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Ultra-Broadband and Low-Loss Silicon-Based Power Splitter Based on Subwavelength Grating-Assisted Multimode Interference Structure

Ultra-Broadband and Low-Loss Silicon-Based Power Splitter Based on Subwavelength Grating-Assisted... hv photonics Communication Ultra-Broadband and Low-Loss Silicon-Based Power Splitter Based on Subwavelength Grating-Assisted Multimode Interference Structure 1 1 1 1 1 1 , 2 , Yuchen Shi , Bo Shao , Zhekang Zhang , Taotao Zhou , Fan Luo and Yin Xu * Department of Electronic Engineering, School of IoT Engineering, Jiangnan University, Wuxi 214122, China; 1038190216@stu.jiangnan.edu.cn (Y.S.); 1038190215@stu.jiangnan.edu.cn (B.S.); 1038190218@stu.jiangnan.edu.cn (Z.Z.); 1038190125@stu.jiangnan.edu.cn (T.Z.); 1038190224@stu.jiangnan.edu.cn (F.L.) Institute of Advanced Technology, Jiangnan University, Wuxi 214122, China * Correspondence: yin.xu@jiangnan.edu.cn Abstract: High-performance and compact power splitters are fundamental components in on-chip photonic integrated circuits (PICs). We propose a silicon-based power splitter based on a subwave- length grating (SWG)-assisted multimode interference (MMI) structure. To shorten the device size and enhance the device performance, an inverse-tapered SWG is embedded in the central region of the MMI and two rows of uniform SWG are embedded on both sides, together with two right-angled cutting structures on the input side. According to the results, the MMI length was obviously reduced to 3.2 m (5.2 m for conventional MMI structure under the same waveguide width), while the insertion loss (IL) and reflection loss were 0.08 dB and <35 dB, respectively. Moreover, the allowable working bandwidth could be extended to 560 nm by keeping IL <0.6 dB, covering the whole optical communication band. On the basis of these features, we believe that such a power splitter is very promising for building on-chip large-scale PICs where power splitting is indispensable. Keywords: subwavelength grating; multimode interference; power splitter Citation: Shi, Y.; Shao, B.; Zhang, Z.; Zhou, T.; Luo, F.; Xu, Y. Ultra-Broadband and Low-Loss Silicon-Based Power Splitter Based on Subwavelength Grating-Assisted 1. Introduction Multimode Interference Structure. Silicon-on-insulator (SOI), a mature and promising platform for silicon photonics, has Photonics 2022, 9, 435. https:// been commonly employed to realize compact, high-performance, and high-yield photonic doi.org/10.3390/photonics9070435 integrated circuits (PICs) [1–5]. To construct such on-chip PICs, power splitters are fun- Received: 21 May 2022 damental and indispensable components, which play a key role in separating the input Accepted: 16 June 2022 light power into different output ports [6–10]. For the power splitter, different waveguide Published: 21 June 2022 structures have been reported, e.g., typical Y-junctions [6], adiabatic tapers [7], directional couplers (DCs) [8], photonic crystals (PCs) [9], and multimode interference (MMI) cou- Publisher’s Note: MDPI stays neutral plers [10]. With overall consideration of the device size, performance, and fabrication with regard to jurisdictional claims in tolerance, MMI couplers are the best choice since Y-branches require a large device size, published maps and institutional affil- while DCs and PCs have limited working bandwidths and tight fabrication tolerances, iations. respectively. Therefore, MMI-based power splitters are vital components applied in on-chip Mach–Zehnder interferometer (MZI) modulators [11,12], optical switches [13,14], and other on-chip optical circuits requiring a light power-splitting function [15,16]. Within these Copyright: © 2022 by the authors. application cases, a smaller device size and better device performance have become the Licensee MDPI, Basel, Switzerland. new requirements for silicon-based power splitters. This article is an open access article To further shorten the device size of MMI-based power splitters (e.g., typical MMI distributed under the terms and length of ~5.2 m under a waveguide width of 2.5 m [17,18]), we should enlarge the conditions of the Creative Commons effective index difference of the transmitted interference modes within the MMI region, Attribution (CC BY) license (https:// which needs to change the refractive index distribution of the conventional MMI structure. creativecommons.org/licenses/by/ Fortunately, a subwavelength grating (SWG) structure whose grating pitch is obviously 4.0/). Photonics 2022, 9, 435. https://doi.org/10.3390/photonics9070435 https://www.mdpi.com/journal/photonics Photonics 2022, 9, 435 2 of 12 shorter than the grating Bragg period behaves as a homogenous medium without a reflec- tion and diffraction effect for the input light (e.g.,  = 1.55 m) [19–22]. Furthermore, the effective refractive index of SWG structure can be easily changed by varying its grating duty cycle, offering a new degree of freedom for the device design [19–22]. Therefore, by adding such an SWG structure into the conventional MMI waveguide, the refractive index distribution of the whole structure becomes no longer uniform in the waveguide region, contributing to a reduction in MMI length [19]. Under this condition, various device schemes have been proposed. For instance, through embedding a row of SWGs in the central region of the MMI, the required MMI length was clearly reduced to 3.8 m (waveg- uide width 2.2 m) for power splitting [23]. Meanwhile, a dual polarization operation could also be achieved with the help of the tunability of the effective refractive index for an SWG structure [23]. To further shrink the MMI length, a tapered SWG structure was embedded in the central region of the MMI along the propagation direction, and the MMI length was reduced to only 1.92 m (waveguide width 2.0 m) with an insertion loss (IL) of 0.39 dB, which is quite beneficial for on-chip compact integration [24]. In addition to these schemes, an SWG-based MMI power splitter was shown to be a useful structure, where the MMI region was formed by SWGs with identical or different orientations for the grating component [25]. The corresponding MMI lengths could even be reduced to 3.2 m (waveguide width 2.8 m) with a large bandwidth of 400 nm (IL < 1 dB) [25]. However, we should note that the IL and working bandwidth of the power splitter still need to be efficiently reduced and increased, respectively, since the fundamental power splitter will be greatly required and heavily used in current and future on-chip large-scale PICs for splitting light power [26–28]. In this paper, we propose a silicon-based MMI power splitter, where the key MMI region is embedded by an inverse-tapered SWG in the center and two rows of uniform SWG slots on both sides along the propagation direction. The embedded central SWG is employed to change the whole refractive index distribution of the multimode silicon waveguide, which can help enlarge the effective index difference between excited modes and further reduce the MMI length. The embedded bilateral SWG slots are used to increase the coupling efficiency with the output waveguides via mode matching, corresponding to a reduction in power splitting loss. Through these two main techniques applied in the MMI structure for the power splitter, the key MMI length could be reduced to 3.2 m (waveguide width 2.5 m), while the obtained IL was only 0.08 dB at a wavelength of 1.55 m, along with a quite low reflection loss (RL) of <35 dB. Note that the device working bandwidth could be over 550 nm (covering the whole optical communication band) even under a strict criterion of IL < 0.6 dB. In addition, the fabrication tolerances of the key structural parameters were also analyzed. We hope that the proposed device can find important applications in the field of on-chip PICs. 2. Device Structure and Principle Figure 1 illustrates the three-dimensional schematic of our proposed SWG-assisted MMI power splitter, which consisted of an inverse-tapered SWG and two rows of uniform SWG slots embedded in the MMI center and on both sides, respectively. For a conventional MMI power splitter, as the input fundamental TE mode is injected into the MMI region from the central port, the new TE and TE mode are excited dominantly within the MMI 0 2 region, thus leading to a clear mode interference along the propagation direction. Once the accumulated phase difference between these two excited modes (TE and TE mode) is 0 2 equal to , a double image of the input TE mode with the same phase can be achieved after mode interference [17]. Finally, using two waveguides to separate and output such a double image, we can realize the function of power splitting. To efficiently shorten the MMI length and reduce the power splitting loss, we embedded an inverse-tapered SWG in the MMI center, where the width of the SWG was linearly tapered from w (=200 nm) to g1 w in a period number of n, and we embedded two rows of uniform SWG slots (period gn number N) on both sides of the MMI region, whereby their central positions along the Photonics 2022, 9, x FOR PEER REVIEW  3  of  12  Photonics 2022, 9, 435 3 of 12 slots (period number N) on both sides of the MMI region, whereby their central positions  along the propagation direction were aligned with those of the output waveguides. These  propagation direction were aligned with those of the output waveguides. These embedded embedded SWG structures had the same grating pitch and duty cycle of  = 200 nm and  SWG structures had the same grating pitch and duty cycle of L = 200 nm and a/L = 0.5, a/ = 0.5, respectively. The gap length between the left side of the inverse‐tapered SWG  respectively. The gap length between the left side of the inverse-tapered SWG (uniform (uniform SWG slot) and the left side of the MMI region was LS (LE), shown in the inset of  SWG slot) and the left side of the MMI region was L (L ), shown in the inset of Figure 1. S E Figure 1. Moreover, the length and width of MMI region were LM and WM (=2.5 μm), re‐ Moreover, the length and width of MMI region were L and W (=2.5 m), respectively. M M spectively. The widths of the central input waveguide and bilateral output waveguides  The widths of the central input waveguide and bilateral output waveguides were tapered were tapered from w1 to w2 in a length of LI and from w3 to w4 in a length of LO, respectively,  from w to w in a length of L and from w to w in a length of L , respectively, where the 1 2 I 3 4 O where the input and output waveguide widths were the same (w1 = w4 = 500 nm). In addi‐ input and output waveguide widths were the same (w = w = 500 nm). In addition, we 1 4 tion, we also introduced two right‐angled cutting structures on both sides of the input  also introduced two right-angled cutting structures on both sides of the input port of MMI port of MMI region symmetrically to further enhance the device performance, where the  region symmetrically to further enhance the device performance, where the corresponding corresponding length and width of the cutting structures were LT and (WM − w2)/2, respec‐ length and width of the cutting structures were L and (W w )/2, respectively. The T M 2 tively. The whole device was analyzed and simulated on the basis of a commercial SOI  whole device was analyzed and simulated on the basis of a commercial SOI wafer with a wafer with a 220 nm thick top silicon layer and a 2 μm thick buried oxide layer (SiO2),  220 nm thick top silicon layer and a 2 m thick buried oxide layer (SiO ), while the upper while the upper cladding was also SiO2 with a thickness of 2 μm.  cladding was also SiO with a thickness of 2 m. Figure 1. Schematic of our proposed power splitter based on SWG-assisted MMI structure, where an Figure 1. Schematic of our proposed power splitter based on SWG‐assisted MMI structure, where  inverse-tapered SWG and two rows of uniform SWG slots were embedded in the center and on both an inverse‐tapered SWG and two rows of uniform SWG slots were embedded in the center and on  sides of the MMI waveguidem respectively. The inset shows the top view of the key MMI region in both sides of the MMI waveguidem respectively. The inset shows the top view of the key MMI  detail. The material and structural parameters are also labeled. region in detail. The material and structural parameters are also labeled.  Figure 2a shows the calculated effective indices n of guided modes under different eff Figure 2a shows the calculated effective indices neff of guided modes under different  waveguide widths, where the TE polarization modes were analyzed. From this figure, waveguide widths, where the TE polarization modes were analyzed. From this figure, we  we can easily find the effective index of every supported mode for the waveguide width. can easily find the effective index of every supported mode for the waveguide width. For  For example, the silicon waveguide could support seven modes (from TE to TE ) when 0 6 example, the silicon waveguide could support seven modes (from TE0 to TE6) when the  the waveguide width was 2.5 m. For the multimode waveguide transmission, only even waveguide width was 2.5 μm. For the multimode waveguide transmission,  only even  modes (TE , TE , TE , TE ) could be adequately excited for the central injection from the 0 2 4 6 modes (TE0, TE2, TE4, TE6) could be adequately excited for the central injection from the  input single-mode waveguide [17]. Meanwhile, the TE and TE modes of the multimode 0 2 input single‐mode waveguide [17]. Meanwhile, the TE0 and TE2 modes of the multimode  waveguide would dominate among the excited modes according to our calculations. On the waveguide would dominate among the excited modes according to our calculations. On  basis of these two modes, we could roughly determine the required multimode waveguide the basis of these two modes, we could roughly determine the required multimode wave‐ length for the power splitting, where more precise length should be optimized using a guide length for the power splitting, where more precise length should be optimized us‐ numerical method. By adding SWG structures into the conventional MMI waveguide, the ing a numerical method. By adding SWG structures into the conventional MMI wave‐ effective index difference of dominant excited modes (TE and TE mode) within the MMI 0 2 guide,  the  effective  index  difference  of  dominant  excited  modes  (TE0  and  TE2  mode)  region was increased, leading to a reduction in beat length L [17–19]. within the MMI region was increased, leading to a reduction in beat length Lπ [17–19].  L =  , (1) 𝐿 ,   (1) 2 n n TE TE 0 2 2 𝑛 𝑛 where n , n are the mode effective indices of the excited TE and TE modes, and l TE0 TE2 0 2 where nTE0, nTE2 are the mode effective indices of the excited TE0 and TE2 modes, and λ is  is the working wavelength. If we set the MMI length L equal to the beat length L , we the working wavelength. If we set the MMI length LM equal to the beat length Lπ, we can  can obtain two TE modes (double image of the input TE mode) with the same phase 0 0 and same power, corresponding to the power splitting. The SWG structure can be treated Photonics 2022, 9, x FOR PEER REVIEW  4  of  12  obtain two TE0 modes (double image of the input TE0 mode) with the same phase and  Photonics 2022, 9, 435 4 of 12 same power, corresponding to the power splitting. The SWG structure can be treated as a  homogeneous medium, and its equivalent refractive index nSWG can be estimated as fol‐ lows [19]:  as a homogeneous medium, and its equivalent refractive index n can be estimated as SWG follows [19]: 𝑎 Λ𝑎 2 2 (2) 𝑛 ∙𝑛 ∙𝑛 ,  SWG a c L a 2 2 Λ Λ n = n + n , (2) SWG cl L L where nc and ncl denote the refractive index of the core (silicon) and cladding (silica) of the  where n and n denote the refractive index of the core (silicon) and cladding (silica) of the cl grating, respectively. Using Equation (2), we can roughly obtain the equivalent refractive  grating, respectively. Using Equation (2), we can roughly obtain the equivalent refractive index of the SWG structure. Figure 2b shows the calculated effective indices neff of guided  index of the SWG structure. Figure 2b shows the calculated effective indices n of guided eff modes  for  the  multimode  waveguide  (WM = 2.5 μm)  embedded  with  the  central  SWG  modes for the multimode waveguide (W = 2.5 m) embedded with the central SWG structure as a function of the SWG width wg. Note that the effective index difference be‐ structure as a function of the SWG width w . Note that the effective index difference tween dominant excited TE0 and TE2 modes is really increased with the increase in em‐ between dominant excited TE and TE modes is really increased with the increase in 0 2 bedded SWG width wg. This is the reason that the required MMI length can be reduced  embedded SWG width w . This is the reason that the required MMI length can be reduced compared with the conventional MMI structure. In the analyses below, we study the em‐ compared with the conventional MMI structure. In the analyses below, we study the bedded SWG structures in detail to achieve larger bandwidth and lower loss compared  embedded SWG structures in detail to achieve larger bandwidth and lower loss compared with with previous previous repor reports ts [2 [233–2 –255] ]..  Figure 2. (a) Effective indices n of guided modes as a function of the waveguide width for the TE eff Figure 2. (a) Effective indices neff of guided modes as a function of the waveguide width for the TE polar‐ polarization state. Insets show the electric field distributions of TE and TE modes. (b) Effective ization state. Insets show the electric field distributions of TE0 and TE2 0modes. (b 2 ) Effective indices neff of  indices n of guided modes for the multimode waveguide embedded with the central SWG structure guided modes for the multimode waveguide embedded with the central SWG structure as a function of  eff th as e SWG a function  width of wthe g. The SWG  mul width timodew wa . The vegu multimode ide width was waveguide  chosen as width  WM = was 2.5 μchosen m. Insets as sh Wow= the 2.5 elec m. tric  field distributions of TE0 and TE2 modes.  Insets show the electric field distributions of TE and TE modes. 0 2 3. Results and Discussion 3. Results and Discussion  For the device performance analyses, the three-dimensional finite-difference time- For the  device performance analyses, the three‐dimensional finite‐difference time‐do‐ domain (3D-FDTD) method was employed to help design and optimize the device pa- main (3D‐FDTD) method was employed to help design and optimize the device parameters  rameters [29,30]. Figure 3 shows the device transmission of several typical silicon-based [29,30]. Figure 3 shows the device transmission of several typical silicon‐based MMI power  MMI power splitters as a function of the MMI length L under the same MMI width splitters as a function of the MMI length LM under the same MMI width (WM = 2.5 μm). As  (W = 2.5 m). As shown in Figure 3, three types of MMI power splitter were considered, shown in Figure 3, three types of MMI power splitter were considered, conventional MMI  conventional MMI structure, uniform SWG embedded MMI structure, and inverse-tapered structure, uniform SWG embedded MMI structure, and inverse‐tapered SWG embedded  SWG embedded MMI structure. One can clearly find that the variation of device transmis- MMI  structure.  One  can  clearly  find  that  the  variation  of  device  transmission  became  sion became small within the calculation range of L when the MMI region was embedded small within the calculation range of LM when the MMI region was embedded with a uni‐ with a uniform or inverse-tapered SWG structure, corresponding to an increased MMI form or inverse‐tapered SWG structure, corresponding to an increased MMI length toler‐ length tolerance. Moreover, we can also observe that the optimum MMI length was ance. Moreover, we can also observe that the optimum MMI length was obviously de‐ obviously decreased from 5.0 m to 3.6 m (3.3 m) due to the embedded uniform (inverse- creased from 5.0 μm to 3.6 μm (3.3 μm) due to the embedded uniform (inverse‐tapered)  tapered) SWG structure in the center of the MMI region along the propagation direction, SWG contributing  structurto e in on-chip  the ce compact nter of th integration. e MMI reg Ifion we alo further ng thadded e prop linearly agationtaper  direed ction, structur  contes rib‐ connecting the input/output waveguides with the MMI region, the device transmission uting to on‐chip compact integration. If we further added linearly tapered structures con‐ could be obviously increased, while the variation range of transmission could be reduced, necting the input/output waveguides with the MMI region, the device transmission could  as shown in Figure 3. By comparison, we can find that the inverse-tapered SWG embedded be obviously increased, while the variation range of transmission could be reduced, as  MMI structure with input and output tapers obtained the best power splitting function shown in Figure 3. By comparison, we can find that the inverse‐tapered SWG embedded  together with largest tolerance for MMI length L , where the device transmission was MMI structure with input and output tapers obtained the best power splitting function  about 0.25 dB at L = 3.3 m.   Photonics 2022, 9, x FOR PEER REVIEW  5  of  12  Photonics 2022, 9, 435 5 of 12 together with largest tolerance for MMI length LM, where the device transmission was  about −0.25 dB at LM = 3.3 μm.  Figure 3. Transmission of several typical silicon-based MMI power splitters as a function of their Figure 3. Transmission of several typical silicon‐based MMI power splitters as a function of their  respective MMI lengths L . (a) I and II represent the conventional MMI structure without and respective MMI lengths LM. (a) I and II represent the conventional MMI structure without and with  with input/output tapers, respectively. (b) III and IV represent the MMI structure embedded with input/output tapers, respectively. (b) III and IV represent the MMI structure embedded with a uni‐ a uniform SWG waveguide without and with input/output tapers, respectively. (c) V and VI form SWG waveguide without and with input/output tapers, respectively. (c) V and VI represent  represent the MMI structure embedded with an inverse-tapered SWG waveguide without and with the MMI structure embedded with an inverse‐tapered SWG waveguide without and with input/out‐ put tapers, respectively.  input/output tapers, respectively. To perform a more detailed analysis of the inverse-tapered SWG structure, the embed- To perform a more detailed analysis of the inverse‐tapered SWG structure, the em‐ ded SWG parameters were defined as follows: bedded SWG parameters were defined as follows:  𝐿 𝐿 L L M S 𝑛 ,   (3) n = , (3) 𝑤 𝑤 𝑘𝑛 1 ,   (4) gn g1 w = w + k(n 1) , (4) gn g1 where k is the width increment of the inverse‐tapered SWG along the y‐direction; k was  where k is the width increment of the inverse-tapered SWG along the y-direction; k was chosen as 50 nm during structural optimization. More details about the choice of k can be  chosen as 50 nm during structural optimization. More details about the choice of k can found in the tolerance analyses described later. Therefore, LM, LS, and n are closely related.  be found in the tolerance analyses described later. Therefore, L , L , and n are closely M S Figure 4a shows the detailed device transmission with MMI length LM, where the optimal  related. Figure 4a shows the detailed device transmission with MMI length L , where the half period number m (n = m/2) of the SWG structure under different LM is also plotted.  optimal half period number m (n = m/2) of the SWG structure under different L is also From Figure 4, we can find that the device transmission was higher than −0.5 dB within the  plotted. From Figure 4, we can find that the device transmission was higher than 0.5 dB whole range from LM = 2.6 to 4.0 μm, and the optimal period number almost increased with  within the whole range from L = 2.6 to 4.0 m, and the optimal period number almost the increase in LM. Note that the device transmission reached a high value with relatively small  increased with the increase in L . Note that the device transmission reached a high value fluctuation when LM varied from 3.2 μm to 3.5 μm, marked by the oval in Figure 4a. By con‐ with relatively small fluctuation when L varied from 3.2 m to 3.5 m, marked by the sideration of the device size and required grating number, we set LM to 3.2 μm for the subse‐ oval in Figure 4a. By consideration of the device size and required grating number, we set quent analysis, where the optimal half period number m was 18 (n = 9). Figure 4b shows the  L to 3.2 m for the subsequent analysis, where the optimal half period number m was device transmission with gap length LS between the left side of the inverse‐tapered SWG and  18 (n = 9). Figure 4b shows the device transmission with gap length L between the left the left side of the MMI region, where LM was equal to 3.2 μm. According to Equation (2), the  side of the inverse-tapered SWG and the left side of the MMI region, where L was equal period number of the embedded SWG structure decreased as the gap length LS increased  to 3.2 m. According to Equation (2), the period number of the embedded SWG structure within the calculation range shown in Figure 4b. Meanwhile, the obtained transmission curve  decreased as the gap length L increased within the calculation range shown in Figure 4b. presented a nearly flat top as LS changed from 1.1 to 1.4 μm, and we chose LS = 1.4 μm, corre‐ Meanwhile, the obtained transmission curve presented a nearly flat top as L changed from sponding to the highest transmission shown in Figure 4b.  1.1 to 1.4 m, and we chose L = 1.4 m, corresponding to the highest transmission shown in Figure 4b. According to above analyses, the best device transmission of the MMI power splitter embedded with the inverse-tapered SWG was limited to about 0.25 dB at the wavelength of 1.55 m. To further enhance the device transmission or reduce the power splitting loss, we embedded two rows of uniform SWG on both sides of the MMI region, where the period number was N. Such embedded uniform SWG structures were employed to match the separated modes (double image of the input TE mode) within the MMI region with the output waveguide modes. Therefore, we set the central positions of embedded uniform SWGs along the propagation direction aligned with those of the output waveguides. Thus, the period number N and relative position L of such a uniform SWG was also determined. Figure 5 illustrates the device transmission as a function of L , where the optimal period   S Photonics 2022, 9, 435 6 of 12 number N and relative position L of the embedded uniform SWG are plotted for every gap length L . The grating parameters of the added uniform SWG were the same as those of the inverse-tapered SWG (grating pitch L = 200 nm, duty cycle a/L = 0.5), and the etching width of the uniform SWG in the y-direction was set as 100 nm, corresponding to the square etching slots. As shown in Figure 5, the optimal value of L was reduced compared with no embedded uniform SWG structure shown in Figure 5b. The reason is that the embedded uniform SWG could reduce the effective index on both sides of the MMI waveguide, and such a structure also required a further reduction in the effective index on the central side, leading to a reduction in L or an increase in period number n of the inverse-tapered SWG. Therefore, L decreased from 1.4 to 0.9 m, corresponding to the optimal values of N = 5 and L = 1.45 m. For the device transmission of our proposed power splitter, its value was obviously reduced to 0.08 dB at a wavelength of 1.55 m upon embedding the extra uniform SWG structures on both sides of the MMI region. Such a low transmission loss of the power splitter would be very beneficial to construct on-chip photonic devices (e.g., MZI modulators [11,12] and optical switches [13,14]) and large-scale PICs. During the calculation process shown in Figure 5, the choice of optimal values of N and L for every gap length L was also important. Here, we used L = 0.9 m as an example, and the results S S are plotted in Figure 6, where the period number of the embedded uniform SWG was set as N = 4, 5, and 6. Note that the obtained device transmissions revealed some fluctuations as the relative position L increased from 0.85 to 2.15 m, and the largest transmission loss was almost lower than 0.5 dB, as shown in Figure 6. These transmission fluctuations may have resulted from the interaction of the separated modes with the uniform SWG structure embedded on both sides of the multimode waveguide, where different interact positions led to different transmission losses due to the wave features of input light. In addition, we also introduced two right-angled cutting structures on both sides of the input MMI side in a symmetric manner (L = 0.25 m) to further reduce the device reflection loss (RL < 35 dB) and stabilize the light evolution through the proposed device. Therefore, through these structural designs and optimizations applied in the MMI region for power splitting, the device transmission loss was reduced to only 0.08 dB, while the required MMI length was Photonics 2022, 9, x FOR PEER REVIEW  6  of  12  3.2 m, representing an improvement compared to the conventional MMI power splitter without an embedded SWG structure. Figure 4. (a) Device transmission with MMI length L and optimal half period number m of the Figure 4. (a) Device transmission with MMI length LM and optimal half period number m of the  embedded SWG structure in the power splitter. SWG period number n = m/2. (b) Device transmission embedded SWG structure in the power splitter. SWG period number n = m/2. (b) Device transmis‐ siwith on with the gap the length gap leLng ,twher h LS,e whe L =re 3.2 LM m. = 3.The 2 μm. marked  The ma regions rkedr epr regions esent rep ther resen ecommended t the reco str mme uctural nded  S M structural parameter ranges.  parameter ranges. Next, we conduct wavelength spectrum analyses for the proposed device, where IL is According to above analyses, the best device transmission of the MMI power splitter  used to denote the device transmission loss. Figure 7 shows the wavelength dependence of embedded with the inverse‐tapered SWG was limited to about −0.25 dB at the wavelength  IL for the proposed device and conventional MMI power splitter, where the inset shows of 1.55 μm. To further enhance the device transmission or reduce the power splitting loss,  the device schematics, and key parameters are also marked. For a better comparison, we we embedded two rows of uniform SWG on both sides of the MMI region, where the  period number was N. Such embedded uniform SWG structures were employed to match  the separated modes (double image of the input TE0 mode) within the MMI region with  the output waveguide modes. Therefore, we set the central positions of embedded uni‐ form SWGs along the propagation direction aligned with those of the output waveguides.  Thus, the period number N and relative position LE of such a uniform SWG was also de‐ termined. Figure 5 illustrates the device transmission as a function of LS, where the opti‐ mal period number N and relative position LE of the embedded uniform SWG are plotted  for every gap length LS. The grating parameters of the added uniform SWG were the same  as those of the inverse‐tapered SWG (grating pitch  = 200 nm, duty cycle a/ = 0.5), and  the etching width of the uniform SWG in the y‐direction was set as 100 nm, corresponding  to the square etching slots. As shown in Figure 5, the optimal value of LS was reduced  compared with no embedded uniform SWG structure shown in Figure 5b. The reason is  that the embedded uniform SWG could reduce the effective index on both sides of the  MMI waveguide, and such a structure also required a further reduction in the effective  index on the central side, leading to a reduction in LS or an increase in period number n of  the inverse‐tapered SWG. Therefore, LS decreased from 1.4 to 0.9 μm, corresponding to  the optimal values of N = 5 and LE = 1.45 μm. For the device transmission of our proposed  power splitter, its value was obviously reduced to −0.08 dB at a wavelength of 1.55 μm  upon embedding the extra uniform SWG structures on both sides of the MMI region. Such  a low transmission loss of the power splitter would be very beneficial to construct on‐chip  photonic devices (e.g., MZI modulators [11,12] and optical switches [13,14]) and large‐ scale PICs. During the calculation process shown in Figure 5, the choice of optimal values  of N and LE for every gap length LS was also important. Here, we used LS = 0.9 μm as an  example, and the results are plotted in Figure 6, where the period number of the embed‐ ded uniform SWG was set as N = 4, 5, and 6. Note that the obtained device transmissions  revealed some fluctuations as the relative position LE increased from 0.85 to 2.15 μm, and  the largest transmission loss was almost lower than 0.5 dB, as shown in Figure 6. These  transmission fluctuations may have resulted from the interaction of the separated modes  with the uniform SWG structure embedded on both sides of the multimode waveguide,  where different interact positions led to different transmission losses due to the wave fea‐ tures of input light. In addition, we also introduced two right‐angled cutting structures  on both sides of the input MMI side in a symmetric manner (LT = 0.25 μm) to further reduce    Photonics 2022, 9, 435 7 of 12 chose quite a large wavelength range calculated from 1.15 to 1.95 m, and the MMI width was set as the same (W = 2.5 m) for both devices, where the material dispersions of silicon and silica were also considered [31]. From Figure 7, we can clearly find that the allowable working bandwidth of the conventional MMI power splitter was very large (1360–1770 nm) when keeping IL < 0.6 dB. This is the main reason for the MMI structure’s superiority over the DC or PC structure for power splitting [8–10]. By comparison, the allowable working bandwidth of our proposed power splitter could be extended from 1240 nm to 1800 nm covering the whole optical communication band if IL < 0.6 dB was also satisfied. Therefore, the obtained working bandwidth (560 nm) of the power splitter Photonics 2022, 9, x FOR PEER REVIEW  7  of  12  based on our proposed structure could be even higher than that of the commonly used  Photonics 2022, 9, x FOR PEER REVIEW  7  of  12  broadband MMI power splitter (410 nm), revealing the ultra-broadband feature of our proposed device. Table 1 compares our proposed power splitter with other MMI power splitters embedded with an SWG structure reported recently, where the MMI dimension, the device reflection loss (RL < −35 dB) and stabilize the light evolution through the pro‐ the device reflection loss (RL < −35 dB) and stabilize the light evolution through the pro‐ IL, RL, and allowable working bandwidth were all considered. It can be noted that the posed device. Therefore, through these structural designs and optimizations applied in  posed device. Therefore, through these structural designs and optimizations applied in  proposed power splitter had obvious advantages of ultra-broadband, low IL, and low RL, the MMI region for power splitting, the device transmission loss was reduced to only 0.08  the MMI region for power splitting, the device transmission loss was reduced to only 0.08  while the required MMI dimension was comparable with other reports. Therefore, the dB, while the required MMI length was 3.2 μm, representing an improvement compared  dB, present  while device  the req can uire bed employed  MMI leng asthan wa efsficient  3.2 μm, and represe broadband ntingpower  an improv splitting ement component  compared  to the conventional MMI power splitter without an embedded SWG structure.  to applied  the conv inention on-chip al  PICs. MMI power splitter without an embedded SWG structure.  Figure 5. Device transmission of the new designed power splitter as a function of its gap length LS,  Figure 5. Device transmission of the new designed power splitter as a function of its gap length L , Figure 5. Device transmission of the new designed power splitter as a function of its gap length LS,  where the optimal period number N and relative position LE of the embedded uniform SWG are  where the optimal period number N and relative position L of the embedded uniform SWG are also where the optimal period number N and relative position LE of the embedded uniform SWG are  also plotted for every gap length LS.  plotted for every gap length L . also plotted for every gap length LS.  Figure 6. Device transmission of the new designed device as a function of its period number N and Figure 6. Device transmission of the new designed device as a function of its period number N and  Figure 6. Device transmission of the new designed device as a function of its period number N and  relative position L of the embedded uniform SWG. L is set as 0.9 m. relative position LE E of the embedded uniform SWG. L SS is set as 0.9 μm.  relative position LE of the embedded uniform SWG. LS is set as 0.9 μm.  Next, we conduct wavelength spectrum analyses for the proposed device, where IL  Next, we conduct wavelength spectrum analyses for the proposed device, where IL  is used to denote the device transmission loss. Figure 7 shows the wavelength dependence  is used to denote the device transmission loss. Figure 7 shows the wavelength dependence  of IL for the proposed device and conventional MMI power splitter, where the inset shows  of IL for the proposed device and conventional MMI power splitter, where the inset shows  the device schematics, and key parameters are also marked. For a better comparison, we  the device schematics, and key parameters are also marked. For a better comparison, we  chose quite a large wavelength range calculated from 1.15 to 1.95 μm, and the MMI width  chose quite a large wavelength range calculated from 1.15 to 1.95 μm, and the MMI width  was set as the same (WM = 2.5 μm) for both devices, where the material dispersions of sili‐ was set as the same (WM = 2.5 μm) for both devices, where the material dispersions of sili‐ con and silica were also considered [31]. From Figure 7, we can clearly find that the allowable  con and silica were also considered [31]. From Figure 7, we can clearly find that the allowable  working bandwidth of the conventional MMI power splitter was very large (1360–1770 nm)  working bandwidth of the conventional MMI power splitter was very large (1360–1770 nm)  when keeping IL <0.6 dB. This is the main reason for the MMI structure’s superiority over the  when keeping IL <0.6 dB. This is the main reason for the MMI structure’s superiority over the  DC or  PC  structure  for  power  splitting  [8–10].  By  comparison,  the  allowable  working  DC or  PC  structure  for  power  splitting  [8–10].  By  comparison,  the  allowable  working  bandwidth of our proposed power splitter could be extended from 1240 nm to 1800 nm  bandwidth of our proposed power splitter could be extended from 1240 nm to 1800 nm  covering the whole optical communication band if IL <0.6 dB was also satisfied. Therefore,  covering the whole optical communication band if IL <0.6 dB was also satisfied. Therefore,  the obtained working bandwidth (560 nm) of the power splitter based on our proposed  the obtained working bandwidth (560 nm) of the power splitter based on our proposed  structure could be even higher than that of the commonly used broadband MMI power  structure could be even higher than that of the commonly used broadband MMI power    Photonics 2022, 9, x FOR PEER REVIEW  8  of  12  splitter (410 nm), revealing the ultra‐broadband feature of our proposed device. Table 1  compares our proposed power splitter with other MMI power splitters embedded with  an SWG structure reported recently, where the MMI dimension, IL, RL, and allowable  working bandwidth were all considered. It can be noted that the proposed power splitter  had obvious advantages of ultra‐broadband, low IL, and low RL, while the required MMI  Photonics 2022, 9, 435 dimension was comparable with other reports. Therefore, the present device can be 8 of em 12 ‐ ployed as an efficient and broadband power splitting component applied in on‐chip PICs.  Figure 7. Wavelength dependence of IL for the conventional MMI power splitter (I) and the pro‐ Figure 7. Wavelength dependence of IL for the conventional MMI power splitter (I) and the proposed posed device (II). The inset shows the corresponding device schematics.  device (II). The inset shows the corresponding device schematics. Table 1. Device comparison of typical MMI power splitters embedded with SWG structure. Table 1. Device comparison of typical MMI power splitters embedded with SWG structure.  Dimension of MMI   Dimension of MMI Reference  IL (dB) @ 1550 nm  RL (dB) @ 1550 nm  Bandwidth (nm)  Reference IL (dB) @ 1550 nm RL (dB) @ 1550 nm Bandwidth (nm) Region (m ) Region (μm )  [23] [23  ] 2.22.2   3.8 3.8  0.0 0.07 7 −28 28.29 .29  280 280 (IL (IL < <0 0.3.3dB)  dB)  [24] 2.0  1.92 0.39 30.51 ~105 (PDL < 0.1 dB) * [24]  2.0    1.92  0.39 −30.51  ~105 (PDL <0.1 dB) *  [25] ** 2.8  3.2 0.20 - 420 (IL < 1.0 dB) [25] ** 2.8    3.2  0.20 ‐  420 (IL <1.0 dB)  This work 2.5  3.2 0.08 35.61 560 (IL < 0.6 dB) This work  2.5    3.2  0.08  −35.61  560 (IL <0.6 dB)  * PDL, polarization-dependent loss. ** Experimental results. “-”: not mentioned. * PDL, polarization‐dependent loss. ** Experimental results. “‐”: not mentioned.  For the device fabrication, we only needed one-step lithography and etching processes For the device fabrication, we only needed one‐step lithography and etching pro‐ on a commercial SOI wafer with 220 nm-thick top silicon layer, since the proposed device cesses on a commercial SOI wafer with 220 nm‐thick top silicon layer, since the proposed  had a uniform etching depth (220 nm). Moreover, the required minimum linewidth was device had a uniform etching depth (220 nm). Moreover, the required minimum linewidth  100 nm, which can be easily achieved by current E-beam lithography [1,32]. Within our was 100 nm, which can be easily achieved by current E‐beam lithography [1,32]. Within  proposed device, the most important structures were the inverse-tapered SWG embedded our proposed device, the most important structures were the inverse‐tapered SWG em‐ in the MMI center and the two rows of uniform SWG embedded on both sides of the MMI bedded in the MMI center and the two rows of uniform SWG embedded on both sides of  region. Here, we mainly considered the device performance affected by the lateral shift of the MMI region. Here, we mainly considered the device performance affected by the lat‐ the embedded SWG structure in the y-direction with respect to the MMI waveguide, and eral shift of the embedded SWG structure in the y‐direction with respect to the MMI wave‐ the results are shown in Figure 8, where Dw and Dw represent the lateral shift (y-direction) S E guide, of the and inverse-taper  the resulted s ar SWG e shoand wn in uniform  FigureSWG  8, wher from e Δ their wS and design  ΔwE a re tedpresent positions  thementioned  lateral shift  (yabove. ‐direction) Mor eover of the , we invintr erse oduce ‐tapered a new  SW index G and called  unifo the rm splitting SWG fro ratio m th(SR) eir design to characterize ated posi‐ the ratio of light power received at output ports due to structural parameter deviations, tions mentioned above. Moreover, we introduce a new index called the splitting ratio (SR)  to characterize the ratio of light power received at output ports due to structural parame‐ Output2 ter deviations,  SR = , (5) Output1 SR ,   (5) where P and P are the receiving power at the two output ports illustrated in Output1 Output2 𝑃 Figure 1. Considering the structural symmetry of our proposed power splitter, performance where POutput1 and POutput2 are the receiving power at the two output ports illustrated in  variation due to lateral shift of Dw was only calculated on one side (positive y-direction, Figure 1. Considering the structural symmetry of our proposed power splitter, perfor‐ Dw > 0), as shown in Figure 8a,b, and the results due to a shift on the other side (negative mance variation due to lateral shift of ΔwS was only calculated on one side (positive y‐ y-direction, Dw < 0) were the same. To keep SR higher than 0.9, Dw should be controlled S S within the interval [30 nm, 30 nm]. Moreover, for the two rows of uniform SWGs embedded on both sides of the MMI region, we considered one row shifting from its   optimal position due to fabrication imperfections, while the other row’s effect on device performance was considered identical due to structural symmetry. As shown in Figure 8c,d, the available variation of Dw was within the interval [140 nm, 200 nm] when keeping SR > 0.9. By comparison, the central SWG structure had a tighter tolerance range with Photonics 2022, 9, x FOR PEER REVIEW  9  of  12  direction, ΔwS > 0), as shown in Figure 8a,b, and the results due to a shift on the other side  (negative y‐direction, ΔwS < 0) were the same. To keep SR higher than 0.9, ΔwS should be  controlled within the interval [−30 nm, 30 nm]. Moreover, for the two rows of uniform  SWGs embedded on both sides of the MMI region, we considered one row shifting from its  optimal position due to fabrication imperfections, while the other row’s effect on device per‐ formance was considered identical due to structural symmetry. As shown in Figure 8c,d, the  available variation of ΔwE was within the interval [−140 nm, 200 nm] when keeping SR > 0.9.  Photonics 2022, 9, 435 9 of 12 By comparison, the central SWG structure had a tighter tolerance range with regard to  device fabrication because such a structure had a strong influence on the mode splitting  in the MMI region. Thus, the variation range of SR for the central inverse‐tapered SWG  regard to device fabrication because such a structure had a strong influence on the mode shift was larger than that for the bilateral uniform SWG shift. Under such conditions, we  splitting in the MMI region. Thus, the variation range of SR for the central inverse-tapered further analyzed the effect of the central inverse‐tapered SWG shift on the power ratio  SWG shift was larger than that for the bilateral uniform SWG shift. Under such conditions, between the two output ports, as shown in Figure 8e. Note that we could achieve a change  we further analyzed the effect of the central inverse-tapered SWG shift on the power ratio in between  powerthe  ratio two from output  neaports, rly 30:as 70shown  to 70:3in 0 by Figur  onley8 sh e.iNote fting that the ce wentcould ral invers achieve e‐tap ae change red SWG  in power ratio from nearly 30:70 to 70:30 by only shifting the central inverse-tapered SWG structure  relative  to  the  silicon  waveguide  along  the  y‐direction.  Such  a  characteristic  structure relative to the silicon waveguide along the y-direction. Such a characteristic would introduce new applications for the power splitter. We also analyzed the effect of  would introduce new applications for the power splitter. We also analyzed the effect of the width increment k of the inverse‐tapered SWG on the device performance, as shown  the width increment k of the inverse-tapered SWG on the device performance, as shown in Figure 9a. As shown in this figure, the highest IL was lower than 0.3 dB within the  in Figure 9a. As shown in this figure, the highest IL was lower than 0.3 dB within the whole calculation range from k = 20 nm to k = 100 nm, and the optimum value of k was  whole calculation range from k = 20 nm to k = 100 nm, and the optimum value of k was located at the position of k = 40 nm or k = 50 nm. This is why we chose k as 50 nm in the  located at the position of k = 40 nm or k = 50 nm. This is why we chose k as 50 nm previous analyses. Figure 9b shows the effect of grating size variation on device perfor‐ in the previous analyses. Figure 9b shows the effect of grating size variation on device mance (IL). Here, we considered the grating width variation along both x‐ and y‐directions.  performance (IL). Here, we considered the grating width variation along both x- and y- For example, a grating size of 100% corresponded to the optimum widths along the x‐ and  directions. For example, a grating size of 100% corresponded to the optimum widths along y‐directions, while a grating size of 120% corresponded to a width increment of 20% rela‐ the x- and y-directions, while a grating size of 120% corresponded to a width increment of tive to the optimum widths along the x‐ and y‐directions. According to the results, the  20% relative to the optimum widths along the x- and y-directions. According to the results, available grating width variation range should be controlled within the range of 53% to  the available grating width variation range should be controlled within the range of 53% to 135% relative to the optimum values by keeping IL <0.3 dB, where 53% indicates a grating  135% relative to the optimum values by keeping IL < 0.3 dB, where 53% indicates a grating width decrement of 47% relative to the optimum width. Such a relatively large width var‐ width decrement of 47% relative to the optimum width. Such a relatively large width iation range is beneficial for device fabrication. Therefore, these obtained tolerance ranges  variation range is beneficial for device fabrication. Therefore, these obtained tolerance of the key embedded SWG structures in the MMI region need to be guaranteed during  ranges of the key embedded SWG structures in the MMI region need to be guaranteed practical device fabrication [32].  during practical device fabrication [32]. Figure 8. Fabrication tolerance analyses. Device performance (transmission, IL, and SR) variation due Figure 8. Fabrication tolerance analyses. Device performance (transmission, IL, and SR) variation  to (a,b) lateral shift (positive y-direction) Dw of inverse-tapered SWG structure, and (c,d) lateral shift due to (a,b) lateral shift (positive y‐direction) ΔwS of inverse‐tapered SWG structure, and (c,d) lateral  (y-direction) Dw of one row of uniform SWG structures embedded in the MMI region. (e) Power shift (y‐direction) ΔwE of one row of uniform SWG structures embedded in the MMI region. (e)  proportion between the two output ports and the obtained device IL as a function of the lateral shift Power proportion between the two output ports and the obtained device IL as a function of the  Dw of the inverse-tapered SWG structure. The inset shows the device schematic. lateral shift ΔwS of the inverse‐tapered SWG structure. The inset shows the device schematic.  On the basis of the abovementioned device design and optimization processes, the final device parameters were as follows: w = w = 0.5 m, w = 0.94 m, w = 0.6 m, 1 4 2 3 L = 1.38 m, L = 2.0 m, W = 2.5 m, L = 3.2 m, L = 0.9 m, L = 1.45 m, I O M M S E L = 0.25 m, m = 23, N = 5, w = 0.2 m, and waveguide thickness = 220 nm. Figure 10 T g1 plots the electric field evolution through the designed power splitter, where the working wavelength was 1.55 m. From Figure 10, we can clearly observe that the input funda- mental TE mode could be evenly separated into the two output ports, and the electric Photonics 2022, 9, x FOR PEER REVIEW  10  of  12  Photonics 2022, 9, 435 10 of 12 field evolution was quite stable without any fluctuations or ripples. In comparison to the conventional MMI structure, no clear periodic interference pattern could be observed. The reason is that the embedded SWG region had a lower refractive index compared with the silicon waveguide, and the inverse-tapered shape of the SWG structure broke the period interference behavior in the conventional MMI structure. Furthermore, we can find that Figure 9. Fabrication tolerance analyses. IL dependence on (a) the width increment k of the inverse‐ its evolution pattern was similar to that of a typical Y splitter. Thus, we cannot find a tapered SWG for the proposed device and (b) the grating size variation. A grating size of 100%  standard period interference pattern in the SWG assisted MMI region, but its working corresponds to the optimum widths along the x‐ and y‐directions. A grating size of 120% corre‐ principle is still based on the MMI effect since the power splitter based on the Y junction sponds to grating width increments relative to the optimum widths along the x‐ and y‐directions.  nearly cannot be realized in a length of only 3.2 m. Both a small branch angle and a large The horizontal line represents IL = 0.3 dB.  conversion length are required for the Y junction-based power splitter. For the proposed power splitter, its total device length is ~6.5 m when both considering the input and On the basis of the abovementioned device design and optimization processes, the  output tapers, while the MMI length is only 3.2 m. Using such a device, we can efficiently final device parameters were as follows: w1 = w4 = 0.5 μm, w2 = 0.94 μm, w3 = 0.6 μm, LI = 1.38 μm,  realize the power splitting function with an ultrabroad bandwidth, low insertion loss, and LO = 2.0 μm, WM = 2.5 μm, LM = 3.2 μm, LS = 0.9 μm, LE = 1.45 μm, LT = 0.25 μm, m = 23, N = 5,  low reflection loss in a compact size, which can be used as the fundamental component Photonics 2022, 9, x FOR PEER REVIEW  10  of  12  wg1 = 0.2 μm, and waveguide thickness = 220 nm. Figure 10 plots the electric field evolution    for constructing other photonic devices and would be very promising for building on-chip th lar ro ge-scale ugh thePICs  desi[g 26 ned –28 power ].  splitter, where the working wavelength was 1.55 μm. From  Figure 10, we can clearly observe that the input fundamental TE mode could be evenly  separated into the two output ports, and the electric field evolution was quite stable with‐ out any fluctuations or ripples. In comparison to the conventional MMI structure, no clear  periodic interference pattern could be observed. The reason is that the embedded SWG  region had a lower refractive index compared with the silicon waveguide, and the inverse‐ tapered shape of the SWG structure broke the period interference behavior in the conven‐ tional MMI structure. Furthermore, we can find that its evolution pattern was similar to  that of a typical Y splitter. Thus, we cannot find a standard period interference pattern in  the SWG assisted MMI region, but its working principle is still based on the MMI effect  since the power splitter based on the Y junction nearly cannot be realized in a length of  only 3.2 μm. Both a small branch angle and a large conversion length are required for the  Y junction‐based power splitter. For the proposed power splitter, its total device length is  ~6.5 μm when both considering the input and output tapers, while the MMI length is only  Figure 9. Fabrication tolerance analyses. IL dependence on (a) the width increment k of the inverse- Figure 9. Fabrication tolerance analyses. IL dependence on (a) the width increment k of the inverse‐ 3.2 μm. Using such a device, we can efficiently realize the power splitting function with  tapered SWG for the proposed device and (b) the grating size variation. A grating size of 100% tapered SWG for the proposed device and (b) the grating size variation. A grating size of 100%  an corr ul esponds trabroa todthe  ban optimum dwidth, widths  low  along insertio thenx -lo and ss,y and -directions.  low re Aflgrating ection size loss of in 120%  a co corr mp esponds act size,  corresponds to the optimum widths along the x‐ and y‐directions. A grating size of 120% corre‐ whi to grating ch can width be used incr as ements  the funda relative mental to the co optimum mponent widths  for constructing along the x- ot and hery photonic -directions. devic Thees  sponds to grating width increments relative to the optimum widths along the x‐ and y‐directions.  and horizontal  would line  be  rvery epresents  prom ILis =ing 0.3 dB. for building on‐chip large‐scale PICs [26–28].  The horizontal line represents IL = 0.3 dB.  On the basis of the abovementioned device design and optimization processes, the  final device parameters were as follows: w1 = w4 = 0.5 μm, w2 = 0.94 μm, w3 = 0.6 μm, LI = 1.38 μm,  LO = 2.0 μm, WM = 2.5 μm, LM = 3.2 μm, LS = 0.9 μm, LE = 1.45 μm, LT = 0.25 μm, m = 23, N = 5,  wg1 = 0.2 μm, and waveguide thickness = 220 nm. Figure 10 plots the electric field evolution  through the designed power splitter, where the working wavelength was 1.55 μm. From  Figure 10, we can clearly observe that the input fundamental TE mode could be evenly  separated into the two output ports, and the electric field evolution was quite stable with‐ out any fluctuations or ripples. In comparison to the conventional MMI structure, no clear  periodic interference pattern could be observed. The reason is that the embedded SWG  region had a lower refractive index compared with the silicon waveguide, and the inverse‐ tapered shape of the SWG structure broke the period interference behavior in the conven‐ Figure 10. Electrical field evolution of input fundamental TE mode (dominant component: E ) along 0 y Figure 10. Electrical field evolution of input fundamental TE0 mode (dominant component: Ey) along  tional MMI structure. Furthermore, we can find that its evolution pattern was similar to  the propagation direction through the proposed device, where the MMI length was 3.2 m. the propagation direction through the proposed device, where the MMI length was 3.2 μm.  that of a typical Y splitter. Thus, we cannot find a standard period interference pattern in  4. Conclusions the SWG assisted MMI region, but its working principle is still based on the MMI effect  In summary, by embedding an inverse-tapered SWG and two rows of uniform SWG since the power splitter based on the Y junction nearly cannot be realized in a length of  structures into the conventional MMI waveguide, the input fundamental TE mode could only 3.2 μm. Both a small branch angle and a large conversion length are required for the  be evenly separated into two output ports, corresponding to a power splitting function. Y junction‐based power splitter. For the proposed power splitter, its total device length is  Compared with the conventional MMI power splitter, the added SWG structures could ~6.5 μm when both considering the input and output tapers, while the MMI length is only  help to shorten the MMI length and enlarge the working bandwidth, as well as reduce 3.2 μm. Using such a device, we can efficiently realize the power splitting function with  an ultrabroad bandwidth, low insertion loss, and low reflection loss in a compact size,  which can be used as the fundamental component for constructing other photonic devices  and would be very promising for building on‐chip large‐scale PICs [26–28].  Figure 10. Electrical field evolution of input fundamental TE0 mode (dominant component: Ey) along  the propagation direction through the proposed device, where the MMI length was 3.2 μm.    Photonics 2022, 9, 435 11 of 12 the insertion loss and reflection loss. According to the results, the required MMI length was reduced to 3.2 m under a waveguide width of 2.5 m, while the IL was only 0.08 dB, together with a low reflection loss <35 dB. Moreover, the device working bandwidth was quite large (>550 nm) while keeping IL < 0.6 dB. Considering its performance and size, the proposed power splitter has obvious advantages compared to previous reports, especially in terms of the working bandwidth and IL. Moreover, the fabrication processes of the proposed device are similar to those of previous reports without introducing extra processing requirements. Therefore, with these advantages, the proposed device could be a good candidate for application in on-chip PICs requiring a power splitting function. Author Contributions: Conceptualization, Y.S. and Y.X.; methodology, Y.S., B.S., Z.Z., T.Z., F.L. and Y.X.; investigation, Y.S. and Y.X.; writing—original draft preparation, Y.S. and Y.X.; writing—review and editing, all authors; supervision, Y.X.; project administration, Y.X. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Natural Science Foundation of Jiangsu Province, grant number BK20200592, and the Fundamental Research Funds for the Central Universities, grant number JUSRP12024. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data that support the findings of this study are available from the corresponding author upon reasonable request. Conflicts of Interest: The authors declare no conflict of interest. References 1. Siew, S.Y.; Li, B.; Gao, F.; Zheng, H.Y.; Zhang, W.; Guo, P.; Xie, S.W.; Song, A.; Dong, B.; Luo, L.W.; et al. 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Ultra-Broadband and Low-Loss Silicon-Based Power Splitter Based on Subwavelength Grating-Assisted Multimode Interference Structure

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hv photonics Communication Ultra-Broadband and Low-Loss Silicon-Based Power Splitter Based on Subwavelength Grating-Assisted Multimode Interference Structure 1 1 1 1 1 1 , 2 , Yuchen Shi , Bo Shao , Zhekang Zhang , Taotao Zhou , Fan Luo and Yin Xu * Department of Electronic Engineering, School of IoT Engineering, Jiangnan University, Wuxi 214122, China; 1038190216@stu.jiangnan.edu.cn (Y.S.); 1038190215@stu.jiangnan.edu.cn (B.S.); 1038190218@stu.jiangnan.edu.cn (Z.Z.); 1038190125@stu.jiangnan.edu.cn (T.Z.); 1038190224@stu.jiangnan.edu.cn (F.L.) Institute of Advanced Technology, Jiangnan University, Wuxi 214122, China * Correspondence: yin.xu@jiangnan.edu.cn Abstract: High-performance and compact power splitters are fundamental components in on-chip photonic integrated circuits (PICs). We propose a silicon-based power splitter based on a subwave- length grating (SWG)-assisted multimode interference (MMI) structure. To shorten the device size and enhance the device performance, an inverse-tapered SWG is embedded in the central region of the MMI and two rows of uniform SWG are embedded on both sides, together with two right-angled cutting structures on the input side. According to the results, the MMI length was obviously reduced to 3.2 m (5.2 m for conventional MMI structure under the same waveguide width), while the insertion loss (IL) and reflection loss were 0.08 dB and <35 dB, respectively. Moreover, the allowable working bandwidth could be extended to 560 nm by keeping IL <0.6 dB, covering the whole optical communication band. On the basis of these features, we believe that such a power splitter is very promising for building on-chip large-scale PICs where power splitting is indispensable. Keywords: subwavelength grating; multimode interference; power splitter Citation: Shi, Y.; Shao, B.; Zhang, Z.; Zhou, T.; Luo, F.; Xu, Y. Ultra-Broadband and Low-Loss Silicon-Based Power Splitter Based on Subwavelength Grating-Assisted 1. Introduction Multimode Interference Structure. Silicon-on-insulator (SOI), a mature and promising platform for silicon photonics, has Photonics 2022, 9, 435. https:// been commonly employed to realize compact, high-performance, and high-yield photonic doi.org/10.3390/photonics9070435 integrated circuits (PICs) [1–5]. To construct such on-chip PICs, power splitters are fun- Received: 21 May 2022 damental and indispensable components, which play a key role in separating the input Accepted: 16 June 2022 light power into different output ports [6–10]. For the power splitter, different waveguide Published: 21 June 2022 structures have been reported, e.g., typical Y-junctions [6], adiabatic tapers [7], directional couplers (DCs) [8], photonic crystals (PCs) [9], and multimode interference (MMI) cou- Publisher’s Note: MDPI stays neutral plers [10]. With overall consideration of the device size, performance, and fabrication with regard to jurisdictional claims in tolerance, MMI couplers are the best choice since Y-branches require a large device size, published maps and institutional affil- while DCs and PCs have limited working bandwidths and tight fabrication tolerances, iations. respectively. Therefore, MMI-based power splitters are vital components applied in on-chip Mach–Zehnder interferometer (MZI) modulators [11,12], optical switches [13,14], and other on-chip optical circuits requiring a light power-splitting function [15,16]. Within these Copyright: © 2022 by the authors. application cases, a smaller device size and better device performance have become the Licensee MDPI, Basel, Switzerland. new requirements for silicon-based power splitters. This article is an open access article To further shorten the device size of MMI-based power splitters (e.g., typical MMI distributed under the terms and length of ~5.2 m under a waveguide width of 2.5 m [17,18]), we should enlarge the conditions of the Creative Commons effective index difference of the transmitted interference modes within the MMI region, Attribution (CC BY) license (https:// which needs to change the refractive index distribution of the conventional MMI structure. creativecommons.org/licenses/by/ Fortunately, a subwavelength grating (SWG) structure whose grating pitch is obviously 4.0/). Photonics 2022, 9, 435. https://doi.org/10.3390/photonics9070435 https://www.mdpi.com/journal/photonics Photonics 2022, 9, 435 2 of 12 shorter than the grating Bragg period behaves as a homogenous medium without a reflec- tion and diffraction effect for the input light (e.g.,  = 1.55 m) [19–22]. Furthermore, the effective refractive index of SWG structure can be easily changed by varying its grating duty cycle, offering a new degree of freedom for the device design [19–22]. Therefore, by adding such an SWG structure into the conventional MMI waveguide, the refractive index distribution of the whole structure becomes no longer uniform in the waveguide region, contributing to a reduction in MMI length [19]. Under this condition, various device schemes have been proposed. For instance, through embedding a row of SWGs in the central region of the MMI, the required MMI length was clearly reduced to 3.8 m (waveg- uide width 2.2 m) for power splitting [23]. Meanwhile, a dual polarization operation could also be achieved with the help of the tunability of the effective refractive index for an SWG structure [23]. To further shrink the MMI length, a tapered SWG structure was embedded in the central region of the MMI along the propagation direction, and the MMI length was reduced to only 1.92 m (waveguide width 2.0 m) with an insertion loss (IL) of 0.39 dB, which is quite beneficial for on-chip compact integration [24]. In addition to these schemes, an SWG-based MMI power splitter was shown to be a useful structure, where the MMI region was formed by SWGs with identical or different orientations for the grating component [25]. The corresponding MMI lengths could even be reduced to 3.2 m (waveguide width 2.8 m) with a large bandwidth of 400 nm (IL < 1 dB) [25]. However, we should note that the IL and working bandwidth of the power splitter still need to be efficiently reduced and increased, respectively, since the fundamental power splitter will be greatly required and heavily used in current and future on-chip large-scale PICs for splitting light power [26–28]. In this paper, we propose a silicon-based MMI power splitter, where the key MMI region is embedded by an inverse-tapered SWG in the center and two rows of uniform SWG slots on both sides along the propagation direction. The embedded central SWG is employed to change the whole refractive index distribution of the multimode silicon waveguide, which can help enlarge the effective index difference between excited modes and further reduce the MMI length. The embedded bilateral SWG slots are used to increase the coupling efficiency with the output waveguides via mode matching, corresponding to a reduction in power splitting loss. Through these two main techniques applied in the MMI structure for the power splitter, the key MMI length could be reduced to 3.2 m (waveguide width 2.5 m), while the obtained IL was only 0.08 dB at a wavelength of 1.55 m, along with a quite low reflection loss (RL) of <35 dB. Note that the device working bandwidth could be over 550 nm (covering the whole optical communication band) even under a strict criterion of IL < 0.6 dB. In addition, the fabrication tolerances of the key structural parameters were also analyzed. We hope that the proposed device can find important applications in the field of on-chip PICs. 2. Device Structure and Principle Figure 1 illustrates the three-dimensional schematic of our proposed SWG-assisted MMI power splitter, which consisted of an inverse-tapered SWG and two rows of uniform SWG slots embedded in the MMI center and on both sides, respectively. For a conventional MMI power splitter, as the input fundamental TE mode is injected into the MMI region from the central port, the new TE and TE mode are excited dominantly within the MMI 0 2 region, thus leading to a clear mode interference along the propagation direction. Once the accumulated phase difference between these two excited modes (TE and TE mode) is 0 2 equal to , a double image of the input TE mode with the same phase can be achieved after mode interference [17]. Finally, using two waveguides to separate and output such a double image, we can realize the function of power splitting. To efficiently shorten the MMI length and reduce the power splitting loss, we embedded an inverse-tapered SWG in the MMI center, where the width of the SWG was linearly tapered from w (=200 nm) to g1 w in a period number of n, and we embedded two rows of uniform SWG slots (period gn number N) on both sides of the MMI region, whereby their central positions along the Photonics 2022, 9, x FOR PEER REVIEW  3  of  12  Photonics 2022, 9, 435 3 of 12 slots (period number N) on both sides of the MMI region, whereby their central positions  along the propagation direction were aligned with those of the output waveguides. These  propagation direction were aligned with those of the output waveguides. These embedded embedded SWG structures had the same grating pitch and duty cycle of  = 200 nm and  SWG structures had the same grating pitch and duty cycle of L = 200 nm and a/L = 0.5, a/ = 0.5, respectively. The gap length between the left side of the inverse‐tapered SWG  respectively. The gap length between the left side of the inverse-tapered SWG (uniform (uniform SWG slot) and the left side of the MMI region was LS (LE), shown in the inset of  SWG slot) and the left side of the MMI region was L (L ), shown in the inset of Figure 1. S E Figure 1. Moreover, the length and width of MMI region were LM and WM (=2.5 μm), re‐ Moreover, the length and width of MMI region were L and W (=2.5 m), respectively. M M spectively. The widths of the central input waveguide and bilateral output waveguides  The widths of the central input waveguide and bilateral output waveguides were tapered were tapered from w1 to w2 in a length of LI and from w3 to w4 in a length of LO, respectively,  from w to w in a length of L and from w to w in a length of L , respectively, where the 1 2 I 3 4 O where the input and output waveguide widths were the same (w1 = w4 = 500 nm). In addi‐ input and output waveguide widths were the same (w = w = 500 nm). In addition, we 1 4 tion, we also introduced two right‐angled cutting structures on both sides of the input  also introduced two right-angled cutting structures on both sides of the input port of MMI port of MMI region symmetrically to further enhance the device performance, where the  region symmetrically to further enhance the device performance, where the corresponding corresponding length and width of the cutting structures were LT and (WM − w2)/2, respec‐ length and width of the cutting structures were L and (W w )/2, respectively. The T M 2 tively. The whole device was analyzed and simulated on the basis of a commercial SOI  whole device was analyzed and simulated on the basis of a commercial SOI wafer with a wafer with a 220 nm thick top silicon layer and a 2 μm thick buried oxide layer (SiO2),  220 nm thick top silicon layer and a 2 m thick buried oxide layer (SiO ), while the upper while the upper cladding was also SiO2 with a thickness of 2 μm.  cladding was also SiO with a thickness of 2 m. Figure 1. Schematic of our proposed power splitter based on SWG-assisted MMI structure, where an Figure 1. Schematic of our proposed power splitter based on SWG‐assisted MMI structure, where  inverse-tapered SWG and two rows of uniform SWG slots were embedded in the center and on both an inverse‐tapered SWG and two rows of uniform SWG slots were embedded in the center and on  sides of the MMI waveguidem respectively. The inset shows the top view of the key MMI region in both sides of the MMI waveguidem respectively. The inset shows the top view of the key MMI  detail. The material and structural parameters are also labeled. region in detail. The material and structural parameters are also labeled.  Figure 2a shows the calculated effective indices n of guided modes under different eff Figure 2a shows the calculated effective indices neff of guided modes under different  waveguide widths, where the TE polarization modes were analyzed. From this figure, waveguide widths, where the TE polarization modes were analyzed. From this figure, we  we can easily find the effective index of every supported mode for the waveguide width. can easily find the effective index of every supported mode for the waveguide width. For  For example, the silicon waveguide could support seven modes (from TE to TE ) when 0 6 example, the silicon waveguide could support seven modes (from TE0 to TE6) when the  the waveguide width was 2.5 m. For the multimode waveguide transmission, only even waveguide width was 2.5 μm. For the multimode waveguide transmission,  only even  modes (TE , TE , TE , TE ) could be adequately excited for the central injection from the 0 2 4 6 modes (TE0, TE2, TE4, TE6) could be adequately excited for the central injection from the  input single-mode waveguide [17]. Meanwhile, the TE and TE modes of the multimode 0 2 input single‐mode waveguide [17]. Meanwhile, the TE0 and TE2 modes of the multimode  waveguide would dominate among the excited modes according to our calculations. On the waveguide would dominate among the excited modes according to our calculations. On  basis of these two modes, we could roughly determine the required multimode waveguide the basis of these two modes, we could roughly determine the required multimode wave‐ length for the power splitting, where more precise length should be optimized using a guide length for the power splitting, where more precise length should be optimized us‐ numerical method. By adding SWG structures into the conventional MMI waveguide, the ing a numerical method. By adding SWG structures into the conventional MMI wave‐ effective index difference of dominant excited modes (TE and TE mode) within the MMI 0 2 guide,  the  effective  index  difference  of  dominant  excited  modes  (TE0  and  TE2  mode)  region was increased, leading to a reduction in beat length L [17–19]. within the MMI region was increased, leading to a reduction in beat length Lπ [17–19].  L =  , (1) 𝐿 ,   (1) 2 n n TE TE 0 2 2 𝑛 𝑛 where n , n are the mode effective indices of the excited TE and TE modes, and l TE0 TE2 0 2 where nTE0, nTE2 are the mode effective indices of the excited TE0 and TE2 modes, and λ is  is the working wavelength. If we set the MMI length L equal to the beat length L , we the working wavelength. If we set the MMI length LM equal to the beat length Lπ, we can  can obtain two TE modes (double image of the input TE mode) with the same phase 0 0 and same power, corresponding to the power splitting. The SWG structure can be treated Photonics 2022, 9, x FOR PEER REVIEW  4  of  12  obtain two TE0 modes (double image of the input TE0 mode) with the same phase and  Photonics 2022, 9, 435 4 of 12 same power, corresponding to the power splitting. The SWG structure can be treated as a  homogeneous medium, and its equivalent refractive index nSWG can be estimated as fol‐ lows [19]:  as a homogeneous medium, and its equivalent refractive index n can be estimated as SWG follows [19]: 𝑎 Λ𝑎 2 2 (2) 𝑛 ∙𝑛 ∙𝑛 ,  SWG a c L a 2 2 Λ Λ n = n + n , (2) SWG cl L L where nc and ncl denote the refractive index of the core (silicon) and cladding (silica) of the  where n and n denote the refractive index of the core (silicon) and cladding (silica) of the cl grating, respectively. Using Equation (2), we can roughly obtain the equivalent refractive  grating, respectively. Using Equation (2), we can roughly obtain the equivalent refractive index of the SWG structure. Figure 2b shows the calculated effective indices neff of guided  index of the SWG structure. Figure 2b shows the calculated effective indices n of guided eff modes  for  the  multimode  waveguide  (WM = 2.5 μm)  embedded  with  the  central  SWG  modes for the multimode waveguide (W = 2.5 m) embedded with the central SWG structure as a function of the SWG width wg. Note that the effective index difference be‐ structure as a function of the SWG width w . Note that the effective index difference tween dominant excited TE0 and TE2 modes is really increased with the increase in em‐ between dominant excited TE and TE modes is really increased with the increase in 0 2 bedded SWG width wg. This is the reason that the required MMI length can be reduced  embedded SWG width w . This is the reason that the required MMI length can be reduced compared with the conventional MMI structure. In the analyses below, we study the em‐ compared with the conventional MMI structure. In the analyses below, we study the bedded SWG structures in detail to achieve larger bandwidth and lower loss compared  embedded SWG structures in detail to achieve larger bandwidth and lower loss compared with with previous previous repor reports ts [2 [233–2 –255] ]..  Figure 2. (a) Effective indices n of guided modes as a function of the waveguide width for the TE eff Figure 2. (a) Effective indices neff of guided modes as a function of the waveguide width for the TE polar‐ polarization state. Insets show the electric field distributions of TE and TE modes. (b) Effective ization state. Insets show the electric field distributions of TE0 and TE2 0modes. (b 2 ) Effective indices neff of  indices n of guided modes for the multimode waveguide embedded with the central SWG structure guided modes for the multimode waveguide embedded with the central SWG structure as a function of  eff th as e SWG a function  width of wthe g. The SWG  mul width timodew wa . The vegu multimode ide width was waveguide  chosen as width  WM = was 2.5 μchosen m. Insets as sh Wow= the 2.5 elec m. tric  field distributions of TE0 and TE2 modes.  Insets show the electric field distributions of TE and TE modes. 0 2 3. Results and Discussion 3. Results and Discussion  For the device performance analyses, the three-dimensional finite-difference time- For the  device performance analyses, the three‐dimensional finite‐difference time‐do‐ domain (3D-FDTD) method was employed to help design and optimize the device pa- main (3D‐FDTD) method was employed to help design and optimize the device parameters  rameters [29,30]. Figure 3 shows the device transmission of several typical silicon-based [29,30]. Figure 3 shows the device transmission of several typical silicon‐based MMI power  MMI power splitters as a function of the MMI length L under the same MMI width splitters as a function of the MMI length LM under the same MMI width (WM = 2.5 μm). As  (W = 2.5 m). As shown in Figure 3, three types of MMI power splitter were considered, shown in Figure 3, three types of MMI power splitter were considered, conventional MMI  conventional MMI structure, uniform SWG embedded MMI structure, and inverse-tapered structure, uniform SWG embedded MMI structure, and inverse‐tapered SWG embedded  SWG embedded MMI structure. One can clearly find that the variation of device transmis- MMI  structure.  One  can  clearly  find  that  the  variation  of  device  transmission  became  sion became small within the calculation range of L when the MMI region was embedded small within the calculation range of LM when the MMI region was embedded with a uni‐ with a uniform or inverse-tapered SWG structure, corresponding to an increased MMI form or inverse‐tapered SWG structure, corresponding to an increased MMI length toler‐ length tolerance. Moreover, we can also observe that the optimum MMI length was ance. Moreover, we can also observe that the optimum MMI length was obviously de‐ obviously decreased from 5.0 m to 3.6 m (3.3 m) due to the embedded uniform (inverse- creased from 5.0 μm to 3.6 μm (3.3 μm) due to the embedded uniform (inverse‐tapered)  tapered) SWG structure in the center of the MMI region along the propagation direction, SWG contributing  structurto e in on-chip  the ce compact nter of th integration. e MMI reg Ifion we alo further ng thadded e prop linearly agationtaper  direed ction, structur  contes rib‐ connecting the input/output waveguides with the MMI region, the device transmission uting to on‐chip compact integration. If we further added linearly tapered structures con‐ could be obviously increased, while the variation range of transmission could be reduced, necting the input/output waveguides with the MMI region, the device transmission could  as shown in Figure 3. By comparison, we can find that the inverse-tapered SWG embedded be obviously increased, while the variation range of transmission could be reduced, as  MMI structure with input and output tapers obtained the best power splitting function shown in Figure 3. By comparison, we can find that the inverse‐tapered SWG embedded  together with largest tolerance for MMI length L , where the device transmission was MMI structure with input and output tapers obtained the best power splitting function  about 0.25 dB at L = 3.3 m.   Photonics 2022, 9, x FOR PEER REVIEW  5  of  12  Photonics 2022, 9, 435 5 of 12 together with largest tolerance for MMI length LM, where the device transmission was  about −0.25 dB at LM = 3.3 μm.  Figure 3. Transmission of several typical silicon-based MMI power splitters as a function of their Figure 3. Transmission of several typical silicon‐based MMI power splitters as a function of their  respective MMI lengths L . (a) I and II represent the conventional MMI structure without and respective MMI lengths LM. (a) I and II represent the conventional MMI structure without and with  with input/output tapers, respectively. (b) III and IV represent the MMI structure embedded with input/output tapers, respectively. (b) III and IV represent the MMI structure embedded with a uni‐ a uniform SWG waveguide without and with input/output tapers, respectively. (c) V and VI form SWG waveguide without and with input/output tapers, respectively. (c) V and VI represent  represent the MMI structure embedded with an inverse-tapered SWG waveguide without and with the MMI structure embedded with an inverse‐tapered SWG waveguide without and with input/out‐ put tapers, respectively.  input/output tapers, respectively. To perform a more detailed analysis of the inverse-tapered SWG structure, the embed- To perform a more detailed analysis of the inverse‐tapered SWG structure, the em‐ ded SWG parameters were defined as follows: bedded SWG parameters were defined as follows:  𝐿 𝐿 L L M S 𝑛 ,   (3) n = , (3) 𝑤 𝑤 𝑘𝑛 1 ,   (4) gn g1 w = w + k(n 1) , (4) gn g1 where k is the width increment of the inverse‐tapered SWG along the y‐direction; k was  where k is the width increment of the inverse-tapered SWG along the y-direction; k was chosen as 50 nm during structural optimization. More details about the choice of k can be  chosen as 50 nm during structural optimization. More details about the choice of k can found in the tolerance analyses described later. Therefore, LM, LS, and n are closely related.  be found in the tolerance analyses described later. Therefore, L , L , and n are closely M S Figure 4a shows the detailed device transmission with MMI length LM, where the optimal  related. Figure 4a shows the detailed device transmission with MMI length L , where the half period number m (n = m/2) of the SWG structure under different LM is also plotted.  optimal half period number m (n = m/2) of the SWG structure under different L is also From Figure 4, we can find that the device transmission was higher than −0.5 dB within the  plotted. From Figure 4, we can find that the device transmission was higher than 0.5 dB whole range from LM = 2.6 to 4.0 μm, and the optimal period number almost increased with  within the whole range from L = 2.6 to 4.0 m, and the optimal period number almost the increase in LM. Note that the device transmission reached a high value with relatively small  increased with the increase in L . Note that the device transmission reached a high value fluctuation when LM varied from 3.2 μm to 3.5 μm, marked by the oval in Figure 4a. By con‐ with relatively small fluctuation when L varied from 3.2 m to 3.5 m, marked by the sideration of the device size and required grating number, we set LM to 3.2 μm for the subse‐ oval in Figure 4a. By consideration of the device size and required grating number, we set quent analysis, where the optimal half period number m was 18 (n = 9). Figure 4b shows the  L to 3.2 m for the subsequent analysis, where the optimal half period number m was device transmission with gap length LS between the left side of the inverse‐tapered SWG and  18 (n = 9). Figure 4b shows the device transmission with gap length L between the left the left side of the MMI region, where LM was equal to 3.2 μm. According to Equation (2), the  side of the inverse-tapered SWG and the left side of the MMI region, where L was equal period number of the embedded SWG structure decreased as the gap length LS increased  to 3.2 m. According to Equation (2), the period number of the embedded SWG structure within the calculation range shown in Figure 4b. Meanwhile, the obtained transmission curve  decreased as the gap length L increased within the calculation range shown in Figure 4b. presented a nearly flat top as LS changed from 1.1 to 1.4 μm, and we chose LS = 1.4 μm, corre‐ Meanwhile, the obtained transmission curve presented a nearly flat top as L changed from sponding to the highest transmission shown in Figure 4b.  1.1 to 1.4 m, and we chose L = 1.4 m, corresponding to the highest transmission shown in Figure 4b. According to above analyses, the best device transmission of the MMI power splitter embedded with the inverse-tapered SWG was limited to about 0.25 dB at the wavelength of 1.55 m. To further enhance the device transmission or reduce the power splitting loss, we embedded two rows of uniform SWG on both sides of the MMI region, where the period number was N. Such embedded uniform SWG structures were employed to match the separated modes (double image of the input TE mode) within the MMI region with the output waveguide modes. Therefore, we set the central positions of embedded uniform SWGs along the propagation direction aligned with those of the output waveguides. Thus, the period number N and relative position L of such a uniform SWG was also determined. Figure 5 illustrates the device transmission as a function of L , where the optimal period   S Photonics 2022, 9, 435 6 of 12 number N and relative position L of the embedded uniform SWG are plotted for every gap length L . The grating parameters of the added uniform SWG were the same as those of the inverse-tapered SWG (grating pitch L = 200 nm, duty cycle a/L = 0.5), and the etching width of the uniform SWG in the y-direction was set as 100 nm, corresponding to the square etching slots. As shown in Figure 5, the optimal value of L was reduced compared with no embedded uniform SWG structure shown in Figure 5b. The reason is that the embedded uniform SWG could reduce the effective index on both sides of the MMI waveguide, and such a structure also required a further reduction in the effective index on the central side, leading to a reduction in L or an increase in period number n of the inverse-tapered SWG. Therefore, L decreased from 1.4 to 0.9 m, corresponding to the optimal values of N = 5 and L = 1.45 m. For the device transmission of our proposed power splitter, its value was obviously reduced to 0.08 dB at a wavelength of 1.55 m upon embedding the extra uniform SWG structures on both sides of the MMI region. Such a low transmission loss of the power splitter would be very beneficial to construct on-chip photonic devices (e.g., MZI modulators [11,12] and optical switches [13,14]) and large-scale PICs. During the calculation process shown in Figure 5, the choice of optimal values of N and L for every gap length L was also important. Here, we used L = 0.9 m as an example, and the results S S are plotted in Figure 6, where the period number of the embedded uniform SWG was set as N = 4, 5, and 6. Note that the obtained device transmissions revealed some fluctuations as the relative position L increased from 0.85 to 2.15 m, and the largest transmission loss was almost lower than 0.5 dB, as shown in Figure 6. These transmission fluctuations may have resulted from the interaction of the separated modes with the uniform SWG structure embedded on both sides of the multimode waveguide, where different interact positions led to different transmission losses due to the wave features of input light. In addition, we also introduced two right-angled cutting structures on both sides of the input MMI side in a symmetric manner (L = 0.25 m) to further reduce the device reflection loss (RL < 35 dB) and stabilize the light evolution through the proposed device. Therefore, through these structural designs and optimizations applied in the MMI region for power splitting, the device transmission loss was reduced to only 0.08 dB, while the required MMI length was Photonics 2022, 9, x FOR PEER REVIEW  6  of  12  3.2 m, representing an improvement compared to the conventional MMI power splitter without an embedded SWG structure. Figure 4. (a) Device transmission with MMI length L and optimal half period number m of the Figure 4. (a) Device transmission with MMI length LM and optimal half period number m of the  embedded SWG structure in the power splitter. SWG period number n = m/2. (b) Device transmission embedded SWG structure in the power splitter. SWG period number n = m/2. (b) Device transmis‐ siwith on with the gap the length gap leLng ,twher h LS,e whe L =re 3.2 LM m. = 3.The 2 μm. marked  The ma regions rkedr epr regions esent rep ther resen ecommended t the reco str mme uctural nded  S M structural parameter ranges.  parameter ranges. Next, we conduct wavelength spectrum analyses for the proposed device, where IL is According to above analyses, the best device transmission of the MMI power splitter  used to denote the device transmission loss. Figure 7 shows the wavelength dependence of embedded with the inverse‐tapered SWG was limited to about −0.25 dB at the wavelength  IL for the proposed device and conventional MMI power splitter, where the inset shows of 1.55 μm. To further enhance the device transmission or reduce the power splitting loss,  the device schematics, and key parameters are also marked. For a better comparison, we we embedded two rows of uniform SWG on both sides of the MMI region, where the  period number was N. Such embedded uniform SWG structures were employed to match  the separated modes (double image of the input TE0 mode) within the MMI region with  the output waveguide modes. Therefore, we set the central positions of embedded uni‐ form SWGs along the propagation direction aligned with those of the output waveguides.  Thus, the period number N and relative position LE of such a uniform SWG was also de‐ termined. Figure 5 illustrates the device transmission as a function of LS, where the opti‐ mal period number N and relative position LE of the embedded uniform SWG are plotted  for every gap length LS. The grating parameters of the added uniform SWG were the same  as those of the inverse‐tapered SWG (grating pitch  = 200 nm, duty cycle a/ = 0.5), and  the etching width of the uniform SWG in the y‐direction was set as 100 nm, corresponding  to the square etching slots. As shown in Figure 5, the optimal value of LS was reduced  compared with no embedded uniform SWG structure shown in Figure 5b. The reason is  that the embedded uniform SWG could reduce the effective index on both sides of the  MMI waveguide, and such a structure also required a further reduction in the effective  index on the central side, leading to a reduction in LS or an increase in period number n of  the inverse‐tapered SWG. Therefore, LS decreased from 1.4 to 0.9 μm, corresponding to  the optimal values of N = 5 and LE = 1.45 μm. For the device transmission of our proposed  power splitter, its value was obviously reduced to −0.08 dB at a wavelength of 1.55 μm  upon embedding the extra uniform SWG structures on both sides of the MMI region. Such  a low transmission loss of the power splitter would be very beneficial to construct on‐chip  photonic devices (e.g., MZI modulators [11,12] and optical switches [13,14]) and large‐ scale PICs. During the calculation process shown in Figure 5, the choice of optimal values  of N and LE for every gap length LS was also important. Here, we used LS = 0.9 μm as an  example, and the results are plotted in Figure 6, where the period number of the embed‐ ded uniform SWG was set as N = 4, 5, and 6. Note that the obtained device transmissions  revealed some fluctuations as the relative position LE increased from 0.85 to 2.15 μm, and  the largest transmission loss was almost lower than 0.5 dB, as shown in Figure 6. These  transmission fluctuations may have resulted from the interaction of the separated modes  with the uniform SWG structure embedded on both sides of the multimode waveguide,  where different interact positions led to different transmission losses due to the wave fea‐ tures of input light. In addition, we also introduced two right‐angled cutting structures  on both sides of the input MMI side in a symmetric manner (LT = 0.25 μm) to further reduce    Photonics 2022, 9, 435 7 of 12 chose quite a large wavelength range calculated from 1.15 to 1.95 m, and the MMI width was set as the same (W = 2.5 m) for both devices, where the material dispersions of silicon and silica were also considered [31]. From Figure 7, we can clearly find that the allowable working bandwidth of the conventional MMI power splitter was very large (1360–1770 nm) when keeping IL < 0.6 dB. This is the main reason for the MMI structure’s superiority over the DC or PC structure for power splitting [8–10]. By comparison, the allowable working bandwidth of our proposed power splitter could be extended from 1240 nm to 1800 nm covering the whole optical communication band if IL < 0.6 dB was also satisfied. Therefore, the obtained working bandwidth (560 nm) of the power splitter Photonics 2022, 9, x FOR PEER REVIEW  7  of  12  based on our proposed structure could be even higher than that of the commonly used  Photonics 2022, 9, x FOR PEER REVIEW  7  of  12  broadband MMI power splitter (410 nm), revealing the ultra-broadband feature of our proposed device. Table 1 compares our proposed power splitter with other MMI power splitters embedded with an SWG structure reported recently, where the MMI dimension, the device reflection loss (RL < −35 dB) and stabilize the light evolution through the pro‐ the device reflection loss (RL < −35 dB) and stabilize the light evolution through the pro‐ IL, RL, and allowable working bandwidth were all considered. It can be noted that the posed device. Therefore, through these structural designs and optimizations applied in  posed device. Therefore, through these structural designs and optimizations applied in  proposed power splitter had obvious advantages of ultra-broadband, low IL, and low RL, the MMI region for power splitting, the device transmission loss was reduced to only 0.08  the MMI region for power splitting, the device transmission loss was reduced to only 0.08  while the required MMI dimension was comparable with other reports. Therefore, the dB, while the required MMI length was 3.2 μm, representing an improvement compared  dB, present  while device  the req can uire bed employed  MMI leng asthan wa efsficient  3.2 μm, and represe broadband ntingpower  an improv splitting ement component  compared  to the conventional MMI power splitter without an embedded SWG structure.  to applied  the conv inention on-chip al  PICs. MMI power splitter without an embedded SWG structure.  Figure 5. Device transmission of the new designed power splitter as a function of its gap length LS,  Figure 5. Device transmission of the new designed power splitter as a function of its gap length L , Figure 5. Device transmission of the new designed power splitter as a function of its gap length LS,  where the optimal period number N and relative position LE of the embedded uniform SWG are  where the optimal period number N and relative position L of the embedded uniform SWG are also where the optimal period number N and relative position LE of the embedded uniform SWG are  also plotted for every gap length LS.  plotted for every gap length L . also plotted for every gap length LS.  Figure 6. Device transmission of the new designed device as a function of its period number N and Figure 6. Device transmission of the new designed device as a function of its period number N and  Figure 6. Device transmission of the new designed device as a function of its period number N and  relative position L of the embedded uniform SWG. L is set as 0.9 m. relative position LE E of the embedded uniform SWG. L SS is set as 0.9 μm.  relative position LE of the embedded uniform SWG. LS is set as 0.9 μm.  Next, we conduct wavelength spectrum analyses for the proposed device, where IL  Next, we conduct wavelength spectrum analyses for the proposed device, where IL  is used to denote the device transmission loss. Figure 7 shows the wavelength dependence  is used to denote the device transmission loss. Figure 7 shows the wavelength dependence  of IL for the proposed device and conventional MMI power splitter, where the inset shows  of IL for the proposed device and conventional MMI power splitter, where the inset shows  the device schematics, and key parameters are also marked. For a better comparison, we  the device schematics, and key parameters are also marked. For a better comparison, we  chose quite a large wavelength range calculated from 1.15 to 1.95 μm, and the MMI width  chose quite a large wavelength range calculated from 1.15 to 1.95 μm, and the MMI width  was set as the same (WM = 2.5 μm) for both devices, where the material dispersions of sili‐ was set as the same (WM = 2.5 μm) for both devices, where the material dispersions of sili‐ con and silica were also considered [31]. From Figure 7, we can clearly find that the allowable  con and silica were also considered [31]. From Figure 7, we can clearly find that the allowable  working bandwidth of the conventional MMI power splitter was very large (1360–1770 nm)  working bandwidth of the conventional MMI power splitter was very large (1360–1770 nm)  when keeping IL <0.6 dB. This is the main reason for the MMI structure’s superiority over the  when keeping IL <0.6 dB. This is the main reason for the MMI structure’s superiority over the  DC or  PC  structure  for  power  splitting  [8–10].  By  comparison,  the  allowable  working  DC or  PC  structure  for  power  splitting  [8–10].  By  comparison,  the  allowable  working  bandwidth of our proposed power splitter could be extended from 1240 nm to 1800 nm  bandwidth of our proposed power splitter could be extended from 1240 nm to 1800 nm  covering the whole optical communication band if IL <0.6 dB was also satisfied. Therefore,  covering the whole optical communication band if IL <0.6 dB was also satisfied. Therefore,  the obtained working bandwidth (560 nm) of the power splitter based on our proposed  the obtained working bandwidth (560 nm) of the power splitter based on our proposed  structure could be even higher than that of the commonly used broadband MMI power  structure could be even higher than that of the commonly used broadband MMI power    Photonics 2022, 9, x FOR PEER REVIEW  8  of  12  splitter (410 nm), revealing the ultra‐broadband feature of our proposed device. Table 1  compares our proposed power splitter with other MMI power splitters embedded with  an SWG structure reported recently, where the MMI dimension, IL, RL, and allowable  working bandwidth were all considered. It can be noted that the proposed power splitter  had obvious advantages of ultra‐broadband, low IL, and low RL, while the required MMI  Photonics 2022, 9, 435 dimension was comparable with other reports. Therefore, the present device can be 8 of em 12 ‐ ployed as an efficient and broadband power splitting component applied in on‐chip PICs.  Figure 7. Wavelength dependence of IL for the conventional MMI power splitter (I) and the pro‐ Figure 7. Wavelength dependence of IL for the conventional MMI power splitter (I) and the proposed posed device (II). The inset shows the corresponding device schematics.  device (II). The inset shows the corresponding device schematics. Table 1. Device comparison of typical MMI power splitters embedded with SWG structure. Table 1. Device comparison of typical MMI power splitters embedded with SWG structure.  Dimension of MMI   Dimension of MMI Reference  IL (dB) @ 1550 nm  RL (dB) @ 1550 nm  Bandwidth (nm)  Reference IL (dB) @ 1550 nm RL (dB) @ 1550 nm Bandwidth (nm) Region (m ) Region (μm )  [23] [23  ] 2.22.2   3.8 3.8  0.0 0.07 7 −28 28.29 .29  280 280 (IL (IL < <0 0.3.3dB)  dB)  [24] 2.0  1.92 0.39 30.51 ~105 (PDL < 0.1 dB) * [24]  2.0    1.92  0.39 −30.51  ~105 (PDL <0.1 dB) *  [25] ** 2.8  3.2 0.20 - 420 (IL < 1.0 dB) [25] ** 2.8    3.2  0.20 ‐  420 (IL <1.0 dB)  This work 2.5  3.2 0.08 35.61 560 (IL < 0.6 dB) This work  2.5    3.2  0.08  −35.61  560 (IL <0.6 dB)  * PDL, polarization-dependent loss. ** Experimental results. “-”: not mentioned. * PDL, polarization‐dependent loss. ** Experimental results. “‐”: not mentioned.  For the device fabrication, we only needed one-step lithography and etching processes For the device fabrication, we only needed one‐step lithography and etching pro‐ on a commercial SOI wafer with 220 nm-thick top silicon layer, since the proposed device cesses on a commercial SOI wafer with 220 nm‐thick top silicon layer, since the proposed  had a uniform etching depth (220 nm). Moreover, the required minimum linewidth was device had a uniform etching depth (220 nm). Moreover, the required minimum linewidth  100 nm, which can be easily achieved by current E-beam lithography [1,32]. Within our was 100 nm, which can be easily achieved by current E‐beam lithography [1,32]. Within  proposed device, the most important structures were the inverse-tapered SWG embedded our proposed device, the most important structures were the inverse‐tapered SWG em‐ in the MMI center and the two rows of uniform SWG embedded on both sides of the MMI bedded in the MMI center and the two rows of uniform SWG embedded on both sides of  region. Here, we mainly considered the device performance affected by the lateral shift of the MMI region. Here, we mainly considered the device performance affected by the lat‐ the embedded SWG structure in the y-direction with respect to the MMI waveguide, and eral shift of the embedded SWG structure in the y‐direction with respect to the MMI wave‐ the results are shown in Figure 8, where Dw and Dw represent the lateral shift (y-direction) S E guide, of the and inverse-taper  the resulted s ar SWG e shoand wn in uniform  FigureSWG  8, wher from e Δ their wS and design  ΔwE a re tedpresent positions  thementioned  lateral shift  (yabove. ‐direction) Mor eover of the , we invintr erse oduce ‐tapered a new  SW index G and called  unifo the rm splitting SWG fro ratio m th(SR) eir design to characterize ated posi‐ the ratio of light power received at output ports due to structural parameter deviations, tions mentioned above. Moreover, we introduce a new index called the splitting ratio (SR)  to characterize the ratio of light power received at output ports due to structural parame‐ Output2 ter deviations,  SR = , (5) Output1 SR ,   (5) where P and P are the receiving power at the two output ports illustrated in Output1 Output2 𝑃 Figure 1. Considering the structural symmetry of our proposed power splitter, performance where POutput1 and POutput2 are the receiving power at the two output ports illustrated in  variation due to lateral shift of Dw was only calculated on one side (positive y-direction, Figure 1. Considering the structural symmetry of our proposed power splitter, perfor‐ Dw > 0), as shown in Figure 8a,b, and the results due to a shift on the other side (negative mance variation due to lateral shift of ΔwS was only calculated on one side (positive y‐ y-direction, Dw < 0) were the same. To keep SR higher than 0.9, Dw should be controlled S S within the interval [30 nm, 30 nm]. Moreover, for the two rows of uniform SWGs embedded on both sides of the MMI region, we considered one row shifting from its   optimal position due to fabrication imperfections, while the other row’s effect on device performance was considered identical due to structural symmetry. As shown in Figure 8c,d, the available variation of Dw was within the interval [140 nm, 200 nm] when keeping SR > 0.9. By comparison, the central SWG structure had a tighter tolerance range with Photonics 2022, 9, x FOR PEER REVIEW  9  of  12  direction, ΔwS > 0), as shown in Figure 8a,b, and the results due to a shift on the other side  (negative y‐direction, ΔwS < 0) were the same. To keep SR higher than 0.9, ΔwS should be  controlled within the interval [−30 nm, 30 nm]. Moreover, for the two rows of uniform  SWGs embedded on both sides of the MMI region, we considered one row shifting from its  optimal position due to fabrication imperfections, while the other row’s effect on device per‐ formance was considered identical due to structural symmetry. As shown in Figure 8c,d, the  available variation of ΔwE was within the interval [−140 nm, 200 nm] when keeping SR > 0.9.  Photonics 2022, 9, 435 9 of 12 By comparison, the central SWG structure had a tighter tolerance range with regard to  device fabrication because such a structure had a strong influence on the mode splitting  in the MMI region. Thus, the variation range of SR for the central inverse‐tapered SWG  regard to device fabrication because such a structure had a strong influence on the mode shift was larger than that for the bilateral uniform SWG shift. Under such conditions, we  splitting in the MMI region. Thus, the variation range of SR for the central inverse-tapered further analyzed the effect of the central inverse‐tapered SWG shift on the power ratio  SWG shift was larger than that for the bilateral uniform SWG shift. Under such conditions, between the two output ports, as shown in Figure 8e. Note that we could achieve a change  we further analyzed the effect of the central inverse-tapered SWG shift on the power ratio in between  powerthe  ratio two from output  neaports, rly 30:as 70shown  to 70:3in 0 by Figur  onley8 sh e.iNote fting that the ce wentcould ral invers achieve e‐tap ae change red SWG  in power ratio from nearly 30:70 to 70:30 by only shifting the central inverse-tapered SWG structure  relative  to  the  silicon  waveguide  along  the  y‐direction.  Such  a  characteristic  structure relative to the silicon waveguide along the y-direction. Such a characteristic would introduce new applications for the power splitter. We also analyzed the effect of  would introduce new applications for the power splitter. We also analyzed the effect of the width increment k of the inverse‐tapered SWG on the device performance, as shown  the width increment k of the inverse-tapered SWG on the device performance, as shown in Figure 9a. As shown in this figure, the highest IL was lower than 0.3 dB within the  in Figure 9a. As shown in this figure, the highest IL was lower than 0.3 dB within the whole calculation range from k = 20 nm to k = 100 nm, and the optimum value of k was  whole calculation range from k = 20 nm to k = 100 nm, and the optimum value of k was located at the position of k = 40 nm or k = 50 nm. This is why we chose k as 50 nm in the  located at the position of k = 40 nm or k = 50 nm. This is why we chose k as 50 nm previous analyses. Figure 9b shows the effect of grating size variation on device perfor‐ in the previous analyses. Figure 9b shows the effect of grating size variation on device mance (IL). Here, we considered the grating width variation along both x‐ and y‐directions.  performance (IL). Here, we considered the grating width variation along both x- and y- For example, a grating size of 100% corresponded to the optimum widths along the x‐ and  directions. For example, a grating size of 100% corresponded to the optimum widths along y‐directions, while a grating size of 120% corresponded to a width increment of 20% rela‐ the x- and y-directions, while a grating size of 120% corresponded to a width increment of tive to the optimum widths along the x‐ and y‐directions. According to the results, the  20% relative to the optimum widths along the x- and y-directions. According to the results, available grating width variation range should be controlled within the range of 53% to  the available grating width variation range should be controlled within the range of 53% to 135% relative to the optimum values by keeping IL <0.3 dB, where 53% indicates a grating  135% relative to the optimum values by keeping IL < 0.3 dB, where 53% indicates a grating width decrement of 47% relative to the optimum width. Such a relatively large width var‐ width decrement of 47% relative to the optimum width. Such a relatively large width iation range is beneficial for device fabrication. Therefore, these obtained tolerance ranges  variation range is beneficial for device fabrication. Therefore, these obtained tolerance of the key embedded SWG structures in the MMI region need to be guaranteed during  ranges of the key embedded SWG structures in the MMI region need to be guaranteed practical device fabrication [32].  during practical device fabrication [32]. Figure 8. Fabrication tolerance analyses. Device performance (transmission, IL, and SR) variation due Figure 8. Fabrication tolerance analyses. Device performance (transmission, IL, and SR) variation  to (a,b) lateral shift (positive y-direction) Dw of inverse-tapered SWG structure, and (c,d) lateral shift due to (a,b) lateral shift (positive y‐direction) ΔwS of inverse‐tapered SWG structure, and (c,d) lateral  (y-direction) Dw of one row of uniform SWG structures embedded in the MMI region. (e) Power shift (y‐direction) ΔwE of one row of uniform SWG structures embedded in the MMI region. (e)  proportion between the two output ports and the obtained device IL as a function of the lateral shift Power proportion between the two output ports and the obtained device IL as a function of the  Dw of the inverse-tapered SWG structure. The inset shows the device schematic. lateral shift ΔwS of the inverse‐tapered SWG structure. The inset shows the device schematic.  On the basis of the abovementioned device design and optimization processes, the final device parameters were as follows: w = w = 0.5 m, w = 0.94 m, w = 0.6 m, 1 4 2 3 L = 1.38 m, L = 2.0 m, W = 2.5 m, L = 3.2 m, L = 0.9 m, L = 1.45 m, I O M M S E L = 0.25 m, m = 23, N = 5, w = 0.2 m, and waveguide thickness = 220 nm. Figure 10 T g1 plots the electric field evolution through the designed power splitter, where the working wavelength was 1.55 m. From Figure 10, we can clearly observe that the input funda- mental TE mode could be evenly separated into the two output ports, and the electric Photonics 2022, 9, x FOR PEER REVIEW  10  of  12  Photonics 2022, 9, 435 10 of 12 field evolution was quite stable without any fluctuations or ripples. In comparison to the conventional MMI structure, no clear periodic interference pattern could be observed. The reason is that the embedded SWG region had a lower refractive index compared with the silicon waveguide, and the inverse-tapered shape of the SWG structure broke the period interference behavior in the conventional MMI structure. Furthermore, we can find that Figure 9. Fabrication tolerance analyses. IL dependence on (a) the width increment k of the inverse‐ its evolution pattern was similar to that of a typical Y splitter. Thus, we cannot find a tapered SWG for the proposed device and (b) the grating size variation. A grating size of 100%  standard period interference pattern in the SWG assisted MMI region, but its working corresponds to the optimum widths along the x‐ and y‐directions. A grating size of 120% corre‐ principle is still based on the MMI effect since the power splitter based on the Y junction sponds to grating width increments relative to the optimum widths along the x‐ and y‐directions.  nearly cannot be realized in a length of only 3.2 m. Both a small branch angle and a large The horizontal line represents IL = 0.3 dB.  conversion length are required for the Y junction-based power splitter. For the proposed power splitter, its total device length is ~6.5 m when both considering the input and On the basis of the abovementioned device design and optimization processes, the  output tapers, while the MMI length is only 3.2 m. Using such a device, we can efficiently final device parameters were as follows: w1 = w4 = 0.5 μm, w2 = 0.94 μm, w3 = 0.6 μm, LI = 1.38 μm,  realize the power splitting function with an ultrabroad bandwidth, low insertion loss, and LO = 2.0 μm, WM = 2.5 μm, LM = 3.2 μm, LS = 0.9 μm, LE = 1.45 μm, LT = 0.25 μm, m = 23, N = 5,  low reflection loss in a compact size, which can be used as the fundamental component Photonics 2022, 9, x FOR PEER REVIEW  10  of  12  wg1 = 0.2 μm, and waveguide thickness = 220 nm. Figure 10 plots the electric field evolution    for constructing other photonic devices and would be very promising for building on-chip th lar ro ge-scale ugh thePICs  desi[g 26 ned –28 power ].  splitter, where the working wavelength was 1.55 μm. From  Figure 10, we can clearly observe that the input fundamental TE mode could be evenly  separated into the two output ports, and the electric field evolution was quite stable with‐ out any fluctuations or ripples. In comparison to the conventional MMI structure, no clear  periodic interference pattern could be observed. The reason is that the embedded SWG  region had a lower refractive index compared with the silicon waveguide, and the inverse‐ tapered shape of the SWG structure broke the period interference behavior in the conven‐ tional MMI structure. Furthermore, we can find that its evolution pattern was similar to  that of a typical Y splitter. Thus, we cannot find a standard period interference pattern in  the SWG assisted MMI region, but its working principle is still based on the MMI effect  since the power splitter based on the Y junction nearly cannot be realized in a length of  only 3.2 μm. Both a small branch angle and a large conversion length are required for the  Y junction‐based power splitter. For the proposed power splitter, its total device length is  ~6.5 μm when both considering the input and output tapers, while the MMI length is only  Figure 9. Fabrication tolerance analyses. IL dependence on (a) the width increment k of the inverse- Figure 9. Fabrication tolerance analyses. IL dependence on (a) the width increment k of the inverse‐ 3.2 μm. Using such a device, we can efficiently realize the power splitting function with  tapered SWG for the proposed device and (b) the grating size variation. A grating size of 100% tapered SWG for the proposed device and (b) the grating size variation. A grating size of 100%  an corr ul esponds trabroa todthe  ban optimum dwidth, widths  low  along insertio thenx -lo and ss,y and -directions.  low re Aflgrating ection size loss of in 120%  a co corr mp esponds act size,  corresponds to the optimum widths along the x‐ and y‐directions. A grating size of 120% corre‐ whi to grating ch can width be used incr as ements  the funda relative mental to the co optimum mponent widths  for constructing along the x- ot and hery photonic -directions. devic Thees  sponds to grating width increments relative to the optimum widths along the x‐ and y‐directions.  and horizontal  would line  be  rvery epresents  prom ILis =ing 0.3 dB. for building on‐chip large‐scale PICs [26–28].  The horizontal line represents IL = 0.3 dB.  On the basis of the abovementioned device design and optimization processes, the  final device parameters were as follows: w1 = w4 = 0.5 μm, w2 = 0.94 μm, w3 = 0.6 μm, LI = 1.38 μm,  LO = 2.0 μm, WM = 2.5 μm, LM = 3.2 μm, LS = 0.9 μm, LE = 1.45 μm, LT = 0.25 μm, m = 23, N = 5,  wg1 = 0.2 μm, and waveguide thickness = 220 nm. Figure 10 plots the electric field evolution  through the designed power splitter, where the working wavelength was 1.55 μm. From  Figure 10, we can clearly observe that the input fundamental TE mode could be evenly  separated into the two output ports, and the electric field evolution was quite stable with‐ out any fluctuations or ripples. In comparison to the conventional MMI structure, no clear  periodic interference pattern could be observed. The reason is that the embedded SWG  region had a lower refractive index compared with the silicon waveguide, and the inverse‐ tapered shape of the SWG structure broke the period interference behavior in the conven‐ Figure 10. Electrical field evolution of input fundamental TE mode (dominant component: E ) along 0 y Figure 10. Electrical field evolution of input fundamental TE0 mode (dominant component: Ey) along  tional MMI structure. Furthermore, we can find that its evolution pattern was similar to  the propagation direction through the proposed device, where the MMI length was 3.2 m. the propagation direction through the proposed device, where the MMI length was 3.2 μm.  that of a typical Y splitter. Thus, we cannot find a standard period interference pattern in  4. Conclusions the SWG assisted MMI region, but its working principle is still based on the MMI effect  In summary, by embedding an inverse-tapered SWG and two rows of uniform SWG since the power splitter based on the Y junction nearly cannot be realized in a length of  structures into the conventional MMI waveguide, the input fundamental TE mode could only 3.2 μm. Both a small branch angle and a large conversion length are required for the  be evenly separated into two output ports, corresponding to a power splitting function. Y junction‐based power splitter. For the proposed power splitter, its total device length is  Compared with the conventional MMI power splitter, the added SWG structures could ~6.5 μm when both considering the input and output tapers, while the MMI length is only  help to shorten the MMI length and enlarge the working bandwidth, as well as reduce 3.2 μm. Using such a device, we can efficiently realize the power splitting function with  an ultrabroad bandwidth, low insertion loss, and low reflection loss in a compact size,  which can be used as the fundamental component for constructing other photonic devices  and would be very promising for building on‐chip large‐scale PICs [26–28].  Figure 10. Electrical field evolution of input fundamental TE0 mode (dominant component: Ey) along  the propagation direction through the proposed device, where the MMI length was 3.2 μm.    Photonics 2022, 9, 435 11 of 12 the insertion loss and reflection loss. According to the results, the required MMI length was reduced to 3.2 m under a waveguide width of 2.5 m, while the IL was only 0.08 dB, together with a low reflection loss <35 dB. Moreover, the device working bandwidth was quite large (>550 nm) while keeping IL < 0.6 dB. Considering its performance and size, the proposed power splitter has obvious advantages compared to previous reports, especially in terms of the working bandwidth and IL. Moreover, the fabrication processes of the proposed device are similar to those of previous reports without introducing extra processing requirements. Therefore, with these advantages, the proposed device could be a good candidate for application in on-chip PICs requiring a power splitting function. Author Contributions: Conceptualization, Y.S. and Y.X.; methodology, Y.S., B.S., Z.Z., T.Z., F.L. and Y.X.; investigation, Y.S. and Y.X.; writing—original draft preparation, Y.S. and Y.X.; writing—review and editing, all authors; supervision, Y.X.; project administration, Y.X. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Natural Science Foundation of Jiangsu Province, grant number BK20200592, and the Fundamental Research Funds for the Central Universities, grant number JUSRP12024. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data that support the findings of this study are available from the corresponding author upon reasonable request. Conflicts of Interest: The authors declare no conflict of interest. References 1. Siew, S.Y.; Li, B.; Gao, F.; Zheng, H.Y.; Zhang, W.; Guo, P.; Xie, S.W.; Song, A.; Dong, B.; Luo, L.W.; et al. 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Journal

PhotonicsMultidisciplinary Digital Publishing Institute

Published: Jun 21, 2022

Keywords: subwavelength grating; multimode interference; power splitter

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