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A Broadband Polarization-Insensitive Graphene Modulator Based on Dual Built-in Orthogonal Slots Plasmonic Waveguide

A Broadband Polarization-Insensitive Graphene Modulator Based on Dual Built-in Orthogonal Slots... Article A Broadband Polarization-Insensitive Graphene Modulator Based on Dual Built-in Orthogonal Slots Plasmonic Waveguide 1 1 1 2 1 1, 1 Wei Chen , Yan Xu , Yang Gao , Lanjing Ji , Xibin Wang , Xiaoqiang Sun * and Daming Zhang State Key Laboratory of Integrated Optoelectronics, College of Electronic Science & Engineering, Jilin University, Changchun 130012, China; chenwei18@mails.jlu.edu.cn (W.C.); xyan17@mails.jlu.edu.cn (Y.X.); ygao17@mails.jlu.edu.cn (Y.G.); xibinwang@jlu.edu.cn (X.W.); zhangdm@jlu.edu.cn (D.Z.) Institute of Marine Science and Technology, Shandong University, Qingdao 250100, China; jilanting@sdu.edu.cn * Correspondence: sunxq@jlu.edu.cn Abstract: A broadband polarization-insensitive graphene modulator has been proposed. The dual built-in orthogonal slots waveguide allows polarization independence for the transverse electric (TE) mode and the transverse magnetic (TM) mode. Due to the introduction of metal slots in both the vertical and horizontal directions, the optical field as well as the electro-absorption of graphene are enhanced by the plasmonic effect. The proposed electro-optic modulator shows a modulation depth of 0.474 and 0.462 dB/μm for two supported modes, respectively. An ultra-low effective index difference of 0.001 can be achieved within the wavelength range from 1100 to 1900 nm. The 3 dB- bandwidth is estimated to be 101 GHz. The power consumption is 271 fJ/bit at a modulation length of 20 μm. The proposed modulator provides high speed broadband solutions in microwave pho- tonic systems. Citation: Chen, W.; Xu, Y.; Gao, Y.; Keywords: graphene; plasmonic modulator; waveguide; polarization-insensitive Ji, L.; Wang, X.; Sun, X.; Zhang, D. A Broadband Polarization-Insensitive Graphene Modulator Based on Dual Built-in Orthogonal Slots Plasmonic 1. Introduction Waveguide. Appl. Sci. 2021, 11, 1897. High performance electro-optic (EO) modulators are highly demanded in wideband https://doi.org/10.3390/app11041897 optics communication networks [1]. The lithium niobite-based modulators are mature but suffer from a large footprint [2]. Silicon modulators are compatible with CMOS technol- Academic Editor: Filippo Giannazzo ogy, while facing the problem of low EO efficiency [3]. III-V based modulators offer a Received: 10 February 2021 small footprint; however, the insertion loss and thermal stability are still to be improved Accepted: 19 February 2021 [4]. SiC-based waveguides also show application potential [5]. Due to the unsatisfactory Published: 21 February 2021 EO properties of the above underlying materials, modulators that meet all requires are still elusive. Graphene with excellent EO characteristics has been well studied and widely Publisher’s Note: MDPI stays neu- adopted in optical modulators [6–9]. In 2011, Liu et al. experimentally presented a gra- tral with regard to jurisdictional phene modulator with a modulation depth (MD, the difference between “ON” state and claims in published maps and institu- “OFF” state) of 0.1 dB/μm [10]. A built-in p-oxide-n-like junction graphene modulator tional affiliations. exhibited an MD of 0.16 dB/μm and a power consumption of 1 pJ/bit [11]. The graphene EO modulator with a high 3 dB-bandwidth of 30 GHz has also been demonstrated [12]. However, the performance of above graphene modulators is limited by the weak interac- tion between the extremely thin graphene flake and the light field that is strongly Copyright: © 2021 by the authors. bounded in the high index dielectric material. If the plasmonic effect is introduced, the Licensee MDPI, Basel, Switzerland. light can propagate as a surface plasmon polarizations (SPPs) mode along the waveguide, This article is an open access article which implies an enhanced optical field intensity. More optical power will be guided to distributed under the terms and the dielectric/graphene interface, facilitating the light–graphene interaction [13–15]. conditions of the Creative Commons Huang et al. proposed a waveguide-coupled hybrid plasmonic graphene modulator with Attribution (CC BY) license (http://creativecommons.org/licenses a 3 dB-bandwidth of 0.48 THz and an energy consumption of 145 fJ/bit [16]. A hybrid /by/4.0/). Appl. Sci. 2021, 11, 1897. https://doi.org/10.3390/app11041897 www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, 1897 2 of 16 plasmonic graphene modulator with a 3 dB-bandwidth of 0.662 THz and a power con- sumption of 118.7 fJ/bit promises good potential for hybrid plasmonic graphene EO mod- ulators [17]. Another issue for the graphene modulator is the polarization sensitivity, which originates from the low absorption rate of 2.3% for the electric field polarization perpendicular to the graphene flake surface. Most reported works can only operate in transverse magnetic (TM) or transverse electric (TE) polarization independently [18]. The introduction of polarization control functions will inevitably complexify the device struc- ture [19]. Therefore, a compact and polarization-insensitive graphene modulator with characteristic of broadband operation is desirable. In this paper, we proposed a graphene modulator based on a dual built-in orthogonal slots waveguide (DBOSW). The geometric parameters of the hybrid plasmonic waveguide are investigated and optimized by finite element method (FEM). The mechanism of po- larization insensitivity and broadband modulation is elaborated in detail. Our proposed waveguide structure overcomes the strict polarization dependence of plasmonic-based waveguides. Moreover, the DBOSW graphene modulator realizes broadband modulation with excellent polarization independence, which shows good potential in microwave pho- tonic systems. 2. Configuration and Structure 2.1. Device Structure As shown in Figure 1, the proposed graphene modulator based on the dual built-in orthogonal slots waveguide consists of a bottom silver layer (Ag, nAg = 0.14447+ 11.366), a middle silica layer (SiO2, nSiO2 = 1.45) and a top silver slot isolated by SiO2. Double 0.33 nm- thick graphene flakes are isolated by 15 nm-thick SiO2 and cover the hybrid waveguide. The metal stacks–graphene contacts form the electrodes [20]. The whole structure is sup- ported by the SiO2 substrate. Figure 1. (a) Two-dimensional (2D) cross section; (b) three-dimensional (3D) view of the graphene modulator with dual built-in orthogonal slots waveguide. Graphene plays a major role in optical modulation of this modulator. As shown in Figure 2a, the transmission spectrum of DBOSW with a modulation length of L = 20 μm covered with graphene-SiO2-graphene stacks but without applied voltage (U = 0 V (μc = 0 eV)) has a sharp drop compared to DBOSW without graphene. This large significant light loss mainly originates from the light absorption effect of graphene, indicating that gra- phene has an effective light modulation function. Appl. Sci. 2021, 11, 1897 3 of 16 Figure 2. (a) Transmission spectrum of the dual built-in orthogonal slots waveguide (DBOSW) with and without graphene; (b) optical absorption in the graphene capacitor structure. Two modes with different electric field polarizations are supported by the dual built- in orthogonal slots waveguide. The distributions of transversal and longitudinal electric field components of the transverse polarization (TM) mode and the complex-polarization mode (complex mode) are illustrated by |Ex| and |Ey|, respectively. As depicted in Figure 3a, the TM mode is mainly distributed in the middle silica layer, which is attributed to the excitation of surface plasmon polarizations (SPPs) constrained by the top and bottom Ag layers. This Ey-dominated plasmonic mode is similar to the optical mode constrained in the metal slot waveguide [21]. As shown in Figure 3b, the complex mode is mainly dis- tributed in the upper slot and extends into the middle SiO2 layer. It should be noted that the complex mode can be seen as a mix of plasmonic modes supported by the crossed vertical metal slot and horizontal metal slot. In this case, both Ey and Ex components exist. The symmetry of both the horizontal and the vertical metal–insulator–metal (MIM) sub- structures lead to the spreading of transversal and longitudinal polarizations into the in- plane graphene-SiO2-graphene layers, which is remarkably favorable to polarization-in- sensitive modulation. Figure 3. The electric field distributions of (a) transverse magnetic (TM) polarized mode and (b) complex-polarization mode. The color bars and arrows represent the intensity and direction of the electric field, respectively. Appl. Sci. 2021, 11, 1897 4 of 16 In order to better illustrate the waveguide optimization and characterize the modu- lation performance of proposed design, the mode power attenuation (MPA), modulation depth (MD) and propagation loss (PL) are defined as follows: MPA 40 (log e) Im(N ) ( 1 ) 10 eff MD MPA OFF MPA ON     ( 2 ) PL MPA ON   ( 3 ) where λ is the incident wavelength, Im(Neff) is the imaginary part of the effective index, MD is defined as the difference between MPA (“ON” state) and MPA (“OFF” state) and PL refers to MPA (“ON” state). 2.2. Graphene Film Graphene is an emerging material with single layer carbon atoms in the form of hex- agons. This unique structure offers graphene optical properties of controllable light ab- sorption, considerable carrier mobility, uniform light absorption rate of 2.3% in a broad- band, etc. [10,22–30]. These favorable properties imply the graphene has good potential in the application of high-speed, low-footprint and low-power consumption devices. As shown in Figure 2b, a plate capacitor is formed by applying bias voltage to gra- phene layers. Light absorption is then controlled by the applied external electric field via the electrostatic doping effect. Since the interband transition in graphene is affected by Fermi level with no consideration of sign, both graphene layers can simultaneously be “transparent” at the high driving voltage, which refers to the "ON" state. An efficient nu- merical calculation method is important [31]. As has been reported [32], the graphene layer can be modeled as a 3D bulk material with a constant thickness or a 2D surface structure. To obtain accurate results, a smaller grid size is required in 3D simulations, which implies longer calculation time and larger memories requirement. On the basis of accuracy, it is desirable to model graphene as a 2D layer for higher efficiency. In this work, the graphene layer is considered a surface conductivity dielectric with a thickness of zero. Benefit from the reduced number of meshes, the calculation time reduces with accuracy guaranteed. The surface conductivity σg of the graphene may be adjusted by its chemical potential μc. This process can be well described by the Kubo formula [33], in which τ cor- responds to the relaxation time, the intraband transition τ1 is 1.2 ps and the interband transition τ2 is 15 fs. Graphene layers exhibit special physical properties at the epsilon- near-zero (ENZ) point, μc(ENZ) ≈ 0.5 eV [34]. When μc is larger than μc(ENZ), graphene shows the characteristics of the dielectric medium. Conversely, graphene behaves like a metallic layer and strong light absorption happens when μc is smaller than μc(ENZ). Equa- tion (4) illustrates the relationship between chemical potential and bias voltage [30]:   ћ  |V V | (4 ) cF g0 where vF is the Fermi velocity of graphene (vF = 2.5 × 10 m/s) [35]] and η = εrε0/de is derived from the parallel capacitor model (εr and d are the permittivity and thickness of SiO2 iso- lation layer, respectively). As shown in Figure 4, μc can shift from 0.2 to 0.6 eV as the applied voltage changes from 0.608 to 5.442 V. Appl. Sci. 2021, 11, 1897 5 of 16 Figure 4. Fermi level μc of graphene versus the change of applied external voltage. 3. Design Optimization To confirm the effect of waveguide dimension on the mode field distribution, the impact of slot width change on the field confinement and metal absorption is investigated, as shown in the Figure 5a–d (g = h = 50) and Figure 5e–h (g = h = 200 nm), respectively. When g and h increase, the field confinement profiles become slack, which handicap the light–graphene interaction. When a smaller slot width (e.g., 50 nm) is adopted, a higher metal absorption can be expected, since the mode power extends more into the metal lay- ers. When a relatively larger slot width (e.g., 200 nm) is adopted, modes are mainly dis- tributed in SiO2, which implies a relatively lower optical loss. Therefore, systematic di- mension analysis is necessary to balance field confinement and metal absorption. In the following geometric discussions, MD is temporarily defined as the difference between MPA (μc = 1 eV) and MPA (μc = 0 eV), and PL refers to MPA (μc = 1 eV) to stress the comparison. The effective index of DBOSW is also calculated at μc = 0 and 1 eV. The po- larization dependence of proposed design is studied by comparison of Neff at different μc and geometric parameters. Figure 5. Comparison of normalized electric field distributions and ohmic loss profiles under different waveguide dimen- sions. When h and g are 50 nm, (a) and (b) are electric field distribution and ohmic loss profile for the TM mode, respec- tively; (c) and (d) are corresponding cases for the complex mode. When h and g are 200 nm; (e) and (f) are electric field distribution and ohmic loss profile for the TM mode, respectively; (g) and (h) are corresponding cases for the complex mode. 3.1. hb As mentioned above, the TM mode and complex mode in this hybrid waveguide can be regarded as compound polarizations supported by the vertical, as well as the horizon- tal Ag-SiO2-Ag structure. The MD, PL and Re(Neff) of the proposed modulator as a func- Appl. Sci. 2021, 11, 1897 6 of 16 tion of bottom Ag slab thickness hb are shown in the Figure 6. The analysis of hb is imple- mented by a similar way adopted in the MIM waveguide model analysis, because it is also with thin metal layers [21]. Compared to complex mode, the TM mode is almost domi- nated by the longitudinal polarization, therefore the dimension change in vertical direc- tion has a larger impact on the TM mode. Figure 6a shows that Re(Neff) of the TM mode is more sensitive to hb than that of complex mode. The Re(Neff) of theTM mode keeps de- creasing with the rising of hb, which decreases from 1.6993 to 1.6464 at μc = 1 eV and 1.718 to 1.6654 at μc = 0 eV. Meanwhile, Re(Neff) of complex mode slowly decreases from hb = 50 nm, and reaches to a stable value at hb = 150 nm. In addition, as shown in Figure 6c, the change in hb has a significant impact on the PL of the TM mode that decreases with the increasing of hb and reaches a stable value at hb = 150 nm. In contrast, PL of complex mode remains at around 0.15 dB/μm that is caused by the fraction of the TM mode distributed in the metal layer. This leads to a larger optical loss. The MD change of two modes versus hb is very small, which is related to the limited influence of hb on the light field distribution. The Re(ΔNeff) of two modes versus hb is shown in Figure 6b. Here, Re(ΔNeff) is determined by ReΔN  | ReN  ReN  | eff eff eff (5 ) TM mode Complex mode Since a low Re(ΔNeff) is more desirable, hb is chosen to be 180 nm. Figure 6. (a, b, c) are Re(Neff), Re(ΔNeff), and modulation depth (MD) as well as propagation loss (PL) of the TM mode and complex mode in the DBOSW modulator as a function of hb, respectively. 3.2. h Figure 7 shows the MD, PL, Re(Neff) and Re(ΔNeff) of two modes in the DBOSW mod- ulator versus the middle silica layer thickness h. As shown Figure 7a, Re(Neff) of both modes reduce consistently with the increasing of h. Furthermore, when h = 100 nm, the Re(Neff) of the TM mode and complex mode show a very close minimum, which can be confirmed in Figure 7b. Though Re(ΔNeff) can already be restrained at a low level (< 0.115) when h is 50 or 200 nm, the thickness of silica layer apparently has a more significant impact on the polarization dependence. As shown in Figure 7c, MD and PL of two modes decrease simultaneously with the increasing of h. These trends are attributed to less con- finement of the light field in the middle silica layer as well as the weakening of the inter- action with graphene. This is depicted in the illustration in Figure 7c. As h decreases, the electric field intensity of the TM mode and the y-axis electric field component of complex mode increases in the middle silica layer. The increment of mode power in the metal layer invites higher optical loss. To be noted, the MD difference between the TM mode and Appl. Sci. 2021, 11, 1897 7 of 16 complex mode remains at a low level when h varies from 50 to 200 nm. However, the PL of the TM mode becomes lower than that of complex mode when h is higher than 95 nm. To constrain the performance difference between the TM mode and complex mode, h is chosen to be 100 nm. Figure 7. Re(Neff), Re(ΔNeff), MD and PL of the TM mode and complex mode in the DBOSW modulator versus h are shown in (a), (b) and (c), respectively. The illustration in (c) shows the variation of electric field distribution for both modes versus h. 3.3. ht When hb = 180 nm, h = 100 nm, Re(Neff) and Re(ΔNeff), the MD and PL of two modes in the DBOSW modulator versus the top layer thickness ht are investigated. As shown in Figure 8a, Re(Neff) of the TM mode decreases with the increment of ht at μc = 0 and 1 eV. When ht is 110 nm, Re(Neff) of the complex mode exhibits a minimum of 1.6722 and 1.6469 at μc = 0 and 1 eV, respectively. It is noteworthy that both modes share the same Re(Neff) when ht is 200 nm and μc is 1 eV. This scenario also can be found when ht is 210 nm and μc is 0 eV. In Figure 8 (b), a maximum Re(ΔNeff) is first presented with the increase of ht as μc −4 = 0 and 1 eV. Then, a minimum Re(ΔNeff) of 6 × 10 (μc = 1 eV) appears when ht is 200 nm. −4 A minimum Re(ΔNeff) of 1 × 10 (μc = 0 eV) can be observed when ht is 210 nm. The differ- ent behaviors of Re(Neff) and Re(ΔNeff) in Figure 8a and Figure 8b can be explained by the change of fringing field distribution as well as the variation in the slot region. This phe- nomenon is similar to what happens to the MIM waveguide [20]. As shown in Figure 8c, the PLs of both the TM mode and the complex mode decrease till ht rises up to 200 nm. As ht increases from 50 nm to 200 nm, the MD of the complex mode decreases by 57.1%, while the MD of the TM mode only reduces by 7.0%. Obviously, the change of ht has a more remarkable impact on the complex mode than that on the TM mode. This can be explained by the field distribution difference that can be observed from the illustration in Figure 8c. With comprehensive consideration, a balanced ht of 200 nm is chosen. Appl. Sci. 2021, 11, 1897 8 of 16 Figure 8. Re(Neff), Re(ΔNeff), MD as well as PL of the TM mode and complex mode in the DBOSW modulator versus ht are shown in (a), (b) and (c), respectively. The illustration in (c) shows the variation of electric field distribution for the TM mode and complex mode versus ht. 3.4. w For the waveguide structure in Figure 1, the width of the Ag strips w will definitely affect the mode field distribution. Therefore, Re(Neff), Re(ΔNeff), MD and PL of the TM mode and complex mode in the DBOSW modulator versus the Ag strips w are investi- gated, when hb = 180 nm, h = 100 nm, and ht = 200 nm. As shown in Figure 9(a), Re(Neff) of the TM mode gradually increases from 1.631 to 1.675 at μc = 0 eV, when w varies from 50 to 150 nm. Re(Neff) of the TM mode remains at 1.675, without changing with the increment in w. Inversely, Re(Neff) of complex mode decreases from 1.712 to 1.673 at μc = 0 eV, when w varies from 50 to 150 nm. A negligible change of Re(Neff) of the complex mode is ob- served when w is over 150 nm. When μc = 1 eV, Re(Neff) of the TM mode and complex mode exhibit similar inverse variation with the increment in w, which leads to a turning point of Re(ΔNeff) at w = 150 nm, as shown in Figure 9b. As w changes from 50 nm to 200 nm, the MDs of the TM mode and complex mode decrease by 55.1 and 30.5%, respectively. Both modes have the same MD at w = 160 nm. When w ranges from 50 to 150 nm, the PL of the TM mode decreases from 0.16 to 0.14 dB/μm, while PL of complex mode from 0.21 to 0.15 dB/μm. Both PLs become stable when w is larger than 150 nm, as shown in Figure 9c. The decrement of the MD and PL can be attributed to the extension of the mode field region with the increment in w, which weak- ens the graphene–light interaction strength, as shown in the illustration in Figure 9c. Since the TM mode and complex mode are distributed differently in the middle slot and the top metal slot, the increment in w has a greater impact on the MD of the TM mode. Moreover, the enlargement of the mode field area will weaken the field intensity, and then the metal absorption, leading to a lower PL. From the above, Re(ΔNeff) shows a minimum, while the MDs and PLs of the two modes are very close at w = 150 nm. Therefore, we choose w to be 150 nm in following work. Appl. Sci. 2021, 11, 1897 9 of 16 Figure 9. Re(Neff), Re(ΔNeff), modulation depth as well as propagation loss of the TM mode and complex mode in the DBOSW modulator versus w are shown in (a), (b) and (c), respectively. The illustration in (c) shows the variation of electric field distribution for both modes versus w. 3.5. g Another parameter to be confirmed in the proposed design is the gap width g be- tween two upper metal parts. When hb = 180 nm, h = 100 nm, w = 150 nm and ht = 200 nm, Re(Neff), Re(ΔNeff), MD and PL of the two modes in the DBOSW modulator versus metal slot width g are investigated. As shown in Figure 10, similar variations of Re(Neff) and Re(ΔNeff) to that in Figure 9 can be observed. The difference is that the change of g has a greater impact on Re(ΔNeff) than that on Re(Neff). As g increases, Re(ΔNeff) decreases firstly and then gradually increases. At g = 50 nm, Re(ΔNeff) shows the maximum of 0.2707 and 0.2691 for μc = 0 and 1 eV, respectively. −4 −4 The minimum Re(ΔNeff) of 6 × 10 and 3 × 10 can be found at g = 125 nm for μc = 0 and 1 eV, respectively. As shown in Figure 10c, the MD of the complex mode is less sensitive to the variation of g than the TM mode, which is due to the enhanced interaction strength between the x- axis electric field component of complex mode caused by the smaller g and the lateral metal slot. This leads to a higher loss and the resulting lower MD. In contrast, for the TM mode, the variation of g only changes its mode area, which is similar to the impact of w on the TM mode, as shown in the illustration in Figure 10c. The almost unchanged PL and linearly decreasing MD of the TM mode depicted in Figure 10c is consistent with the EA graphene modulator based on the MIM waveguide [36]. Since the difference of MD and PL between the two modes remains at a low level, when g is larger than 125 nm, g is chosen to be 125 nm in this design. Appl. Sci. 2021, 11, 1897 10 of 16 Figure 10. (a, b, c) are Re(Neff), Re(ΔNeff), modulation depth as well as propagation loss of the TM mode and complex mode in the DBOSW modulator versus g, respectively; the illustration in (c) shows the variation of electric field distribution for both modes versus g. 3.6. μ. c Response The relationships between Re(Neff) (Re(ΔNeff)), PL, Im(Neff) and the chemical potential μc also have been investigated. Figure 11a shows that Re(Neff) of the TM mode first in- creases from 1.6699 to the peak value of 1.6772 as μc increases from 0 to 0.4 eV. Subse- quently, it decreases to 1.6511 as μc continues to increase to 1 eV. Similar trends for Re(Neff) of the complex mode can also be observed. Furthermore, the Re(ΔNeff) remains at a low −4 level with an average of 3.6 × 10 in the range of μc = 0 to 1 eV. Figure 11b shows that the PL decreases rapidly as μc decreases from 0.2 to 0.6 eV. Therefore, the “ON” and the “OFF” state of DBOSW modulator is defined at μc = 0.6 and 0.2 eV, respectively. In this case, the MD of the TM mode up to 0.474 dB/μm can be obtained, while the MD of the complex mode is 0.462 dB/μm. The calculated ΔMD (|MDTM mode − MDComplex mode|) is only 0.012 dB/μm at λ = 1550 nm. Figure 11. Re(Neff) and Re(ΔNeff), Im(Neff) and PL of the TM mode and complex mode versus Femi level (chemical potential μc) from 0 to 1 eV are shown in (a) and (b), respectively. 4. Performance and Discussion 4.1. Optical Bandwidth To confirm the optical bandwidth of the DBOSW modulator with the above geomet- ric parameters, the relationships between Re(Neff) and Re(ΔNeff) of the two modes as a Appl. Sci. 2021, 11, 1897 11 of 16 function of the incident wavelength are investigated when μc ranges from 0.2 to 0.6 eV. As shown in Figure 12a, Re(Neff) decreases with the increment in wavelength. When λ = 1.1 μm and μc = 0.6 eV, the maximum Re(Neff) of the TM mode and the complex mode is 1.7135 and 1.7163, respectively. When λ = 1.1 μm and μc = 0.2 eV, Re(Neff) of the TM mode and complex mode is 1.7096 and 1.7127, respectively. When λ = 1.9 μmand μc = 0.6 eV, Re(Neff) of the TM mode and complex mode is 1.6438 and 1.6427, respectively. When λ = 1.9 μm and μc = 0.2 eV, Re(Neff) of the TM mode and complex mode is 1.6586 and 1.6574, respectively. It can be observed that a very low Re(ΔNeff) of around 0.001 can be obtained within a wavelength range from 1.1 to 1.9 μm. In Figure 12b, when the wavelength varies from 1.1 to 1.9 μm, Im(Neff) of the TM mode quickly increases from 0.01207 to 0.02164 at μc = 0.2 eV; meanwhile, Im(Neff) of the complex mode increases from 0.01160 to 0.02177 at μc = 0.2 eV, which mainly results from the enhancement of the graphene–light interaction due to the increasing dielectric con- stant with the increment in optical wavelength. To be mentioned, the MPA change of both two modes is very limited within the wavelength range. The MDs of the TM mode are 0.40918 dB/μm at λ = 1.1 μm and 0.46931 dB/μm at λ = 1.9 μm, respectively. While, the MDs of the complex mode are 0.38416 dB/μm at λ = 1.1 μm and 0.46415 dB/μm at λ = 1.9 μm, respectively. Therefore, the proposed modulator shows good polarization-independ- ence characteristics over a broad optical bandwidth. Figure 12. (a) Re(Neff) and Re(ΔNeff), (b) Im(Neff) and MPA of the TM mode and complex mode versus the incident wave- length at μc = 0.2 and 0.6 eV, respectively. 4.2. Frequency Response Here, the 3 dB-bandwidth (f3dB) and power consumption of the proposed DBOSW modulator with optimized geometric parameters are also confirmed. An equivalent cir- cuit model is adopted to estimate the dynamic response of the DBOSW modulator, which is shown in Figure 13. Figure 13. The equivalent circuit model. Appl. Sci. 2021, 11, 1897 12 of 16 In this model, the capacitance Cair exists between two electrodes and the air, which is 12 fF [37]. The capacitance C that consists of the two graphene layers and SiO2 isolation layer includes both the dielectric capacitance CD and the quantum capacitor CQ. Assuming the graphene layer is undoped (ns = 0), then we have CQ = 0. Hence, the capacitance C can be described by the following capacitor model: C  w Ld / ( 6 ) r 0 ol where L = 20 μm and wol = 1385 nm are the graphene modulation length and the overlap width of two graphene layers, respectively. εr and d are the permittivity and the thickness of SiO2 isolation layer, respectively. Rtotal is the total resistance, which includes the gra- phene sheet resistance Rs of 100 Ω/□ [38], and the metal electrode contact resistance to graphene layer Rc of 150 Ω-μm [20]. According to Equation (6) below, Rtotal is calculated to be about 33.85 Ω [24,30], where the effective graphene width wg is set to be 1.885 μm. 2R R  2R ( 7 ) total s L L Based on Equation (8), the 3 dB-bandwidth is dominantly limited by RC delay. Ac- cording to Equations (5–7), the DBOSW modulator shows a high f3dB of 101 GHz. For the proposed device structure, the silica as an isolation layer that is with a relatively low per- mittivity and a small thickness of 15 nm is favorable to compensate the disadvantages of the large effective width and overlapping area of graphene layers. In addition, the sheet resistance Rs and contact resistance Rc are values adopted in related Ref. [17]. f  ( 8 ) 3dB 2RC total total The power consumption (Ebit = Ctotal(ΔU) /4) is estimated to be 0.271 pJ/bit at L = 20 μm, where the applied voltage change ΔU is 4.834 V. This is in accordance with the change of chemical potential from 0.2 to 0.6 eV. To clarify the merits of proposed design, the theoretical performance of the reported polarization-insensitive graphene modulators is comprehensively compared with that of this work. As shown in Table 1, the proposed modulator has the largest optical bandwidth and the smallest Re(ΔNeff). Moderate MD and ΔMD also can be obtained. The characteris- tics of f3dB and Ebit are also better than most reported works. Appl. Sci. 2021, 11, 1897 13 of 16 Table 1. Performance comparison with reported polarization-insensitive graphene modulators at λ = 1.55 μm. Ref. Bandwidth (nm) Re(ΔNeff) MD (dB/μm) ΔMD (dB/μm) f3dB (GHz) Ebit (fJ/bit) [39] 1500–1600 - 0.06 0 13.4 - [40] 1500–1600 - 0.08 0 80 - mode A: 1.05, Min: 0.08 [41] 1200–1600 - mode B: 1.13, 95 138.8 Max: 0.61 mode C: 0.52 TM mode: ~0.2975, −3 −3 [42] 1530–1565 4.7 × 10 ~8 × 10 30.2 2980 TE mode: ~0.2895 TM mode: 1.113, −3 [43] 1367–1771 ~ 0.5 ~6 × 10 6.1 7800 TE mode: 1.119 TM mode: 1.392, [44] 1450– 1650 ~ 0.1 0.045 ~100 - TE mode: 1.347 −3 [45] 1300–1800 1.2 × 10 - - 135.6 - TM mode: 0.474, −4 This work 1100–1900 6 × 10 0.012 101 271 complex mode: 0.462 The proposed DBOSW modulator can be implemented through the following fabri- cation process. The fabrication process starts with a commercial silica wafer. The E-beam evaporation deposits a silver layer with a thickness of 180 nm (hb) onto the silica surface, serving as a bottom layer. Subsequently, the plasma-enhanced chemical vapor deposition (PECVD) can be used to deposit the 100 nm-thick SiO2 (h) middle layer. Next, the thermal evaporation is used to deposit a 200 nm-thick (ht) silver layer followed by electron-beam lithography (EBL) and inductively coupled plasma etching. The 125 nm-wide metal slot substructure (g) is then filled with SiO2 by PECVD. The subsequent surface chemical me- chanical polishing as well as the etching to three layers above can form a hybrid ridge with a width of 425 nm (w × 2 + g). After that, the bottom graphene sheet grown can be wet-transferred to the hybrid ridge waveguide. The graphene-covered region can be de- fined by EBL processing to remove the excess graphene. Whereas, the graphene on the other side extends 500 nm to form an electrode contact. A 15 nm-thick SiO2 isolation layer is deposited on the bottom graphene flake. The second graphene flake is transferred onto the SiO2 isolation layer and handled with the same process applied on the bottom gra- phene layer, constructing a complete hybrid waveguide structure. Considering the structural complexity of the proposed DBOSW, the influence of manufacturing errors on the modulator is also evaluated. Firstly, the influence of inequal- ity of the top Ag strip δ (the asymmetry of DBOSW) on the modulator performance is investigated, as shown in Figure 14. The geometric parameters used here are the optimal values discussed in above sections. It can be seen that the DBOSW modulator exhibits stable polarization insensitivity in the fluctuation of one side w from 135 to 165 nm (−15 −3 nm > δ > 15 nm). The maximum Re(ΔNeff) at δ = 15 nm is 4 × 10 , which is still lower than the optimal value in Ref. [40]. ΔMD remains at a low level, which is still competitive com- pared with reported works. The undulation of ΔMD relates to the difference between the mutative MD of the TM mode and the relatively constant MD of the complex mode, as shown in Figure 14 (c). PLs exhibit good stability. As discussed in Section 3, though the proposed design has a relatively large fabrication tolerance, g needs to be treated carefully. A significant negative effect on Re(Neff) may damage the modulation performance at small g. Appl. Sci. 2021, 11, 1897 14 of 16 Figure 14. The inequality of the top Ag strip δ on (a) Re(ΔNeff); (b) ΔMD; and (c) MD, PL of the TM mode and complex mode. The illustration in (b) shows the unequal condition of the DBOSW modulator, when δ < 0 the width of the right Ag stripe is smaller than that of the left one. 5. Conclusions In summary, to achieve the polarization-insensitive modulation and enhance the modulation capability of the graphene layer, a broadband polarization-insensitive gra- phene modulator based on plasmonic effect with DBOSW is proposed and comprehen- sively investigated. By introducing the two slot-like structure in the waveguide, the DBOSW can support two modes simultaneously, which enables the modulation of both the longitudinal and the transverse polarization electric fields in a broadband bandwidth. When the external bias voltage shifts from 0.608 to 5.442 V, the MD of 0.474 and 0.462 dB/μm for the TM mode and complex mode can be obtained, respectively. A low effective index difference with an average of 0.001 is achieved within a wide optical band range from 1.1 to 1.9 μm. The 3 dB-bandwidth of 101 GHz and a power consumption of 0.271 pJ/bit at a modulation length of 20 μm can be obtained. The proposed graphene modulator has potential in microwave photonic systems. Author Contributions: W.C. proposed the idea, carried out the simulations and wrote the manu- script. Y.X. and Y.G. plotted the figures and provided suggestions. X.W. supervised the simula- tions. X.S. and D.Z. supervised the whole work, interpreted the results and improved the manu- script. All authors reviewed the manuscript. All authors have read and agreed to the published version of the manuscript. Funding: This study was supported by the National Key Research and Development Program of China (2019YFB2203001), National Natural Science Foundation of China (61675087, 61875069), and The Education Department of Jilin Province (JJKH20190118KJ) Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Conflicts of Interest: The authors declare no conflict of interest. References 1. Marris-Morini, D.; Lyan, P.; Rivallin, P.; Halbwax, M.; Laval, S.; Vivien, L.; Rasigade, G.; Fedeli, J.-M.; Cassan, E.; Le Roux, X.; et al. Recent Progress in High-Speed Silicon-Based Optical Modulators. Proc. IEEE 2009, 97, 1199–1215. 2. Wang, C.; Zhang, M.; Chen, X.; Bertrand, M.; Shams-Ansari, A.; Chandrasekhar, S.; Winzer, P.; Lončar, M. Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages. Nature 2018, 562, 101–104. 3. Pérez-Galacho, D.; Marris-Morini, D.; Stoffer, R.; Cassan, E.; Vivien, L. Simplified modeling and optimization of silicon modu- lators based on free-carrier plasma dispersion effect. Opt. Express 2016, 24, 26332–26337. 4. Park, J.-K.; Takagi, S.; Takenaka, M. InGaAsP Mach–Zehnder interferometer optical modulator monolithically integrated with InGaAs driver MOSFET on a III-V CMOS photonics platform. Opt. Express 2018, 26, 4842–4852. 5. Nickelson, L.; Gric, T.; Asmontas, S.; Martavicius, R. Electric Field Distributions of the Fast and Slow Modes Propagated in the Open Rod SiC Waveguide. Elektron. Elektrotech. 2009, 93, 87–90. Appl. Sci. 2021, 11, 1897 15 of 16 6. Hu, Y.; Pantouvaki, M.; Van Campenhout, J.; Brems, S.; Asselberghs, I.; Huyghebaert, C.; Absil, P.; Van Thourhout, D. Broad- band 10 Gb/s operation of graphene electro-absorption modulator on silicon. Laser Photon. Rev. 2016, 10, 307–316. 7. Mohsin, M.; Schall, D.; Otto, M.; Noculak, A.; Neumaier, D.; Kurz, H. Graphene based low insertion loss electro-absorption modulator on SOI waveguide. Opt. Express 2014, 22, 15292–15297. 8. Dalir, H.; Xia, Y.; Wang, Y.; Zhang, X. Athermal Broadband Graphene Optical Modulator with 35 GHz Speed. ACS Photonics 2016, 3, 1564–1568. 9. Phatak, A.; Cheng, Z.Z.; Qin, C.Y.; Goda, K. Design of electro-optic modulators based on graphene-on-silicon slot waveguides. Opt. Lett. 2016, 41, 2501–2504. 10. Liu, M.; Yin, X.; Ulin-Avila, E.; Geng, B.; Zentgraf, T.; Ju, L.; Wang, F.; Zhang, X. A graphene-based broadband optical modula- tor. Nature 2011, 474, 64–67. 11. Liu, M.; Yin, X.; Zhang, X. Double-Layer Graphene Optical Modulator. Nano Lett. 2012, 12, 1482–1485. 12. Phare, C.T.; Daniel Lee, Y.-H.; Cardenas, J.; Lipson, M. Graphene electro-optic modulator with 30 GHz bandwidth. Nat. Photon- ics 2015, 9, 511–514. 13. Schuller, J.A.; Barnard, E.S.; Cai, W.; Jun, Y.C.; White, J.S.; Brongersma, M.L. Plasmonics for extreme light concentration and manipulation. Nat. Mater. 2010, 9, 193–204. 14. Bozhevolnyi, S.I.; Volkov, V.S.; Devaux, E.; Laluet, J.Y.; Ebbesen, T.W. Channel plasmon subwavelength waveguide compo- nents including interferometers and ring resonators. Nature 2006, 440, 508–511. 15. Gramotnev, D.K.; Bozhevolnyi, S.I. Plasmonics beyond the diffraction limit. Nat. Photonics 2010, 4, 83–91. 16. Huang, B.-H.; Lu, W.-B.; Li, X.-B.; Wang, J.; Liu, Z.-G. Waveguide-coupled hybrid plasmonic modulator based on graphene. Appl. Optics 2016, 55, 5598–5602. 17. Zheng, P.; Yang, H.; Fan, M.; Hu, G.; Zhang, R.; Yun, B.; Cui, Y. A Hybrid Plasmonic Modulator Based on Graphene on Channel Plasmonic Polariton Waveguide. Plasmonics 2018, 13, 2029–2035. 18. Bao, Q.; Zhang, H.; Wang, B.; Ni, Z.; Lim, C.H.Y.X.; Wang, Y.; Tang, D.Y.; Loh, K.P. Broadband graphene polarizer. Nat. Pho- tonics 2011, 5, 411–415. 19. Chang, L.-M.; Liu, L.; Gong, Y.-H.; Tan, M.-Q.; Yu, Y.-D.; Li, Z.-Y. Polarization-independent directional coupler and polarization beam splitter based on asymmetric cross-slot waveguides. Appl. Optics 2018, 57, 678–683. 20. Zhong, H.; Zhang, Z.Y.; Chen, B.Y.; Xu, H.T.; Yu, D.M.; Huang, L.; Peng, L.M. Realization of low contact resistance close to theoretical limit in graphene transistors. Nano Res. 2015, 8, 1669–1679. 21. Veronis, G.; Fan, S. Modes of Subwavelength Plasmonic Slot Waveguides. J. Lightwave Technol. 2007, 25, 2511–2521. 22. Geim, A.K.; Novoselov, K.S. The rise of graphene. Nat. Mater. 2009, 6, 183–191. 23. Schwierz, F. Graphene transistors. Nat. Nanotechnol. 2010, 5, 487–496. 24. Bonaccorso, F.; Hasan, T.; Sun, Z.; Ferrari, A.C. Graphene photonics and optoelectronics. Nat. Photonics 2010, 4, 611–622. 25. Kusuma, J.; Balakrishna, R.G.; Patil, S.; Jyothi, M.S.; Chandan, H.R.; Shwetharani, R. Exploration of graphene oxide nanoribbons as excellent electron conducting network for third generation solar cells. Solar Energy Mater. Solar Cells 2018, 183, 211–219. 26. Avouris, P.; Chen, Z.; Perebeinos, V. Carbon Based Electronics. Nat. Nanotechnol. 2007, 2, 605–615. 27. Bolotin, K.I.; Sikes, K.J.; Jiang, Z.; Klima, M.; Fudenberg, G.; Hone, J.; Kim, P.; Stormer, H.L. Ultrahigh electron mobility in suspended graphene. Solid State Commun. 2008, 146, 351–355. 28. Nair, R.R.; Blake, P.; Grigorenko, A.N.; Novoselov, K.S.; Booth, T.J.; Stauber, T.; Peres, N.M.R.; Geim, A.K. Fine Structure Con- stant Defines Visual Transparency of Graphene. Science 2008, 320, 1308–1308. 29. Mak, K.F.; Sfeir, M.Y.; Wu, Y.; Lui, C.H.; Misewich, J.A.; Heinz, T.F. Measurement of the Optical Conductivity of Graphene. Phys. Rev. Lett. 2008, 101, 196405–196408. 30. Sensale-Rodriguez, B.; Yan, R.; Kelly, M.M.; Fang, T.; Tahy, K.; Hwang, W.S.; Jena, D.; Liu, L.; Xing, H.G. Broadband graphene terahertz modulators enabled by intraband transitions. Nat. Commun. 2012, 3, 780–786. 31. Gric, T.; Nickelson, L.; Asmontas, S. Electrodynamical characteristic particularity of open metamaterial square and circular waveguides. Prog. Electromagn. Res. 2010, 109, 361–379. 32. Ye, L.; Sui, K.; Zhang, Y.; Liu, Q.H. Broadband optical waveguide modulators based on strongly coupled hybrid graphene and metal nanoribbons for near-infrared applications. Nanoscale 2019, 11, 3229–3239. 33. Hanson, G.W. Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene. J. Appl. Phys. 2007, 103, 064302–064309. 34. Kwon, M.-S. Discussion of the Epsilon-Near-Zero Effect of Graphene in a Horizontal Slot Waveguide. IEEE Photonics J. 2014, 6, 1–9. 35. Hwang, C.; Siegel, D.A.; Mo, S.K.; Regan, W.; Ismach, A.; Zhang, Y.; Zettl, A.; Lanzara, A. Fermi velocity engineering in gra- phene by substrate modification. Sci. Rep. 2012, 2, 590–593. 36. Ding, Y.; Guan, X.; Zhu, X.; Hao, H.; Xiao, S. Effective electro-optic modulation in low-loss graphene-plasmonic slot waveguides. Nanoscale 2017, 9, 15576–15581. 37. Hu, Y.; Xiao, X.; Xu, H.; Li, X.; Xiong, K.; Li, Z.; Chu, T.; Yu, Y.; Yu, J. High-speed silicon modulator based on cascaded microring resonators. Opt. Express 2012, 20, 15079–15085. 38. Abdollahi Shiramin, L.; Van Thourhout, D. Graphene Modulators and Switches Integrated on Silicon and Silicon Nitride Wave- guide. IEEE J. Sel. Top. Quantum Electron. 2016, 23, 94–100. Appl. Sci. 2021, 11, 1897 16 of 16 39. Yang, Z.; Lu, R.; Cai, S.; Wang, Y.; Zhang, Y.; Wang, X.; Liu, Y. A CMOS-compatible and polarization-insensitive graphene optical modulator. Opt. Commun. 2019, 450, 130–135. 40. Yang, Z.; Lu, R.; Wang, Y.; Cai, S.; Zhang, Y.; Wang, X.; Liu, Y. A fabrication-friendly graphene-based polarization insensitive optical modulator. Optik 2019, 182, 1093–1098. 41. Shirdel, M.; Mansouri-Birjandi, M.A. Broadband graphene modulator based on a plus-shaped plasmonic slot waveguide. Appl. Optics 2019, 58, 8174–8179. 42. Hu, X.; Wang, J. Design of graphene-based polarization-insensitive optical modulator. Nanophotonics 2018, 7, 651–658. 43. Xu, Y.; Li, F.; Kang, Z.; Huang, D.; Zhang, X.; Tam, H.-Y.; Wai, P. Hybrid Graphene-Silicon Based Polarization-Insensitive Elec- tro-Absorption Modulator with High-Modulation Efficiency and Ultra-Broad Bandwidth. Nanomaterials 2019, 9, 157–171. 44. Ye, S.W.; Liang, D.; Lu, R.-G.; Shah, M.K.; Zou, X.-H.; Yang, F.; Yuan, F.; Liu, Y. Polarization Independent Modulator by Partly Tilted Graphene Induced Electro-Absorption Effect. IEEE Photonics Technol. Lett. 2016, 29, 23–26. 45. Zou, X.H.; Zhang, Y.J.; Li, Z.H.; Yang, Y.W.; Zhang, S.J.; Zhang, Z.Y.; Zhang, Y.L.; Liu, Y. Polarization-Insensitive Phase Modulators Based on an Embedded Silicon-Graphene-Silicon Waveguide. Appl. Sci.-Basel 2019, 9, 429-436. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Sciences Multidisciplinary Digital Publishing Institute

A Broadband Polarization-Insensitive Graphene Modulator Based on Dual Built-in Orthogonal Slots Plasmonic Waveguide

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Article A Broadband Polarization-Insensitive Graphene Modulator Based on Dual Built-in Orthogonal Slots Plasmonic Waveguide 1 1 1 2 1 1, 1 Wei Chen , Yan Xu , Yang Gao , Lanjing Ji , Xibin Wang , Xiaoqiang Sun * and Daming Zhang State Key Laboratory of Integrated Optoelectronics, College of Electronic Science & Engineering, Jilin University, Changchun 130012, China; chenwei18@mails.jlu.edu.cn (W.C.); xyan17@mails.jlu.edu.cn (Y.X.); ygao17@mails.jlu.edu.cn (Y.G.); xibinwang@jlu.edu.cn (X.W.); zhangdm@jlu.edu.cn (D.Z.) Institute of Marine Science and Technology, Shandong University, Qingdao 250100, China; jilanting@sdu.edu.cn * Correspondence: sunxq@jlu.edu.cn Abstract: A broadband polarization-insensitive graphene modulator has been proposed. The dual built-in orthogonal slots waveguide allows polarization independence for the transverse electric (TE) mode and the transverse magnetic (TM) mode. Due to the introduction of metal slots in both the vertical and horizontal directions, the optical field as well as the electro-absorption of graphene are enhanced by the plasmonic effect. The proposed electro-optic modulator shows a modulation depth of 0.474 and 0.462 dB/μm for two supported modes, respectively. An ultra-low effective index difference of 0.001 can be achieved within the wavelength range from 1100 to 1900 nm. The 3 dB- bandwidth is estimated to be 101 GHz. The power consumption is 271 fJ/bit at a modulation length of 20 μm. The proposed modulator provides high speed broadband solutions in microwave pho- tonic systems. Citation: Chen, W.; Xu, Y.; Gao, Y.; Keywords: graphene; plasmonic modulator; waveguide; polarization-insensitive Ji, L.; Wang, X.; Sun, X.; Zhang, D. A Broadband Polarization-Insensitive Graphene Modulator Based on Dual Built-in Orthogonal Slots Plasmonic 1. Introduction Waveguide. Appl. Sci. 2021, 11, 1897. High performance electro-optic (EO) modulators are highly demanded in wideband https://doi.org/10.3390/app11041897 optics communication networks [1]. The lithium niobite-based modulators are mature but suffer from a large footprint [2]. Silicon modulators are compatible with CMOS technol- Academic Editor: Filippo Giannazzo ogy, while facing the problem of low EO efficiency [3]. III-V based modulators offer a Received: 10 February 2021 small footprint; however, the insertion loss and thermal stability are still to be improved Accepted: 19 February 2021 [4]. SiC-based waveguides also show application potential [5]. Due to the unsatisfactory Published: 21 February 2021 EO properties of the above underlying materials, modulators that meet all requires are still elusive. Graphene with excellent EO characteristics has been well studied and widely Publisher’s Note: MDPI stays neu- adopted in optical modulators [6–9]. In 2011, Liu et al. experimentally presented a gra- tral with regard to jurisdictional phene modulator with a modulation depth (MD, the difference between “ON” state and claims in published maps and institu- “OFF” state) of 0.1 dB/μm [10]. A built-in p-oxide-n-like junction graphene modulator tional affiliations. exhibited an MD of 0.16 dB/μm and a power consumption of 1 pJ/bit [11]. The graphene EO modulator with a high 3 dB-bandwidth of 30 GHz has also been demonstrated [12]. However, the performance of above graphene modulators is limited by the weak interac- tion between the extremely thin graphene flake and the light field that is strongly Copyright: © 2021 by the authors. bounded in the high index dielectric material. If the plasmonic effect is introduced, the Licensee MDPI, Basel, Switzerland. light can propagate as a surface plasmon polarizations (SPPs) mode along the waveguide, This article is an open access article which implies an enhanced optical field intensity. More optical power will be guided to distributed under the terms and the dielectric/graphene interface, facilitating the light–graphene interaction [13–15]. conditions of the Creative Commons Huang et al. proposed a waveguide-coupled hybrid plasmonic graphene modulator with Attribution (CC BY) license (http://creativecommons.org/licenses a 3 dB-bandwidth of 0.48 THz and an energy consumption of 145 fJ/bit [16]. A hybrid /by/4.0/). Appl. Sci. 2021, 11, 1897. https://doi.org/10.3390/app11041897 www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, 1897 2 of 16 plasmonic graphene modulator with a 3 dB-bandwidth of 0.662 THz and a power con- sumption of 118.7 fJ/bit promises good potential for hybrid plasmonic graphene EO mod- ulators [17]. Another issue for the graphene modulator is the polarization sensitivity, which originates from the low absorption rate of 2.3% for the electric field polarization perpendicular to the graphene flake surface. Most reported works can only operate in transverse magnetic (TM) or transverse electric (TE) polarization independently [18]. The introduction of polarization control functions will inevitably complexify the device struc- ture [19]. Therefore, a compact and polarization-insensitive graphene modulator with characteristic of broadband operation is desirable. In this paper, we proposed a graphene modulator based on a dual built-in orthogonal slots waveguide (DBOSW). The geometric parameters of the hybrid plasmonic waveguide are investigated and optimized by finite element method (FEM). The mechanism of po- larization insensitivity and broadband modulation is elaborated in detail. Our proposed waveguide structure overcomes the strict polarization dependence of plasmonic-based waveguides. Moreover, the DBOSW graphene modulator realizes broadband modulation with excellent polarization independence, which shows good potential in microwave pho- tonic systems. 2. Configuration and Structure 2.1. Device Structure As shown in Figure 1, the proposed graphene modulator based on the dual built-in orthogonal slots waveguide consists of a bottom silver layer (Ag, nAg = 0.14447+ 11.366), a middle silica layer (SiO2, nSiO2 = 1.45) and a top silver slot isolated by SiO2. Double 0.33 nm- thick graphene flakes are isolated by 15 nm-thick SiO2 and cover the hybrid waveguide. The metal stacks–graphene contacts form the electrodes [20]. The whole structure is sup- ported by the SiO2 substrate. Figure 1. (a) Two-dimensional (2D) cross section; (b) three-dimensional (3D) view of the graphene modulator with dual built-in orthogonal slots waveguide. Graphene plays a major role in optical modulation of this modulator. As shown in Figure 2a, the transmission spectrum of DBOSW with a modulation length of L = 20 μm covered with graphene-SiO2-graphene stacks but without applied voltage (U = 0 V (μc = 0 eV)) has a sharp drop compared to DBOSW without graphene. This large significant light loss mainly originates from the light absorption effect of graphene, indicating that gra- phene has an effective light modulation function. Appl. Sci. 2021, 11, 1897 3 of 16 Figure 2. (a) Transmission spectrum of the dual built-in orthogonal slots waveguide (DBOSW) with and without graphene; (b) optical absorption in the graphene capacitor structure. Two modes with different electric field polarizations are supported by the dual built- in orthogonal slots waveguide. The distributions of transversal and longitudinal electric field components of the transverse polarization (TM) mode and the complex-polarization mode (complex mode) are illustrated by |Ex| and |Ey|, respectively. As depicted in Figure 3a, the TM mode is mainly distributed in the middle silica layer, which is attributed to the excitation of surface plasmon polarizations (SPPs) constrained by the top and bottom Ag layers. This Ey-dominated plasmonic mode is similar to the optical mode constrained in the metal slot waveguide [21]. As shown in Figure 3b, the complex mode is mainly dis- tributed in the upper slot and extends into the middle SiO2 layer. It should be noted that the complex mode can be seen as a mix of plasmonic modes supported by the crossed vertical metal slot and horizontal metal slot. In this case, both Ey and Ex components exist. The symmetry of both the horizontal and the vertical metal–insulator–metal (MIM) sub- structures lead to the spreading of transversal and longitudinal polarizations into the in- plane graphene-SiO2-graphene layers, which is remarkably favorable to polarization-in- sensitive modulation. Figure 3. The electric field distributions of (a) transverse magnetic (TM) polarized mode and (b) complex-polarization mode. The color bars and arrows represent the intensity and direction of the electric field, respectively. Appl. Sci. 2021, 11, 1897 4 of 16 In order to better illustrate the waveguide optimization and characterize the modu- lation performance of proposed design, the mode power attenuation (MPA), modulation depth (MD) and propagation loss (PL) are defined as follows: MPA 40 (log e) Im(N ) ( 1 ) 10 eff MD MPA OFF MPA ON     ( 2 ) PL MPA ON   ( 3 ) where λ is the incident wavelength, Im(Neff) is the imaginary part of the effective index, MD is defined as the difference between MPA (“ON” state) and MPA (“OFF” state) and PL refers to MPA (“ON” state). 2.2. Graphene Film Graphene is an emerging material with single layer carbon atoms in the form of hex- agons. This unique structure offers graphene optical properties of controllable light ab- sorption, considerable carrier mobility, uniform light absorption rate of 2.3% in a broad- band, etc. [10,22–30]. These favorable properties imply the graphene has good potential in the application of high-speed, low-footprint and low-power consumption devices. As shown in Figure 2b, a plate capacitor is formed by applying bias voltage to gra- phene layers. Light absorption is then controlled by the applied external electric field via the electrostatic doping effect. Since the interband transition in graphene is affected by Fermi level with no consideration of sign, both graphene layers can simultaneously be “transparent” at the high driving voltage, which refers to the "ON" state. An efficient nu- merical calculation method is important [31]. As has been reported [32], the graphene layer can be modeled as a 3D bulk material with a constant thickness or a 2D surface structure. To obtain accurate results, a smaller grid size is required in 3D simulations, which implies longer calculation time and larger memories requirement. On the basis of accuracy, it is desirable to model graphene as a 2D layer for higher efficiency. In this work, the graphene layer is considered a surface conductivity dielectric with a thickness of zero. Benefit from the reduced number of meshes, the calculation time reduces with accuracy guaranteed. The surface conductivity σg of the graphene may be adjusted by its chemical potential μc. This process can be well described by the Kubo formula [33], in which τ cor- responds to the relaxation time, the intraband transition τ1 is 1.2 ps and the interband transition τ2 is 15 fs. Graphene layers exhibit special physical properties at the epsilon- near-zero (ENZ) point, μc(ENZ) ≈ 0.5 eV [34]. When μc is larger than μc(ENZ), graphene shows the characteristics of the dielectric medium. Conversely, graphene behaves like a metallic layer and strong light absorption happens when μc is smaller than μc(ENZ). Equa- tion (4) illustrates the relationship between chemical potential and bias voltage [30]:   ћ  |V V | (4 ) cF g0 where vF is the Fermi velocity of graphene (vF = 2.5 × 10 m/s) [35]] and η = εrε0/de is derived from the parallel capacitor model (εr and d are the permittivity and thickness of SiO2 iso- lation layer, respectively). As shown in Figure 4, μc can shift from 0.2 to 0.6 eV as the applied voltage changes from 0.608 to 5.442 V. Appl. Sci. 2021, 11, 1897 5 of 16 Figure 4. Fermi level μc of graphene versus the change of applied external voltage. 3. Design Optimization To confirm the effect of waveguide dimension on the mode field distribution, the impact of slot width change on the field confinement and metal absorption is investigated, as shown in the Figure 5a–d (g = h = 50) and Figure 5e–h (g = h = 200 nm), respectively. When g and h increase, the field confinement profiles become slack, which handicap the light–graphene interaction. When a smaller slot width (e.g., 50 nm) is adopted, a higher metal absorption can be expected, since the mode power extends more into the metal lay- ers. When a relatively larger slot width (e.g., 200 nm) is adopted, modes are mainly dis- tributed in SiO2, which implies a relatively lower optical loss. Therefore, systematic di- mension analysis is necessary to balance field confinement and metal absorption. In the following geometric discussions, MD is temporarily defined as the difference between MPA (μc = 1 eV) and MPA (μc = 0 eV), and PL refers to MPA (μc = 1 eV) to stress the comparison. The effective index of DBOSW is also calculated at μc = 0 and 1 eV. The po- larization dependence of proposed design is studied by comparison of Neff at different μc and geometric parameters. Figure 5. Comparison of normalized electric field distributions and ohmic loss profiles under different waveguide dimen- sions. When h and g are 50 nm, (a) and (b) are electric field distribution and ohmic loss profile for the TM mode, respec- tively; (c) and (d) are corresponding cases for the complex mode. When h and g are 200 nm; (e) and (f) are electric field distribution and ohmic loss profile for the TM mode, respectively; (g) and (h) are corresponding cases for the complex mode. 3.1. hb As mentioned above, the TM mode and complex mode in this hybrid waveguide can be regarded as compound polarizations supported by the vertical, as well as the horizon- tal Ag-SiO2-Ag structure. The MD, PL and Re(Neff) of the proposed modulator as a func- Appl. Sci. 2021, 11, 1897 6 of 16 tion of bottom Ag slab thickness hb are shown in the Figure 6. The analysis of hb is imple- mented by a similar way adopted in the MIM waveguide model analysis, because it is also with thin metal layers [21]. Compared to complex mode, the TM mode is almost domi- nated by the longitudinal polarization, therefore the dimension change in vertical direc- tion has a larger impact on the TM mode. Figure 6a shows that Re(Neff) of the TM mode is more sensitive to hb than that of complex mode. The Re(Neff) of theTM mode keeps de- creasing with the rising of hb, which decreases from 1.6993 to 1.6464 at μc = 1 eV and 1.718 to 1.6654 at μc = 0 eV. Meanwhile, Re(Neff) of complex mode slowly decreases from hb = 50 nm, and reaches to a stable value at hb = 150 nm. In addition, as shown in Figure 6c, the change in hb has a significant impact on the PL of the TM mode that decreases with the increasing of hb and reaches a stable value at hb = 150 nm. In contrast, PL of complex mode remains at around 0.15 dB/μm that is caused by the fraction of the TM mode distributed in the metal layer. This leads to a larger optical loss. The MD change of two modes versus hb is very small, which is related to the limited influence of hb on the light field distribution. The Re(ΔNeff) of two modes versus hb is shown in Figure 6b. Here, Re(ΔNeff) is determined by ReΔN  | ReN  ReN  | eff eff eff (5 ) TM mode Complex mode Since a low Re(ΔNeff) is more desirable, hb is chosen to be 180 nm. Figure 6. (a, b, c) are Re(Neff), Re(ΔNeff), and modulation depth (MD) as well as propagation loss (PL) of the TM mode and complex mode in the DBOSW modulator as a function of hb, respectively. 3.2. h Figure 7 shows the MD, PL, Re(Neff) and Re(ΔNeff) of two modes in the DBOSW mod- ulator versus the middle silica layer thickness h. As shown Figure 7a, Re(Neff) of both modes reduce consistently with the increasing of h. Furthermore, when h = 100 nm, the Re(Neff) of the TM mode and complex mode show a very close minimum, which can be confirmed in Figure 7b. Though Re(ΔNeff) can already be restrained at a low level (< 0.115) when h is 50 or 200 nm, the thickness of silica layer apparently has a more significant impact on the polarization dependence. As shown in Figure 7c, MD and PL of two modes decrease simultaneously with the increasing of h. These trends are attributed to less con- finement of the light field in the middle silica layer as well as the weakening of the inter- action with graphene. This is depicted in the illustration in Figure 7c. As h decreases, the electric field intensity of the TM mode and the y-axis electric field component of complex mode increases in the middle silica layer. The increment of mode power in the metal layer invites higher optical loss. To be noted, the MD difference between the TM mode and Appl. Sci. 2021, 11, 1897 7 of 16 complex mode remains at a low level when h varies from 50 to 200 nm. However, the PL of the TM mode becomes lower than that of complex mode when h is higher than 95 nm. To constrain the performance difference between the TM mode and complex mode, h is chosen to be 100 nm. Figure 7. Re(Neff), Re(ΔNeff), MD and PL of the TM mode and complex mode in the DBOSW modulator versus h are shown in (a), (b) and (c), respectively. The illustration in (c) shows the variation of electric field distribution for both modes versus h. 3.3. ht When hb = 180 nm, h = 100 nm, Re(Neff) and Re(ΔNeff), the MD and PL of two modes in the DBOSW modulator versus the top layer thickness ht are investigated. As shown in Figure 8a, Re(Neff) of the TM mode decreases with the increment of ht at μc = 0 and 1 eV. When ht is 110 nm, Re(Neff) of the complex mode exhibits a minimum of 1.6722 and 1.6469 at μc = 0 and 1 eV, respectively. It is noteworthy that both modes share the same Re(Neff) when ht is 200 nm and μc is 1 eV. This scenario also can be found when ht is 210 nm and μc is 0 eV. In Figure 8 (b), a maximum Re(ΔNeff) is first presented with the increase of ht as μc −4 = 0 and 1 eV. Then, a minimum Re(ΔNeff) of 6 × 10 (μc = 1 eV) appears when ht is 200 nm. −4 A minimum Re(ΔNeff) of 1 × 10 (μc = 0 eV) can be observed when ht is 210 nm. The differ- ent behaviors of Re(Neff) and Re(ΔNeff) in Figure 8a and Figure 8b can be explained by the change of fringing field distribution as well as the variation in the slot region. This phe- nomenon is similar to what happens to the MIM waveguide [20]. As shown in Figure 8c, the PLs of both the TM mode and the complex mode decrease till ht rises up to 200 nm. As ht increases from 50 nm to 200 nm, the MD of the complex mode decreases by 57.1%, while the MD of the TM mode only reduces by 7.0%. Obviously, the change of ht has a more remarkable impact on the complex mode than that on the TM mode. This can be explained by the field distribution difference that can be observed from the illustration in Figure 8c. With comprehensive consideration, a balanced ht of 200 nm is chosen. Appl. Sci. 2021, 11, 1897 8 of 16 Figure 8. Re(Neff), Re(ΔNeff), MD as well as PL of the TM mode and complex mode in the DBOSW modulator versus ht are shown in (a), (b) and (c), respectively. The illustration in (c) shows the variation of electric field distribution for the TM mode and complex mode versus ht. 3.4. w For the waveguide structure in Figure 1, the width of the Ag strips w will definitely affect the mode field distribution. Therefore, Re(Neff), Re(ΔNeff), MD and PL of the TM mode and complex mode in the DBOSW modulator versus the Ag strips w are investi- gated, when hb = 180 nm, h = 100 nm, and ht = 200 nm. As shown in Figure 9(a), Re(Neff) of the TM mode gradually increases from 1.631 to 1.675 at μc = 0 eV, when w varies from 50 to 150 nm. Re(Neff) of the TM mode remains at 1.675, without changing with the increment in w. Inversely, Re(Neff) of complex mode decreases from 1.712 to 1.673 at μc = 0 eV, when w varies from 50 to 150 nm. A negligible change of Re(Neff) of the complex mode is ob- served when w is over 150 nm. When μc = 1 eV, Re(Neff) of the TM mode and complex mode exhibit similar inverse variation with the increment in w, which leads to a turning point of Re(ΔNeff) at w = 150 nm, as shown in Figure 9b. As w changes from 50 nm to 200 nm, the MDs of the TM mode and complex mode decrease by 55.1 and 30.5%, respectively. Both modes have the same MD at w = 160 nm. When w ranges from 50 to 150 nm, the PL of the TM mode decreases from 0.16 to 0.14 dB/μm, while PL of complex mode from 0.21 to 0.15 dB/μm. Both PLs become stable when w is larger than 150 nm, as shown in Figure 9c. The decrement of the MD and PL can be attributed to the extension of the mode field region with the increment in w, which weak- ens the graphene–light interaction strength, as shown in the illustration in Figure 9c. Since the TM mode and complex mode are distributed differently in the middle slot and the top metal slot, the increment in w has a greater impact on the MD of the TM mode. Moreover, the enlargement of the mode field area will weaken the field intensity, and then the metal absorption, leading to a lower PL. From the above, Re(ΔNeff) shows a minimum, while the MDs and PLs of the two modes are very close at w = 150 nm. Therefore, we choose w to be 150 nm in following work. Appl. Sci. 2021, 11, 1897 9 of 16 Figure 9. Re(Neff), Re(ΔNeff), modulation depth as well as propagation loss of the TM mode and complex mode in the DBOSW modulator versus w are shown in (a), (b) and (c), respectively. The illustration in (c) shows the variation of electric field distribution for both modes versus w. 3.5. g Another parameter to be confirmed in the proposed design is the gap width g be- tween two upper metal parts. When hb = 180 nm, h = 100 nm, w = 150 nm and ht = 200 nm, Re(Neff), Re(ΔNeff), MD and PL of the two modes in the DBOSW modulator versus metal slot width g are investigated. As shown in Figure 10, similar variations of Re(Neff) and Re(ΔNeff) to that in Figure 9 can be observed. The difference is that the change of g has a greater impact on Re(ΔNeff) than that on Re(Neff). As g increases, Re(ΔNeff) decreases firstly and then gradually increases. At g = 50 nm, Re(ΔNeff) shows the maximum of 0.2707 and 0.2691 for μc = 0 and 1 eV, respectively. −4 −4 The minimum Re(ΔNeff) of 6 × 10 and 3 × 10 can be found at g = 125 nm for μc = 0 and 1 eV, respectively. As shown in Figure 10c, the MD of the complex mode is less sensitive to the variation of g than the TM mode, which is due to the enhanced interaction strength between the x- axis electric field component of complex mode caused by the smaller g and the lateral metal slot. This leads to a higher loss and the resulting lower MD. In contrast, for the TM mode, the variation of g only changes its mode area, which is similar to the impact of w on the TM mode, as shown in the illustration in Figure 10c. The almost unchanged PL and linearly decreasing MD of the TM mode depicted in Figure 10c is consistent with the EA graphene modulator based on the MIM waveguide [36]. Since the difference of MD and PL between the two modes remains at a low level, when g is larger than 125 nm, g is chosen to be 125 nm in this design. Appl. Sci. 2021, 11, 1897 10 of 16 Figure 10. (a, b, c) are Re(Neff), Re(ΔNeff), modulation depth as well as propagation loss of the TM mode and complex mode in the DBOSW modulator versus g, respectively; the illustration in (c) shows the variation of electric field distribution for both modes versus g. 3.6. μ. c Response The relationships between Re(Neff) (Re(ΔNeff)), PL, Im(Neff) and the chemical potential μc also have been investigated. Figure 11a shows that Re(Neff) of the TM mode first in- creases from 1.6699 to the peak value of 1.6772 as μc increases from 0 to 0.4 eV. Subse- quently, it decreases to 1.6511 as μc continues to increase to 1 eV. Similar trends for Re(Neff) of the complex mode can also be observed. Furthermore, the Re(ΔNeff) remains at a low −4 level with an average of 3.6 × 10 in the range of μc = 0 to 1 eV. Figure 11b shows that the PL decreases rapidly as μc decreases from 0.2 to 0.6 eV. Therefore, the “ON” and the “OFF” state of DBOSW modulator is defined at μc = 0.6 and 0.2 eV, respectively. In this case, the MD of the TM mode up to 0.474 dB/μm can be obtained, while the MD of the complex mode is 0.462 dB/μm. The calculated ΔMD (|MDTM mode − MDComplex mode|) is only 0.012 dB/μm at λ = 1550 nm. Figure 11. Re(Neff) and Re(ΔNeff), Im(Neff) and PL of the TM mode and complex mode versus Femi level (chemical potential μc) from 0 to 1 eV are shown in (a) and (b), respectively. 4. Performance and Discussion 4.1. Optical Bandwidth To confirm the optical bandwidth of the DBOSW modulator with the above geomet- ric parameters, the relationships between Re(Neff) and Re(ΔNeff) of the two modes as a Appl. Sci. 2021, 11, 1897 11 of 16 function of the incident wavelength are investigated when μc ranges from 0.2 to 0.6 eV. As shown in Figure 12a, Re(Neff) decreases with the increment in wavelength. When λ = 1.1 μm and μc = 0.6 eV, the maximum Re(Neff) of the TM mode and the complex mode is 1.7135 and 1.7163, respectively. When λ = 1.1 μm and μc = 0.2 eV, Re(Neff) of the TM mode and complex mode is 1.7096 and 1.7127, respectively. When λ = 1.9 μmand μc = 0.6 eV, Re(Neff) of the TM mode and complex mode is 1.6438 and 1.6427, respectively. When λ = 1.9 μm and μc = 0.2 eV, Re(Neff) of the TM mode and complex mode is 1.6586 and 1.6574, respectively. It can be observed that a very low Re(ΔNeff) of around 0.001 can be obtained within a wavelength range from 1.1 to 1.9 μm. In Figure 12b, when the wavelength varies from 1.1 to 1.9 μm, Im(Neff) of the TM mode quickly increases from 0.01207 to 0.02164 at μc = 0.2 eV; meanwhile, Im(Neff) of the complex mode increases from 0.01160 to 0.02177 at μc = 0.2 eV, which mainly results from the enhancement of the graphene–light interaction due to the increasing dielectric con- stant with the increment in optical wavelength. To be mentioned, the MPA change of both two modes is very limited within the wavelength range. The MDs of the TM mode are 0.40918 dB/μm at λ = 1.1 μm and 0.46931 dB/μm at λ = 1.9 μm, respectively. While, the MDs of the complex mode are 0.38416 dB/μm at λ = 1.1 μm and 0.46415 dB/μm at λ = 1.9 μm, respectively. Therefore, the proposed modulator shows good polarization-independ- ence characteristics over a broad optical bandwidth. Figure 12. (a) Re(Neff) and Re(ΔNeff), (b) Im(Neff) and MPA of the TM mode and complex mode versus the incident wave- length at μc = 0.2 and 0.6 eV, respectively. 4.2. Frequency Response Here, the 3 dB-bandwidth (f3dB) and power consumption of the proposed DBOSW modulator with optimized geometric parameters are also confirmed. An equivalent cir- cuit model is adopted to estimate the dynamic response of the DBOSW modulator, which is shown in Figure 13. Figure 13. The equivalent circuit model. Appl. Sci. 2021, 11, 1897 12 of 16 In this model, the capacitance Cair exists between two electrodes and the air, which is 12 fF [37]. The capacitance C that consists of the two graphene layers and SiO2 isolation layer includes both the dielectric capacitance CD and the quantum capacitor CQ. Assuming the graphene layer is undoped (ns = 0), then we have CQ = 0. Hence, the capacitance C can be described by the following capacitor model: C  w Ld / ( 6 ) r 0 ol where L = 20 μm and wol = 1385 nm are the graphene modulation length and the overlap width of two graphene layers, respectively. εr and d are the permittivity and the thickness of SiO2 isolation layer, respectively. Rtotal is the total resistance, which includes the gra- phene sheet resistance Rs of 100 Ω/□ [38], and the metal electrode contact resistance to graphene layer Rc of 150 Ω-μm [20]. According to Equation (6) below, Rtotal is calculated to be about 33.85 Ω [24,30], where the effective graphene width wg is set to be 1.885 μm. 2R R  2R ( 7 ) total s L L Based on Equation (8), the 3 dB-bandwidth is dominantly limited by RC delay. Ac- cording to Equations (5–7), the DBOSW modulator shows a high f3dB of 101 GHz. For the proposed device structure, the silica as an isolation layer that is with a relatively low per- mittivity and a small thickness of 15 nm is favorable to compensate the disadvantages of the large effective width and overlapping area of graphene layers. In addition, the sheet resistance Rs and contact resistance Rc are values adopted in related Ref. [17]. f  ( 8 ) 3dB 2RC total total The power consumption (Ebit = Ctotal(ΔU) /4) is estimated to be 0.271 pJ/bit at L = 20 μm, where the applied voltage change ΔU is 4.834 V. This is in accordance with the change of chemical potential from 0.2 to 0.6 eV. To clarify the merits of proposed design, the theoretical performance of the reported polarization-insensitive graphene modulators is comprehensively compared with that of this work. As shown in Table 1, the proposed modulator has the largest optical bandwidth and the smallest Re(ΔNeff). Moderate MD and ΔMD also can be obtained. The characteris- tics of f3dB and Ebit are also better than most reported works. Appl. Sci. 2021, 11, 1897 13 of 16 Table 1. Performance comparison with reported polarization-insensitive graphene modulators at λ = 1.55 μm. Ref. Bandwidth (nm) Re(ΔNeff) MD (dB/μm) ΔMD (dB/μm) f3dB (GHz) Ebit (fJ/bit) [39] 1500–1600 - 0.06 0 13.4 - [40] 1500–1600 - 0.08 0 80 - mode A: 1.05, Min: 0.08 [41] 1200–1600 - mode B: 1.13, 95 138.8 Max: 0.61 mode C: 0.52 TM mode: ~0.2975, −3 −3 [42] 1530–1565 4.7 × 10 ~8 × 10 30.2 2980 TE mode: ~0.2895 TM mode: 1.113, −3 [43] 1367–1771 ~ 0.5 ~6 × 10 6.1 7800 TE mode: 1.119 TM mode: 1.392, [44] 1450– 1650 ~ 0.1 0.045 ~100 - TE mode: 1.347 −3 [45] 1300–1800 1.2 × 10 - - 135.6 - TM mode: 0.474, −4 This work 1100–1900 6 × 10 0.012 101 271 complex mode: 0.462 The proposed DBOSW modulator can be implemented through the following fabri- cation process. The fabrication process starts with a commercial silica wafer. The E-beam evaporation deposits a silver layer with a thickness of 180 nm (hb) onto the silica surface, serving as a bottom layer. Subsequently, the plasma-enhanced chemical vapor deposition (PECVD) can be used to deposit the 100 nm-thick SiO2 (h) middle layer. Next, the thermal evaporation is used to deposit a 200 nm-thick (ht) silver layer followed by electron-beam lithography (EBL) and inductively coupled plasma etching. The 125 nm-wide metal slot substructure (g) is then filled with SiO2 by PECVD. The subsequent surface chemical me- chanical polishing as well as the etching to three layers above can form a hybrid ridge with a width of 425 nm (w × 2 + g). After that, the bottom graphene sheet grown can be wet-transferred to the hybrid ridge waveguide. The graphene-covered region can be de- fined by EBL processing to remove the excess graphene. Whereas, the graphene on the other side extends 500 nm to form an electrode contact. A 15 nm-thick SiO2 isolation layer is deposited on the bottom graphene flake. The second graphene flake is transferred onto the SiO2 isolation layer and handled with the same process applied on the bottom gra- phene layer, constructing a complete hybrid waveguide structure. Considering the structural complexity of the proposed DBOSW, the influence of manufacturing errors on the modulator is also evaluated. Firstly, the influence of inequal- ity of the top Ag strip δ (the asymmetry of DBOSW) on the modulator performance is investigated, as shown in Figure 14. The geometric parameters used here are the optimal values discussed in above sections. It can be seen that the DBOSW modulator exhibits stable polarization insensitivity in the fluctuation of one side w from 135 to 165 nm (−15 −3 nm > δ > 15 nm). The maximum Re(ΔNeff) at δ = 15 nm is 4 × 10 , which is still lower than the optimal value in Ref. [40]. ΔMD remains at a low level, which is still competitive com- pared with reported works. The undulation of ΔMD relates to the difference between the mutative MD of the TM mode and the relatively constant MD of the complex mode, as shown in Figure 14 (c). PLs exhibit good stability. As discussed in Section 3, though the proposed design has a relatively large fabrication tolerance, g needs to be treated carefully. A significant negative effect on Re(Neff) may damage the modulation performance at small g. Appl. Sci. 2021, 11, 1897 14 of 16 Figure 14. The inequality of the top Ag strip δ on (a) Re(ΔNeff); (b) ΔMD; and (c) MD, PL of the TM mode and complex mode. The illustration in (b) shows the unequal condition of the DBOSW modulator, when δ < 0 the width of the right Ag stripe is smaller than that of the left one. 5. Conclusions In summary, to achieve the polarization-insensitive modulation and enhance the modulation capability of the graphene layer, a broadband polarization-insensitive gra- phene modulator based on plasmonic effect with DBOSW is proposed and comprehen- sively investigated. By introducing the two slot-like structure in the waveguide, the DBOSW can support two modes simultaneously, which enables the modulation of both the longitudinal and the transverse polarization electric fields in a broadband bandwidth. When the external bias voltage shifts from 0.608 to 5.442 V, the MD of 0.474 and 0.462 dB/μm for the TM mode and complex mode can be obtained, respectively. A low effective index difference with an average of 0.001 is achieved within a wide optical band range from 1.1 to 1.9 μm. The 3 dB-bandwidth of 101 GHz and a power consumption of 0.271 pJ/bit at a modulation length of 20 μm can be obtained. The proposed graphene modulator has potential in microwave photonic systems. Author Contributions: W.C. proposed the idea, carried out the simulations and wrote the manu- script. Y.X. and Y.G. plotted the figures and provided suggestions. X.W. supervised the simula- tions. X.S. and D.Z. supervised the whole work, interpreted the results and improved the manu- script. All authors reviewed the manuscript. All authors have read and agreed to the published version of the manuscript. Funding: This study was supported by the National Key Research and Development Program of China (2019YFB2203001), National Natural Science Foundation of China (61675087, 61875069), and The Education Department of Jilin Province (JJKH20190118KJ) Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Conflicts of Interest: The authors declare no conflict of interest. References 1. Marris-Morini, D.; Lyan, P.; Rivallin, P.; Halbwax, M.; Laval, S.; Vivien, L.; Rasigade, G.; Fedeli, J.-M.; Cassan, E.; Le Roux, X.; et al. Recent Progress in High-Speed Silicon-Based Optical Modulators. Proc. IEEE 2009, 97, 1199–1215. 2. Wang, C.; Zhang, M.; Chen, X.; Bertrand, M.; Shams-Ansari, A.; Chandrasekhar, S.; Winzer, P.; Lončar, M. Integrated lithium niobate electro-optic modulators operating at CMOS-compatible voltages. Nature 2018, 562, 101–104. 3. Pérez-Galacho, D.; Marris-Morini, D.; Stoffer, R.; Cassan, E.; Vivien, L. Simplified modeling and optimization of silicon modu- lators based on free-carrier plasma dispersion effect. Opt. Express 2016, 24, 26332–26337. 4. Park, J.-K.; Takagi, S.; Takenaka, M. InGaAsP Mach–Zehnder interferometer optical modulator monolithically integrated with InGaAs driver MOSFET on a III-V CMOS photonics platform. Opt. Express 2018, 26, 4842–4852. 5. Nickelson, L.; Gric, T.; Asmontas, S.; Martavicius, R. Electric Field Distributions of the Fast and Slow Modes Propagated in the Open Rod SiC Waveguide. Elektron. Elektrotech. 2009, 93, 87–90. Appl. Sci. 2021, 11, 1897 15 of 16 6. Hu, Y.; Pantouvaki, M.; Van Campenhout, J.; Brems, S.; Asselberghs, I.; Huyghebaert, C.; Absil, P.; Van Thourhout, D. Broad- band 10 Gb/s operation of graphene electro-absorption modulator on silicon. Laser Photon. Rev. 2016, 10, 307–316. 7. Mohsin, M.; Schall, D.; Otto, M.; Noculak, A.; Neumaier, D.; Kurz, H. Graphene based low insertion loss electro-absorption modulator on SOI waveguide. Opt. Express 2014, 22, 15292–15297. 8. Dalir, H.; Xia, Y.; Wang, Y.; Zhang, X. Athermal Broadband Graphene Optical Modulator with 35 GHz Speed. ACS Photonics 2016, 3, 1564–1568. 9. Phatak, A.; Cheng, Z.Z.; Qin, C.Y.; Goda, K. Design of electro-optic modulators based on graphene-on-silicon slot waveguides. Opt. Lett. 2016, 41, 2501–2504. 10. Liu, M.; Yin, X.; Ulin-Avila, E.; Geng, B.; Zentgraf, T.; Ju, L.; Wang, F.; Zhang, X. A graphene-based broadband optical modula- tor. Nature 2011, 474, 64–67. 11. Liu, M.; Yin, X.; Zhang, X. Double-Layer Graphene Optical Modulator. Nano Lett. 2012, 12, 1482–1485. 12. Phare, C.T.; Daniel Lee, Y.-H.; Cardenas, J.; Lipson, M. Graphene electro-optic modulator with 30 GHz bandwidth. Nat. Photon- ics 2015, 9, 511–514. 13. Schuller, J.A.; Barnard, E.S.; Cai, W.; Jun, Y.C.; White, J.S.; Brongersma, M.L. Plasmonics for extreme light concentration and manipulation. Nat. Mater. 2010, 9, 193–204. 14. Bozhevolnyi, S.I.; Volkov, V.S.; Devaux, E.; Laluet, J.Y.; Ebbesen, T.W. Channel plasmon subwavelength waveguide compo- nents including interferometers and ring resonators. Nature 2006, 440, 508–511. 15. Gramotnev, D.K.; Bozhevolnyi, S.I. Plasmonics beyond the diffraction limit. Nat. Photonics 2010, 4, 83–91. 16. Huang, B.-H.; Lu, W.-B.; Li, X.-B.; Wang, J.; Liu, Z.-G. Waveguide-coupled hybrid plasmonic modulator based on graphene. Appl. Optics 2016, 55, 5598–5602. 17. Zheng, P.; Yang, H.; Fan, M.; Hu, G.; Zhang, R.; Yun, B.; Cui, Y. A Hybrid Plasmonic Modulator Based on Graphene on Channel Plasmonic Polariton Waveguide. Plasmonics 2018, 13, 2029–2035. 18. Bao, Q.; Zhang, H.; Wang, B.; Ni, Z.; Lim, C.H.Y.X.; Wang, Y.; Tang, D.Y.; Loh, K.P. Broadband graphene polarizer. Nat. Pho- tonics 2011, 5, 411–415. 19. Chang, L.-M.; Liu, L.; Gong, Y.-H.; Tan, M.-Q.; Yu, Y.-D.; Li, Z.-Y. Polarization-independent directional coupler and polarization beam splitter based on asymmetric cross-slot waveguides. Appl. Optics 2018, 57, 678–683. 20. Zhong, H.; Zhang, Z.Y.; Chen, B.Y.; Xu, H.T.; Yu, D.M.; Huang, L.; Peng, L.M. Realization of low contact resistance close to theoretical limit in graphene transistors. Nano Res. 2015, 8, 1669–1679. 21. Veronis, G.; Fan, S. Modes of Subwavelength Plasmonic Slot Waveguides. J. Lightwave Technol. 2007, 25, 2511–2521. 22. Geim, A.K.; Novoselov, K.S. The rise of graphene. Nat. Mater. 2009, 6, 183–191. 23. Schwierz, F. Graphene transistors. Nat. Nanotechnol. 2010, 5, 487–496. 24. Bonaccorso, F.; Hasan, T.; Sun, Z.; Ferrari, A.C. Graphene photonics and optoelectronics. Nat. Photonics 2010, 4, 611–622. 25. Kusuma, J.; Balakrishna, R.G.; Patil, S.; Jyothi, M.S.; Chandan, H.R.; Shwetharani, R. Exploration of graphene oxide nanoribbons as excellent electron conducting network for third generation solar cells. Solar Energy Mater. Solar Cells 2018, 183, 211–219. 26. Avouris, P.; Chen, Z.; Perebeinos, V. Carbon Based Electronics. Nat. Nanotechnol. 2007, 2, 605–615. 27. Bolotin, K.I.; Sikes, K.J.; Jiang, Z.; Klima, M.; Fudenberg, G.; Hone, J.; Kim, P.; Stormer, H.L. Ultrahigh electron mobility in suspended graphene. Solid State Commun. 2008, 146, 351–355. 28. Nair, R.R.; Blake, P.; Grigorenko, A.N.; Novoselov, K.S.; Booth, T.J.; Stauber, T.; Peres, N.M.R.; Geim, A.K. Fine Structure Con- stant Defines Visual Transparency of Graphene. Science 2008, 320, 1308–1308. 29. Mak, K.F.; Sfeir, M.Y.; Wu, Y.; Lui, C.H.; Misewich, J.A.; Heinz, T.F. Measurement of the Optical Conductivity of Graphene. Phys. Rev. Lett. 2008, 101, 196405–196408. 30. Sensale-Rodriguez, B.; Yan, R.; Kelly, M.M.; Fang, T.; Tahy, K.; Hwang, W.S.; Jena, D.; Liu, L.; Xing, H.G. Broadband graphene terahertz modulators enabled by intraband transitions. Nat. Commun. 2012, 3, 780–786. 31. Gric, T.; Nickelson, L.; Asmontas, S. Electrodynamical characteristic particularity of open metamaterial square and circular waveguides. Prog. Electromagn. Res. 2010, 109, 361–379. 32. Ye, L.; Sui, K.; Zhang, Y.; Liu, Q.H. Broadband optical waveguide modulators based on strongly coupled hybrid graphene and metal nanoribbons for near-infrared applications. Nanoscale 2019, 11, 3229–3239. 33. Hanson, G.W. Dyadic Green’s functions and guided surface waves for a surface conductivity model of graphene. J. Appl. Phys. 2007, 103, 064302–064309. 34. Kwon, M.-S. Discussion of the Epsilon-Near-Zero Effect of Graphene in a Horizontal Slot Waveguide. IEEE Photonics J. 2014, 6, 1–9. 35. Hwang, C.; Siegel, D.A.; Mo, S.K.; Regan, W.; Ismach, A.; Zhang, Y.; Zettl, A.; Lanzara, A. Fermi velocity engineering in gra- phene by substrate modification. Sci. Rep. 2012, 2, 590–593. 36. Ding, Y.; Guan, X.; Zhu, X.; Hao, H.; Xiao, S. Effective electro-optic modulation in low-loss graphene-plasmonic slot waveguides. Nanoscale 2017, 9, 15576–15581. 37. Hu, Y.; Xiao, X.; Xu, H.; Li, X.; Xiong, K.; Li, Z.; Chu, T.; Yu, Y.; Yu, J. High-speed silicon modulator based on cascaded microring resonators. Opt. Express 2012, 20, 15079–15085. 38. Abdollahi Shiramin, L.; Van Thourhout, D. Graphene Modulators and Switches Integrated on Silicon and Silicon Nitride Wave- guide. IEEE J. Sel. Top. Quantum Electron. 2016, 23, 94–100. Appl. Sci. 2021, 11, 1897 16 of 16 39. Yang, Z.; Lu, R.; Cai, S.; Wang, Y.; Zhang, Y.; Wang, X.; Liu, Y. A CMOS-compatible and polarization-insensitive graphene optical modulator. Opt. Commun. 2019, 450, 130–135. 40. Yang, Z.; Lu, R.; Wang, Y.; Cai, S.; Zhang, Y.; Wang, X.; Liu, Y. A fabrication-friendly graphene-based polarization insensitive optical modulator. Optik 2019, 182, 1093–1098. 41. Shirdel, M.; Mansouri-Birjandi, M.A. Broadband graphene modulator based on a plus-shaped plasmonic slot waveguide. Appl. Optics 2019, 58, 8174–8179. 42. Hu, X.; Wang, J. Design of graphene-based polarization-insensitive optical modulator. Nanophotonics 2018, 7, 651–658. 43. Xu, Y.; Li, F.; Kang, Z.; Huang, D.; Zhang, X.; Tam, H.-Y.; Wai, P. Hybrid Graphene-Silicon Based Polarization-Insensitive Elec- tro-Absorption Modulator with High-Modulation Efficiency and Ultra-Broad Bandwidth. Nanomaterials 2019, 9, 157–171. 44. Ye, S.W.; Liang, D.; Lu, R.-G.; Shah, M.K.; Zou, X.-H.; Yang, F.; Yuan, F.; Liu, Y. Polarization Independent Modulator by Partly Tilted Graphene Induced Electro-Absorption Effect. IEEE Photonics Technol. Lett. 2016, 29, 23–26. 45. Zou, X.H.; Zhang, Y.J.; Li, Z.H.; Yang, Y.W.; Zhang, S.J.; Zhang, Z.Y.; Zhang, Y.L.; Liu, Y. Polarization-Insensitive Phase Modulators Based on an Embedded Silicon-Graphene-Silicon Waveguide. Appl. Sci.-Basel 2019, 9, 429-436.

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Applied Sciences – Multidisciplinary Digital Publishing Institute

Published: Feb 21, 2021

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