A Proposal for Optical Antenna in VLC Communication Receiver System
A Proposal for Optical Antenna in VLC Communication Receiver System
Chamani, Shaghayegh;Dehgani, Roya;Rostami, Ali;Mirtagioglu, Hamit;Mirtaheri, Peyman
2022-04-05 00:00:00
hv photonics Article A Proposal for Optical Antenna in VLC Communication Receiver System 1 1 1 , 2 , 3 4 Shaghayegh Chamani , Roya Dehgani , Ali Rostami * , Hamit Mirtagioglu and Peyman Mirtaheri Photonics and Nanocrystal Research Lab. (PNRL), University of Tabriz, Tabriz 5166614761, Iran; shaghayegh_chamani98@ms.tabrizu.ac.ir (S.C.); roya_dehghani98@ms.tabrizu.ac.ir (R.D.) SP-EPT Lab., ASEPE Company, Industrial Park of Advanced Technologies, Tabriz 5169654916, Iran Department of Statistics, Faculty of Science and Literature, University of Bitlis Eren, Bitlis 13100, Turkey; hmirtagioglu@beu.edu.tr Department of Mechanical, Electronics and Chemical Engineering, OsloMet-Oslo Metropolitan University, 0167 Oslo, Norway; peyman.mirtaheri@oslomet.no * Correspondence: rostami@tabrizu.ac.ir Abstract: Visible Light Communication (VLC) is an important emerging choice for high-speed wireless communication. In this perspective, light-emitting diodes as illuminators will be modulated to transmit data simultaneously. However, the receivers bring severe difficulties due to cost, response time, and sensitivity with a wide Field Of View (FOV). To avoid these problems, one approach is to apply a large area photodetector; however, this solution is slow and costly. Another method is to focus light on a fast photodetector by optical components, but the photodetector ’s FOV decreases, resulting from the conservation of etendue. Another option is Luminescent Solar Concentrators (LSCs). This paper demonstrates a novel shape of LSC with advantages such as inexpensive, fast response time, small antenna area for VLC purposes with significant geometrical gain, FOV, and ultra-broad bandwidth. It does not require any complex tracking system and active pointing but, due to its tiny size, it can also be adapted in integrating and mobile devices. Numerical simulation is done using Monte-Carlo raytracing, and the results are demonstrated in the spectral domain. The optical efficiency of the proposed antenna is obtained at 1.058%, which is about 0.4% better than the Citation: Chamani, S.; Dehgani, R.; efficiency levels reported in other works, and the geometric gain of the antenna is reported to be 44, Rostami, A.; Mirtagioglu, H.; which is significant. Mirtaheri, P. A Proposal for Optical Antenna in VLC Communication Keywords: visible light communication; Monte-Carlo simulation; luminescent solar concentrators; Receiver System. Photonics 2022, 9, optical antenna 241. https://doi.org/10.3390/ photonics9040241 Received: 16 February 2022 Accepted: 15 March 2022 1. Introduction Published: 5 April 2022 In the contemporary world, an extension of numerous digital technologies has made Publisher’s Note: MDPI stays neutral wireless technology an essential means of connection [1,2]. Wireless communication tech- with regard to jurisdictional claims in nology is one of the flourishing fields of communication through which people can com- published maps and institutional affil- municate from anywhere and at any instant using electromagnetic (EM) waves wirelessly. iations. Hence, it has become a significant transmission medium [1,3]. Transmission applications in wireless networks have caused unexampled solicitations. Therefore, supplying high- performance wireless transmission is of great importance [4]. Although Radio Frequency (RF) communication as a subset of wireless communication is widely used for an extensive Copyright: © 2022 by the authors. range of applications due to its small electromagnetic (EM) interference and decent cov- Licensee MDPI, Basel, Switzerland. erage, the network traffic has experienced incredible congestion because of the excessive This article is an open access article users and heavy data-hungry applications [3,5]. Over time, it has faced some challenges, distributed under the terms and such as increasing demand for high Quality of Service (QoS), achieving a high data rate conditions of the Creative Commons (beyond Gbps toward Tb/s regime), limited channel capacity, limited bandwidth, and the Attribution (CC BY) license (https:// emergence of fifth- and sixth-generation (5G and 6G) networks [5–8]. As its management by creativecommons.org/licenses/by/ 4.0/). the limited RF spectrum has become a growing concern, there was a severe need to develop Photonics 2022, 9, 241. https://doi.org/10.3390/photonics9040241 https://www.mdpi.com/journal/photonics Photonics 2022, 9, 241 2 of 19 a new technology to avoid the defects of previous technologies. In this regard, Optical Wireless Communication (OWC) technology was proposed as an alternative technology, especially for indoor communications [9], which transmits data using light pulses instead of radio waves [3]. OWC works in the optical region of the electromagnetic (EM) spectrum (300 GHz to 30 PHz), which is license-free and nonhazardous. Hence, it provides a high data rate, high capacity, broad bandwidth (in range of THz), security, and safety acute in the RF region [1,3,6,8]. Additionally, OWC possesses many other features, including high energy efficiency and low cost [1]. At first, OWC focused on wireless infrared communication. Then, it extended to the visible region of the EM spectrum, and it was called Visible Light Communication (VLC) [8]. VLC is an attractive developing field in OWC technology to fulfill the RF-based wireless fidelity (Wi-Fi) [10,11]. Through it, data are transmitted by intensity modulation of an optical source operating in the visible range of the EM spectrum (400–800 THz) at a very high rate [5]. The human eye cannot detect pulses and preserves them as a constant light [12]. Nowadays, revolutionary choices for optical sources are Light Emitting Diodes (LEDs) because not only are they able to illuminate an area thanks to their low energy (they can reduce energy consumption by 80% [3]) and higher lifetime, but also they can transmit data with less cost and a smaller carbon footprint [13]. Since serious environmental problems such as energy shortage, greenhouse gases emission, and global warming are growing [14–16], using LED as a source of VLC on the global scale can play a helpful role in preventing the condition from getting worse. This is why VLC has been very successful in attracting many research interests [13]. To indicate the importance of VLC, some examples can be emphasized, such as underwater VLC [17], high-speed indoor VLC [18], Non-Orthogonal Multiple Access (NOMA) for VLC systems [19], Power Domain Non-Orthogonal Multiple Access (PD-NOMA) for 6G networks [20], intelligent reflecting surfaces to aid VLC [21] and cooperative and non-cooperative relying on VLC channels [22]. To accomplish a VLC-based system, a modulated light source and a receiver are also needed. Antennas, therefore, are important and inseparable parts of VLC [4,23]. There are two substantial quantities in VLC: bandwidth and signal-to-noise ratio (S/N) [3,9]. In a high-speed VLC data link, the combination of a large signal-to-noise ratio and high bandwidth is crucial, not only in transmitters but also in receivers. Principally, these two factors determine the channel capacity of a VLC system [11]. Since VLC uses the illuminator LED as a data carrier and its bandwidth is limited to 20 MHz or less [24], it will restrict the bandwidth of the VLC system, so achieving a large bandwidth using existing LED technology is out of reach. Thus, improving the latter quantity, a high signal-to-noise ratio, is of great importance in VLC. Obtaining a large signal can be possible by collecting a large fraction of the light from a transmitter. In this case, there is a need for a large photodetector, which would normally have a slow response time and be expensive [9,11]. On the other hand, a typical photodetector with a bandwidth of GHz level has an active area of around 1 mm or less. Thus, the common way to improve the SNR in this much smaller photodetector is focusing the light onto it using an optical element that works based on reflection and refraction (for example, an optical lens or compound parabolic reflectors), thereby conserving the etendue in geometric optics. The conservation of etendue declares that if the wavelength of an optical system does not change, the maximum concentration gain of the system (C ) and field of view (FOV) are related max 2 2 inversely by C = n /sin (), where n is the refractive index of the concentrator and max is the acceptance angle that describes the FOV (range of solid angles for which the photodetector accepts light) [9,11,25]. However, if the wavelength of the optical system changes, etendue does not need to be conserved, and it is possible to obtain both high concentration gain and a wide FOV simultaneously [25,26]. In this regard, non-imaging optical concentrators called Luminescent Solar Concentrators (LSCs) have emerged recently as a reassuring receiver technology to realize VLC-based systems. Originally, they were Photonics 2022, 9, 241 3 of 19 fabricated to gather and concentrate the solar energy efficiently and guide it toward solar panels attached on all side edges of the LSC at an affordable cost. Apart from photovoltaics, they attracted a wide range of interests for numerous ap- plications, including microreactors [27], greenhouse coatings [28], dark-field imaging [29], dynamic systems (where the arrival time of photon is of the essence) such as image record- ing and movement detection technologies [30] and especially as an antenna in VLC-based systems very recently [25]. In the latter case, LSC has been made from a transparent host matrix doped with fluorophores. They are recommended to collect both direct and diffuse light of modulated LEDs from wide FOV in VLC systems. Then, fluorophores absorb the incident light and re-emit it at a longer wavelength by a down conversion [31]. This wavelength change is known as the Stokes shift. Thus, high concentration gain, a wide FOV, and consequently a high signal-to-noise ratio are accessible simultaneously without any other limitation [7]. The general schematic of an LSC has been illustrated in different references. So far, several shapes and sizes of waveguides and different types of fluo- rophores and host matrixes have been investigated to evaluate LSC performances [32] in terms of optical efficiency and FOV [25]. Since they can concentrate both direct and diffuse intended light, no tracking system is required [32,33]. LSC with a communication purpose includes a thin host matrix doped with fluorophores and the photodetector of receiver mounted on one specific edge. First, fluorophores absorb incident light signals from a large surface area, and secondly they re-emit photons at lower energy. The difference between refractive indices of the host matrix and surrounding medium causes the newly generated photons to be waveguided or retained inside the LSC because of the total internal reflection (TIR) phenomena. TIR leads to trapping these re-emitted photons inside the optical waveguide and concentrating them onto the edge of the LSC device [31]. Eventually, part of the photons is collected by a photodetector attached to the specific narrow edge or small end facet of the LSC [11,32]. Since the 1970s, various types of fluorophores have been applied to enhance the optical efficiency of the LSC [31]. Different types of fluorophores can be classified into organic dyes [34,35], lanthanide complex hybrids [36,37], perovskites [38,39] and Quan- tum Dots (QDs) [40,41]. Primarily, organic dyes, such as coumarin and rhodamine, are indicated as the high-performance fluorophores of LSCs owing to their large absorption coefficient, high photoluminescence quantum yield (PLQY), and good solubility [31,42,43]. Nevertheless, some unavoidable drawbacks of them including an unfriendly photodegra- dation effect and narrow absorption spectra affected their position. QDs, meanwhile, have significant pros over others, such as adjustable absorption and emission spectra, stability, a high quantum yield (QY), and a large absorption cross-section [32]. Most recently, wide research has been conducted focusing on LSCs in a variety of fields, such as photovoltaic systems, optical communication systems, and others. In the photovoltaic field, H. Zhao et al. in 2018 perused two perovskite LSCs and utilized spin-coated carbon dot LSC in the tandem structure. For carbon dot, green-emitting perovskite, and the red-emitting perovskite layer, optical efficiency was 0.3%, 1.1%, and 1.65%, respectively. In the end, combining three layers in one tandem structure improved optical efficiency to 3.0% [44]. In the most recent research, M. R. Mirzaei et al. modeled LSC based on different QDs with dimensions of 60 60 1.25 cm . The optical efficiency was written up as 11.8%, 13.8% and 31% for three different QYs (0.4, 0.6, and 1, respectively) [32]. On the other hand, different geometries have been studied in the communication field to increase optical efficiency, bit rate, and FOV. In 2016, Manousiadis et al. designed a dye-doped planar LSC sandwiched between microscope slides. FOV and data rate were reported as 60 and 190 Mb/s, respectively [11]. In the meantime, in another research, Peyronel et al. demonstrated a ball-shaped fiber-based LSC, reporting the FOV of 3.9 and data rates of 2.1 Gb/s [45]. In Table 1, the properties of previous works are summarized. Considering the number of utilized edges, this work has achieved better results. Photonics 2022, 9, 241 4 of 19 Table 1. Summary of previous works. Number of Optical Field of Structure of Ref. Fluorophore Utilized Efficiency Research LSC End Facets (%) Photovoltaics [44] Single layer Carbon dot 4 edges 0.3 Photovoltaics [44] Single layer Carbon dot 4 edges 1.1 Photovoltaics [44] Single-layer Carbon dot 4 edges 1.65 Photovoltaics [44] Tandem Carbon dot 4 edges 3 Photovoltaics [32] Single layer Quantum dot 4 edges 31 Communication [11] Single layer dye 1 edge 0.612% Communication This work Single-layer Quantum dot 1 edge 1.058% Communication This work Single-layer Quantum dot 4 edges 31.344% A large surface sufficient for collecting light from a large FOV offers LSCs exemplary merits because they do not need any tracking systems and active pointing. These ad- vantages lead to reduce cost and complexity and provide better adaptability with mobile devices such as wireless virtual reality headsets, quadcopters, etc. In any manner, there are still many shortcomings, especially about the efficiency of LSCs in optical communication that hinders their high performance. Up to now, many thermodynamic, theoretical, and light tracing models have been developed for modeling the LSC prototype devices, because theoretical simulation is an essential method to analyze and confirm the parameters of LSC prototype devices. Monte-Carlo ray-tracing simulation is one of the common methods to model LSCs because of their presumptive nature, diverse possible outcomes, and greater flexibility. Among all, Monte-Carlo simulation as a numerical method has a cogent usage in the situations wherein variables have coupled degrees of freedom, or there is no deterministic algorithm to solve the problem. It possesses a generally accepted popularity in differ- ent sciences including physics, statistics, engineering, finance, project management, and mathematics [40]. This paper aims at presenting a promising and novel schematic for the optical antenna using LSCs based on graphene QDs. Optimistically, not only can it partially address the mentioned problems, but it also allows for the application of a very small photodetector that is very fast, sensitive, and cost-effective. Our approach in this paper is introducing a new shape of an antenna suitable for VLC to take advantage of various factors. First, LED as a light source is used to provide a high data rate, low energy consumption, a high lifetime, less cost, and a smaller carbon footprint. Second, LSC is the main structure for the antenna to achieve a wide FOV and high concentration gain (due to stokes-shift), and it does not need any tracking system and active pointing. Third, a new antenna shape is used to attach a small photodetector that is fast, sensitive, and cost-effective, and to reach high geometric gain. Fourth, small size and dimensions are used to be adaptable with electronic devices and integration systems. The proposed antenna is analyzed using Monte-Carlo ray-tracing simulation. Moreover, we have calculated the percentage of every event and extracted corresponding spectra. Additionally, we have simulated the bandwidth of the passive component theoretically. We anticipate that our results will be a turning point for future research on Graphene Quantum Dot (GQD)-based LSC devices for communication purposes. The rest of this paper is organized as follows. First, in Section 2, we described the structure and shape of the proposed optical antenna and possible events that occur in it as well. Furthermore, the Monte-Carlo algorithm and followed steps were depicted in Section 2. Then, in Section 3, we provided related simulation results of the proposed scheme. Finally, a conclusion is drawn and future works are outlined in Section 4. Photonics 2022, 9, x FOR PEER REVIEW 5 of 20 as well. Furthermore, the Monte-Carlo algorithm and followed steps were depicted in Section 2. Then, in Section 3, we provided related simulation results of the proposed scheme. Finally, a conclusion is drawn and future works are outlined in Section 4. Photonics 2022, 9, 241 5 of 19 2. LSC Structure and Possible Phenomena An optical antenna is assumed to have a semi-sharp shape in our proposed structure. The schematic diagram of the LSC configuration is demonstrated in Figure 1. The host 2. LSC Structure and Possible Phenomena matrix consists of polyvinyl alcohol (PVA), and Graphene Quantum Dots (GQDs) are em- An optical antenna is assumed to have a semi-sharp shape in our proposed structure. bedded. Further, the photodetector of the receiver is placed on the tip of the antenna The schematic diagram of the LSC configuration is demonstrated in Figure 1. The host which is a small end facet of the LSC. The source of input light is a blue 450 nm LED, and matrix consists of polyvinyl alcohol (PVA), and Graphene Quantum Dots (GQDs) are it is irradiated on the front surface of the antenna. Generally, incoming photons are ab- embedded. Further, the photodetector of the receiver is placed on the tip of the antenna which sorbed by is a small GQDs an end facet d the of the n re-em LSC. The itted in a sourcelong of input er wavel lighteis ngth. Due to tota a blue 450 nm LED, l interna and itl reflec- is irradiated on the front surface of the antenna. Generally, incoming photons are absorbed tion phenomena, the re-emitted photons can be trapped inside the waveguide. They are by GQDs and then re-emitted in a longer wavelength. Due to total internal reflection then guided toward the tip of the LSC, which will be further detected by a photodetector phenomena, the re-emitted photons can be trapped inside the waveguide. They are then and converted into an electrical signal. Thus, the LSC plus the attached photodetector is a guided toward the tip of the LSC, which will be further detected by a photodetector and system to transmit light signal and convert it into electrical signals for data transmission converted into an electrical signal. Thus, the LSC plus the attached photodetector is a system purposes. to transmit light signal and convert it into electrical signals for data transmission purposes. (a) (b) Figure 1. Schematics of the proposed optical antenna. (a) Dimensions of the proposed optical an- Figure 1. Schematics of the proposed optical antenna. (a) Dimensions of the proposed optical tenna. (b) Configuration of components in the optical antenna (host matrix, Graphene Quantum antenna. (b) Configuration of components in the optical antenna (host matrix, Graphene Quantum Dots (GQDs), photodetector, incident light, and guiding light). Dots (GQDs), photodetector, incident light, and guiding light). Different phenomena occur when a light beam is an incident on the front surface of Different phenomena occur when a light beam is an incident on the front surface LSC. Those are illustrated in Figure 2. First, a photon may be reflected from the top surface of LSC. Those are illustrated in Figure 2. First, a photon may be reflected from the top surface without even entering the without even enteringLSC du the LSC e to th due to e differenc the differ eence in refr inactive indices o refractive indices f the two medi- of the two ums. medi A ums. fter eAfter ntering t entering he remain the remaining ing photons, t photons, herether is a pos e is aspossibility ibility thatthat eitheither er a ph aoton is photon is absorbed by the GQDs or passes through the LSC without being absorbed. The absorbed by the GQDs or passes through the LSC without being absorbed. The absorbed absorbed photon may be re-emitted by GQDs at an angle incidence greater than the critical photon may be re-emitted by GQDs at an angle incidence greater than the critical angle, angle, resulting in Total Internal Reflection (TIR), and, finally, the photon may reach the resulting in Total Internal Reflection (TIR), and, finally, the photon may reach the photo- photodetector after some TIR. Furthermore, there is a possibility that the photon will be detector after some TIR. Furthermore, there is a possibility that the photon will be re- re-emitted in a direction resulting in the direct collection at the tip of the LSC without any emitted in a direction resulting in the direct collection at the tip of the LSC without any prior TIR. prior TIR. Moreover, some percentage of the newly emitted photon escapes from LSC due to Moreover, some percentage of the newly emitted photon escapes from LSC due to escape-cone loss. Additionally, the re-emitted photon can be re-absorbed by the adjacent escape-cone loss. Additionally, the re-emitted photon can be re-absorbed by the adjacent GQDs; this mechanism is known as self-absorption. Further, the absorbed photon may GQDs; this mechanism is known as self-absorption. Further, the absorbed photon may be be quenched by non-radiative decay. Rarely, the host matrix can absorb and quench the quenched by non-radiative decay. Rarely, the host matrix can absorb and quench the pho- photon; however, due to its low probability of occurrence, it will be ignored in this paper. ton; however, due to its low probability of occurrence, it will be ignored in this paper. The The process can be simulated by the Monte-Carlo method that will be described in the process can be simulated by the Monte-Carlo method that will be described in the next next section. section. Photonics 2022, 9, x FOR PEER REVIEW 6 of 20 Photonics 2022, 9, 241 6 of 19 Figure 2. Physical process in optical antenna. Figure 2. Physical process in optical antenna. LSC Monte-Carlo Ray-Tracing Simulation The Monte-Carlo technique is a versatile statistical approach for modeling the propaga- tion of photons through a system. The Monte-Carlo simulation works based on mathemati- LSC Monte-Carlo Ray-Tracing Simulation cal relevant equations such as the Beer–Lambert law, Snell’s law, Fresnel law, and empirical data such as the absorption spectrum, photoluminescence spectrum, and quantum yield The Monte-Carlo technique is a versatile statistical approach for modeling the prop- of fluorophores. The ultimate fate of each photon is determined via this simulation under physical phenomena such as reflection, absorption, emission, and transmission proce- agation of photons through a system. The Monte-Carlo simulation works based on math- dures. Using this method leads to the avoidance of complex radiation transfer equations. Monte-Carlo simulation is expanded to model and optimize the operation and performance ematical relevant equations such as the Beer–Lambert law, Snell’s law, Fresnel law, and of LSCs. The algorithm used to create discussed Monte-Carlo simulation to model the proposed device is shown in the flow chart in Figure 3. Each time the algorithm is run, empirical data such as the absorption spectrum, photoluminescence spectrum, and quan- only one randomly generated photon is accounted for. The goal of this simulation is to detect whether the single photon will be collected or lost. Moreover, it can determine the tum yield of fluorophores. The ultimate fate of each photon is determined via this simu- type of loss among the probable losses, such as reflection, non-radiative recombination, lation under physical phenomena such as reflection, absorption, emission, and transmis- transmission, and escape-cone loss. The Monte-Carlo algorithm applied to model the proposed LSC (Figure 4) is depicted sion procedures. Using this method leads to the avoidance of complex radiation transfer as follows [46,47]: 1. The first step is to sample the wavelengths of incident photons from the spectrum of a equations. Monte-Carlo simulation is expanded to model and optimize the operation and 450 nm blue LED. This sampling process dawns on generating a Probability Density Function (PDF) [32] of the spectrum of the LED directly. Figure 5a represents the PDF performance of LSCs. The algorithm used to create discussed Monte-Carlo simulation to of the 450 nm blue LED. model the proposed device is shown in the flow chart in Figure 3. Each time the algorithm PDF = (Distribution/Area of the Curve) (1) is run, only one randomly generated photon is accounted for. The goal of this simulation Then, the PDF is converted to the Cumulative Distribution Function (CDF) [32], through which the wavelength of each photon is generated using the inverse transform is to detect whether the single photon will be collected or lost. Moreover, it can determine sampling method. (PDF +PDF )(l l ) j+1 j i j+1 j the type of loss among the probable losses, such as reflection, non-radiative recombina- j=1 CDF = (2) (PDF +PDF )(l l ) k j+1 j j+1 j tion, transmission, and escape-cone j=1 loss. Photonics 2022, 9, x FOR PEER REVIEW 7 of 20 Photonics 2022, 9, 241 7 of 19 Photonics 2022, 9, x FOR PEER REVIEW 8 of 20 5b points out the CDF of the 450 nm blue LED. In total, 100,000 initial photons with uni- form distribution on the upper surface of LSC and flood illumination are assumed during this simulation. The upper flat surface of LSC encounters a typical incidence, while the upper inclined surface will have the incident light with a non-zero input angle. This is calculated by using trigonometric relations. 2. Some percent of initial photons are reflected from the upper surfaces of LSC results from the different refractive index for waveguide and the surrounding medium. In this work, it is assumed that the LED is TE polarized. Hence, the probability of re- flection is calculated from Fresnel reflection equations [48] as Equation (3). Air nn cos(θθ )−− 1 ( sin( )) Air i LSC i nn cos(θθ ) − cos( ) 2 LSC Air i LSC t (1) RR==() = nn cos(θθ ) + cos( ) Air i LSC t Air nn cos(θθ )+− 1 ( sin( )) Air i LSC i LSC where θi and θt are the incidence angle and transmission angle, respectively. In the upper inclined surface, the incidence angle is non-zero, as shown in Figure 4. Thus, Equation (3) is used to determine the percentage of reflected photons. Whereas the flat surface sees the zero-incidence angle, Equation (3) is changed to Equation (4) after some simplifications [48]. nn − Air LSC R =() (4) nn + Air LSC Since nAir = 1, and nLSC is assumed to be the refractive index of PVA, which is approx- imately 1.49 in the visible light region [49], totally about 4% of primary photons are re- flected from the top surface, regarded as reflection loss. Figure 3. Monte-Carlo algorithm for numerical simulation. Figure 3. Monte-Carlo algorithm for numerical simulation. The Monte-Carlo algorithm applied to model the proposed LSC (Figure 4) is depicted as follows [46,47]: 1. The first step is to sample the wavelengths of incident photons from the spectrum of a 450 nm blue LED. This sampling process dawns on generating a Probability Density Function (PDF) [32] of the spectrum of the LED directly. Figure 5a represents the PDF of the 450 nm blue LED. PDF = (Distribution/Area of the Curve) (1) Then, the PDF is converted to the Cumulative Distribution Function (CDF) [32], through which the wavelength of each photon is generated using the inverse transform Figure 4. The incident light on the optical antenna. sampling method. Figure 4. The incident light on the optical antenna. (PDF+− PDF)(λλ ) j+1 j j +1 j j =1 CDF = (2) (PDF +PDF)(λλ − ) j+1 j jj +1 j =1 The CDF is defined as the area of the PDF curve until the i-th term, to the whole area of the PDF. Equation (2) depicts the relation applied to calculate the area under the curve, where λj is the j-th term of the wavelength, and k is the wavelength vector’s length. Figure Photonics 2022, 9, x FOR PEER REVIEW 9 of 20 Photonics 2022, 9, 241 8 of 19 (a) (b) PDF for emission spectrum of graphene 1.5 0.5 300 400 500 600 700 Wavelength (nm) (c) (d) Figure 5. Probability density function (PDF) and cumulative distribution function (CDF) for blue Figure 5. Probability density function (PDF) and cumulative distribution function (CDF) for blue 450 nm LED (a,b) and graphene quantum dots (c,d) respectively. 450 nm LED (a,b) and graphene quantum dots (c,d) respectively. 3. Once a photon enters the LSC, it must be determined whether absorption occurs. To The CDF is defined as the area of the PDF curve until the i-th term, to the whole achieve such a property, the Beer–Lambert law is an adequate tool to work out the area of the PDF. Equation (2) depicts the relation applied to calculate the area under the probability of a photon that is absorbed through the absorption path length. Frac- curve, where l is the j-th term of the wavelength, and k is the wavelength vector ’s length. tional absorbance, A [50], is a CDF and gives the probability that a photon will be Figure 5b points out the CDF of the 450 nm blue LED. In total, 100,000 initial photons absorbed. with uniform distribution on the upper surface of LSC and flood illumination are assumed during this simulation. The upper flat surface of LSC encounters a typical incidence, while −ελ()cl A =−110 (5) the upper inclined surface will have the incident light with a non-zero input angle. This is calculated by using trigonometric relations. where ε(λ) is the wavelength-dependent extinction coefficient, c is the concentration of 2 Some percent of initial photons are reflected from the upper surfaces of LSC results the GQDs that should match the extinction coefficient unit and is the path length in from the different refractive index for waveguide and the surrounding medium. In cm. Moreover [50], this work, it is assumed that the LED is TE polarized. Hence, the probability of log 1− A () reflection is calculated from Fresnel reflection equations [48] as Equation (3). l =− (6) ελ()c 2 3 Air n cos(q ) n 1 ( sin(q )) Air i LSC i n cosAbsorpt (q ) n ion p cos robabil (q ) ity is specified by a random num n ber in this simulation. By intro- Air i LSC LSC 4 5 R = R = ( ) = q (3) n cos(q )ξ+ n cos(q ) n Air i LSC t Air ducing , which is a random number in n cos(q )the range o + n 1 f [0(,1], the rela sin(q )) tion can be written as Air i LSC i LSC Equation (7) [50]. where q and q are the incidence angle and transmission angle, respectively. In the upper i t log(ξ) inclined surface, the incidence angle is non-zero, as shown in Figure 4. Thus, Equation (3) ld =− =Δ (7) ελ()c Probability (PDF) Probability (PDF) Probability (CDF) Probability (CDF) Photonics 2022, 9, 241 9 of 19 is used to determine the percentage of reflected photons. Whereas the flat surface sees the zero-incidence angle, Equation (3) is changed to Equation (4) after some simplifications [48]. n n LSC Air R = ( ) (4) n + n Air LSC Since n = 1, and n is assumed to be the refractive index of PVA, which is approxi- Air LSC mately 1.49 in the visible light region [49], totally about 4% of primary photons are reflected from the top surface, regarded as reflection loss. 3 Once a photon enters the LSC, it must be determined whether absorption occurs. To achieve such a property, the Beer–Lambert law is an adequate tool to work out the probability of a photon that is absorbed through the absorption path length. Fractional absorbance, A [50], is a CDF and gives the probability that a photon will be absorbed. #(l)cl A = 1 10 (5) where #(l) is the wavelength-dependent extinction coefficient, c is the concentration of the GQDs that should match the extinction coefficient unit and l is the path length in cm. Moreover [50], log(1 A) l = (6) #(l)c Absorption probability is specified by a random number in this simulation. By intro- ducing x, which is a random number in the range of [0,1], the relation can be written as Equation (7) [50]. log(x) l = = Dd (7) #(l)c where Dd represents the distance, a photon will travel before being absorbed. If the Dd found is smaller than the LSC thickness and simultaneously its wavelength is valid in the absorption region of the GQDs, QGDs will absorb the photon. Otherwise, it will pass through the LSC without any absorption known as transmission loss. The position of the absorbed photon is stored for the rest of the simulation. 4 In this step, it must become clear whether GQDs would emit the absorbed photon or not. It is done according to the quantum yield, which is defined by the ratio of the emitted photons to the total number of the absorbed photons [51], and a randomly generated number (b) between 0 and 1. If b < QY, the photon would be re-emitted. Otherwise, it would undergo non-radiative decay known as non-radiative recombination loss [31]. After re-emission, the new position of the photon must be updated. Moreover, the emission angle is obtained randomly (uniform distribution), and the wavelength of the new photon is obtained simply from the PDF and modeling of the emission spectrum of the GQDs. Figure 5c,d demonstrate the PDF and CDF for the emission spectra of GQDs. The crossed distance by the re-emitted photon is given in Equation (8) [50]. log(b) Dd = (8) a(l) Moreover [50], a(l) = #(l)c (9) 5 Now, it must be checked if the newly generated photon is still inside the LSC structure. If the answer is yes, the previous steps must repeat the photon. If not, the photon must interact with LSC surfaces. 6 The last objective is to determine the interacted surface. If the photon reaches the tip surface of the LSC, it will be harvested by the photodetector. Otherwise, two separate scenarios can be the outcome if it hits the other surfaces. First, the photon Photonics 2022, 9, 241 10 of 19 is reflected due to TIR, and whether it returns into the LSC or interacts with another surface is determined. Second, the photon escapes from the interacted surface and is consequently lost due to escape-cone loss. The steps mentioned above are repeated for all the 100,000 initial photons one by one to complete the simulation and trace the fate of each photon. To evaluate the performance of the LSC, we define some relations as follows. The optical efficiency [32] of the LSC can be illustrated as Equation (10). Photonics 2022, 9, x FOR PEER REVIEW 11 of 20 = (Collected Photons/Incident Photons) (10) Geometric gain is another parameter to assess the concentration of the LSC, although 3. Results and Discussion we have defined optical power efficiency until now. Geometric gain [32] is described as Equation (11). It measures the maximum possible photon flux concentration of an LSC To realize a VLC antenna, LSC technology has been used. The host matrix material when all the other factors are ideal. was PVA with a refractive index of 1.49, and for the fluorophores of the structure, GQDs have been considered. We designed the size of the GQDs experimentally to obtain its pho- LSC G = (11) tophysical characterization, including absorp PD tion and photoluminescence spectra and QY. The resulting absorption and photoluminescence spectra are exhibited in Figure 6. As is where A is the total area of the upper faces of the LSC (both flat and inclined) and A LSC PD apparent from the figure, GQDs can absorb a wide range of the visible band, convert it to is the area of the attached photodetector. Ultimately, the product of optical efficiency and around 520 nm by stokes-shift and emit only the green color. This means that, in addition geometric gain is defined as optical flux gain [32], as written in Equation (12). to the 450 nm blue LED, the designed GQDs also can absorb other colors. Thus, our sug- FG = G (12) opt gested antenna design will have a greater degr opt ee of freedom to work with several colors of LEDs used in ambient lighting. Additionally, QY of GQDs has acquired 0.99 thanks to 3. Results and Discussion the synthesis method, so this is considered throughout the study. To realize a VLC antenna, LSC technology has been used. The host matrix material Monte-Carlo ray-tracing simulation requires five different input parameters, includ- was PVA with a refractive index of 1.49, and for the fluorophores of the structure, GQDs ing LSC waveguide dimensions, refractive indices of LSC and the surrounding medium, have been considered. We designed the size of the GQDs experimentally to obtain its quantum yield, concentration and absorption, and photoluminescence spectra of fluoro- photophysical characterization, including absorption and photoluminescence spectra and phores. Depending on the synthesis methods, the quantum yields of fluorophores vary QY. The resulting absorption and photoluminescence spectra are exhibited in Figure 6. As between zero and unity. In this study, we considered the dimensions as shown in Figure is apparent from the figure, GQDs can absorb a wide range of the visible band, convert 1a. it to Moreover around 520 , we nm have by stokes-shift assumed the re and emit fract only ive the inde gr x of LSC een color con . This stant an meansd e that, qual to the in addition to the 450 nm blue LED, the designed GQDs also can absorb other colors. Thus, refractive index of the host matrix because the concentration of the QGDs is not high our suggested antenna design will have a greater degree of freedom to work with several enough to change the refractive index of the host material. The concentration of GQDs is colors of LEDs used in ambient lighting. Additionally, QY of GQDs has acquired 0.99 approximately 120 PPM and the surrounding medium is air. thanks to the synthesis method, so this is considered throughout the study. Absorption and emission spectrum of graphene Absorption Emission 1.5 0.5 300 400 500 600 700 Wavelength (nm) Figure 6. Absorption and emission spectrum of graphene. Figure 6. Absorption and emission spectrum of graphene. After completing the simulation, according to Equation (10), the optical efficiency of the LSC is acquired at 1.058%. Meanwhile, geometric gain, which assesses the aspect ratio of the device and plays an inevitable role in the overall performance of the LSC is calcu- lated from Equation (11) and is 44. The ultimate goal of designing an antenna using LSC technology is acceding to the cost-effective, sensitive, small, and fast antenna for VLC pur- poses. This objective can be fulfilled by geometric gain enlargement. Because the tiny end facet on which the photodetector is attached would be far smaller than the front surface of the LSC. In our structure, due to the geometry, it is possible to have an ultra-high geo- metric gain because the front surface of our structure is much larger than its tip surface and the export of the semi-sharp-shape LSC has a better match with high bandwidth pho- todetectors compared with the rectangular LSCs. Nevertheless, the absorption and subsequently the output power of the LSC depend on the thickness of the LSC directly. Therefore, in a mandatory manner, optical power efficiency and energy flux gain have a tradeoff relation. To evaluate our proposed struc- ture, we have tracked the fate of each interfering photon in the simulation. Intensity (a.u.) Photonics 2022, 9, 241 11 of 19 Monte-Carlo ray-tracing simulation requires five different input parameters, including LSC waveguide dimensions, refractive indices of LSC and the surrounding medium, quan- tum yield, concentration and absorption, and photoluminescence spectra of fluorophores. Depending on the synthesis methods, the quantum yields of fluorophores vary between zero and unity. In this study, we considered the dimensions as shown in Figure 1a. More- over, we have assumed the refractive index of LSC constant and equal to the refractive index of the host matrix because the concentration of the QGDs is not high enough to change the refractive index of the host material. The concentration of GQDs is approximately 120 PPM and the surrounding medium is air. After completing the simulation, according to Equation (10), the optical efficiency of the LSC is acquired at 1.058%. Meanwhile, geometric gain, which assesses the aspect ratio of the device and plays an inevitable role in the overall performance of the LSC is calculated from Equation (11) and is 44. The ultimate goal of designing an antenna using LSC technology is acceding to the cost-effective, sensitive, small, and fast antenna for VLC purposes. This objective can be fulfilled by geometric gain enlargement. Because the tiny end facet on which the photodetector is attached would be far smaller than the front surface of the LSC. In our structure, due to the geometry, it is possible to have an ultra-high geometric gain because the front surface of our structure is much larger than its tip surface and the export of the semi-sharp-shape LSC has a better match with high bandwidth photodetectors compared with the rectangular LSCs. Nevertheless, the absorption and subsequently the output power of the LSC depend on the thickness of the LSC directly. Therefore, in a mandatory manner, optical power efficiency and energy flux gain have a tradeoff relation. To evaluate our proposed structure, we have tracked the fate of each interfering photon in the simulation. According to the Monte-Carlo simulation, 3.887% of the initial 10 photons are re- flected from the top surface of the LSC due to the refractive indices difference between the surrounding medium and the waveguide, which is known as reflection loss. Moreover, 3.728% of the photons entering the structure are passed through the LSC without being absorbed, which is called transmission loss. Finally, 92.385% of the leftover photons are absorbed by the GQDs. However, not all of these photons have a chance of finding a way to the exit aperture. In this regard, 10.865% of them are lost due to non-unity quantum yield, which is known as non-irradiative recombination. Additionally, the photodetector collected 1.058% of the absorbed photons. At the same time, 30.286% of the absorbed photons are exited from the other edges of the LSC. A total of 50.176% of the absorbed photons are lost due to escape-cone loss. We anticipate that, in future work, we could concentrate this amount of the photons toward the photodetector using the existence optical elements to enhance the optical efficiency extraordinarily. For instance, this can be achieved by attaching a 99% mirror on the other edges of the antenna. To make the percentages more comprehensive, we summarized the fate of each photon in Figure 7. As a comparison with previous works, different indicators should be considered. For example, in photovoltaic applications, solar panels are attached to all edges of the LSC. This means that collected photons from all the edges are beneficial and converted to electrical power, while in communication applications the photodetector is attached on only one edge. In this way, the optical efficiency of the LSC will be reduced by at least a quarter of the solar LSCs (depending on the shape of the LSC). With all this, the optical efficiency of our structure is much better than the reported ones in [44]. This is because, if we include other edges of the LSC, its optical efficiency will be enhanced to 30.286%, whereas the most considerable reported optical efficiency was 3.05% with the tandem structure in [44]. For communication purposes, it is inadequate to use all the edges of the LSC because it needs more photodetectors, which are very costly, so the mentioned quantitative report was only for indicating the amount of improvement. On the other hand, in [32], 31% optical efficiency was written up due to the considerable size of the LSC, which is almost several hundred times larger than our proposed LSC. It is worth mentioning that, in the communication field, the smaller antenna, the better the installation of electrical appliances. Previous Photonics 2022, 9, x FOR PEER REVIEW 12 of 20 According to the Monte-Carlo simulation, 3.887% of the initial 10 photons are re- flected from the top surface of the LSC due to the refractive indices difference between the surrounding medium and the waveguide, which is known as reflection loss. Moreover, 3.728% of the photons entering the structure are passed through the LSC without being absorbed, which is called transmission loss. Finally, 92.385% of the leftover photons are absorbed by the GQDs. However, not all of these photons have a chance of finding a way to the exit aperture. In this regard, 10.865% of them are lost due to non-unity quantum yield, which is known as non-irradiative recombination. Additionally, the photodetector Photonics 2022, 9, 241 12 of 19 collected 1.058% of the absorbed photons. At the same time, 30.286% of the absorbed pho- tons are exited from the other edges of the LSC. A total of 50.176% of the absorbed photons are lost due to escape-cone loss. We anticipate that, in future work, we could concentrate this amount of the photons toward the photodetector using the existence optical elements work [11] in the field of communication that has introduced an optical antenna had 0.612% to enhance the optical efficiency extraordinarily. For instance, this can be achieved by at- optical efficiency based on its data resulting from Monte-Carlo ray-tracing simulation and taching a 99% mirror on the other edges of the antenna. To make the percentages more Equation (10). Contrastingly, we have achieved an optical efficiency of 1.058% in this work, comprehensive, we so about a 0.4% impr summ ovement arized is the fa evident. te of each photon in Figure 7. (a) (b) Figure 7. The fate of photons after simulation. (a) Contribution of reflected, transmitted, and ab- Figure 7. The fate of photons after simulation. (a) Contribution of reflected, transmitted, and absorbed sorbed photons. (b) Contribution of losses (non-radiative recombination, escape-cone loss) and ben- photons. (b) Contribution of losses (non-radiative recombination, escape-cone loss) and beneficial eficial photons (reached the photodetector and other edges). photons (reached the photodetector and other edges). As a comparison with previous works, different indicators should be considered. For Meanwhile, we have extracted the spectra of the aforementioned event to analyze the example, in photovoltaic applications, solar panels are attached to all edges of the LSC. structure visually. First off, the randomly generated initial photons spectrum is shown in This means that collected photons from all the edges are beneficial and converted to elec- Figure 8a. It is evident from the figure that the spectrum of the initial photons is bounded trical power, while in communication applications the photodetector is attached on only in the as same range as the 450 nm blue LED spectrum. The reflected and transmitted one edge. In this way, the optical efficiency of the LSC will be reduced by at least a quarter photons spectra are illustrated in Figure 8b,c, respectively. Furthermore, the spectrum of of the solar LSCs (depending on the shape of the LSC). With all this, the optical efficiency the absorbed photons is presented in Figure 8d. Following this, the quenched photons of our structure is much better than the reported ones in [44]. This is because, if we include spectrum is exhibited in Figure 8e. In addition, sequentially, the spectrum of photons came other edges of the LSC, its optical efficiency will be enhanced to 30.286%, whereas the out from all edges, and the spectrum of the harvested photons is pointed out in Figure 8f,g. most considerable reported optical efficiency was 3.05% with the tandem structure in [44]. The difference in peak position and the shoulder appearance is due to the self-absorption For communication purposes, it is inadequate to use all the edges of the LSC because it of the emitted light because of the overlap between the absorption and emission spectra of needs more photodetectors, which are very costly, so the mentioned quantitative report GQDs (see Figure 8h). This overlap also brings about a few wavelength differences between was only for indicating the amount of improvement. On the other hand, in [32], 31% op- emission spectra of the graphene and collected photons spectra in the antenna. Since it is ti mor cal ef e important ficiency wa tos wri havetten up a broadband due to t absorption he consider spectr able size o um for GQDs f the LSC (see, wh Figur ich e 6 is ) to almost make several h the antenna und competitive red times lar with ger than o different ur color proposed LEDsLSC. It is worth used in lightening, mentioning t we forgive hat, in the this little communi wavelength catidif on f ferie ence. ld, the Tosma sumllup, er awe ntenna summarized , the better the i all the spectra nstallation of in Figur el eectri 8i. cal appli- ances. Prev At theio last us wor attempt k [11] , we in the field computed o the f communi proposed cati stron tha ucture’s t ha bandwidth s introduced an opti by applying caa l ant modulated enna had input. 0.612% opt During ica this l effic simulation iency based step, on it weshav date a r replaced esultingthe from Mont modulated e-Carlo spectr ra um y- of 450 nm blue LED instead of the non-modulated spectrum by applying a wide range of tracing simulation and Equation (10). Contrastingly, we have achieved an optical effi- modulation frequencies. The non-modulated spectrum of 450 nm blue LED was shown in ciency of 1.058% in this work, so about a 0.4% improvement is evident. Figure 5a. In the time domain, the temporal response of the normal LED is as Equation (13), Meanwhile, we have extracted the spectra of the aforementioned event to analyze the equivalent to Equation (14) after Fourier transforms to conveniently perform mathematical structure visually. First off, the randomly generated initial photons spectrum is shown in and simulation operations in the frequency domain. Figure 8a. It is evident from the figure that the spectrum of the initial photons is bounded f (t) = f (t) (13) LED F(w) = F (w) (14) LED Following these relations, the time-domain function and Fourier transform of the amplitude-modulated LED signal [52] are given as Equations (15) and (16), respectively, where m is the modulation index, which can vary between 0 and 1 [52]. We have assumed m = 0.2 throughout the simulation. Moreover, w is the modulation frequency. By applying a wide range of modulation frequencies (as shown in Figure 9), we have recorded the Photonics 2022, 9, 241 13 of 19 Photonics 2022, 9, x FOR PEER REVIEW 13 of 20 number of the harvested photons to make the bandwidth of our proposed structure evident. In this analysis, we only investigate the frequency response of the optical antenna. in the as same range as the 450 nm blue LED spectrum. The reflected and transmitted f (t) = f (t)(1 + m. cos(w t)) (15) LED photons spectra are illustrated in Figure 8b,c, respectively. Furthermore, the spectrum of the absorbed photons is presented in F F(w) = F (w) + m[iF gure( 8d w . Following this, the quench w ) + F (w + w )] ed photons (16) LED LED m LED m spectrum is exhibited in Figure 8e. In addition, sequentially, the spectrum of photons The resulted theoretical bandwidth for the passive component is presented in Figure 10. came out from all edges, and the spectrum of the harvested photons is pointed out in It is clear that the passive structure possesses an ultra-broadband bandwidth in the THz Figure 8f and Figure 8g. The difference in peak position and the shoulder appearance is regime. It is worth mentioning that the bandwidth of the structure is significantly greater due to the self-absorption of the emitted light because of the overlap between the absorp- than the typical LEDs designated for illumination, whose bandwidths are limited to 20 MHz tion and emission spectra of GQDs (see Figure 8h). This overlap also brings about a few or less [11]. Thus, our antenna will not limit the bandwidth of the VLC systems channel, and wavelength differences between emission spectra of the graphene and collected photons any bandwidth restriction will result from the LED or other optical or electrical elements spect inrthe a in t commu he ant nication enna. Sin system. ce it isThe moachievable re important data to hav ratesein a b a r communication oadband absorp system tion sp ar ec e - trum for GQ proportionate Ds (see F to theig system’s ure 6) to make t bandwidth he antenn at a particular a competitive wit signal-to-noise h differ ratio.ent color LED We, therefore,s simulated the antenna’s bandwidth, and simultaneously, using the LSC technology, we used in lightening, we forgive this little wavelength difference. To sum up, we summa- provided the condition for a high signal-to-noise ratio. rized all the spectra in Figure 8i. Randomly generated initial photons vs 450 nm blue LED spectrum 0.8 450 nm blue LED spectrum Randomly generated initial photons 0.6 0.4 0.2 400 420 440 460 480 500 Wavelength (nm) (a) (b) Transmitted photons Absorbed photons 250 5000 200 4000 150 3000 100 2000 50 1000 0 0 400 420 440 460 480 500 400 420 440 460 480 500 Wavelength (nm) Wavelength (nm) (c) (d) Figure 8. Cont. Number (count) Photonics Photonics 2022 2022 , 9,,241 9, x FOR PEER REVIEW 14 14 of of 20 19 Quenched photons Photons came out from all edges 0 0 400 420 440 460 480 500 350 400 450 500 550 600 650 Wavelength (nm) Wavelength (nm) (e) (f) Photons reached the photodetector 350 400 450 500 550 600 650 Wavelength (nm) (g) (h) (i) Figure 8. Results after Monte-Carlo simulation. (a) Incident photons (randomly generated). (b) Re- Figure 8. Results after Monte-Carlo simulation. (a) Incident photons (randomly generated). (b) Reflected flected photons. (c) Transmitted photons. (d) Absorbed photons. (e) Quenched photons. (f) Photons photons. (c) Transmitted photons. (d) Absorbed photons. (e) Quenched photons. (f) Photons came came out from all edges. (g) Photons reached the photodetector. (h) Emission spectra of graphene out from all edges. (g) Photons reached the photodetector. (h) Emission spectra of graphene collected collected photons, and photons came out from all edges in one figure. (i) All events in one figure. photons, and photons came out from all edges in one figure. (i) All events in one figure. Number (count) Normalized intensity Photonics 2022, 9, x FOR PEER REVIEW 15 of 20 At the last attempt, we computed the proposed structure’s bandwidth by applying a modulated input. During this simulation step, we have replaced the modulated spectrum of 450 nm blue LED instead of the non-modulated spectrum by applying a wide range of modulation frequencies. The non-modulated spectrum of 450 nm blue LED was shown in Figure 5a. In the time domain, the temporal response of the normal LED is as Equation (13), equivalent to Equation (14) after Fourier transforms to conveniently perform mathe- matical and simulation operations in the frequency domain. f ()tf = ()t (13) LED F(ωω ) =F ( ) (14) LED Following these relations, the time-domain function and Fourier transform of the am- plitude-modulated LED signal [52] are given as Equations (15) and (16), respectively, where m is the modulation index, which can vary between 0 and 1 [52]. We have assumed m = 0.2 throughout the simulation. Moreover, ωm is the modulation frequency. By apply- ing a wide range of modulation frequencies (as shown in Figure 9), we have recorded the number of the harvested photons to make the bandwidth of our proposed structure evi- dent. In this analysis, we only investigate the frequency response of the optical antenna. f ()tf=+ ()t (1 m.cos(ωt)) (15) LED m F(ωω )=+ F ( ) m[F (ω−ω )+F (ω+ω )] (16) LED LED mm LED The resulted theoretical bandwidth for the passive component is presented in Figure 10. It is clear that the passive structure possesses an ultra-broadband bandwidth in the THz regime. It is worth mentioning that the bandwidth of the structure is significantly greater than the typical LEDs designated for illumination, whose bandwidths are limited to 20 MHz or less [11]. Thus, our antenna will not limit the bandwidth of the VLC systems channel, and any bandwidth restriction will result from the LED or other optical or elec- trical elements in the communication system. The achievable data rates in a communica- tion system are proportionate to the system’s bandwidth at a particular signal-to-noise Photonics 2022, 9, 241 15 of 19 ratio. We, therefore, simulated the antenna’s bandwidth, and simultaneously, using the LSC technology, we provided the condition for a high signal-to-noise ratio. Photonics 2022, 9, x FOR PEER REVIEW 16 of 20 (a) (b) (c) (d) (e) (f) Figure 9. The spectrum of the modulated input light by LED. (a) Modulated LED light for 100 GHz. Figure 9. The spectrum of the modulated input light by LED. (a) Modulated LED light for 100 GHz. (b) Modulated LED light for 100 MHz. (c) Modulated LED light for 1 THz. (d) Modulated LED light (b) Modulated LED light for 100 MHz. (c) Modulated LED light for 1 THz. (d) Modulated LED light for 10 THz. (e) Modulated LED light for 100 THz. (f) Modulated LED light for 500 THz. for 10 THz. (e) Modulated LED light for 100 THz. (f) Modulated LED light for 500 THz. Bandwidth 0.8 0.6 0.4 0.2 0 200 400 600 800 1000 Frequency (THz) Figure 10. The total number of photons in the output port of the proposed device versus modulation frequency (total number of photons = summation on photons in the output band). Intensity (a.u.) Intensity (a.u.) Normalized amplitude Intensity (a.u.) Intensity (a.u.) Photonics 2022, 9, x FOR PEER REVIEW 16 of 20 (c) (d) (e) (f) Figure 9. The spectrum of the modulated input light by LED. (a) Modulated LED light for 100 GHz. (b) Modulated LED light for 100 MHz. (c) Modulated LED light for 1 THz. (d) Modulated LED light Photonics 2022, 9, 241 16 of 19 for 10 THz. (e) Modulated LED light for 100 THz. (f) Modulated LED light for 500 THz. Bandwidth 0.8 0.6 0.4 0.2 0 200 400 600 800 1000 Frequency (THz) Figure 10. The total number of photons in the output port of the proposed device versus modulation Figure 10. The total number of photons in the output port of the proposed device versus modulation frequency (total number of photons = summation on photons in the output band). frequency (total number of photons = summation on photons in the output band). In this figure, we simulated the effect of the input signal with different frequencies and calculated how many photons come out from the device and in which frequencies. Since the output spectrum is constant and determined by graphene nanoparticles, we calculate the whole photon number in the emission stock shifted band. On the other hand, with a variation of the input modulation frequency, the number of photons in the emission band is changed. Thus, this figure shows in each input modulation frequency how many photons come out in the output stock shifted band. On the other hand, the effect of the input modulation frequency on the performance of the antenna is calculated. 4. Conclusions In summary, we have demonstrated a new shape of LSCs to verify simple, fast, sensitive, small, and inexpensive optical receiving antennas for VLC systems. The LSC configuration with a PVA host matrix containing QGDs overcomes the etendue limitation, i.e., high concentration gain, a large FOV, and, eventually, a large signal-to-noise ratio are available at the same time. To model the LSC, the Monte-Carlo ray-tracing method was developed, and the results were reported in the form of spectra. Furthermore, the optical efficiency of 1.058% and geometric gain of 44 were obtained. Due to the novel geometry for LSC, since its front surface is considerably larger than its facet edge on which a small pho- todetector is attached, a significant geometric gain has resulted. The large light-collecting surface and FOV free the LSC from any tracking system and active pointing for VLC. In addition, loss percentages have been calculated in detail and reported. Since the proposed antenna is very small and cost-effective, it becomes a promising candidate for integrating and incorporating mobile devices such as smart mobile phones, computers, tablets, virtual reality headsets, quadcopters, and even clothing that enables rapid mobile communication. Nevertheless, the performance of the LSC can be improved by increasing the optical efficiency. In future work, we aim to realize better performance for the LSC by utilizing different sizes with different absorption and emission spectra for QGDs instead of single- size QGDs. Further, we will be using white LED with a broad emission spectrum instead of single-color LED, modeling a tandem structure instead of a single layer, and attaching a 99% mirror on the other edges of the LSC. Intensity (a.u.) Intensity (a.u.) Normalized amplitude Intensity (a.u.) Photonics 2022, 9, 241 17 of 19 Author Contributions: S.C. and R.D. provided draft for the paper and simulated the proposed design. A.R. proposed the concept, modeled the structure, edit the paper, and supervised the project. H.M. and P.M. edited the paper and supervised the project. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Conflicts of Interest: There is no conflict of interest in this work. Abbreviations Abbreviation Expression VLC Visible light communication LED Light-emitting diode FOV Field of view LSC Luminescent solar concentrator RF Radiofrequency EM Electromagnetic QoS Quality of service OWC Optical wireless communication Wi-fi Wireless fidelity TIR Total internal reflection QDs Quantum dots PLQY Photoluminescence quantum yield QY Quantum yield GQDs Graphene quantum dots PVA Polyvinyl alcohol PDF Probability density function CDF Cumulative distribution function NOMA Non-orthogonal multiple access PDNOMA Power domain non-orthogonal multiple access References 1. Yahia, S.; Meraihi, Y.; Ramdane-Cherif, A.; Gabis, A.B.; Acheli, D.; Guan, H. A Survey of Channel Modeling Techniques for Visible Light Communications. J. Netw. Comput. Appl. 2021, 194, 2016–2034. [CrossRef] 2. Dawy, Z.; Saad, W.; Ghosh, A.; Andrews, J.G.; Yaacoub, E. Toward Massive Machine Type Cellular Communications. IEEE Wirel. Commun. 2017, 24, 120–128. [CrossRef] 3. Mukherjee, M. 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