Optics Communications

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1 Optics Communications 285 (202) Contents lists available at SciVerse ScienceDirect Optics Communications journal homepage: Double-structure, bidirectional and polarization-independent subwavelength grating beam splitter Junbo Yang a,b, Zhiping Zhou a,c, a State Key Laboratory on Advanced Optical Communication Systems and Networks, Peking University, Beijing 0087, China b Center of Material Science, National University of Defense Technology, Changsha 4007, China c School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia 02, USA article info abstract Article history: Received 27 February 20 Received in revised form 5 October 20 Accepted 2 October 20 Available online 0 October 20 Keywords: Grating coupler Beam splitter Rigorous coupled-wave analysis Silicon-on-insulator A novel broadband beam splitter (BS) at a wavelength of.55 μm is proposed and demonstrated, which is based on the form birefringence of subwavelength binary blazed grating and effective-medium theory. Rigorous coupled-wave analysis (RCWA) is used to optimize the design of this beam splitter. In order to achieve high coupling efficiency and equal power separation, the grating depth, period and wavelength are optimized, and the double-structure design which consists of symmetrical subwavelength gratings is adopted. Finally, the additional reflectors are also discussed and analyzed. Simulation results for TE polarized wave and TM polarized wave are presented. Using three reflectors, the BS for TE light are designed to split incident light beam into two beams of nearly equal power (4% and 4%), and the power difference of two output ports is less than % over a 20 nm wavelength bandwidth range. Simultaneously, the coupling efficiency of TM model for the right and the left branches of waveguide are % and 40%, respectively. The power differences of two ports of waveguide are lower than 0% with 80 nm wavelength bandwidth. Both theoretical analysis and simulation results show that the beam splitter designed here has advantages of high coupling efficiency, compact structure and polarization independence. 20 Elsevier B.V. All rights reserved.. Introduction In the last decade a lot of research was geared towards silicon photonic integrated circuits, due to the scaling in size that can be accomplished because of the high refractive index contrast available on silicon-on-insulator (SOI) material platform. Subwavelength binary blazed grating based on SOI structure exhibits lots of interesting effects such as high-efficiency [], high extinction ratio polarizing beam splitter (PBS) [2], and beam splitter (BS) [,4]. The beam splitter is a device commonly used in various optical systems, such as optical information processing, optical computing, holography and metrology. Most commercial splitters based on multilayer coatings have the disadvantages of complicated fabrication procedures, thermal deformations [] and energy loss [4,5] caused by thermal gradients and rapid damage near coating defects. Beam splitter based on pure dielectric grating has numerous benefits, such as compact structure, low energy loss, high diffraction efficiency, and stable performance. Fahr et al. designed a reflective 50/50 subwavelength beam splitter grating operated at a wavelength of 064 nm and in TE polarization for high-power laser interferometers []. Other several BS gratings have been designed or fabricated, which Corresponding author at: State Key Laboratory on Advanced Optical Communication Systems and Networks, Peking University, Beijing 0087, China. address: zjzhou@pku.edu.cn (Z. Zhou). can separate TE (electric field vector parallel to the grating groove) and TM (magnetic field vector parallel to the grating groove) polarized beams into its reflected 0th order and transmitted 0th order respectively, such as multilayer dielectric gratings [6], metallic wire-grid gratings [7], sub-wavelength gratings in the quasi-static domain [8], and embedded metal-wire nano-gratings [9]. However, most reported beam splitters are designed for one definite polarization [0 6]. As well known,for practical application, a polarization-independent two-port beam splitter grating would be more favorable [7 22]. In this paper, we theoretically investigated polarization-independent subwavelength binary blazed grating beam splitter, which consists of double symmetrical grating structure. A signal beam with information can be equally split into two output beams using this grating. The effective-medium theory is used to illustrate the coupling and splitting process in the grating layer. Design equations are then given for separating the TE and TM polarized waves along Si waveguide. Coupling efficiency are obtained by using rigorous coupled-wave analysis (RCWA) and finite difference time-domain (FDTD) simulation, which prove the validity of the design equations and corresponding parameters. BS gratings can be optimized to function over a wide band with both high coupling efficiencies and low power difference. Simple analysis of the physical essence of such a grating by the modal method and waveguide theory is presented firstly in Section 2. In Section, the guideline for the beam splitter grating design and the approximate grating parameters are obtained. Using RCWA method /$ see front matter 20 Elsevier B.V. All rights reserved. doi:0.06/j.optcom

2 J. Yang, Z. Zhou / Optics Communications 285 (202) with parameters varying around the approximate ones, the exact optimum grating parameters can be found. Discussions and analysis of coupling efficiency is given in Section 4. Simple summary and conclusion are shown in Section Waveguide theory analysis of subwavelength grating splitter Fig. is the schematic diagram of conventional planar waveguide structure. a is the depth of waveguide. n c and n s denote the refractive index at two sides of the waveguide, respectively. n w is the refractive index of waveguide. According to planar waveguide theory, the effective refractive indices (ERIs, N eff ) of TE and TM mode as a function of wavelength and the depth of waveguide satisfy the following equations: 2 n 2 w N 2 2π eff =2 λ a ¼ mπ þ tan C N2 eff n 2 4 c n 2 w N 2 eff 2 þ tan C 2 N2 eff n 2 4 s n 2 w N 2 eff C ¼ C 2 ¼ ðtemodeþ C ¼ ðn w =n c Þ 2 ; C 2 ¼ ðn w =n s Þ 2 ðtmmodeþ :! =2! =2 Thus, for SOI planar waveguide structure, n w =.5(Si), n c =(air), n s =.45(SiO 2 ), we can obtain the effective refractive index of TE and TM mode when the depth of waveguide is equal to 220 nm, and λ=550 nm. N TE eff 2:875; 5 5 ðþ N TM :975 ð2þ eff According to the phase match condition between the gratings and the waveguide mode, the grating period, denoted by T, should be: T N eff n sinθ ¼ mλ ðm ¼ 0; ; 2 Þ: ðþ Therefore, when we consider normal incidence and vertical coupling, i.e. θ=0, m=, the grating period T can also be acquired based on above Eqs. () and (). T TM 785 nm; T TE 59 nm ð4þ The effective refractive indices of binary gratings with a localized subwavelength structure (n eff ) consisting of ridges of material n with material n 2 in between can be obtained through 8 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n ðþ TE ¼ fn 2 þ ð f Þn2 2 >< vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n eff ¼ n ðþ TM ¼ u t f þ ð f Þ : ð5þ >: n 2 n 2 2 For TE and TM polarization, respectively, where f is the fill factor, which is defined as the ratio of pillar width to grating subperiod. We can control the width of each pillar to obtain the desired refractive index distribution. For the subwavelength binary blazed gratings, rigorous diffraction theory must be applied to describe their behavior. The basic design procedure and discrete processing are shown in Fig. 2, and apply a Fig.. Planar waveguide. n c n w n s the rigorous diffraction analysis to the localized subwavelength features within the grating period, and optimize it by the simulated annealing method [2]. Assume that the conventional grating has an index of refraction n and a height H. The surrounding medium has an index of refraction n 2. The height of each of the discrete multilevel grating is h i (i=,2,, N). H denotes the height of binary subwavelength blazed grating, and the fill factor of each subperiod is f i (i=,2,, N), then h i ¼ 2 H N i þ H N ði Þ ¼ ð2i ÞH 2N ði ¼ ; 2; NÞ ð6þ h i H n þ H h i H n 2 ¼ n eff ð7þ According to Eqs. (5) (7), we have 8 2i H 2 2 ðn 2N H n 2 Þþn n n 2 n2 2 >< 2 2 f i ¼ n n i H 5 ðn 2N H n 2 Þþn 2 >: n 2 n2 2 n 2 2 ðteþ ðtmþ ði ¼ ; 2; NÞ: With the assumptions and the calculations given above, all the data required for constructing a ridge-width-modulated grating with localized subwavelength features by straightforward quantization of the conventional grating can be computed.. Beam splitter design.. Design parameters For TE polarization, fill factor can be given as the following equations when N=4, ð2i ÞH ð:5 Þþ 8 H f i ¼ 6 ð2i ÞH þ H ¼ :5 2 :25 n 2 n (a) Conventional blazed grating h h 2 h h 4 (b) Discrete multilevel grating f f 2 f f 4 H H 2 H (c) Binary subwavelength blazed grating Fig. 2. Comparison of the different grating. ð8þ ð9þ

3 496 J. Yang, Z. Zhou / Optics Communications 285 (202) T Δ Δ2 Δ Δ4 Si H a SiO 2 Si L Fig.. Schematic diagram of binary blazed grating splitter. then, 5 H 2 5 H 2 þ 25 H 2 þ þ 6 H f ¼ 6 H, f :25 2 ¼ 6 H, f :25 ¼, and :25. 5 H 2 þ 6 H f 4 ¼ :25 According to the definition of fill factor, f 4 must satisfy that 5 H 2 þ 6 H f 4 ¼ ; :25 thus 5 H 2 þ 6 H 2:25; and H 8 H 7 :4 In our design, H H ¼ 8 7, and H =0.08 μm. Finally, the ridge-width of each of grating can be obtained, f ¼ 0:075; f 2 ¼ 0:29; f ¼ 0:60; f 4 ¼ ; Δ ¼ 0:0 μm; Δ 2 ¼ 0:09 μm; Δ ¼ 0:08 μm; Δ 4 ¼ 0:5 μm; Simultaneously, the finite-difference time-domain method, a powerful and accurate method for finite size structure, is chosen to simulate and design this device. The input field is chosen to be TE mode (λ=.55 μm). The subwavelength blazed grating beam splitter designed here is shown in Fig.. The length of beam splitter L is equal to 6 μm..2. Simulation results Using FDTD compute and simulation based on above parameters, the coupling efficiency for the right (η right ) and the left branches (η left ) of waveguide are about 49% and 4%, respectively, when we consider the TE mode and normal incidence. Poynting Vector Sz is given in Fig. 4. Fig. 5. Distribution of coupling power in waveguide. The difference value can reach to about 5% when compared of the coupling efficiencies between the right and the left branches of waveguide. Obviously, most part of power of incident light is coupled into the right branch of waveguide, as clearly shown in Fig Double-structure and symmetrically optimum design Too large power difference between two branches is not desired for beam splitter. In order to realize nearly equal power separation and splitting, we optimize the architecture design of waveguide grating by double-structure pattern, which consists of grating above discussed and its symmetrical counterpart, as shown in Fig. 6. In terms of the influence of fill factor on the effective refractive index, and the phase modulation discipline of binary blazed grating, this type of design pattern can remodulate the distribution of fill factor, furthermore, affect the coupling efficiency of grating, and result in equal power coupling and splitting in waveguide. For TE polarization and normal incidence, the distribution of Poynting vector Sz is given in Fig. 7. The power distribution of double-structure symmetrical waveguide grating is also shown in Fig. 8. It is obvious that the power coupling into two branches of waveguide is nearly identical. When compared with the wave profile of the right and the left ports, as shown in Fig. 9, their corresponding coupling efficiencies are 2% and 25%, respectively. Fig. 4. Distribution of Poynting vector.

4 J. Yang, Z. Zhou / Optics Communications 285 (202) T Symmetrical line H Δ Δ2 Δ Δ4 Δ4 Δ Δ2 Δ a L Fig. 6. Symmetrical structure of binary blazed grating splitter. Fig. 9 indicates that their corresponding wave profile of two branches is very robust, in which fundamental models are strictly confined into the waveguide region of.6 to 2.28 μm. According to our design, the coordinates of the top and the down surface of the Si waveguide are.95 and 2.55 μm, and the width of the waveguide is 0.22 μm. Consequently, the simulation results agree well with the theoretical values. Identically, for TM polarization, the distribution of Poynting vector Sz is given in Fig. 0. The coupling efficiency of the right branch is 0%, which is nearly equal to that of the left branch %. Although the double-structure grating splitter above design can realize nearly equal power separation, the coupling efficiencies are not high enough to be utilized in practical applications due to large portions of incident light power directly transmitting through the waveguide. Thus, some efforts must be underway to increase the coupling efficiency of double-structure waveguide grating beam splitter..4. Additional reflect layers design An alternative approach potentially capable of realizing high coupling efficiency uses additional reflect layers (i.e. Bragg reflector) under substrate. An optimum design of grating beam splitter is given in Fig., which adds three reflect layers under substrate. According to the requirements and properties of DBR reflector, the height of each layer is equal to λ/4n, where n is the refractive index of material, i.e. n SiO2 =.45, and n Si =.5. Thus, their corresponding heights are μm and 0. μm, respectively. Same as the above discussion and simulation, for TE model, Poynting vector Sz and power distribution are also given in Fig. 2. Fig. indicates that their corresponding wave profile of two branches is very robust, in which fundamental models are strictly confined into the waveguide region. The coupling efficiencies of two branches are also given respectively, η right ¼ 4%; η left ¼ 4%. Obviously, adopting reflect layer structure design can not only effectively improve the coupling efficiency, but also keep equal power splitting. Simultaneously, for TM model, Poynting vector Sz and power distribution are also given in Fig. 4 based on the identical discussion and simulation above. The coupling efficiencies of two branches are also given respectively, η right ¼ %; η left ¼ 40%. It is noted that the coupling efficiencies have also been significantly increased, simultaneously, the power differences between two branches of the waveguide are rather small which fully meet practical requirements. 4. Discussion and analysis In practical applications, the influences of wavelength bandwidth on coupling efficiencies and power differences between two ports of waveguide are very important. Thus, the relationship between incident wavelength, coupling efficiency, and splitting function will be discussed and analyzed in detail. 4.. TE model Fig. 8. Distribution of coupling power in waveguide. For TE polarization, the value relationship of wavelength, coupling efficiency and power difference is given in Table. The computing data as a function of the wavelength from.5 to.59 μm are plotted in Fig. 5. Apparently, from.5 to.57 μm, the coupling efficiencies of two ports of the waveguide are relatively high, and power differences as low as 6% also are achieved, which correspond to about 40 nm Fig. 7. Distribution of Poynting vector.

5 498 J. Yang, Z. Zhou / Optics Communications 285 (202) (a) right port reflect layer Fig.. Binary blazed grating splitter with three reflect layers. (a) Distribution of Poynting vector Sz (b) left port (b) Distribution of coupling power in waveguide Fig. 9. Wave profile and coupling efficiency of right-left port. wavelength bandwidth. Particularly, the coupling efficiency can reach above 0% in the range of μm, simultaneously, the power difference of two ports is only about 2% %. Consequently, it nearly accomplishes equal power splitting function with a 20 nm wavelength bandwidth TM model For TM polarization, the computing data are given in Table 2, and plotted in Fig. 6. Fig. 2. Properties of power distribution of symmetrical binary blazed grating coupler. Fig. 0. Poynting vector of TM model.

6 J. Yang, Z. Zhou / Optics Communications 285 (202) (a) right port (a) Distribution of Poynting vector Sz (b) Distribution of coupling power in waveguide (b) left port Fig. 4. Properties of power distribution of symmetrical binary blazed grating coupler. Fig.. Wave profile and coupling efficiency of right-left port. From.5 to.59 μm, the power differences of two ports of the waveguide are lower than 0%. Consequently, incident light is divided into two beams with 80 nm wavelength bandwidth, which have nearly equal power. From the above discussion and analysis, we know that the subwavelength grating beam splitter design here has a property of polarization independence due to both TE and TM model are effectively coupled and split simultaneously. It gives a very useful and important approach in optical information processing. Table The relationship of wavelength and coupling efficiency. Wavelength (μm) Coupling efficiency Right Left Difference Conclusion In this paper, we proposed a subwavelength double-structure grating splitter for efficient, high performance, and broadband coupling and splitting. We studied the performance of this grating splitter by simulation and optimum design with coupling efficiencies exceeding 0% at a wavelength of.55 μm. For TE polarization, the coupling efficiency can reach above 40% in the range of.55 μm. It nearly accomplishes equal power splitting function with 20 nm wavelength bandwidth. For the TM model, relative high coupling efficiency is also demonstrated at a wavelength of.55 μm. The power differences of two ports of the waveguide are lower than 0% with 80 nm wavelength bandwidth. The theoretical results are in good agreement with simulation results. Subwavelength grating splitter is compact in structure, efficient in performance, and insensitive to polarization. Because of the mature fabrication process suitable for mass Fig. 5. The curve between wavelength and coupling efficiency.

7 500 J. Yang, Z. Zhou / Optics Communications 285 (202) Table 2 The relationship of wavelength and coupling efficiency. Wavelength (μm) Coupling efficiency Right Left Difference AA0002), the National Natural Science Foundation of China (grant nos , ), the Major International (Regional) Cooperation and Exchange Program of the National Natural Science Foundation of China (grant no ), the Doctoral Program Foundation of Institutions of Higher Education of China (grant no ), and Open Research Fund of SKLTOP (grant no. SKLST20090). References Fig. 6. The curve between wavelength and coupling efficiency. production of the etched silicon grating as a beam splitter, it is easy to realize large-scale integration with other photoelectronic elements. This device should have potential applications in the future. Acknowledgments This work is partially supported by National High Technology Research and Development Program of China (86 Program) (grant no. [] S. Wang, C. Zhou, Y. Zhang, H. Ru, Applied Optics 45 (2) (2006) [2] B. Wang, C. Zhou, S. Wang, J. Feng, Optics Letters 2 (0) (2007) 299. [] S. Fahr, T. Clausnitzer, E.-B. Kley, A. Tünnermann, Applied Optics 46 (24) (2007) [4] R. Borghi, G. Cincotti, M. Santarsiero, Journal of the Optical Society of America. A 7 () (2000) 6. [5] D.S. Hobbs, B.D. Macleod, J.R. Riccobono, Proceedings of SPIE The International Society for Optical Engineering 6545 (2007) 65450Y. [6] R. Tyan, P. Sun, A. Scherer, Y. Fainman, Optics Letters 2 (0) (996) 76. [7] H. Tamada, T. Doumuki, T. Yamaguchi, S. Matsumoto, Optics Letters 22 (6) (997) 49. [8] D. Yi, Y. Yan, H. Liu, S. Lu, G. Jin, Optics Letters 29 (7) (2004) 754. [9] L. Zhou, W. Liu, Optics Letters 0 (2) (2005) 44. [0] Yuan Zhang, Yurong Jiang, Wei Xue, Sailing He, Optics Express 5 (22) (2007) 46. [] Fung J. Wen, Po S. Chung, Proceedings of SPIE 65 (2006). [2] Deer Yi, Yingbai Yan, Haitao Liu, Lu. Si, Guofan Jin, Optics Letters 29 (7) (2004) 754. [] Libing Zhou, Wen Liu, Optics Letters 0 (2) (2005) 44. [4] Jae-Hong Park, Yu. Chang-Jae, Jinyool Kim, Sung-Yeop Chung, Sin-Doo Lee, Applied Physics Letters 8 (0) (200) 98. [5] Dewei Gong, Zhongxiang Zhou, Hongpeng Liu, Jian Wang, Hongyue Gao, Optics and Lasers in Engineering 47 (2009) 662. [6] Jiangjun Zheng, Chanhe Zhou, Jijun Feng, Hongchao Cao, Lu. Peng, Optics Communications 282 (2009) 069. [7] Wenliang Wang, Shengming Xiong, Yundong Zhang, Applied Optics 46 (6) (2007) 85. [8] Lara Pajewski, Riccardo Borghi, Giuseppe Schettini, Fabrizion Frezza, Massimo Santarsiero, Applied Optics 40 (2) (200) [9] Yan-Lin Liao, Zheng-Fu Han, Zhuo-Liang Cao, Optics Communications 27 (2007) 569. [20] C. Alonso-Ramos, A. Ortega-Monux, I. Molina-fernandez, P. Cheben, L. Zavargo- Pech, R. Halir, Optics Express 8 (4) (200) 589. [2] R.M.A. Azzam, Applied Optics 45 (9) (2006) [22] Jijun Feng, Changhe Zhou, Jiangjun Zheng, Bo Wang, Optics Communications 28 (2008) [2] Zhou Zhiping, Timothy J. Drabik, Journal of the Optical Society of America. A 2 (5) (995) 04.