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Design and fabrication of 1× N polarization-insensitive beam splitters based on 2D subwavelength gratings
Journal Pre-proof Design and fabrication of 1×N polarization-insensitive beam splitters based on 2D subwavelength gratings Gang Wu, Yongqing Huang, Xiaofeng Duan, Kai Liu, Xiaokai Ma, Tao Liu, Huanhuan Wang, Xiaomin Ren
PII: DOI: Reference:
S0030-4018(19)30756-4 https://doi.org/10.1016/j.optcom.2019.124458 OPTICS 124458
To appear in:
Optics Communications
Received date : 23 April 2019 Revised date : 20 August 2019 Accepted date : 25 August 2019 Please cite this article as: G. Wu, Y. Huang, X. Duan et al., Design and fabrication of 1×N polarization-insensitive beam splitters based on 2D subwavelength gratings, Optics Communications (2019), doi: https://doi.org/10.1016/j.optcom.2019.124458. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
*Manuscript of Revised Submission Click here to view linked References
Journal Pre-proof
Design and fabrication of 1×N polarization-insensitive beam splitters based on 2D subwavelength gratings Gang Wua,b, Yongqing Huanga,*, Xiaofeng Duana, Kai Liua, Xiaokai Maa, Tao Liua, Huanhuan Wanga and Xiaomin Rena a
State Key Laboratory of Information Photonics and Optical Communications; Institute of Information Photonics and Optical Communications, Beijing
University of Posts and Telecommunications, Beijing 100876, China b
School of science, Lanzhou University of Technology, 730050, China
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*Corresponding author: [email protected] (Yongqing Huang)
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ABSTRACT
1. Introduction
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Based upon the wave front control of transmitted light using 2D high index contrast subwavelength gratings, a kind of 1×N polarization-insensitive beam splitters are proposed and demonstrated, which could redistribute the incident light into N beams while each of them converges to a spot respectively in the relevant subregion. 1×3 and 1×4 beam splitters as typical instances are designed applying the rigorous coupled-wave analysis (RCWA) results, of which the characterizations are tested by numerical simulation and the samples are fabricated on a silicon-on-insulator (SOI) wafer. Both numerical and experimental results demonstrate that good splitting ability without polarization sensitivity can be achieved while simultaneously maintaining high transmissivity under normal incidence at a wavelength of 1.55 µm. Keywords: beam splitter; subwavelength grating; polarization-insensitive; focusing ability; phase contral
In integrated photonics, optical beam splitters are one of the fundamental beam-delivery elements that can redistribute signals from one input port into an arbitrary array of beam spots, which have been widely used in optical interconnection and optical transmission for signal routing and signal processing, such as optical coupler [1, 2], optical modulators [3], switches [4], and multiplexers [5], moreover, they play an active part in investigating the quantum nature of light and multiphoton interference effects [6]. Conventional beam splitters based on multilayer coatings, fused fibers and slot waveguides suffer from light power loss and large size, consequently, they are more difficult to integrate with other optical devices. In recent years, several novel schemes for beam splitters have been presented e.g., multimode interference (MMI) coupler [7], photonic crystal (PhC) splitters [8, 9], binary-phase grating or metasurface based splitters [10, 11], subwavelength grating (SWG) couplers [12, 13], and hybrid plasmonic couplers [14], most of these devices take advantages of the complementary metal oxide semiconductor (CMOS) compatibility and strong optical confinement of the SOI wafer, and have benefits of compact structures and low power loss. However, the beam splitters or couplers mentioned above are usually planer structure and have difficulties in integrating with large area semiconductor laser array, photodiode array, photodetector array or other three-dimensional devices. Furthermore, some corresponding polarization-independent devices are not applicable for polarization-insensitive systems. In this work, we propose a kind of 1×N polarization-insensitive beam splitters based on 2D subwavelength high index contrast gratings (HCGs) at a wavelength of 1.55 µm, they have the
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Journal Pre-proof advantage of focusing ability and polarization-insensitivity, and can be achieved on an SOI platform due to the design flexibility. Firstly, as examples, a 1×3 beam splitter and a 1×4 beam splitter are designed based on the RCWA method, then the excellent performance of them is simulated using the finite element method (FEM). Finally, the fabrication and characterization of splitters realized on an SOI wafer is presented and discussed.
2. Design and simulation
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Focusing lens and focusing reflectors using 2D blocky HCGs have been reported in [15] and [16] respectively, both of them have 2D sub-wavelength structures of which the grating blocks and surrounding media have a big refractive index difference. The waves, guided by high-index blocks, are rapidly scattered into the zeroth diffracted order, a constructive result is that high reflection/transmission feature can be observed and the phase front of the reflected/transmitted beam can be manipulated. A similar design philosophy is employed in this study, 1×3 and 1×4 beam splitters as typical instances of the proposed 1×N polarization-insensitive beam splitters are calculated and simulated, and the fabrication of them is realized on an SOI wafer. Schematic diagrams of a 1×3 beam splitter and a 1×4 beam splitter based on 2D SWGs are shown in Fig. 1 and Fig. 2 respectively, the gratings consist of several high refractive index silicon blocks of different sizes in the top layer of an SOI wafer that surrounded by air and a buried oxide layer as the low refractive index media, the schematic of a block is indicated in the top-left corner of Fig. 1(a), each block is square and the width is denoted as w while all the blocks have the same height h1, and the center-to-center distance between two adjacent blocks along the x-axis or y-axis is defined as grating period Λ which is a constant in this letter. The height of the buried oxide layer is denoted as h2, the refractive indices of the silicon blocks and the oxide layer are 3.47 and 1.47 respectively. Because commonly used SOI wafers cannot meet the requirements of our design, in order to obtain higher transmittance, optimal values of the blocks height h1, buried oxide layer height h2 and grating period Λ are set to be 0.65 µm, 0.5 µm and 0.6 μm respectively on the basis of numeration and detailed comparison, thus the transmission characteristics of the grating will depend only on the blocks width w. Fig. 1(b) shows the schematic of a circular 1×3 beam splitter, whose transmission plane is divided into three subregions in the Cartesian coordinate system illustrated in Fig. 1(b), the transmitted light in each subregion will converge to a spot (the focus) respectively, thus the incident light will be split into three beams. The grating center of the 1×3 beam splitter as coordinate origin is denoted as O1, the projective spots on the transmission plane of three foci are denoted as F1, F2 and F3, the distance between the grating center and the projective spot F1/F2/F3 is denoted as d1. Fig. 2 (a) shows the schematic of a square 1×4 beam splitter, analogously, the transmission plane is divided into four subregions indicated in Fig. 2 (b).
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Fig. 1. (a) Schematic of investigated 1×3 beam splitter, (b) illustration of splitting characterization setup
Fig. 2. (a) Schematic of investigated 1×4 beam splitter, (b) illustration of splitting characterization setup
The design procedures of a polarization-insensitive focusing lens based on 2D SWGs have been reported in the related work [15], it is mentioned that the nonperiodic blocky grating achieving the focusing function or other performance depends on the phase profile of the wave front, and the local phase depends only on the local geometry of the blocks around that point. So to design a 2D SWGs based splitter, we have to arrange the grating blocks with appropriate size to make sure that the phase response for splitting could be obtained while maintaining high transmissivity. Initially, transmittance and wave front phase of the transmitted light for 2D periodic SWGs (all the blocks have a uniform size) are numerically calculated based on the RCWA method under normal incidence at a wavelength of 1.55 μm, the transmittance and phase spectrum as the function of the blocks width w for TE and TM mixed incident waves are shown in Fig. 3, it is thus clear that high transmissivity can be obtained and the phase spectrum span a full 2π range when the width w varies from 0.01 μm to 0.48 μm. It is important to note that this phase spectrum is a phase look-up table for getting the necessary phase change in the design process of the gratings with special performance.
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Fig. 3. (a) Transmittance spectrum and (b) phase spectrum of periodic 2D subwavelength gratings
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By applying the similar approach in the study of focusing lens, we have designed a 1×3 beam splitter and a 1×4 beam splitter just assuring that the collimated beams of normal incidence passed through the grating in each subregion converge to a spot (the focus) respectively (indicated in Fig. 1 and Fig. 2). Because the blocks size of the grating will affect the state of the magnetic resonance and determine the phase profile of the transmitted light, we should arrange the blocks with different geometries in the right order, it’s a critical factor for the focusing functionality in each subregion. It could be concluded from the analysis that the desired phase profile of the transmitted light wave front is a parabola in each subregion, which is demonstrated below for a 1×3 beam splitter corresponding to Fig. 1(b):
x d1
2
y2 f 2 f 0
2 2 d1 3d1 2 f f 0 x y 2 2 2 2 d1 3d1 2 f f 0 x y 2 2
(in region I)
(in region II)
(1)
(in region III)
where Φ(x, y) is the local phase of the transmitted light wave front on the transmission plane in transverse rectangular coordinates (x, y). Φ0 is the local phase at the center of the grating (origin of coordinates), λ is the vacuum wavelength of the incident light, d1 is the distance between the grating center and the projective spots of the foci, and f is the focal length of each subregion. For a 1×4 beam splitter corresponding to Fig. 2(b), the phase profile of transmitted light is as follows:
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f f f
x d2 y d2
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f 2 f 0
(in region i)
x d2 y d2
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(in region ii)
x d2 y d2
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x d2 y d2
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2
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(2) 0
(in region iii)
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where d2 is the distance from the projective spots of the foci to x-axis or y-axis. Here, f is chosen to be 10 μm for the purpose of reducing computational complexity both in 1×3 beam splitter and 1×4 beam splitter. Fig.4 shows the phase profiles of a 1×3 beam splitter and a 1×4 beam splitter corresponding to (1) and (2) respectively, and both of them possess good symmetry.
Fig. 4. Phase profiles of (a) a 1×3 beam splitter and (b) a 1×4 beam splitter with focal length of 10 μm
According to the goal parabolic phase change represented by (1) and (2), grating units on the transmission plane will be selected one by one from center to periphery in each subregion, this process is realized by searching the phase look-up table shown in Fig.3 (b) under the condition of higher transmissivity. It should be noted that the phases been selected are discontinuous because they are the local phases at the center of the blocks. At first, the lower limit of the transmittance is set to be 85%, that is to say, the blocks width shown in Fig. 3(a) ranging from about 0.27 μm to 0.36 μm will be rejected, and the corresponding phases shown in Fig. 3(b) ranging from 3.3 rad to 5.4 rad cannot be selected too, therefore the phases of the transmitted beam could not cover a full 2π range of variation. In order to solve this problem, lower limit of the transmittance in this range must be reduced so that the whole phase spectrum is continuous all the phases could be selected from. After that, a new phase look-up table will be produced as indicated in Fig. 5, then the blocks size will be configured from it according to the phase profile of the designed grating.
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Fig. 5. Phase look-up table of the splitters
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On the basis of the design process mentioned above, a 1×3 beam splitter and a 1×4 beam splitter based on nonperiodic 2D subwavelength gratings with focal length of 10 μm at a wavelength of 1.55 μm are designed. The 1×3 beam splitter is round with radius of 6.9 μm while d1 is set to be 6.6 μm, three foci of the splitter are axisymmetrically distributed. Meanwhile, the 1×4 beam splitter is square with side length of 12.6 μm while d2 is set to be 6 μm, the foci of it are axisymmetrically distributed too. The performance of the proposed polarization-insensitive beam splitters is assessed by the FEM, which is carried out by the commercial software COMSOL Multiphysics. TE and TM mixed normal incident waves illuminate upon the substrate of the wafer and pass through the top silicon blocks layer, the local phases of the wavefront are modulated by the local blocks, then the split beams converge to a spot in specific subregion respectively. The simulation results are indicated in Fig. 6 and Fig. 7.
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Fig. 6. (a) 3D field distribution of 1×3 beam splitter, (b) 2D slicing field distribution of the focal plane, (c) field distribution on slice 1, (d) field distribution on slice 4 and (e) E-field intensity distribution around the foci in two orthogonal directions on the focal plane
Fig. 6 shows 3D field distribution and 2D slicing field distribution of the simulated 1×3 beam splitter, it is apparent that the incident light is split into three beams, and converge to three spots which are about 9.5 μm away from the incident plane, the deviation is only 0.5 µm from the designed
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focal length. The distance between the grating center and the projective spots of the foci is about 6.5 µm, which is in essential agreement with the design value. The foci are not round because the blocks in each subregion show un-axial-symmetrical distribution. The total transmittance of the grating is about 89%, and the FWHMs of the electric field intensity at foci are about 1.65 µm on the slice 1 and about 1.78 µm on the slice 4. The 3D field distribution and 2D slicing field distribution on three orthogonal planes of the 1×4 beam splitter are indicated in Fig. 7, as expected, the incident light is split into four beams and each of them converges to a spot in their respective subregion, the focal length is about 9.7 μm. The distance between two adjacent foci along the x-axis or y-axis is about 12 μm, it’s identical with the design value. The total transmittance of the grating is about 87.2%, and the FWHMs of the electric field intensity at two foci on the slice 6 are about 1.61 μm and 1.64 μm respectively while on the slice 7 are about 1.7 μm and 1.66 μm respectively. The conclusion can be drawn from the above simulation that good splitting performance could be observed for 1×N beam splitter based on 2D nonperiodic subwavelength gratings, which can be used as the individual components or optical systems integrated with laser array and photodetector array.
Fig. 7. (a) 3D field distribution of 1×4 beam splitter, (b) 2D slicing field distribution of the focal plane, (c) field distribution on slice 6, (d) field distribution on slice 7 and (e) E-field intensity distribution around the foci in two orthogonal directions on the focal plane
3. Experimental demostration
In order to verify the theoretical models, a 1×3 beam splitter and a 1×4 beam splitter based on 2D subwavelength gratings with focal length of 150 µm are fabricated on an SOI wafer, 0.65 µm think silicon layer and 0.5 µm think buried oxide layer, other parameters are as follows: Λ=0.6 µm, d1=75 µm, d2=75 µm, λ=1.55 µm, and the radius of the circular 1×3 beam splitter is 216 µm while the side length of the square 1×4 beam splitter is 370 µm. The production processes mainly include electron beam lithography (EBL) and inductively coupled-plasma (ICP) etching. The optical microscope images of the fabricated 1×3 and 1×4 beam splitters are shown in Fig. 8, and Fig. 9 shows scanning electron microscope (SEM) images of them, it can be seen that the roof shapes of some smaller blocks became domes due to the excessive lateral etching.
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Fig. 8. The optical microscope images of (a) 1×3 beam splitter and (b) 1×4 beam splitter
Fig. 9. SEM images of fabricated splitters on an SOI wafer
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To test the beam splitting capability of proposed devices, the samples are illuminated normally from the back substrate by an Anritsu Tunics SCL tunable laser with a wavelength of 1.55 μm and a power of 1 mW, the beam is collimated by a single mode pigtailed GRIN fiber collimator with a beam diameter of 500 µm. The transmitted light is detected by optical power meter through another fiber collimator with smaller beam diameter. When the transmitted light is scanned by the fiber collimator on a 2D plane behind the grating sample, the intensity distribution of transmitted beam on the focal plane will be obtained. Fig. 10 shows the normalized intensity distributions of the 1×3 beam splitter and 1×4 beam splitter on the focal plane near 170 μm, approximative Gaussian shaped foci are presented in each diagram. The observed data of d1 for 1×3 beam splitter is about 90 μm while d2 for 1×4 beam splitter is about 80 μm, which are close to the design values. The beam profile would not be exactly Gaussian, and difference between theoretical values and the measurements may be caused by asymmetry of the gratings and some other uncertainty introduced by the setup, or the inaccuracy of the focal plane measured. Moreover, the error of technology or manufacture and the excessive lateral etching will lead to poorer convergence performance and foci position shift. The fabricated samples have been used in integration with photodetector array due to the better splitting ability and focusing ability.
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Fig. 10. The intensity distribution at 170 µm outside of the grating surface for (a) 1×3 beam splitter and (b) 1×4 beam splitter
4. Conclusion
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A kind of high-transmittance, polarization insensitive 1×N beam splitters using 2D blocky subwavelength gratings have been presented. In order to achieve beam splitting performance, we only need to divide the grating plane into several regions and make the transmitted light in each subregion converge to a spot taking advantage of the steering ability of subwavelength gratings. A 1×3 beam splitter and a 1×4 beam splitter with focal length of 10 μm are simulated by the finite element method, results exhibit excellent splitting performance while simultaneously maintaining high transmissivity under normal incidence at a wavelength of 1.55 μm. Samples of 1×3 beam splitter and 1×4 beam splitter with focal length of 150 μm are fabricated on an SOI wafer, the experimental results show that the focus in each subregion could be observed clearly, and the focal plane is about 170 μm away from the gratings surface, which is in a reasonable agreement with the theoretical value. The design procedures would provide helpful guidelines for research of the grating array and integration with other optoelectronic devices.
Acknowledgment
This work was funded by National Nature and Science Foundation of China (NSFC) (61574019, 61674018, and 61674020) and Fund of State Key Laboratory of Information Photonics and Optical Communications and the Specialized Research Fund for the Doctoral Program of Higher Education of China (20130005130001).
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References
[1] H. Yun, Y. Wang, F. Zhang, Z. Lu, S. Lin, L. Chrostowski, and N. A. F. Jaeger, Broadband 2×2 adiabatic 3 dB coupler using silicon-on-insulator sub-wavelength grating waveguides, Opt. Lett. 41(13) (2016) 3041–3044. [2] L. Xu, Y. Wang, A. Kumar, E. El-Fiky, D. Mao, H. Tamazin, M. Jacques, Z. Xing, M. G. Saber, and D. V. Plant, Compact high-performance adiabatic 3-dB coupler enabled by subwavelength grating slot in the siliconon-insulator platform, Opt. Express 26(23) (2018) 29873–29885.
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[3] T. Li, J. Zhang, H. Yi, W. Tan, Q. Long, Z. Zhou, X. Wang, and H. Wu, Low-voltage, high speed, compact silicon modulator for BPSK modulation, Opt. Express 21(20) (2013) 23410–23415. [4] S. Tomofuji, S. Matsuo, T. Kakitsuka, and K. Kitayama, Dynamic switching characteristics of InGaAsP/InP multimode interference optical waveguide switch, Opt. Express 17(26) (2009) 23380–23388. [5] Y. Ding, H. Ou, J. Xu, and C. Peucheret, Silicon photonic integrated circuit mode multiplexer, IEEE Photonics Technol. Lett. 25(7) (2013) 648–651. [6] R. Yang, J. Li, X. Song, et al., Experimental realization of a 2×2 polarization-independent split-ratio-tunable optical beam splitter, Opt. Express 24(25) (2016) 28519-28528. [7] Z. Sheng, Z. Wang, C. Qiu, L. Li, A. Pang, A. Wu, X. Wang, S. Zou, and F. Gann, A compact and low-loss MMI coupler fabricated with CMOS technology, IEEE Photonics J. 4(6) (2012) 2272–2277. [8] M. Zhang, R. Malureanu, A. C. Krüger, and M. Kristensen, 1 × 3 beam splitter for TE polarization based on self-imaging phenomena in photonic crystal waveguides, Opt. Express 18(14) (2010) 14944–14949. [9] D. C. Tee, N. Tamchek, Y. G. Shee and F. R. Mahamd Adikan, Numerical investigation on cascaded 1×3 photonic crystal power splitter based on asymmetric and symmetric 1×2 photonic crystal splitters designed with flexible structural defects, Opt. Express 22(20) (2014) 24241-24255. [10] B. Wang, C. Zhou, et al., Wideband two-port beam splitter of a binary fused-silica phase grating, Appl. Optics 47 (22) (2008) 4004-4008. [11] D. Zhang, M. Ren, W. Wu, et al., Nanoscale beam splitters based on gradient metasurfaces, Opt. Letters 43(2) (2018) 267-270. [12] L. Xu, Y. Wang, A. Kumar, E. El-Fiky, D. Mao, H. Tamazin, M. Jacques, Z. Xing, M. G. Saber, and D. V. Plant, Compact high-performance adiabatic 3-dB coupler enabled by subwavelength grating slot in the siliconon-insulator platform, Opt. Express 26(23) (2018) 29873–29885. [13] B. Ni, J. Xiao, Ultracompact and broadband silicon-based TE-pass 1 × 2 power splitter using subwavelength grating couplers and hybrid plasmonic gratings, Opt. Express, 23(26) (2018) 33942-33955. [14] J. N. Caspers and M. Mojahedi, Measurement of a compact colorless 3 dB hybrid plasmonic directional coupler, Opt. Letters 39(11) (2014) 3262–3265. [15] C. Ma, Y. Huang, X. Duan, G. Dou, M. Mao, and X. Ren, Polarization-insensitive focusing lens using 2D blocky high-contrast gratings, IEEE Photon. Technol. Lett. 27(7) (2015) 697-700. [16] X. Duan, M. Zhang, Y. Huang, K. Liu, Y. Shang, and X. Ren, Polarization-independent focusing reflectors using two-dimensional SWG, IEEE Photon. Technol. Lett., 29(2) (2017) 209–212.
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PII: DOI: Reference:
S0030-4018(19)30756-4 https://doi.org/10.1016/j.optcom.2019.124458 OPTICS 124458
To appear in:
Optics Communications
Received date : 23 April 2019 Revised date : 20 August 2019 Accepted date : 25 August 2019 Please cite this article as: G. Wu, Y. Huang, X. Duan et al., Design and fabrication of 1×N polarization-insensitive beam splitters based on 2D subwavelength gratings, Optics Communications (2019), doi: https://doi.org/10.1016/j.optcom.2019.124458. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier B.V.
*Manuscript of Revised Submission Click here to view linked References
Journal Pre-proof
Design and fabrication of 1×N polarization-insensitive beam splitters based on 2D subwavelength gratings Gang Wua,b, Yongqing Huanga,*, Xiaofeng Duana, Kai Liua, Xiaokai Maa, Tao Liua, Huanhuan Wanga and Xiaomin Rena a
State Key Laboratory of Information Photonics and Optical Communications; Institute of Information Photonics and Optical Communications, Beijing
University of Posts and Telecommunications, Beijing 100876, China b
School of science, Lanzhou University of Technology, 730050, China
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*Corresponding author: [email protected] (Yongqing Huang)
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ABSTRACT
1. Introduction
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Based upon the wave front control of transmitted light using 2D high index contrast subwavelength gratings, a kind of 1×N polarization-insensitive beam splitters are proposed and demonstrated, which could redistribute the incident light into N beams while each of them converges to a spot respectively in the relevant subregion. 1×3 and 1×4 beam splitters as typical instances are designed applying the rigorous coupled-wave analysis (RCWA) results, of which the characterizations are tested by numerical simulation and the samples are fabricated on a silicon-on-insulator (SOI) wafer. Both numerical and experimental results demonstrate that good splitting ability without polarization sensitivity can be achieved while simultaneously maintaining high transmissivity under normal incidence at a wavelength of 1.55 µm. Keywords: beam splitter; subwavelength grating; polarization-insensitive; focusing ability; phase contral
In integrated photonics, optical beam splitters are one of the fundamental beam-delivery elements that can redistribute signals from one input port into an arbitrary array of beam spots, which have been widely used in optical interconnection and optical transmission for signal routing and signal processing, such as optical coupler [1, 2], optical modulators [3], switches [4], and multiplexers [5], moreover, they play an active part in investigating the quantum nature of light and multiphoton interference effects [6]. Conventional beam splitters based on multilayer coatings, fused fibers and slot waveguides suffer from light power loss and large size, consequently, they are more difficult to integrate with other optical devices. In recent years, several novel schemes for beam splitters have been presented e.g., multimode interference (MMI) coupler [7], photonic crystal (PhC) splitters [8, 9], binary-phase grating or metasurface based splitters [10, 11], subwavelength grating (SWG) couplers [12, 13], and hybrid plasmonic couplers [14], most of these devices take advantages of the complementary metal oxide semiconductor (CMOS) compatibility and strong optical confinement of the SOI wafer, and have benefits of compact structures and low power loss. However, the beam splitters or couplers mentioned above are usually planer structure and have difficulties in integrating with large area semiconductor laser array, photodiode array, photodetector array or other three-dimensional devices. Furthermore, some corresponding polarization-independent devices are not applicable for polarization-insensitive systems. In this work, we propose a kind of 1×N polarization-insensitive beam splitters based on 2D subwavelength high index contrast gratings (HCGs) at a wavelength of 1.55 µm, they have the
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Journal Pre-proof advantage of focusing ability and polarization-insensitivity, and can be achieved on an SOI platform due to the design flexibility. Firstly, as examples, a 1×3 beam splitter and a 1×4 beam splitter are designed based on the RCWA method, then the excellent performance of them is simulated using the finite element method (FEM). Finally, the fabrication and characterization of splitters realized on an SOI wafer is presented and discussed.
2. Design and simulation
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Focusing lens and focusing reflectors using 2D blocky HCGs have been reported in [15] and [16] respectively, both of them have 2D sub-wavelength structures of which the grating blocks and surrounding media have a big refractive index difference. The waves, guided by high-index blocks, are rapidly scattered into the zeroth diffracted order, a constructive result is that high reflection/transmission feature can be observed and the phase front of the reflected/transmitted beam can be manipulated. A similar design philosophy is employed in this study, 1×3 and 1×4 beam splitters as typical instances of the proposed 1×N polarization-insensitive beam splitters are calculated and simulated, and the fabrication of them is realized on an SOI wafer. Schematic diagrams of a 1×3 beam splitter and a 1×4 beam splitter based on 2D SWGs are shown in Fig. 1 and Fig. 2 respectively, the gratings consist of several high refractive index silicon blocks of different sizes in the top layer of an SOI wafer that surrounded by air and a buried oxide layer as the low refractive index media, the schematic of a block is indicated in the top-left corner of Fig. 1(a), each block is square and the width is denoted as w while all the blocks have the same height h1, and the center-to-center distance between two adjacent blocks along the x-axis or y-axis is defined as grating period Λ which is a constant in this letter. The height of the buried oxide layer is denoted as h2, the refractive indices of the silicon blocks and the oxide layer are 3.47 and 1.47 respectively. Because commonly used SOI wafers cannot meet the requirements of our design, in order to obtain higher transmittance, optimal values of the blocks height h1, buried oxide layer height h2 and grating period Λ are set to be 0.65 µm, 0.5 µm and 0.6 μm respectively on the basis of numeration and detailed comparison, thus the transmission characteristics of the grating will depend only on the blocks width w. Fig. 1(b) shows the schematic of a circular 1×3 beam splitter, whose transmission plane is divided into three subregions in the Cartesian coordinate system illustrated in Fig. 1(b), the transmitted light in each subregion will converge to a spot (the focus) respectively, thus the incident light will be split into three beams. The grating center of the 1×3 beam splitter as coordinate origin is denoted as O1, the projective spots on the transmission plane of three foci are denoted as F1, F2 and F3, the distance between the grating center and the projective spot F1/F2/F3 is denoted as d1. Fig. 2 (a) shows the schematic of a square 1×4 beam splitter, analogously, the transmission plane is divided into four subregions indicated in Fig. 2 (b).
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Fig. 1. (a) Schematic of investigated 1×3 beam splitter, (b) illustration of splitting characterization setup
Fig. 2. (a) Schematic of investigated 1×4 beam splitter, (b) illustration of splitting characterization setup
The design procedures of a polarization-insensitive focusing lens based on 2D SWGs have been reported in the related work [15], it is mentioned that the nonperiodic blocky grating achieving the focusing function or other performance depends on the phase profile of the wave front, and the local phase depends only on the local geometry of the blocks around that point. So to design a 2D SWGs based splitter, we have to arrange the grating blocks with appropriate size to make sure that the phase response for splitting could be obtained while maintaining high transmissivity. Initially, transmittance and wave front phase of the transmitted light for 2D periodic SWGs (all the blocks have a uniform size) are numerically calculated based on the RCWA method under normal incidence at a wavelength of 1.55 μm, the transmittance and phase spectrum as the function of the blocks width w for TE and TM mixed incident waves are shown in Fig. 3, it is thus clear that high transmissivity can be obtained and the phase spectrum span a full 2π range when the width w varies from 0.01 μm to 0.48 μm. It is important to note that this phase spectrum is a phase look-up table for getting the necessary phase change in the design process of the gratings with special performance.
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Fig. 3. (a) Transmittance spectrum and (b) phase spectrum of periodic 2D subwavelength gratings
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By applying the similar approach in the study of focusing lens, we have designed a 1×3 beam splitter and a 1×4 beam splitter just assuring that the collimated beams of normal incidence passed through the grating in each subregion converge to a spot (the focus) respectively (indicated in Fig. 1 and Fig. 2). Because the blocks size of the grating will affect the state of the magnetic resonance and determine the phase profile of the transmitted light, we should arrange the blocks with different geometries in the right order, it’s a critical factor for the focusing functionality in each subregion. It could be concluded from the analysis that the desired phase profile of the transmitted light wave front is a parabola in each subregion, which is demonstrated below for a 1×3 beam splitter corresponding to Fig. 1(b):
x d1
2
y2 f 2 f 0
2 2 d1 3d1 2 f f 0 x y 2 2 2 2 d1 3d1 2 f f 0 x y 2 2
(in region I)
(in region II)
(1)
(in region III)
where Φ(x, y) is the local phase of the transmitted light wave front on the transmission plane in transverse rectangular coordinates (x, y). Φ0 is the local phase at the center of the grating (origin of coordinates), λ is the vacuum wavelength of the incident light, d1 is the distance between the grating center and the projective spots of the foci, and f is the focal length of each subregion. For a 1×4 beam splitter corresponding to Fig. 2(b), the phase profile of transmitted light is as follows:
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f f f
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x d2 y d2
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x d2 y d2
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x d2 y d2
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2
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where d2 is the distance from the projective spots of the foci to x-axis or y-axis. Here, f is chosen to be 10 μm for the purpose of reducing computational complexity both in 1×3 beam splitter and 1×4 beam splitter. Fig.4 shows the phase profiles of a 1×3 beam splitter and a 1×4 beam splitter corresponding to (1) and (2) respectively, and both of them possess good symmetry.
Fig. 4. Phase profiles of (a) a 1×3 beam splitter and (b) a 1×4 beam splitter with focal length of 10 μm
According to the goal parabolic phase change represented by (1) and (2), grating units on the transmission plane will be selected one by one from center to periphery in each subregion, this process is realized by searching the phase look-up table shown in Fig.3 (b) under the condition of higher transmissivity. It should be noted that the phases been selected are discontinuous because they are the local phases at the center of the blocks. At first, the lower limit of the transmittance is set to be 85%, that is to say, the blocks width shown in Fig. 3(a) ranging from about 0.27 μm to 0.36 μm will be rejected, and the corresponding phases shown in Fig. 3(b) ranging from 3.3 rad to 5.4 rad cannot be selected too, therefore the phases of the transmitted beam could not cover a full 2π range of variation. In order to solve this problem, lower limit of the transmittance in this range must be reduced so that the whole phase spectrum is continuous all the phases could be selected from. After that, a new phase look-up table will be produced as indicated in Fig. 5, then the blocks size will be configured from it according to the phase profile of the designed grating.
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Fig. 5. Phase look-up table of the splitters
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On the basis of the design process mentioned above, a 1×3 beam splitter and a 1×4 beam splitter based on nonperiodic 2D subwavelength gratings with focal length of 10 μm at a wavelength of 1.55 μm are designed. The 1×3 beam splitter is round with radius of 6.9 μm while d1 is set to be 6.6 μm, three foci of the splitter are axisymmetrically distributed. Meanwhile, the 1×4 beam splitter is square with side length of 12.6 μm while d2 is set to be 6 μm, the foci of it are axisymmetrically distributed too. The performance of the proposed polarization-insensitive beam splitters is assessed by the FEM, which is carried out by the commercial software COMSOL Multiphysics. TE and TM mixed normal incident waves illuminate upon the substrate of the wafer and pass through the top silicon blocks layer, the local phases of the wavefront are modulated by the local blocks, then the split beams converge to a spot in specific subregion respectively. The simulation results are indicated in Fig. 6 and Fig. 7.
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Fig. 6. (a) 3D field distribution of 1×3 beam splitter, (b) 2D slicing field distribution of the focal plane, (c) field distribution on slice 1, (d) field distribution on slice 4 and (e) E-field intensity distribution around the foci in two orthogonal directions on the focal plane
Fig. 6 shows 3D field distribution and 2D slicing field distribution of the simulated 1×3 beam splitter, it is apparent that the incident light is split into three beams, and converge to three spots which are about 9.5 μm away from the incident plane, the deviation is only 0.5 µm from the designed
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focal length. The distance between the grating center and the projective spots of the foci is about 6.5 µm, which is in essential agreement with the design value. The foci are not round because the blocks in each subregion show un-axial-symmetrical distribution. The total transmittance of the grating is about 89%, and the FWHMs of the electric field intensity at foci are about 1.65 µm on the slice 1 and about 1.78 µm on the slice 4. The 3D field distribution and 2D slicing field distribution on three orthogonal planes of the 1×4 beam splitter are indicated in Fig. 7, as expected, the incident light is split into four beams and each of them converges to a spot in their respective subregion, the focal length is about 9.7 μm. The distance between two adjacent foci along the x-axis or y-axis is about 12 μm, it’s identical with the design value. The total transmittance of the grating is about 87.2%, and the FWHMs of the electric field intensity at two foci on the slice 6 are about 1.61 μm and 1.64 μm respectively while on the slice 7 are about 1.7 μm and 1.66 μm respectively. The conclusion can be drawn from the above simulation that good splitting performance could be observed for 1×N beam splitter based on 2D nonperiodic subwavelength gratings, which can be used as the individual components or optical systems integrated with laser array and photodetector array.
Fig. 7. (a) 3D field distribution of 1×4 beam splitter, (b) 2D slicing field distribution of the focal plane, (c) field distribution on slice 6, (d) field distribution on slice 7 and (e) E-field intensity distribution around the foci in two orthogonal directions on the focal plane
3. Experimental demostration
In order to verify the theoretical models, a 1×3 beam splitter and a 1×4 beam splitter based on 2D subwavelength gratings with focal length of 150 µm are fabricated on an SOI wafer, 0.65 µm think silicon layer and 0.5 µm think buried oxide layer, other parameters are as follows: Λ=0.6 µm, d1=75 µm, d2=75 µm, λ=1.55 µm, and the radius of the circular 1×3 beam splitter is 216 µm while the side length of the square 1×4 beam splitter is 370 µm. The production processes mainly include electron beam lithography (EBL) and inductively coupled-plasma (ICP) etching. The optical microscope images of the fabricated 1×3 and 1×4 beam splitters are shown in Fig. 8, and Fig. 9 shows scanning electron microscope (SEM) images of them, it can be seen that the roof shapes of some smaller blocks became domes due to the excessive lateral etching.
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Fig. 8. The optical microscope images of (a) 1×3 beam splitter and (b) 1×4 beam splitter
Fig. 9. SEM images of fabricated splitters on an SOI wafer
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To test the beam splitting capability of proposed devices, the samples are illuminated normally from the back substrate by an Anritsu Tunics SCL tunable laser with a wavelength of 1.55 μm and a power of 1 mW, the beam is collimated by a single mode pigtailed GRIN fiber collimator with a beam diameter of 500 µm. The transmitted light is detected by optical power meter through another fiber collimator with smaller beam diameter. When the transmitted light is scanned by the fiber collimator on a 2D plane behind the grating sample, the intensity distribution of transmitted beam on the focal plane will be obtained. Fig. 10 shows the normalized intensity distributions of the 1×3 beam splitter and 1×4 beam splitter on the focal plane near 170 μm, approximative Gaussian shaped foci are presented in each diagram. The observed data of d1 for 1×3 beam splitter is about 90 μm while d2 for 1×4 beam splitter is about 80 μm, which are close to the design values. The beam profile would not be exactly Gaussian, and difference between theoretical values and the measurements may be caused by asymmetry of the gratings and some other uncertainty introduced by the setup, or the inaccuracy of the focal plane measured. Moreover, the error of technology or manufacture and the excessive lateral etching will lead to poorer convergence performance and foci position shift. The fabricated samples have been used in integration with photodetector array due to the better splitting ability and focusing ability.
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Fig. 10. The intensity distribution at 170 µm outside of the grating surface for (a) 1×3 beam splitter and (b) 1×4 beam splitter
4. Conclusion
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A kind of high-transmittance, polarization insensitive 1×N beam splitters using 2D blocky subwavelength gratings have been presented. In order to achieve beam splitting performance, we only need to divide the grating plane into several regions and make the transmitted light in each subregion converge to a spot taking advantage of the steering ability of subwavelength gratings. A 1×3 beam splitter and a 1×4 beam splitter with focal length of 10 μm are simulated by the finite element method, results exhibit excellent splitting performance while simultaneously maintaining high transmissivity under normal incidence at a wavelength of 1.55 μm. Samples of 1×3 beam splitter and 1×4 beam splitter with focal length of 150 μm are fabricated on an SOI wafer, the experimental results show that the focus in each subregion could be observed clearly, and the focal plane is about 170 μm away from the gratings surface, which is in a reasonable agreement with the theoretical value. The design procedures would provide helpful guidelines for research of the grating array and integration with other optoelectronic devices.
Acknowledgment
This work was funded by National Nature and Science Foundation of China (NSFC) (61574019, 61674018, and 61674020) and Fund of State Key Laboratory of Information Photonics and Optical Communications and the Specialized Research Fund for the Doctoral Program of Higher Education of China (20130005130001).
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