Abstract

In this paper, we innovatively demonstrate a rotatable direct-binary-search algorithm. Based on this unique inverse design method, the coupling region of nanophotonic device can be realized with multi-shape and multi-rotation pixels. In addition, the novel 1× 2 mode converters with multipurpose design goals on a 220 nm-thick top silicon-on-insulator platform are proposed by utilizing this enhanced algorithm, which can simultaneously achieve power splitting and mode conversion. By 3D fine difference time domain solutions, the 1 × 2 mode converter that converts TE0 mode into TE1, with a footprint of 2.7 µm × 2.4 µm, exhibits the excess loss of 0.1 - 0.2 dB (TE1 mode), crosstalk of lower than -20.6 dB (TE0 mode) and reflection loss of lower than -19.5 dB (TE0 mode) from 1500 nm to 1600 nm. The 1 × 2 mode converter that transforms TE0 into TE2 occupies the footprint of 3.6 µm × 3 µm. The excess loss is 0.3 - 0.4 dB (TE2 mode) in the wavelength range of 1500 - 1600 nm. The crosstalks are lower than -17.5 dB (TE1 mode) and -25.1 dB (TE0 mode), and the reflection loss is lower than -18.3 dB (TE0 mode). Besides, the fabrication tolerances caused by both expansion or contraction of etched pattern contour and round corner effect are also investigated.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2020 (3)

H. Xie, Y. Liu, S. Wang, Y. Wang, Y. Yao, Q. Song, J. Du, Z. He, and K. Xu, “Highly Compact and Efficient Four-mode Multiplexer based on Pixelated Waveguides,” IEEE Photonics Technol. Lett. 32(3), 166–169 (2020)..
[Crossref]

H. Ma, J. Huang, K. Zhang, and J. Yang, “Arbitrary-direction, multichannel and ultra-compact power splitters by inverse design method,” Opt. Commun. 462, 125329 (2020)..
[Crossref]

H. Xie, Y. Liu, Y. Wang, Y. Wang, Y. Yao, Q. Song, J. Du, Z. He, and K. Xu, “An Ultra-Compact 3-dB Power Splitter for Three Modes Based on Pixelated Meta-Structure,” IEEE Photonics Technol. Lett. 32(6), 341–344 (2020)..
[Crossref]

2019 (6)

Y. Liu, K. Xu, S. Wang, W. Shen, H. Xie, Y. Wang, S. Xiao, Y. Yao, J. Du, Z. He, and Q. Song, “Arbitrarily routed mode-division multiplexed photonic circuits for dense integration,” Nat. Commun. 10(1), 3263 (2019).
[Crossref]

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[Crossref]

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[Crossref]

J. Huang, J. Yang, D. Chen, W. Bai, J. Han, Z. Zhang, J. Zhang, X. He, Y. Han, and L. Liang, “Implementation of on-chip multi-channel focusing wavelength demultiplexer with regularized digital metamaterials,” Nanophotonics 9(1), 159–166 (2019)..
[Crossref]

M. H. Tahersima, K. Kojima, T. Koike-Akino, D. Jha, B. Wang, C. Lin, and K. Parsons, “Deep neural network inverse design of integrated photonic power splitters,” Sci. Rep. 9(1), 1368 (2019)..
[Crossref]

W. Ma, F. Cheng, Y. Xu, Q. Wen, and Y. Liu, “Probabilistic Representation and Inverse Design of Metamaterials Based on a Deep Generative Model with Semi-Supervised Learning Strategy,” Adv. Mater. 31(35), 1901111 (2019)..
[Crossref]

2018 (5)

W. Ma, F. Cheng, and Y. Liu, “Deep-learning-enabled on-demand design of chiral metamaterials,” ACS Nano 12(6), 6326–6334 (2018)..
[Crossref]

W. Chang, L. Lu, X. Ren, D. Li, Z. Pan, M. Cheng, D. Liu, and M. Zhang, “Ultracompact dual-mode waveguide crossing based on subwavelength multimode-interference couplers,” Photonics Res. 6(7), 660–665 (2018)..
[Crossref]

J. Huang, J. Yang, D. Chen, X. He, Y. Han, J. Zhang, and Z. Zhang, “Ultra-compact broadband polarization beam splitter with strong expansibility,” Photonics Res. 6(6), 574–578 (2018)..
[Crossref]

W. Chang, L. Lu, X. Ren, D. Li, Z. Pan, M. Cheng, D. Liu, and M. Zhang, “Ultra-compact mode (de) multiplexer based on subwavelength asymmetric Y-junction,” Opt. Express 26(7), 8162–8170 (2018)..
[Crossref]

Y. Liu, W. Sun, H. Xie, N. Zhang, K. Xu, Y. Yao, S. Xiao, and Q. Song, “Very sharp adiabatic bends based on an inverse design,” Opt. Lett. 43(11), 2482–2485 (2018)..
[Crossref]

2017 (3)

2016 (1)

2015 (2)

Z. Zhang, X. Hu, and J. Wang, “On-chip optical mode exchange using tapered directional coupler,” Sci. Rep. 5(1), 16072 (2015).
[Crossref]

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4× 2.4 µm2 footprint,” Nat. Photonics 9(6), 378–382 (2015)..
[Crossref]

2014 (4)

J. Wang, S. He, and D. Dai, “On-chip silicon 8-channel hybrid (de) multiplexer enabling simultaneous mode-and polarization-division-multiplexing,” Laser Photonics Rev. 8(2), L18–L22 (2014)..
[Crossref]

M. Ye, Y. Yu, J. Zou, W. Yang, and X. Zhang, “On-chip multiplexing conversion between wavelength division multiplexing–polarization division multiplexing and wavelength division multiplexing-mode division multiplexing,” Opt. Express 39(4), 758–761 (2014).
[Crossref]

J. Wang, P. Chen, S. shen, Y. shi, and D. Dai, “Improved 8-channel silicon mode demultiplexer with grating polarizers,” Opt. Express 22(11), 12799–12807 (2014)..
[Crossref]

B. Shen, P. Wang, R. Polson, and R. Menon, “Integrated metamaterials for efficient and compact free-space-to-waveguide coupling,” Opt. Express 22(22), 27175–27182 (2014)..
[Crossref]

2013 (3)

2012 (2)

2011 (1)

2010 (1)

2007 (1)

J. H. Schmid, B. Lamontagne, P. Cheben, A. Delâge, S. Janz, A. Densmore, J. Lapointe, E. Post, P. Waldron, and D. Xu, “Mode converters for coupling to high aspect ratio silicon-on-insulator channel waveguides,” IEEE Photonics Technol. Lett. 19(11), 855–857 (2007)..
[Crossref]

2006 (2)

D. Dai, S. He, and H. K. Tsang, “Bilevel mode converter between a silicon nanowire waveguide and a larger waveguide,” J. Lightwave Technol. 24(6), 2428–2433 (2006)..
[Crossref]

T. Aalto, K. Solehmainen, M. Harjanne, M. Kapulainen, and P. Heimala, “Low-loss converters between optical silicon waveguides of different sizes and types,” IEEE Photonics Technol. Lett. 18(5), 709–711 (2006)..
[Crossref]

2005 (1)

P. I. Borel, L. H. Frandsen, A. Harpøth, M. Kristensen, J. S. Jensen, and O. Sigmund, “Topology optimised broadband photonic crystal Y-splitter,” Electron. Lett. 41(2), 69–71 (2005)..
[Crossref]

1999 (1)

1975 (1)

W. K. Burns and A. Milton, “Mode conversion in planar-dielectric separating waveguides,” IEEE J. Quantum Electron. 11(1), 32–39 (1975)..
[Crossref]

Aalto, T.

T. Aalto, K. Solehmainen, M. Harjanne, M. Kapulainen, and P. Heimala, “Low-loss converters between optical silicon waveguides of different sizes and types,” IEEE Photonics Technol. Lett. 18(5), 709–711 (2006)..
[Crossref]

Baets, R.

D. Vermeulen, K. Van Acoleyen, S. Ghosh, W. De Cort, N. A. Yebo, E. Hallynck, K. De Vos, P. Debackere, P. Dumon, W. Bogaerts, G. Roelkens, D. Van Thourhout, and R. Baets, “Efficient tapering to the fundamental quasi-TM mode in asymmetrical waveguides,” presented at the 15th European conference on Integrated Optics (ECIO 2010). 2010.

Bai, W.

J. Huang, J. Yang, D. Chen, W. Bai, J. Han, Z. Zhang, J. Zhang, X. He, Y. Han, and L. Liang, “Implementation of on-chip multi-channel focusing wavelength demultiplexer with regularized digital metamaterials,” Nanophotonics 9(1), 159–166 (2019)..
[Crossref]

Bock, P. J.

Bogaerts, W.

D. Vermeulen, K. Van Acoleyen, S. Ghosh, W. De Cort, N. A. Yebo, E. Hallynck, K. De Vos, P. Debackere, P. Dumon, W. Bogaerts, G. Roelkens, D. Van Thourhout, and R. Baets, “Efficient tapering to the fundamental quasi-TM mode in asymmetrical waveguides,” presented at the 15th European conference on Integrated Optics (ECIO 2010). 2010.

Borel, P. I.

P. I. Borel, L. H. Frandsen, A. Harpøth, M. Kristensen, J. S. Jensen, and O. Sigmund, “Topology optimised broadband photonic crystal Y-splitter,” Electron. Lett. 41(2), 69–71 (2005)..
[Crossref]

Bowers, J. E.

Burns, W. K.

W. K. Burns and A. Milton, “Mode conversion in planar-dielectric separating waveguides,” IEEE J. Quantum Electron. 11(1), 32–39 (1975)..
[Crossref]

Chang, W.

W. Chang, L. Lu, X. Ren, D. Li, Z. Pan, M. Cheng, D. Liu, and M. Zhang, “Ultra-compact mode (de) multiplexer based on subwavelength asymmetric Y-junction,” Opt. Express 26(7), 8162–8170 (2018)..
[Crossref]

W. Chang, L. Lu, X. Ren, D. Li, Z. Pan, M. Cheng, D. Liu, and M. Zhang, “Ultracompact dual-mode waveguide crossing based on subwavelength multimode-interference couplers,” Photonics Res. 6(7), 660–665 (2018)..
[Crossref]

L. Lu, M. Zhang, F. Zhou, W. Chang, J. Tang, D. Li, X. Ren, Z. Pan, M. Cheng, and D. Liu, “Inverse-designed ultra-compact star-crossings based on PhC-like subwavelength structures for optical intercross connect,” Opt. Express 25(15), 18355–18364 (2017)..
[Crossref]

F. Zhou, L. Lu, M. Zhang, W. Chang, D. Li, L. Deng, and D. Liu, “Ultra-compact, low-loss and low-crosstalk wavelength demultiplexer for CWDM system based on the photonic-crystal-like metamaterial structure,” in Proceedings of 2017 Conference on Lasers and Electro-Optics (CLEO). IEEE, 1 (2017).

W. Chang, L. Lu, D. Liu, and M. zhang, “Ultra-compact silicon multi-mode waveguide bend based on subwavelength asymmetric Y-junction,” in Proceedings of Optical Fiber Communication Conference (Optical Society of America, 2018), Tu3A.1.

W. Chang, L. Lu, D. Liu, and M. Zhang, “An Ultra-Compact Colorless Dual-Mode 3 dB Power Splitter Based on Axisymmetrical Subwavelength Structure,” CLEO: Science and Innovations (Optical Society of America, 2018), JW2A. 47.

Cheben, P.

P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delage, and S. Janz, “Subwavelength grating periodic structures in silicon-on-insulator: a new type of microphotonic waveguide,” Opt. Express 18(19), 20251 (2010)..
[Crossref]

J. H. Schmid, B. Lamontagne, P. Cheben, A. Delâge, S. Janz, A. Densmore, J. Lapointe, E. Post, P. Waldron, and D. Xu, “Mode converters for coupling to high aspect ratio silicon-on-insulator channel waveguides,” IEEE Photonics Technol. Lett. 19(11), 855–857 (2007)..
[Crossref]

Chen, D.

J. Huang, J. Yang, D. Chen, W. Bai, J. Han, Z. Zhang, J. Zhang, X. He, Y. Han, and L. Liang, “Implementation of on-chip multi-channel focusing wavelength demultiplexer with regularized digital metamaterials,” Nanophotonics 9(1), 159–166 (2019)..
[Crossref]

J. Huang, J. Yang, D. Chen, X. He, Y. Han, J. Zhang, and Z. Zhang, “Ultra-compact broadband polarization beam splitter with strong expansibility,” Photonics Res. 6(6), 574–578 (2018)..
[Crossref]

Chen, P.

Chen, W.

Cheng, F.

W. Ma, F. Cheng, Y. Xu, Q. Wen, and Y. Liu, “Probabilistic Representation and Inverse Design of Metamaterials Based on a Deep Generative Model with Semi-Supervised Learning Strategy,” Adv. Mater. 31(35), 1901111 (2019)..
[Crossref]

W. Ma, F. Cheng, and Y. Liu, “Deep-learning-enabled on-demand design of chiral metamaterials,” ACS Nano 12(6), 6326–6334 (2018)..
[Crossref]

Cheng, M.

Cui, H.

Dadap, J. I.

Dai, D.

Dai, T.

De Cort, W.

D. Vermeulen, K. Van Acoleyen, S. Ghosh, W. De Cort, N. A. Yebo, E. Hallynck, K. De Vos, P. Debackere, P. Dumon, W. Bogaerts, G. Roelkens, D. Van Thourhout, and R. Baets, “Efficient tapering to the fundamental quasi-TM mode in asymmetrical waveguides,” presented at the 15th European conference on Integrated Optics (ECIO 2010). 2010.

De Vos, K.

D. Vermeulen, K. Van Acoleyen, S. Ghosh, W. De Cort, N. A. Yebo, E. Hallynck, K. De Vos, P. Debackere, P. Dumon, W. Bogaerts, G. Roelkens, D. Van Thourhout, and R. Baets, “Efficient tapering to the fundamental quasi-TM mode in asymmetrical waveguides,” presented at the 15th European conference on Integrated Optics (ECIO 2010). 2010.

Debackere, P.

D. Vermeulen, K. Van Acoleyen, S. Ghosh, W. De Cort, N. A. Yebo, E. Hallynck, K. De Vos, P. Debackere, P. Dumon, W. Bogaerts, G. Roelkens, D. Van Thourhout, and R. Baets, “Efficient tapering to the fundamental quasi-TM mode in asymmetrical waveguides,” presented at the 15th European conference on Integrated Optics (ECIO 2010). 2010.

Delage, A.

Delâge, A.

J. H. Schmid, B. Lamontagne, P. Cheben, A. Delâge, S. Janz, A. Densmore, J. Lapointe, E. Post, P. Waldron, and D. Xu, “Mode converters for coupling to high aspect ratio silicon-on-insulator channel waveguides,” IEEE Photonics Technol. Lett. 19(11), 855–857 (2007)..
[Crossref]

Deng, L.

F. Zhou, L. Lu, M. Zhang, W. Chang, D. Li, L. Deng, and D. Liu, “Ultra-compact, low-loss and low-crosstalk wavelength demultiplexer for CWDM system based on the photonic-crystal-like metamaterial structure,” in Proceedings of 2017 Conference on Lasers and Electro-Optics (CLEO). IEEE, 1 (2017).

Densmore, A.

J. H. Schmid, B. Lamontagne, P. Cheben, A. Delâge, S. Janz, A. Densmore, J. Lapointe, E. Post, P. Waldron, and D. Xu, “Mode converters for coupling to high aspect ratio silicon-on-insulator channel waveguides,” IEEE Photonics Technol. Lett. 19(11), 855–857 (2007)..
[Crossref]

Driscoll, J. B.

Du, J.

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J. Huang, J. Yang, D. Chen, X. He, Y. Han, J. Zhang, and Z. Zhang, “Ultra-compact broadband polarization beam splitter with strong expansibility,” Photonics Res. 6(6), 574–578 (2018)..
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H. Xie, Y. Liu, S. Wang, Y. Wang, Y. Yao, Q. Song, J. Du, Z. He, and K. Xu, “Highly Compact and Efficient Four-mode Multiplexer based on Pixelated Waveguides,” IEEE Photonics Technol. Lett. 32(3), 166–169 (2020)..
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W. Chang, L. Lu, D. Liu, and M. zhang, “Ultra-compact silicon multi-mode waveguide bend based on subwavelength asymmetric Y-junction,” in Proceedings of Optical Fiber Communication Conference (Optical Society of America, 2018), Tu3A.1.

L. Lu, M. Zhang, F. Zhou, and D. Liu, “An ultra-compact colorless 50: 50 coupler based on PhC-like metamaterial structure,” in Proceedings of 2016 Optical Fiber Communications Conference and Exhibition (OFC). IEEE, 1–3 (2016).

W. Chang, L. Lu, D. Liu, and M. Zhang, “An Ultra-Compact Colorless Dual-Mode 3 dB Power Splitter Based on Axisymmetrical Subwavelength Structure,” CLEO: Science and Innovations (Optical Society of America, 2018), JW2A. 47.

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H. Ma, J. Huang, K. Zhang, and J. Yang, “Arbitrary-direction, multichannel and ultra-compact power splitters by inverse design method,” Opt. Commun. 462, 125329 (2020)..
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W. Ma, F. Cheng, Y. Xu, Q. Wen, and Y. Liu, “Probabilistic Representation and Inverse Design of Metamaterials Based on a Deep Generative Model with Semi-Supervised Learning Strategy,” Adv. Mater. 31(35), 1901111 (2019)..
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J. H. Schmid, B. Lamontagne, P. Cheben, A. Delâge, S. Janz, A. Densmore, J. Lapointe, E. Post, P. Waldron, and D. Xu, “Mode converters for coupling to high aspect ratio silicon-on-insulator channel waveguides,” IEEE Photonics Technol. Lett. 19(11), 855–857 (2007)..
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T. Aalto, K. Solehmainen, M. Harjanne, M. Kapulainen, and P. Heimala, “Low-loss converters between optical silicon waveguides of different sizes and types,” IEEE Photonics Technol. Lett. 18(5), 709–711 (2006)..
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H. Xie, Y. Liu, Y. Wang, Y. Wang, Y. Yao, Q. Song, J. Du, Z. He, and K. Xu, “An Ultra-Compact 3-dB Power Splitter for Three Modes Based on Pixelated Meta-Structure,” IEEE Photonics Technol. Lett. 32(6), 341–344 (2020)..
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D. Vermeulen, K. Van Acoleyen, S. Ghosh, W. De Cort, N. A. Yebo, E. Hallynck, K. De Vos, P. Debackere, P. Dumon, W. Bogaerts, G. Roelkens, D. Van Thourhout, and R. Baets, “Efficient tapering to the fundamental quasi-TM mode in asymmetrical waveguides,” presented at the 15th European conference on Integrated Optics (ECIO 2010). 2010.

Vermeulen, D.

D. Vermeulen, K. Van Acoleyen, S. Ghosh, W. De Cort, N. A. Yebo, E. Hallynck, K. De Vos, P. Debackere, P. Dumon, W. Bogaerts, G. Roelkens, D. Van Thourhout, and R. Baets, “Efficient tapering to the fundamental quasi-TM mode in asymmetrical waveguides,” presented at the 15th European conference on Integrated Optics (ECIO 2010). 2010.

Vuckovic, J.

Waldron, P.

J. H. Schmid, B. Lamontagne, P. Cheben, A. Delâge, S. Janz, A. Densmore, J. Lapointe, E. Post, P. Waldron, and D. Xu, “Mode converters for coupling to high aspect ratio silicon-on-insulator channel waveguides,” IEEE Photonics Technol. Lett. 19(11), 855–857 (2007)..
[Crossref]

Wang, B.

M. H. Tahersima, K. Kojima, T. Koike-Akino, D. Jha, B. Wang, C. Lin, and K. Parsons, “Deep neural network inverse design of integrated photonic power splitters,” Sci. Rep. 9(1), 1368 (2019)..
[Crossref]

Wang, G.

Wang, H. Q.

Wang, J.

Z. Zhang, X. Hu, and J. Wang, “On-chip optical mode exchange using tapered directional coupler,” Sci. Rep. 5(1), 16072 (2015).
[Crossref]

J. Wang, P. Chen, S. shen, Y. shi, and D. Dai, “Improved 8-channel silicon mode demultiplexer with grating polarizers,” Opt. Express 22(11), 12799–12807 (2014)..
[Crossref]

J. Wang, S. He, and D. Dai, “On-chip silicon 8-channel hybrid (de) multiplexer enabling simultaneous mode-and polarization-division-multiplexing,” Laser Photonics Rev. 8(2), L18–L22 (2014)..
[Crossref]

D. Dai, J. Wang, and Y. Shi, “Silicon mode (de) multiplexer enabling high capacity photonic networks-on-chip with a single-wavelength-carrier light,” Opt. Express 38(9), 1422–1424 (2013).
[Crossref]

Wang, P.

Wang, S.

H. Xie, Y. Liu, S. Wang, Y. Wang, Y. Yao, Q. Song, J. Du, Z. He, and K. Xu, “Highly Compact and Efficient Four-mode Multiplexer based on Pixelated Waveguides,” IEEE Photonics Technol. Lett. 32(3), 166–169 (2020)..
[Crossref]

Y. Liu, K. Xu, S. Wang, W. Shen, H. Xie, Y. Wang, S. Xiao, Y. Yao, J. Du, Z. He, and Q. Song, “Arbitrarily routed mode-division multiplexed photonic circuits for dense integration,” Nat. Commun. 10(1), 3263 (2019).
[Crossref]

Y. Liu, S. Wang, Y. Wang, W. Liu, H. Xie, Y. Yao, Q. Song, X. Zhang, Y. Yu, and K. Xu, “Subwavelength polarization splitter–rotator with ultra-compact footprint,” Opt. Lett. 44(18), 4495–4498 (2019)..
[Crossref]

Wang, Y.

H. Xie, Y. Liu, S. Wang, Y. Wang, Y. Yao, Q. Song, J. Du, Z. He, and K. Xu, “Highly Compact and Efficient Four-mode Multiplexer based on Pixelated Waveguides,” IEEE Photonics Technol. Lett. 32(3), 166–169 (2020)..
[Crossref]

H. Xie, Y. Liu, Y. Wang, Y. Wang, Y. Yao, Q. Song, J. Du, Z. He, and K. Xu, “An Ultra-Compact 3-dB Power Splitter for Three Modes Based on Pixelated Meta-Structure,” IEEE Photonics Technol. Lett. 32(6), 341–344 (2020)..
[Crossref]

H. Xie, Y. Liu, Y. Wang, Y. Wang, Y. Yao, Q. Song, J. Du, Z. He, and K. Xu, “An Ultra-Compact 3-dB Power Splitter for Three Modes Based on Pixelated Meta-Structure,” IEEE Photonics Technol. Lett. 32(6), 341–344 (2020)..
[Crossref]

Y. Liu, K. Xu, S. Wang, W. Shen, H. Xie, Y. Wang, S. Xiao, Y. Yao, J. Du, Z. He, and Q. Song, “Arbitrarily routed mode-division multiplexed photonic circuits for dense integration,” Nat. Commun. 10(1), 3263 (2019).
[Crossref]

Y. Liu, S. Wang, Y. Wang, W. Liu, H. Xie, Y. Yao, Q. Song, X. Zhang, Y. Yu, and K. Xu, “Subwavelength polarization splitter–rotator with ultra-compact footprint,” Opt. Lett. 44(18), 4495–4498 (2019)..
[Crossref]

Wen, Q.

W. Ma, F. Cheng, Y. Xu, Q. Wen, and Y. Liu, “Probabilistic Representation and Inverse Design of Metamaterials Based on a Deep Generative Model with Semi-Supervised Learning Strategy,” Adv. Mater. 31(35), 1901111 (2019)..
[Crossref]

Wen, X.

Wu, Y.

Xiao, S.

Xiao, Z.

Xie, H.

H. Xie, Y. Liu, Y. Wang, Y. Wang, Y. Yao, Q. Song, J. Du, Z. He, and K. Xu, “An Ultra-Compact 3-dB Power Splitter for Three Modes Based on Pixelated Meta-Structure,” IEEE Photonics Technol. Lett. 32(6), 341–344 (2020)..
[Crossref]

H. Xie, Y. Liu, S. Wang, Y. Wang, Y. Yao, Q. Song, J. Du, Z. He, and K. Xu, “Highly Compact and Efficient Four-mode Multiplexer based on Pixelated Waveguides,” IEEE Photonics Technol. Lett. 32(3), 166–169 (2020)..
[Crossref]

Y. Liu, K. Xu, S. Wang, W. Shen, H. Xie, Y. Wang, S. Xiao, Y. Yao, J. Du, Z. He, and Q. Song, “Arbitrarily routed mode-division multiplexed photonic circuits for dense integration,” Nat. Commun. 10(1), 3263 (2019).
[Crossref]

Y. Liu, S. Wang, Y. Wang, W. Liu, H. Xie, Y. Yao, Q. Song, X. Zhang, Y. Yu, and K. Xu, “Subwavelength polarization splitter–rotator with ultra-compact footprint,” Opt. Lett. 44(18), 4495–4498 (2019)..
[Crossref]

Y. Liu, W. Sun, H. Xie, N. Zhang, K. Xu, Y. Yao, S. Xiao, and Q. Song, “Very sharp adiabatic bends based on an inverse design,” Opt. Lett. 43(11), 2482–2485 (2018)..
[Crossref]

Xu, D.

J. H. Schmid, B. Lamontagne, P. Cheben, A. Delâge, S. Janz, A. Densmore, J. Lapointe, E. Post, P. Waldron, and D. Xu, “Mode converters for coupling to high aspect ratio silicon-on-insulator channel waveguides,” IEEE Photonics Technol. Lett. 19(11), 855–857 (2007)..
[Crossref]

Xu, K.

H. Xie, Y. Liu, S. Wang, Y. Wang, Y. Yao, Q. Song, J. Du, Z. He, and K. Xu, “Highly Compact and Efficient Four-mode Multiplexer based on Pixelated Waveguides,” IEEE Photonics Technol. Lett. 32(3), 166–169 (2020)..
[Crossref]

H. Xie, Y. Liu, Y. Wang, Y. Wang, Y. Yao, Q. Song, J. Du, Z. He, and K. Xu, “An Ultra-Compact 3-dB Power Splitter for Three Modes Based on Pixelated Meta-Structure,” IEEE Photonics Technol. Lett. 32(6), 341–344 (2020)..
[Crossref]

Y. Liu, K. Xu, S. Wang, W. Shen, H. Xie, Y. Wang, S. Xiao, Y. Yao, J. Du, Z. He, and Q. Song, “Arbitrarily routed mode-division multiplexed photonic circuits for dense integration,” Nat. Commun. 10(1), 3263 (2019).
[Crossref]

Y. Liu, S. Wang, Y. Wang, W. Liu, H. Xie, Y. Yao, Q. Song, X. Zhang, Y. Yu, and K. Xu, “Subwavelength polarization splitter–rotator with ultra-compact footprint,” Opt. Lett. 44(18), 4495–4498 (2019)..
[Crossref]

Y. Liu, W. Sun, H. Xie, N. Zhang, K. Xu, Y. Yao, S. Xiao, and Q. Song, “Very sharp adiabatic bends based on an inverse design,” Opt. Lett. 43(11), 2482–2485 (2018)..
[Crossref]

K. Xu, L. Liu, X. Wen, W. Sun, N. Zhang, N. Yi, S. Sun, S. Xiao, and Q. Song, “Integrated photonic power divider with arbitrary power ratios,” Opt. Lett. 42(4), 855–858 (2017)..
[Crossref]

Xu, Y.

W. Ma, F. Cheng, Y. Xu, Q. Wen, and Y. Liu, “Probabilistic Representation and Inverse Design of Metamaterials Based on a Deep Generative Model with Semi-Supervised Learning Strategy,” Adv. Mater. 31(35), 1901111 (2019)..
[Crossref]

Yang, J.

H. Ma, J. Huang, K. Zhang, and J. Yang, “Arbitrary-direction, multichannel and ultra-compact power splitters by inverse design method,” Opt. Commun. 462, 125329 (2020)..
[Crossref]

J. Huang, J. Yang, D. Chen, W. Bai, J. Han, Z. Zhang, J. Zhang, X. He, Y. Han, and L. Liang, “Implementation of on-chip multi-channel focusing wavelength demultiplexer with regularized digital metamaterials,” Nanophotonics 9(1), 159–166 (2019)..
[Crossref]

J. Huang, J. Yang, D. Chen, X. He, Y. Han, J. Zhang, and Z. Zhang, “Ultra-compact broadband polarization beam splitter with strong expansibility,” Photonics Res. 6(6), 574–578 (2018)..
[Crossref]

W. Chen, P. Wang, T. Yang, G. Wang, T. Dai, Y. Zhang, L. Zhou, X. Jiang, and J. Yang, “Silicon three-mode (de) multiplexer based on cascaded asymmetric Y junctions,” Opt. Lett. 41(12), 2851–2854 (2016)..
[Crossref]

Z. Li, Z. Zhang, J. Huang, and J. Yang, “Genetically Designed Ultra-compact Wideband Multiple-use Reflectors with High Reflectivity Appling to Optics Communication,” in Proceedings of 2019 IEEE 19th International Conference on Communication Technology (ICCT). IEEE, 724–728 (2019).

Yang, T.

Yang, W.

M. Ye, Y. Yu, J. Zou, W. Yang, and X. Zhang, “On-chip multiplexing conversion between wavelength division multiplexing–polarization division multiplexing and wavelength division multiplexing-mode division multiplexing,” Opt. Express 39(4), 758–761 (2014).
[Crossref]

Yao, Y.

H. Xie, Y. Liu, Y. Wang, Y. Wang, Y. Yao, Q. Song, J. Du, Z. He, and K. Xu, “An Ultra-Compact 3-dB Power Splitter for Three Modes Based on Pixelated Meta-Structure,” IEEE Photonics Technol. Lett. 32(6), 341–344 (2020)..
[Crossref]

H. Xie, Y. Liu, S. Wang, Y. Wang, Y. Yao, Q. Song, J. Du, Z. He, and K. Xu, “Highly Compact and Efficient Four-mode Multiplexer based on Pixelated Waveguides,” IEEE Photonics Technol. Lett. 32(3), 166–169 (2020)..
[Crossref]

Y. Liu, K. Xu, S. Wang, W. Shen, H. Xie, Y. Wang, S. Xiao, Y. Yao, J. Du, Z. He, and Q. Song, “Arbitrarily routed mode-division multiplexed photonic circuits for dense integration,” Nat. Commun. 10(1), 3263 (2019).
[Crossref]

Y. Liu, S. Wang, Y. Wang, W. Liu, H. Xie, Y. Yao, Q. Song, X. Zhang, Y. Yu, and K. Xu, “Subwavelength polarization splitter–rotator with ultra-compact footprint,” Opt. Lett. 44(18), 4495–4498 (2019)..
[Crossref]

Y. Liu, W. Sun, H. Xie, N. Zhang, K. Xu, Y. Yao, S. Xiao, and Q. Song, “Very sharp adiabatic bends based on an inverse design,” Opt. Lett. 43(11), 2482–2485 (2018)..
[Crossref]

Ye, M.

M. Ye, Y. Yu, J. Zou, W. Yang, and X. Zhang, “On-chip multiplexing conversion between wavelength division multiplexing–polarization division multiplexing and wavelength division multiplexing-mode division multiplexing,” Opt. Express 39(4), 758–761 (2014).
[Crossref]

Yebo, N. A.

D. Vermeulen, K. Van Acoleyen, S. Ghosh, W. De Cort, N. A. Yebo, E. Hallynck, K. De Vos, P. Debackere, P. Dumon, W. Bogaerts, G. Roelkens, D. Van Thourhout, and R. Baets, “Efficient tapering to the fundamental quasi-TM mode in asymmetrical waveguides,” presented at the 15th European conference on Integrated Optics (ECIO 2010). 2010.

Yi, N.

Yu, Y.

Y. Liu, S. Wang, Y. Wang, W. Liu, H. Xie, Y. Yao, Q. Song, X. Zhang, Y. Yu, and K. Xu, “Subwavelength polarization splitter–rotator with ultra-compact footprint,” Opt. Lett. 44(18), 4495–4498 (2019)..
[Crossref]

M. Ye, Y. Yu, J. Zou, W. Yang, and X. Zhang, “On-chip multiplexing conversion between wavelength division multiplexing–polarization division multiplexing and wavelength division multiplexing-mode division multiplexing,” Opt. Express 39(4), 758–761 (2014).
[Crossref]

Yu, Z.

Zhang, H.

Zhang, J.

J. Huang, J. Yang, D. Chen, W. Bai, J. Han, Z. Zhang, J. Zhang, X. He, Y. Han, and L. Liang, “Implementation of on-chip multi-channel focusing wavelength demultiplexer with regularized digital metamaterials,” Nanophotonics 9(1), 159–166 (2019)..
[Crossref]

J. Huang, J. Yang, D. Chen, X. He, Y. Han, J. Zhang, and Z. Zhang, “Ultra-compact broadband polarization beam splitter with strong expansibility,” Photonics Res. 6(6), 574–578 (2018)..
[Crossref]

Zhang, K.

H. Ma, J. Huang, K. Zhang, and J. Yang, “Arbitrary-direction, multichannel and ultra-compact power splitters by inverse design method,” Opt. Commun. 462, 125329 (2020)..
[Crossref]

Zhang, M.

W. Chang, L. Lu, X. Ren, D. Li, Z. Pan, M. Cheng, D. Liu, and M. Zhang, “Ultra-compact mode (de) multiplexer based on subwavelength asymmetric Y-junction,” Opt. Express 26(7), 8162–8170 (2018)..
[Crossref]

W. Chang, L. Lu, X. Ren, D. Li, Z. Pan, M. Cheng, D. Liu, and M. Zhang, “Ultracompact dual-mode waveguide crossing based on subwavelength multimode-interference couplers,” Photonics Res. 6(7), 660–665 (2018)..
[Crossref]

L. Lu, M. Zhang, F. Zhou, W. Chang, J. Tang, D. Li, X. Ren, Z. Pan, M. Cheng, and D. Liu, “Inverse-designed ultra-compact star-crossings based on PhC-like subwavelength structures for optical intercross connect,” Opt. Express 25(15), 18355–18364 (2017)..
[Crossref]

F. Zhou, L. Lu, M. Zhang, W. Chang, D. Li, L. Deng, and D. Liu, “Ultra-compact, low-loss and low-crosstalk wavelength demultiplexer for CWDM system based on the photonic-crystal-like metamaterial structure,” in Proceedings of 2017 Conference on Lasers and Electro-Optics (CLEO). IEEE, 1 (2017).

W. Chang, L. Lu, D. Liu, and M. zhang, “Ultra-compact silicon multi-mode waveguide bend based on subwavelength asymmetric Y-junction,” in Proceedings of Optical Fiber Communication Conference (Optical Society of America, 2018), Tu3A.1.

L. Lu, M. Zhang, F. Zhou, and D. Liu, “An ultra-compact colorless 50: 50 coupler based on PhC-like metamaterial structure,” in Proceedings of 2016 Optical Fiber Communications Conference and Exhibition (OFC). IEEE, 1–3 (2016).

W. Chang, L. Lu, D. Liu, and M. Zhang, “An Ultra-Compact Colorless Dual-Mode 3 dB Power Splitter Based on Axisymmetrical Subwavelength Structure,” CLEO: Science and Innovations (Optical Society of America, 2018), JW2A. 47.

Zhang, N.

Zhang, X.

Zhang, Y.

Zhang, Z.

J. Huang, J. Yang, D. Chen, W. Bai, J. Han, Z. Zhang, J. Zhang, X. He, Y. Han, and L. Liang, “Implementation of on-chip multi-channel focusing wavelength demultiplexer with regularized digital metamaterials,” Nanophotonics 9(1), 159–166 (2019)..
[Crossref]

J. Huang, J. Yang, D. Chen, X. He, Y. Han, J. Zhang, and Z. Zhang, “Ultra-compact broadband polarization beam splitter with strong expansibility,” Photonics Res. 6(6), 574–578 (2018)..
[Crossref]

Z. Zhang, X. Hu, and J. Wang, “On-chip optical mode exchange using tapered directional coupler,” Sci. Rep. 5(1), 16072 (2015).
[Crossref]

Z. Li, Z. Zhang, J. Huang, and J. Yang, “Genetically Designed Ultra-compact Wideband Multiple-use Reflectors with High Reflectivity Appling to Optics Communication,” in Proceedings of 2019 IEEE 19th International Conference on Communication Technology (ICCT). IEEE, 724–728 (2019).

Zhou, F.

L. Lu, M. Zhang, F. Zhou, W. Chang, J. Tang, D. Li, X. Ren, Z. Pan, M. Cheng, and D. Liu, “Inverse-designed ultra-compact star-crossings based on PhC-like subwavelength structures for optical intercross connect,” Opt. Express 25(15), 18355–18364 (2017)..
[Crossref]

F. Zhou, L. Lu, M. Zhang, W. Chang, D. Li, L. Deng, and D. Liu, “Ultra-compact, low-loss and low-crosstalk wavelength demultiplexer for CWDM system based on the photonic-crystal-like metamaterial structure,” in Proceedings of 2017 Conference on Lasers and Electro-Optics (CLEO). IEEE, 1 (2017).

L. Lu, M. Zhang, F. Zhou, and D. Liu, “An ultra-compact colorless 50: 50 coupler based on PhC-like metamaterial structure,” in Proceedings of 2016 Optical Fiber Communications Conference and Exhibition (OFC). IEEE, 1–3 (2016).

Zhou, L.

Zou, J.

M. Ye, Y. Yu, J. Zou, W. Yang, and X. Zhang, “On-chip multiplexing conversion between wavelength division multiplexing–polarization division multiplexing and wavelength division multiplexing-mode division multiplexing,” Opt. Express 39(4), 758–761 (2014).
[Crossref]

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W. Ma, F. Cheng, and Y. Liu, “Deep-learning-enabled on-demand design of chiral metamaterials,” ACS Nano 12(6), 6326–6334 (2018)..
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W. Ma, F. Cheng, Y. Xu, Q. Wen, and Y. Liu, “Probabilistic Representation and Inverse Design of Metamaterials Based on a Deep Generative Model with Semi-Supervised Learning Strategy,” Adv. Mater. 31(35), 1901111 (2019)..
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[Crossref]

H. Xie, Y. Liu, S. Wang, Y. Wang, Y. Yao, Q. Song, J. Du, Z. He, and K. Xu, “Highly Compact and Efficient Four-mode Multiplexer based on Pixelated Waveguides,” IEEE Photonics Technol. Lett. 32(3), 166–169 (2020)..
[Crossref]

H. Xie, Y. Liu, Y. Wang, Y. Wang, Y. Yao, Q. Song, J. Du, Z. He, and K. Xu, “An Ultra-Compact 3-dB Power Splitter for Three Modes Based on Pixelated Meta-Structure,” IEEE Photonics Technol. Lett. 32(6), 341–344 (2020)..
[Crossref]

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J. Wang, S. He, and D. Dai, “On-chip silicon 8-channel hybrid (de) multiplexer enabling simultaneous mode-and polarization-division-multiplexing,” Laser Photonics Rev. 8(2), L18–L22 (2014)..
[Crossref]

Nanophotonics (1)

J. Huang, J. Yang, D. Chen, W. Bai, J. Han, Z. Zhang, J. Zhang, X. He, Y. Han, and L. Liang, “Implementation of on-chip multi-channel focusing wavelength demultiplexer with regularized digital metamaterials,” Nanophotonics 9(1), 159–166 (2019)..
[Crossref]

Nat. Commun. (1)

Y. Liu, K. Xu, S. Wang, W. Shen, H. Xie, Y. Wang, S. Xiao, Y. Yao, J. Du, Z. He, and Q. Song, “Arbitrarily routed mode-division multiplexed photonic circuits for dense integration,” Nat. Commun. 10(1), 3263 (2019).
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Nat. Photonics (1)

B. Shen, P. Wang, R. Polson, and R. Menon, “An integrated-nanophotonics polarization beamsplitter with 2.4× 2.4 µm2 footprint,” Nat. Photonics 9(6), 378–382 (2015)..
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H. Ma, J. Huang, K. Zhang, and J. Yang, “Arbitrary-direction, multichannel and ultra-compact power splitters by inverse design method,” Opt. Commun. 462, 125329 (2020)..
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P. J. Bock, P. Cheben, J. H. Schmid, J. Lapointe, A. Delage, and S. Janz, “Subwavelength grating periodic structures in silicon-on-insulator: a new type of microphotonic waveguide,” Opt. Express 18(19), 20251 (2010)..
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D. Dai and J. E. Bowers, “Novel concept for ultracompact polarization splitter-rotator based on silicon nanowires[J],” Opt. Express 19(11), 10940–10949 (2011)..
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D. Dai, Y. Tang, and J. E. Bowers, “Mode conversion in tapered submicron silicon ridge optical waveguides,” Opt. Express 20(12), 13425–13439 (2012)..
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J. Lu and J. Vučković, “Nanophotonic computational design,” Opt. Express 21(11), 13351–13367 (2013)..
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J. Wang, P. Chen, S. shen, Y. shi, and D. Dai, “Improved 8-channel silicon mode demultiplexer with grating polarizers,” Opt. Express 22(11), 12799–12807 (2014)..
[Crossref]

B. Shen, P. Wang, R. Polson, and R. Menon, “Integrated metamaterials for efficient and compact free-space-to-waveguide coupling,” Opt. Express 22(22), 27175–27182 (2014)..
[Crossref]

D. Dai, J. Wang, and Y. Shi, “Silicon mode (de) multiplexer enabling high capacity photonic networks-on-chip with a single-wavelength-carrier light,” Opt. Express 38(9), 1422–1424 (2013).
[Crossref]

M. Ye, Y. Yu, J. Zou, W. Yang, and X. Zhang, “On-chip multiplexing conversion between wavelength division multiplexing–polarization division multiplexing and wavelength division multiplexing-mode division multiplexing,” Opt. Express 39(4), 758–761 (2014).
[Crossref]

L. Lu, M. Zhang, F. Zhou, W. Chang, J. Tang, D. Li, X. Ren, Z. Pan, M. Cheng, and D. Liu, “Inverse-designed ultra-compact star-crossings based on PhC-like subwavelength structures for optical intercross connect,” Opt. Express 25(15), 18355–18364 (2017)..
[Crossref]

W. Chang, L. Lu, X. Ren, D. Li, Z. Pan, M. Cheng, D. Liu, and M. Zhang, “Ultra-compact mode (de) multiplexer based on subwavelength asymmetric Y-junction,” Opt. Express 26(7), 8162–8170 (2018)..
[Crossref]

Opt. Lett. (6)

Optica (1)

Photonics Res. (2)

W. Chang, L. Lu, X. Ren, D. Li, Z. Pan, M. Cheng, D. Liu, and M. Zhang, “Ultracompact dual-mode waveguide crossing based on subwavelength multimode-interference couplers,” Photonics Res. 6(7), 660–665 (2018)..
[Crossref]

J. Huang, J. Yang, D. Chen, X. He, Y. Han, J. Zhang, and Z. Zhang, “Ultra-compact broadband polarization beam splitter with strong expansibility,” Photonics Res. 6(6), 574–578 (2018)..
[Crossref]

Sci. Rep. (2)

M. H. Tahersima, K. Kojima, T. Koike-Akino, D. Jha, B. Wang, C. Lin, and K. Parsons, “Deep neural network inverse design of integrated photonic power splitters,” Sci. Rep. 9(1), 1368 (2019)..
[Crossref]

Z. Zhang, X. Hu, and J. Wang, “On-chip optical mode exchange using tapered directional coupler,” Sci. Rep. 5(1), 16072 (2015).
[Crossref]

Other (7)

D. Vermeulen, K. Van Acoleyen, S. Ghosh, W. De Cort, N. A. Yebo, E. Hallynck, K. De Vos, P. Debackere, P. Dumon, W. Bogaerts, G. Roelkens, D. Van Thourhout, and R. Baets, “Efficient tapering to the fundamental quasi-TM mode in asymmetrical waveguides,” presented at the 15th European conference on Integrated Optics (ECIO 2010). 2010.

F. Zhou, L. Lu, M. Zhang, W. Chang, D. Li, L. Deng, and D. Liu, “Ultra-compact, low-loss and low-crosstalk wavelength demultiplexer for CWDM system based on the photonic-crystal-like metamaterial structure,” in Proceedings of 2017 Conference on Lasers and Electro-Optics (CLEO). IEEE, 1 (2017).

W. Chang, L. Lu, D. Liu, and M. zhang, “Ultra-compact silicon multi-mode waveguide bend based on subwavelength asymmetric Y-junction,” in Proceedings of Optical Fiber Communication Conference (Optical Society of America, 2018), Tu3A.1.

Z. Li, Z. Zhang, J. Huang, and J. Yang, “Genetically Designed Ultra-compact Wideband Multiple-use Reflectors with High Reflectivity Appling to Optics Communication,” in Proceedings of 2019 IEEE 19th International Conference on Communication Technology (ICCT). IEEE, 724–728 (2019).

A. Y. Piggott, “Automated Design of Photonic Devices,” (Stanford University, 2018). https://c3.glgoo.top/scholar?q=PIGGOTT%2C+Alexander%2C+Y.+Automated+design+of+photonic+devices.+Doctoral+dissertation%2C+Stanford+University%2C+2018+ .

L. Lu, M. Zhang, F. Zhou, and D. Liu, “An ultra-compact colorless 50: 50 coupler based on PhC-like metamaterial structure,” in Proceedings of 2016 Optical Fiber Communications Conference and Exhibition (OFC). IEEE, 1–3 (2016).

W. Chang, L. Lu, D. Liu, and M. Zhang, “An Ultra-Compact Colorless Dual-Mode 3 dB Power Splitter Based on Axisymmetrical Subwavelength Structure,” CLEO: Science and Innovations (Optical Society of America, 2018), JW2A. 47.

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Figures (7)

Fig. 1.
Fig. 1. The different shapes of basic pixel. (a) The rectangular pixels in silicon layer. (b) The triangular pixels in silicon layer. (c) The circular pixels in silicon layer.
Fig. 2.
Fig. 2. The flow chart of RDBS algorithm
Fig. 3.
Fig. 3. The simulated results of comparing DBS algorithm with RDBS. (a) and (e) The initial patterns of DBS and RDBS algorithms. (b) and (f) The top views optimized by DBS and RDBS algorithms. (c) and (g) The corresponding light field distributions. (d) The shortest distances between adjacent pixels in DBS and RDBS algorithms. (h) The simulated spectral responses of transmission loss for different algorithms.
Fig. 4.
Fig. 4. The simulated results of 1 × 2 mode converter of dual-mode version. (a) The top view. (b) The corresponding light field distribution. (c) The simulated spectral responses of the transmission loss.
Fig. 5.
Fig. 5. The simulated results of 1 × 2 mode converter of three-mode version. (a) The top view. (b) The corresponding light field distribution. (c) The simulated spectral responses of the transmission loss.
Fig. 6.
Fig. 6. The analysis of fabrication tolerance for 1 × 2 mode converter of dual-mode version. (a) - (c) The simulated spectral responses under the variations of pixel side from -10 nm to 10 nm.
Fig. 7.
Fig. 7. The analysis of fabrication tolerance for 1 × 2 mode converter of three-mode version. (a) The sharp corner and rounding radius of triangular pixel. (b) - (d) The simulated spectral responses considering the fabrication tolerance of different rounding radii (0 nm, 10 nm and 20 nm).

Tables (1)

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Table 1. Performance comparison of different power splitters

Equations (2)

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E L m = 10 × log ( t m T )
C T n = 10 × log ( t n T )