Abstract

A novel silicon-on-insulator (SOI) polarization splitter-rotator (PSR) with a large fabrication tolerance is proposed based on cascaded multimode interference (MMI) couplers and an assisted mode-evolution taper. The tapers are designed to adiabatically convert the input TM0 mode into the TE1 mode, which will output as the TE0 mode after processed by the subsequent MMI mode converter, 90-degree phase shifter (PS) and MMI 3 dB coupler. The numerical simulation results show that the proposed device has a < 0.5 dB insertion loss with < −17 dB crosstalk in C optical communication band. Fabrication tolerance analysis is also performed with respect to the deviations of MMI coupler width, PS width, slab height and upper-cladding refractive index, showing that this device could work well even when affected by considerable fabrication errors. With such a robust performance with a large bandwidth, this device offers potential applications for CMOS-compatible polarization diversity, especially in the booming 100 Gb/s coherent optical communications based on silicon photonics technology.

© 2014 Optical Society of America

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2014 (11)

D. Xu, J. H. Schmid, G. T. Reed, G. Z. Mashanovich, D. J. Thomson, M. Nedeljkovic, X. Chen, D. V. Thourhout, S. Keyvaninia, and S. K. Selvaraja, “Silicon photonic integration platform-have we found the sweet spot?” IEEE J. Sel. Top. Quantum Electron. 20(4), 189–205 (2014).
[Crossref]

A. Rickman, “The commercialization of silicon photonics,” Nat. Photonics 8(8), 579–582 (2014).
[Crossref]

A. E. J. Lim, J. Song, F. Qing, C. Li, X. Tu, N. Duan, K. K. Chen, R. P. C. Tern, and T. Y. Liow, “Review of silicon photonics foundry efforts,” IEEE J. Sel. Top. Quantum Electron. 20(4), 1–12 (2014).
[Crossref]

P. Dong, X. Liu, S. Chandrasekhar, L. L. Buhl, R. Aroca, and Y.-K. Chen, “Monolithic silicon photonic integrated circuits for compact 100 Gb/s coherent optical receivers and transmitters,” IEEE J. Sel. Top. Quantum Electron. 20(4), 1–8 (2014).

H. Guan, A. Novack, M. Streshinsky, R. Shi, Q. Fang, A. E. Lim, G. Q. Lo, T. Baehr-Jones, and M. Hochberg, “CMOS-compatible highly efficient polarization splitter and rotator based on a double-etched directional coupler,” Opt. Express 22(3), 2489–2496 (2014).
[Crossref] [PubMed]

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. Lett. 39(4), 758–761 (2014).
[Crossref] [PubMed]

J. Wang, B. Niu, Z. Sheng, A. Wu, X. Wang, S. Zou, M. Qi, and F. Gan, “Design of a SiO₂ top-cladding and compact polarization splitter-rotator based on a rib directional coupler,” Opt. Express 22(4), 4137–4143 (2014).
[Crossref] [PubMed]

J. Wang, Z. Sheng, L. Li, A. Pang, A. Wu, W. Li, X. Wang, S. Zou, M. Qi, and F. Gan, “Low-loss and low-crosstalk 8 × 8 silicon nanowire AWG routers fabricated with CMOS technology,” Opt. Express 22(8), 9395–9403 (2014).
[Crossref] [PubMed]

K. Goi, A. Oka, H. Kusaka, Y. Terada, K. Ogawa, T. Y. Liow, X. G. Tu, G. Q. Lo, and D. L. Kwong, “Low-loss high-speed silicon IQ modulator for QPSK/DQPSK in C and L bands,” Opt. Express 22(9), 10703–10709 (2014).
[Crossref] [PubMed]

J. Wang, B. Niu, Z. Sheng, A. Wu, W. Li, X. Wang, S. Zou, M. Qi, and F. Gan, “Novel ultra-broadband polarization splitter-rotator based on mode-evolution tapers and a mode-sorting asymmetric Y-junction,” Opt. Express 22(11), 13565–13571 (2014).
[Crossref] [PubMed]

C. Qiu, Z. Sheng, H. Li, W. Liu, L. Li, A. Pang, A. Wu, X. Wang, S. Zou, and F. Gan, “Fabrication, characterization and loss analysis of silicon nanowaveguides,” J. Lightwave Technol. 32(13), 2303–2307 (2014).
[Crossref]

2013 (2)

2012 (5)

2011 (2)

2007 (3)

T. Lang, J. J. He, J. G. Kuang, and S. He, “Birefringence compensated AWG demultiplexer with angled star couplers,” Opt. Express 15(23), 15022–15028 (2007).
[Crossref] [PubMed]

Z. Wang, D. Dai, and S. He, “Polarization-insensitive ultrasmall microring resonator design based on optimized Si sandwich nanowires,” IEEE Photon. Technol. Lett. 19(20), 1580–1582 (2007).
[Crossref]

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kartner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
[Crossref]

2005 (2)

2002 (1)

Y. Kawaguchi and K. Tsutsumi, “Mode multiplexing and demultiplexing devices using multimode interference couplers,” Electron. Lett. 38(25), 1701–1702 (2002).
[Crossref]

1995 (1)

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13(4), 615–627 (1995).
[Crossref]

Aroca, R.

P. Dong, X. Liu, S. Chandrasekhar, L. L. Buhl, R. Aroca, and Y.-K. Chen, “Monolithic silicon photonic integrated circuits for compact 100 Gb/s coherent optical receivers and transmitters,” IEEE J. Sel. Top. Quantum Electron. 20(4), 1–8 (2014).

Baehr-Jones, T.

Baets, R.

Barwicz, T.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kartner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
[Crossref]

Bienstman, P.

Bowers, J. E.

Buhl, L. L.

P. Dong, X. Liu, S. Chandrasekhar, L. L. Buhl, R. Aroca, and Y.-K. Chen, “Monolithic silicon photonic integrated circuits for compact 100 Gb/s coherent optical receivers and transmitters,” IEEE J. Sel. Top. Quantum Electron. 20(4), 1–8 (2014).

Cao, T.

Cao, Y.

Chandrasekhar, S.

P. Dong, X. Liu, S. Chandrasekhar, L. L. Buhl, R. Aroca, and Y.-K. Chen, “Monolithic silicon photonic integrated circuits for compact 100 Gb/s coherent optical receivers and transmitters,” IEEE J. Sel. Top. Quantum Electron. 20(4), 1–8 (2014).

Cheben, P.

Chen, K. K.

A. E. J. Lim, J. Song, F. Qing, C. Li, X. Tu, N. Duan, K. K. Chen, R. P. C. Tern, and T. Y. Liow, “Review of silicon photonics foundry efforts,” IEEE J. Sel. Top. Quantum Electron. 20(4), 1–12 (2014).
[Crossref]

Chen, S.

Chen, X.

D. Xu, J. H. Schmid, G. T. Reed, G. Z. Mashanovich, D. J. Thomson, M. Nedeljkovic, X. Chen, D. V. Thourhout, S. Keyvaninia, and S. K. Selvaraja, “Silicon photonic integration platform-have we found the sweet spot?” IEEE J. Sel. Top. Quantum Electron. 20(4), 189–205 (2014).
[Crossref]

Chen, Y.-K.

P. Dong, X. Liu, S. Chandrasekhar, L. L. Buhl, R. Aroca, and Y.-K. Chen, “Monolithic silicon photonic integrated circuits for compact 100 Gb/s coherent optical receivers and transmitters,” IEEE J. Sel. Top. Quantum Electron. 20(4), 1–8 (2014).

Dai, D.

Ding, Y.

Dong, P.

P. Dong, X. Liu, S. Chandrasekhar, L. L. Buhl, R. Aroca, and Y.-K. Chen, “Monolithic silicon photonic integrated circuits for compact 100 Gb/s coherent optical receivers and transmitters,” IEEE J. Sel. Top. Quantum Electron. 20(4), 1–8 (2014).

Duan, N.

A. E. J. Lim, J. Song, F. Qing, C. Li, X. Tu, N. Duan, K. K. Chen, R. P. C. Tern, and T. Y. Liow, “Review of silicon photonics foundry efforts,” IEEE J. Sel. Top. Quantum Electron. 20(4), 1–12 (2014).
[Crossref]

Dumon, P.

Fang, Q.

Fei, Y.

Gan, F.

Goi, K.

Guan, H.

Halir, R.

Haus, H. A.

He, J. J.

He, S.

T. Lang, J. J. He, J. G. Kuang, and S. He, “Birefringence compensated AWG demultiplexer with angled star couplers,” Opt. Express 15(23), 15022–15028 (2007).
[Crossref] [PubMed]

Z. Wang, D. Dai, and S. He, “Polarization-insensitive ultrasmall microring resonator design based on optimized Si sandwich nanowires,” IEEE Photon. Technol. Lett. 19(20), 1580–1582 (2007).
[Crossref]

Hochberg, M.

Hvam, J. M.

Ippen, E. P.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kartner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
[Crossref]

M. R. Watts, H. A. Haus, and E. P. Ippen, “Integrated mode-evolution-based polarization splitter,” Opt. Lett. 30(9), 967–969 (2005).
[Crossref] [PubMed]

Ishizaka, Y.

Kartner, F. X.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kartner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
[Crossref]

Kawaguchi, Y.

Keyvaninia, S.

D. Xu, J. H. Schmid, G. T. Reed, G. Z. Mashanovich, D. J. Thomson, M. Nedeljkovic, X. Chen, D. V. Thourhout, S. Keyvaninia, and S. K. Selvaraja, “Silicon photonic integration platform-have we found the sweet spot?” IEEE J. Sel. Top. Quantum Electron. 20(4), 189–205 (2014).
[Crossref]

Koshiba, M.

Kuang, J. G.

Kusaka, H.

Kwong, D. L.

Lang, T.

Li, C.

A. E. J. Lim, J. Song, F. Qing, C. Li, X. Tu, N. Duan, K. K. Chen, R. P. C. Tern, and T. Y. Liow, “Review of silicon photonics foundry efforts,” IEEE J. Sel. Top. Quantum Electron. 20(4), 1–12 (2014).
[Crossref]

Li, H.

Li, L.

Li, W.

Lim, A. E.

Lim, A. E. J.

A. E. J. Lim, J. Song, F. Qing, C. Li, X. Tu, N. Duan, K. K. Chen, R. P. C. Tern, and T. Y. Liow, “Review of silicon photonics foundry efforts,” IEEE J. Sel. Top. Quantum Electron. 20(4), 1–12 (2014).
[Crossref]

Ling, W.

Liow, T. Y.

A. E. J. Lim, J. Song, F. Qing, C. Li, X. Tu, N. Duan, K. K. Chen, R. P. C. Tern, and T. Y. Liow, “Review of silicon photonics foundry efforts,” IEEE J. Sel. Top. Quantum Electron. 20(4), 1–12 (2014).
[Crossref]

K. Goi, A. Oka, H. Kusaka, Y. Terada, K. Ogawa, T. Y. Liow, X. G. Tu, G. Q. Lo, and D. L. Kwong, “Low-loss high-speed silicon IQ modulator for QPSK/DQPSK in C and L bands,” Opt. Express 22(9), 10703–10709 (2014).
[Crossref] [PubMed]

Liu, L.

Liu, W.

Liu, X.

P. Dong, X. Liu, S. Chandrasekhar, L. L. Buhl, R. Aroca, and Y.-K. Chen, “Monolithic silicon photonic integrated circuits for compact 100 Gb/s coherent optical receivers and transmitters,” IEEE J. Sel. Top. Quantum Electron. 20(4), 1–8 (2014).

Lo, G. Q.

Luyssaert, B.

Maese-Novo, A.

Mashanovich, G. Z.

D. Xu, J. H. Schmid, G. T. Reed, G. Z. Mashanovich, D. J. Thomson, M. Nedeljkovic, X. Chen, D. V. Thourhout, S. Keyvaninia, and S. K. Selvaraja, “Silicon photonic integration platform-have we found the sweet spot?” IEEE J. Sel. Top. Quantum Electron. 20(4), 189–205 (2014).
[Crossref]

Molina-Fernández, I.

Nedeljkovic, M.

D. Xu, J. H. Schmid, G. T. Reed, G. Z. Mashanovich, D. J. Thomson, M. Nedeljkovic, X. Chen, D. V. Thourhout, S. Keyvaninia, and S. K. Selvaraja, “Silicon photonic integration platform-have we found the sweet spot?” IEEE J. Sel. Top. Quantum Electron. 20(4), 189–205 (2014).
[Crossref]

Niu, B.

Novack, A.

Ogawa, K.

Oka, A.

Ortega-Moñux, A.

Ou, H.

Pang, A.

Pennings, E. C. M.

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13(4), 615–627 (1995).
[Crossref]

Pérez-Galacho, D.

Peucheret, C.

Popovic, M. A.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kartner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
[Crossref]

Qi, M.

Qing, F.

A. E. J. Lim, J. Song, F. Qing, C. Li, X. Tu, N. Duan, K. K. Chen, R. P. C. Tern, and T. Y. Liow, “Review of silicon photonics foundry efforts,” IEEE J. Sel. Top. Quantum Electron. 20(4), 1–12 (2014).
[Crossref]

Qiu, C.

Rakich, P. T.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kartner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
[Crossref]

Reed, G. T.

D. Xu, J. H. Schmid, G. T. Reed, G. Z. Mashanovich, D. J. Thomson, M. Nedeljkovic, X. Chen, D. V. Thourhout, S. Keyvaninia, and S. K. Selvaraja, “Silicon photonic integration platform-have we found the sweet spot?” IEEE J. Sel. Top. Quantum Electron. 20(4), 189–205 (2014).
[Crossref]

Rickman, A.

A. Rickman, “The commercialization of silicon photonics,” Nat. Photonics 8(8), 579–582 (2014).
[Crossref]

Romero-García, S.

Saitoh, K.

Schmid, J. H.

D. Xu, J. H. Schmid, G. T. Reed, G. Z. Mashanovich, D. J. Thomson, M. Nedeljkovic, X. Chen, D. V. Thourhout, S. Keyvaninia, and S. K. Selvaraja, “Silicon photonic integration platform-have we found the sweet spot?” IEEE J. Sel. Top. Quantum Electron. 20(4), 189–205 (2014).
[Crossref]

Selvaraja, S. K.

D. Xu, J. H. Schmid, G. T. Reed, G. Z. Mashanovich, D. J. Thomson, M. Nedeljkovic, X. Chen, D. V. Thourhout, S. Keyvaninia, and S. K. Selvaraja, “Silicon photonic integration platform-have we found the sweet spot?” IEEE J. Sel. Top. Quantum Electron. 20(4), 189–205 (2014).
[Crossref]

Sheng, Z.

Shi, R.

Smith, H. I.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kartner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
[Crossref]

Socci, L.

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kartner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
[Crossref]

Soldano, L. B.

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Appl. Opt. (1)

Electron. Lett. (1)

Y. Kawaguchi and K. Tsutsumi, “Mode multiplexing and demultiplexing devices using multimode interference couplers,” Electron. Lett. 38(25), 1701–1702 (2002).
[Crossref]

IEEE J. Sel. Top. Quantum Electron. (3)

D. Xu, J. H. Schmid, G. T. Reed, G. Z. Mashanovich, D. J. Thomson, M. Nedeljkovic, X. Chen, D. V. Thourhout, S. Keyvaninia, and S. K. Selvaraja, “Silicon photonic integration platform-have we found the sweet spot?” IEEE J. Sel. Top. Quantum Electron. 20(4), 189–205 (2014).
[Crossref]

A. E. J. Lim, J. Song, F. Qing, C. Li, X. Tu, N. Duan, K. K. Chen, R. P. C. Tern, and T. Y. Liow, “Review of silicon photonics foundry efforts,” IEEE J. Sel. Top. Quantum Electron. 20(4), 1–12 (2014).
[Crossref]

P. Dong, X. Liu, S. Chandrasekhar, L. L. Buhl, R. Aroca, and Y.-K. Chen, “Monolithic silicon photonic integrated circuits for compact 100 Gb/s coherent optical receivers and transmitters,” IEEE J. Sel. Top. Quantum Electron. 20(4), 1–8 (2014).

IEEE Photon. J. (1)

Z. Sheng, Z. Q. Wang, C. Qiu, L. Li, A. Pang, A. Wu, X. Wang, S. Zou, and F. Gan, “A compact and low-loss MMI coupler fabricated with CMOS technology,” IEEE Photon. J. 4(6), 2272–2277 (2012).
[Crossref]

IEEE Photon. Technol. Lett. (1)

Z. Wang, D. Dai, and S. He, “Polarization-insensitive ultrasmall microring resonator design based on optimized Si sandwich nanowires,” IEEE Photon. Technol. Lett. 19(20), 1580–1582 (2007).
[Crossref]

J. Lightwave Technol. (5)

Nat. Photonics (2)

A. Rickman, “The commercialization of silicon photonics,” Nat. Photonics 8(8), 579–582 (2014).
[Crossref]

T. Barwicz, M. R. Watts, M. A. Popovic, P. T. Rakich, L. Socci, F. X. Kartner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
[Crossref]

Opt. Express (11)

J. Wang, Z. Sheng, L. Li, A. Pang, A. Wu, W. Li, X. Wang, S. Zou, M. Qi, and F. Gan, “Low-loss and low-crosstalk 8 × 8 silicon nanowire AWG routers fabricated with CMOS technology,” Opt. Express 22(8), 9395–9403 (2014).
[Crossref] [PubMed]

T. Lang, J. J. He, J. G. Kuang, and S. He, “Birefringence compensated AWG demultiplexer with angled star couplers,” Opt. Express 15(23), 15022–15028 (2007).
[Crossref] [PubMed]

L. Liu, Y. Ding, K. Yvind, and J. M. Hvam, “Silicon-on-insulator polarization splitting and rotating device for polarization diversity circuits,” Opt. Express 19(13), 12646–12651 (2011).
[Crossref] [PubMed]

D. Dai and J. E. Bowers, “Novel concept for ultracompact polarization splitter-rotator based on silicon nanowires,” Opt. Express 19(11), 10940–10949 (2011).
[Crossref] [PubMed]

Y. Ding, L. Liu, C. Peucheret, and H. Ou, “Fabrication tolerant polarization splitter and rotator based on a tapered directional coupler,” Opt. Express 20(18), 20021–20027 (2012).
[Crossref] [PubMed]

K. Goi, A. Oka, H. Kusaka, Y. Terada, K. Ogawa, T. Y. Liow, X. G. Tu, G. Q. Lo, and D. L. Kwong, “Low-loss high-speed silicon IQ modulator for QPSK/DQPSK in C and L bands,” Opt. Express 22(9), 10703–10709 (2014).
[Crossref] [PubMed]

A. Maese-Novo, R. Halir, S. Romero-García, D. Pérez-Galacho, L. Zavargo-Peche, A. Ortega-Moñux, I. Molina-Fernández, J. G. Wangüemert-Pérez, and P. Cheben, “Wavelength independent multimode interference coupler,” Opt. Express 21(6), 7033–7040 (2013).
[Crossref] [PubMed]

J. Wang, B. Niu, Z. Sheng, A. Wu, X. Wang, S. Zou, M. Qi, and F. Gan, “Design of a SiO₂ top-cladding and compact polarization splitter-rotator based on a rib directional coupler,” Opt. Express 22(4), 4137–4143 (2014).
[Crossref] [PubMed]

H. Guan, A. Novack, M. Streshinsky, R. Shi, Q. Fang, A. E. Lim, G. Q. Lo, T. Baehr-Jones, and M. Hochberg, “CMOS-compatible highly efficient polarization splitter and rotator based on a double-etched directional coupler,” Opt. Express 22(3), 2489–2496 (2014).
[Crossref] [PubMed]

J. Wang, B. Niu, Z. Sheng, A. Wu, W. Li, X. Wang, S. Zou, M. Qi, and F. Gan, “Novel ultra-broadband polarization splitter-rotator based on mode-evolution tapers and a mode-sorting asymmetric Y-junction,” Opt. Express 22(11), 13565–13571 (2014).
[Crossref] [PubMed]

D. Dai, Y. Tang, and J. E. Bowers, “Mode conversion in tapered submicron silicon ridge optical waveguides,” Opt. Express 20(12), 13425–13439 (2012).
[Crossref] [PubMed]

Opt. Lett. (2)

Other (3)

J. C. Wirth, J. Wang, B. Niu, Y. Xuan, L. Fan, L. Varghese, D. E. Leaird, M. Qi, and A. Weiner, “Efficient silicon-on-insulator polarization rotator based on mode evolution,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2012), paper JW4A.83.
[Crossref]

C. R. Doerr, L. Chen, D. Vermeulen, T. Nielsen, S. Azemati, S. Stulz, G. McBrien, X. Xu, B. Mikkelsen, M. Givehchi, C. Rasmussen, and S. Y. Park, “Single-chip silicon photonics 100-Gb/s coherent transceiver,” in Optical Fiber Communication Conference: Postdeadline Papers, (Optical Society of America, 2014), paper Th5C.1.
[Crossref]

B. Milivojevic, C. Raabe, A. Shastri, M. Webster, P. Metz, S. Sunder, B. Chattin, S. Wiese, B. Dama, and K. Shastri, “112Gb/s DP-QPSK transmission over 2427km SSMF using small-size silicon photonic IQ modulator and low-power CMOS driver,” in Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper OTh1D.1.
[Crossref]

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Figures (9)

Fig. 1
Fig. 1 (a) Schematic of a normal linear taper based on the symmetric strip SOI waveguide. (b) The calculated effective refractive indices of the first three modes in the waveguide cross-section along this taper. Insets: the profiles of the second and third modes. (c) The mode propagation in the taper for the input TM0 mode.
Fig. 2
Fig. 2 (a) Schematic of a linear taper based on the asymmetric rib SOI waveguide. (b) The calculated effective refractive indices of the first three modes in the waveguide cross-section along this taper. Insets: the profiles of the second and third modes. (c) The mode propagation in the taper for the input TM0 mode.
Fig. 3
Fig. 3 (a-b) The mode propagation in the MMI coupler for the input TE0 and TE1 mode, respectively. Insets: the mode profile at the input plane and the position of z = 3Lπ/4.
Fig. 4
Fig. 4 Schematic of the proposed PSR which consists of a bi-level taper, a MMI mode converter, a 90-degree PS and a MMI 3 dB coupler. The overall device is designed in the SOI waveguide with a waveguide height H = 220 nm while the bi-level taper section needs an additional etch (i.e., the slab height Hslab = 90 nm).
Fig. 5
Fig. 5 (a) Effective refractive indices of the first three modes in the waveguide cross-section along the bi-level taper. Insets: the profiles of the zero-, first- and second-order modes in the cross-section along this taper. All the simulations were run at 1550 nm wavelength.
Fig. 6
Fig. 6 (a) Mode conversion efficiency from TM0 to TE1 in the bi-level taper as a function of Ltp1 with Ltp2 varying from 5 μm (red) to 25 μm (pink). Inset: the wavelength dependence of the mode conversion efficiency from TM0 to TE1 when Ltp1 = 35 μm and Ltp2 = 20 μm. (b-c) Mode propagation in the bi-level taper when the input is TE0 and TM0, respectively. All the simulations were run at 1550 nm wavelength.
Fig. 7
Fig. 7 (a) Optimization for the first MMI coupler with different input/output taper lengths (i.e., Ltp3 = 5, 10, 15, and 20 μm). The MMI width WMMI is chosen to be 3.4 μm here. (b) Phase difference between lights propagating through a straight waveguide and a PS with the same length LPS = 10 μm. (c-d) Mode propagation in the right section of the PSR for the incoming TE0 mode and TE1 mode, respectively. All the simulations were run at 1550 nm wavelength.
Fig. 8
Fig. 8 (a-b) Mode propagation in our proposed PSR at 1550 wavelength for input TE0 mode and TM0 mode, respectively. (c) Wavelength dependence of the PSR performance in terms of the insertion loss (IL) and crosstalk (CT) for different input modes. The points with value higher than 30 dB are not shown here.
Fig. 9
Fig. 9 Fabrication tolerance analysis to the deviations of (a1-a3) slab height ΔHslab in the bi-level taper, (b1-b3) MMI width ΔWMMI, (c1-c3) PS width ΔdW, and (d1-d3) refractive index of the upper-cladding ΔnSiO2/nSiO2 at wavelengths of 1.52 μm, 1.55 μm and 1.63 μm, respectively. The points with value higher than 30 dB are not shown here.

Equations (8)

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ψ ( x , y , 0 ) = v c v φ v ( x , y ) ,
c v = ψ ( x , y , 0 ) φ v ( x , y ) d x d y φ v 2 ( x , y ) d x d y .
ψ ( x , y , z ) = v c v φ v ( x , y ) exp [ j v ( v + 2 ) π 3 L π z ] ,
L π = π β 0 β 1
ψ ( x , y , 3 2 L π ) = v e v e n c v φ v ( x , y ) + v o d d ( j ) c v φ v ( x , y ) = 1 j 2 ψ ( x , y , 0 ) + 1 + j 2 ψ ( x , y , 0 ) .
ψ ( x , y , 3 2 L π ) = ψ ( x , y , 0 ) .
ψ ( x , y , 0 ) = ϕ ( x , y , 0 ) + ϕ ( x , y , 0 ) exp ( j π 2 ) ,
ψ ( x , y , 3 2 L π ) = ( 1 + j ) ϕ ( x , y , 0 ) ,

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