Abstract

We experimentally realize a compact wideband polarization splitter and rotator (PSR) with CMOS compatibility. The fabricated PSR is then tested by utilizing a fabrication-tolerant TE-pass on-chip polarizer we propose to practically solve the issue of accurately aligning the polarizations in fiber and modes on chip. Both of these polarization handling devices take the advantage of bend structure that confines TE mode better than TM mode. The fabricated PSR has a high TM-TE and TE-TE mode conversion efficiency of −0.4 dB and −0.2 dB at 1310 nm, while the extinction ratio is better than 18 dB and the broad bandwidth exceeds 100 nm.

© 2017 Optical Society of America

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References

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  1. A. Rickman, “The commercialization of silicon photonics,” Nat. Photonics 8(8), 579–582 (2014).
    [Crossref]
  2. T. Baehr-Jones, T. Pinguet, P. Lo Guo-Qiang, S. Danziger, D. Prather, and M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6(4), 206–208 (2012).
    [Crossref]
  3. T. Barwicz, M. R. Watts, M. A. Popović, P. T. Rakich, L. Socci, F. X. Kärtner, E. P. Ippen, and H. I. Smith, “Polarization-transparent microphotonic devices in the strong confinement limit,” Nat. Photonics 1(1), 57–60 (2007).
    [Crossref]
  4. J. Wang, D. Bonneau, M. Villa, J. W. Silverstone, R. Santagati, S. Miki, T. Yamashita, M. Fujiwara, M. Sasaki, H. Terai, M. G. Tanner, C. M. Natarajan, R. H. Hadfield, J. L. O’Brien, and M. G. Thompson, “Chip-to-chip quantum photonic interconnect by path-polarization interconversion,” Optica 3(4), 407–413 (2016).
    [Crossref]
  5. W. D. Sacher, T. Barwicz, B. J. F. Taylor, and J. K. S. Poon, “Polarization rotator-splitters in standard active silicon photonics platforms,” Opt. Express 22(4), 3777–3786 (2014).
    [Crossref] [PubMed]
  6. Z. Su, E. Timurdogan, E. S. Hosseini, J. Sun, G. Leake, D. D. Coolbaugh, and M. R. Watts, “Four-port integrated polarizing beam splitter,” Opt. Lett. 39(4), 965–968 (2014).
    [Crossref] [PubMed]
  7. 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]
  8. H. Guan, A. Novack, M. Streshinsky, R. Shi, Y. Liu, Q. Fang, A. E. Lim, G. Lo, T. Baehr-Jones, and M. Hochberg, “High-Efficiency Low-Crosstalk 1310-nm Polarization Splitter and Rotator,” IEEE Photonics Technol. Lett. 26(9), 925–928 (2014).
    [Crossref]
  9. J. Wang, M. Qi, Y. Xuan, H. Huang, Y. Li, M. Li, X. Chen, Q. Jia, Z. Sheng, A. Wu, W. Li, X. Wang, S. Zou, and F. Gan, “Proposal for fabrication-tolerant SOI polarization splitter-rotator based on cascaded MMI couplers and an assisted bi-level taper,” Opt. Express 22(23), 27869–27879 (2014).
    [Crossref] [PubMed]
  10. 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]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  15. L. H. Gabrielli, D. Liu, S. G. Johnson, and M. Lipson, “On-chip transformation optics for multimode waveguide bends,” Nat. Commun. 3, 1217 (2012).
    [Crossref] [PubMed]
  16. 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]
  17. Y. Huang, S. Zhu, H. Zhang, T.-Y. Liow, and G.-Q. Lo, “CMOS compatible horizontal nanoplasmonic slot waveguides TE-pass polarizer on silicon-on-insulator platform,” Opt. Express 21(10), 12790–12796 (2013).
    [Crossref] [PubMed]
  18. W. D. Sacher, Y. Huang, L. Ding, T. Barwicz, J. C. Mikkelsen, B. J. F. Taylor, G.-Q. Lo, and J. K. S. Poon, “Polarization rotator-splitters and controllers in a Si3N4-on-SOI integrated photonics platform,” Opt. Express 22(9), 11167–11174 (2014).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2016 (4)

2014 (9)

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

H. Guan, A. Novack, M. Streshinsky, R. Shi, Y. Liu, Q. Fang, A. E. Lim, G. Lo, T. Baehr-Jones, and M. Hochberg, “High-Efficiency Low-Crosstalk 1310-nm Polarization Splitter and Rotator,” IEEE Photonics Technol. Lett. 26(9), 925–928 (2014).
[Crossref]

Z. Su, E. Timurdogan, E. S. Hosseini, J. Sun, G. Leake, D. D. Coolbaugh, and M. R. Watts, “Four-port integrated polarizing beam splitter,” Opt. Lett. 39(4), 965–968 (2014).
[Crossref] [PubMed]

W. D. Sacher, T. Barwicz, B. J. F. Taylor, and J. K. S. Poon, “Polarization rotator-splitters in standard active silicon photonics platforms,” Opt. Express 22(4), 3777–3786 (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]

W. D. Sacher, Y. Huang, L. Ding, T. Barwicz, J. C. Mikkelsen, B. J. F. Taylor, G.-Q. Lo, and J. K. S. Poon, “Polarization rotator-splitters and controllers in a Si3N4-on-SOI integrated photonics platform,” Opt. Express 22(9), 11167–11174 (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]

Y. Huang, J. Song, X. Luo, T.-Y. Liow, and G.-Q. Lo, “CMOS compatible monolithic multi-layer Si3N4− on-SOI platform for low-loss high performance silicon photonics dense integration,” Opt. Express 22(18), 21859–21865 (2014).
[Crossref] [PubMed]

J. Wang, M. Qi, Y. Xuan, H. Huang, Y. Li, M. Li, X. Chen, Q. Jia, Z. Sheng, A. Wu, W. Li, X. Wang, S. Zou, and F. Gan, “Proposal for fabrication-tolerant SOI polarization splitter-rotator based on cascaded MMI couplers and an assisted bi-level taper,” Opt. Express 22(23), 27869–27879 (2014).
[Crossref] [PubMed]

2013 (2)

2012 (3)

L. H. Gabrielli, D. Liu, S. G. Johnson, and M. Lipson, “On-chip transformation optics for multimode waveguide bends,” Nat. Commun. 3, 1217 (2012).
[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]

T. Baehr-Jones, T. Pinguet, P. Lo Guo-Qiang, S. Danziger, D. Prather, and M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6(4), 206–208 (2012).
[Crossref]

2007 (1)

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

Baehr-Jones, T.

H. Guan, A. Novack, M. Streshinsky, R. Shi, Y. Liu, Q. Fang, A. E. Lim, G. Lo, T. Baehr-Jones, and M. Hochberg, “High-Efficiency Low-Crosstalk 1310-nm Polarization Splitter and Rotator,” IEEE Photonics Technol. Lett. 26(9), 925–928 (2014).
[Crossref]

T. Baehr-Jones, T. Pinguet, P. Lo Guo-Qiang, S. Danziger, D. Prather, and M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6(4), 206–208 (2012).
[Crossref]

Barwicz, T.

Bonneau, D.

Chen, G.

Chen, L.

Chen, X.

Coolbaugh, D. D.

Dai, D.

Danziger, S.

T. Baehr-Jones, T. Pinguet, P. Lo Guo-Qiang, S. Danziger, D. Prather, and M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6(4), 206–208 (2012).
[Crossref]

Ding, L.

Ding, W.

Ding, Y.

Fang, Q.

H. Guan, A. Novack, M. Streshinsky, R. Shi, Y. Liu, Q. Fang, A. E. Lim, G. Lo, T. Baehr-Jones, and M. Hochberg, “High-Efficiency Low-Crosstalk 1310-nm Polarization Splitter and Rotator,” IEEE Photonics Technol. Lett. 26(9), 925–928 (2014).
[Crossref]

Feng, R.

Fujiwara, M.

Gabrielli, L. H.

L. H. Gabrielli, D. Liu, S. G. Johnson, and M. Lipson, “On-chip transformation optics for multimode waveguide bends,” Nat. Commun. 3, 1217 (2012).
[Crossref] [PubMed]

Gan, F.

Guan, H.

H. Guan, A. Novack, M. Streshinsky, R. Shi, Y. Liu, Q. Fang, A. E. Lim, G. Lo, T. Baehr-Jones, and M. Hochberg, “High-Efficiency Low-Crosstalk 1310-nm Polarization Splitter and Rotator,” IEEE Photonics Technol. Lett. 26(9), 925–928 (2014).
[Crossref]

Hadfield, R. H.

Hochberg, M.

H. Guan, A. Novack, M. Streshinsky, R. Shi, Y. Liu, Q. Fang, A. E. Lim, G. Lo, T. Baehr-Jones, and M. Hochberg, “High-Efficiency Low-Crosstalk 1310-nm Polarization Splitter and Rotator,” IEEE Photonics Technol. Lett. 26(9), 925–928 (2014).
[Crossref]

T. Baehr-Jones, T. Pinguet, P. Lo Guo-Qiang, S. Danziger, D. Prather, and M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6(4), 206–208 (2012).
[Crossref]

Hosseini, E. S.

Huang, H.

Huang, Y.

Ippen, E. P.

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

Jia, Q.

Johnson, S. G.

L. H. Gabrielli, D. Liu, S. G. Johnson, and M. Lipson, “On-chip transformation optics for multimode waveguide bends,” Nat. Commun. 3, 1217 (2012).
[Crossref] [PubMed]

Kärtner, F. X.

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

Leake, G.

Lee, C.

Li, M.

Li, W.

Li, Y.

Lim, A. E.

H. Guan, A. Novack, M. Streshinsky, R. Shi, Y. Liu, Q. Fang, A. E. Lim, G. Lo, T. Baehr-Jones, and M. Hochberg, “High-Efficiency Low-Crosstalk 1310-nm Polarization Splitter and Rotator,” IEEE Photonics Technol. Lett. 26(9), 925–928 (2014).
[Crossref]

Liow, T.-Y.

Lipson, M.

L. H. Gabrielli, D. Liu, S. G. Johnson, and M. Lipson, “On-chip transformation optics for multimode waveguide bends,” Nat. Commun. 3, 1217 (2012).
[Crossref] [PubMed]

Liu, D.

L. H. Gabrielli, D. Liu, S. G. Johnson, and M. Lipson, “On-chip transformation optics for multimode waveguide bends,” Nat. Commun. 3, 1217 (2012).
[Crossref] [PubMed]

Liu, L.

Liu, Y.

H. Guan, A. Novack, M. Streshinsky, R. Shi, Y. Liu, Q. Fang, A. E. Lim, G. Lo, T. Baehr-Jones, and M. Hochberg, “High-Efficiency Low-Crosstalk 1310-nm Polarization Splitter and Rotator,” IEEE Photonics Technol. Lett. 26(9), 925–928 (2014).
[Crossref]

Lo, G.

H. Guan, A. Novack, M. Streshinsky, R. Shi, Y. Liu, Q. Fang, A. E. Lim, G. Lo, T. Baehr-Jones, and M. Hochberg, “High-Efficiency Low-Crosstalk 1310-nm Polarization Splitter and Rotator,” IEEE Photonics Technol. Lett. 26(9), 925–928 (2014).
[Crossref]

Lo, G.-Q.

Lo Guo-Qiang, P.

T. Baehr-Jones, T. Pinguet, P. Lo Guo-Qiang, S. Danziger, D. Prather, and M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6(4), 206–208 (2012).
[Crossref]

Luo, X.

Miki, S.

Mikkelsen, J. C.

Natarajan, C. M.

Niu, B.

Novack, A.

H. Guan, A. Novack, M. Streshinsky, R. Shi, Y. Liu, Q. Fang, A. E. Lim, G. Lo, T. Baehr-Jones, and M. Hochberg, “High-Efficiency Low-Crosstalk 1310-nm Polarization Splitter and Rotator,” IEEE Photonics Technol. Lett. 26(9), 925–928 (2014).
[Crossref]

O’Brien, J. L.

Ou, H.

Peucheret, C.

Pinguet, T.

T. Baehr-Jones, T. Pinguet, P. Lo Guo-Qiang, S. Danziger, D. Prather, and M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6(4), 206–208 (2012).
[Crossref]

Poon, J. K. S.

Popovic, M. A.

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

Prather, D.

T. Baehr-Jones, T. Pinguet, P. Lo Guo-Qiang, S. Danziger, D. Prather, and M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6(4), 206–208 (2012).
[Crossref]

Qi, M.

Rakich, P. T.

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

Rickman, A.

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

Sacher, W. D.

Santagati, R.

Sasaki, M.

Sheng, Z.

Shi, R.

H. Guan, A. Novack, M. Streshinsky, R. Shi, Y. Liu, Q. Fang, A. E. Lim, G. Lo, T. Baehr-Jones, and M. Hochberg, “High-Efficiency Low-Crosstalk 1310-nm Polarization Splitter and Rotator,” IEEE Photonics Technol. Lett. 26(9), 925–928 (2014).
[Crossref]

Silverstone, J. W.

Smith, H. I.

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

Song, J.

Streshinsky, M.

H. Guan, A. Novack, M. Streshinsky, R. Shi, Y. Liu, Q. Fang, A. E. Lim, G. Lo, T. Baehr-Jones, and M. Hochberg, “High-Efficiency Low-Crosstalk 1310-nm Polarization Splitter and Rotator,” IEEE Photonics Technol. Lett. 26(9), 925–928 (2014).
[Crossref]

Su, Z.

Sun, F.

Sun, J.

Sun, Y.

Tan, K.

Tanner, M. G.

Taylor, B. J. F.

Terai, H.

Thompson, M. G.

Timurdogan, E.

Villa, M.

Wang, J.

Wang, X.

Watts, M. R.

Z. Su, E. Timurdogan, E. S. Hosseini, J. Sun, G. Leake, D. D. Coolbaugh, and M. R. Watts, “Four-port integrated polarizing beam splitter,” Opt. Lett. 39(4), 965–968 (2014).
[Crossref] [PubMed]

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

Wu, A.

Wu, H.

Xiong, Y.

Xuan, Y.

Yamashita, T.

Ye, W. N.

Yu, C.

Zhang, H.

Zhu, S.

Zou, S.

IEEE Photonics Technol. Lett. (1)

H. Guan, A. Novack, M. Streshinsky, R. Shi, Y. Liu, Q. Fang, A. E. Lim, G. Lo, T. Baehr-Jones, and M. Hochberg, “High-Efficiency Low-Crosstalk 1310-nm Polarization Splitter and Rotator,” IEEE Photonics Technol. Lett. 26(9), 925–928 (2014).
[Crossref]

Nat. Commun. (1)

L. H. Gabrielli, D. Liu, S. G. Johnson, and M. Lipson, “On-chip transformation optics for multimode waveguide bends,” Nat. Commun. 3, 1217 (2012).
[Crossref] [PubMed]

Nat. Photonics (3)

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

T. Baehr-Jones, T. Pinguet, P. Lo Guo-Qiang, S. Danziger, D. Prather, and M. Hochberg, “Myths and rumours of silicon photonics,” Nat. Photonics 6(4), 206–208 (2012).
[Crossref]

T. Barwicz, M. R. Watts, M. A. Popović, P. T. Rakich, L. Socci, F. X. Kärtner, 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 (9)

J. Wang, M. Qi, Y. Xuan, H. Huang, Y. Li, M. Li, X. Chen, Q. Jia, Z. Sheng, A. Wu, W. Li, X. Wang, S. Zou, and F. Gan, “Proposal for fabrication-tolerant SOI polarization splitter-rotator based on cascaded MMI couplers and an assisted bi-level taper,” Opt. Express 22(23), 27869–27879 (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]

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]

Y. Huang, S. Zhu, H. Zhang, T.-Y. Liow, and G.-Q. Lo, “CMOS compatible horizontal nanoplasmonic slot waveguides TE-pass polarizer on silicon-on-insulator platform,” Opt. Express 21(10), 12790–12796 (2013).
[Crossref] [PubMed]

W. D. Sacher, Y. Huang, L. Ding, T. Barwicz, J. C. Mikkelsen, B. J. F. Taylor, G.-Q. Lo, and J. K. S. Poon, “Polarization rotator-splitters and controllers in a Si3N4-on-SOI integrated photonics platform,” Opt. Express 22(9), 11167–11174 (2014).
[Crossref] [PubMed]

W. D. Sacher, T. Barwicz, B. J. F. Taylor, and J. K. S. Poon, “Polarization rotator-splitters in standard active silicon photonics platforms,” Opt. Express 22(4), 3777–3786 (2014).
[Crossref] [PubMed]

Y. Huang, J. Song, X. Luo, T.-Y. Liow, and G.-Q. Lo, “CMOS compatible monolithic multi-layer Si3N4− on-SOI platform for low-loss high performance silicon photonics dense integration,” Opt. Express 22(18), 21859–21865 (2014).
[Crossref] [PubMed]

K. Tan, Y. Huang, G.-Q. Lo, C. Lee, and C. Yu, “Compact highly-efficient polarization splitter and rotator based on 90° bends,” Opt. Express 24(13), 14506–14512 (2016).
[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]

Opt. Lett. (4)

Optica (1)

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Figures (7)

Fig. 1
Fig. 1 (a) SEM image of the whole PSR. (b) SEM photo of the bend structure.

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Fig. 2
Fig. 2 Schematic structure of proposed on-chip TE-pass polarizer, which comprises of 364 90° bends cascaded in series. Only the starting part is shown.

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Fig. 3
Fig. 3 Experimental setup for accurate polarization alignment and on-chip PSR measurement.

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Fig. 4
Fig. 4 The transmission efficiency of proposed on-chip TE-pass polarizer as a function of the bend radius.

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Fig. 5
Fig. 5 The mode conversion efficiency as a function of the wavelength in the cross output port (a) and through output port (b). The dashed lines are simulation results, while the solid ones are experimental data. Sim. and Exp. are short for simulation and experiment, respectively. The conversion efficiency below −40 dB is not shown.

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Fig. 6
Fig. 6 The CE as a function of rib width W2 at cross output port (a) and through output port (b). Sim. and Exp. are short for simulation and experiment, respectively. The wavelength is set to be 1310 nm.

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Fig. 7
Fig. 7 The CE as a function of slab width W3 at cross output port (a) and through output port (b). Sim. and Exp. are short for simulation and experiment, respectively. The wavelength is set to be 1310 nm.

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Equations (3)

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PER(dB)=10× log 10 ( T TE T TM ).
{ C E TM−TE Cross (dB)=10× log 10 ( P TM−TE Cross / P TM Input ) C E TE−TE Through (dB)=10× log 10 ( P TE−TE Through / P TE Input ) .
{ E R TM−TE Cross (dB)=10× log 10 ( P TM−TE Cross / P TM−TE Through ) E R TE−TE Through (dB)=10× log 10 ( P TE−TE Through / P TE−TE Cross ) .

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