Abstract

Chiral light–matter interaction is currently revolutionizing the fundamental research on light and its applications. This interaction has traditionally faced the challenges of low directionality and efficiency based on the spin–orbit interaction of light in microscopic waveguides. It is important to exploit photonic integrated circuits to efficiently engineer photonic chiral behavior. In this paper, we propose and demonstrate ultra-directional high-efficiency chiral coupling in silicon photonic circuits based on low-to-high-order mode conversion and interference. We show that the directionality of chiral coupling can, in principle, approach ±1 with circular polarization inputs by benefiting from the underlying mechanism of complete destructive and constructive interference. The efficiency of chiral coupling can exceed 70%, with negligible scattering to unguided modes, and this is considerably higher than the efficiency of conventional coupling mechanisms. Moreover, chiral silicon photonic circuits can function as perfect 3 dB power splitters for arbitrarily linear polarization inputs. These offer the possibility of on-chip chirality determination and management using photonic integrated circuits for flourishing development in chiral optics.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2018 (4)

G. Li, A. S. Sheremet, R. Ge, T. C. H. Liew, and A. V. Kavokin, “Design for a nanoscale single-photon spin splitter for modes with orbital angular momentum,” Phys. Rev. Lett. 121, 053901 (2018).
[Crossref]

S. Gong, F. Alpeggiani, B. Sciacca, E. C. Garnett, and L. Kuipers, “Nanoscale chiral valley-photon interface through optical spin-orbit coupling,” Science 359, 443–447 (2018).
[Crossref]

J. Wang and Y. Long, “On-chip silicon photonic signaling and processing: a review,” Sci. Bull. 63, 1267–1310 (2018).

J. Wang, “Metasurfaces enabling structured light manipulation: advances and perspectives [Invited],” Chin. Opt. Lett. 16, 050006 (2018).

2017 (4)

L. Fang and J. Wang, “Intrinsic transverse spin angular momentum of fiber eigenmodes,” Phys. Rev. A 95, 053827 (2017).
[Crossref]

S. Xiao, J. Wang, F. Liu, S. Zhang, X. Yin, and J. Li, “Spin-dependent optics with metasurfaces,” Nanophotonics 6, 215–234 (2017).
[Crossref]

P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541, 473–480 (2017).
[Crossref]

X. Ling, X. Zhou, K. Huang, Y. Liu, C. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80, 066401 (2017).
[Crossref]

2016 (3)

M. Scheucher, A. Hilico, E. Will, J. Volz, and A. Rauschenbeute, “Quantum optical circulator controlled by a single chirally coupled atom,” Science 354, 1577–1580 (2016).
[Crossref]

R. J. Coles, D. M. Price, J. E. Dixon, B. Royall, E. Clarke, P. Kok, M. S. Skolnick, A. M. Fox, and M. N. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7, 11183 (2016).
[Crossref]

M. Khorasaninejad, W. T. Chen, A. Y. Zhu, J. Oh, R. C. Devlin, D. Rousso, and F. Capasso, “Multispectral chiral imaging with a metalens,” Nano Lett. 16, 4595–4600 (2016).
[Crossref]

2015 (6)

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9, 796–808 (2015).
[Crossref]

B. L. Feber, N. Rotenberg, and L. Kuipers, “Nanophotonic control of circular dipole emission,” Nat. Commun. 6, 6695 (2015).
[Crossref]

K. Y. Bliokh, D. Smirnova, and F. Nori, “Quantum spin Hall effect of light,” Science 348, 1448–1451 (2015).
[Crossref]

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9, 789–795 (2015).
[Crossref]

A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse spin and momentum in two-wave interference,” Phys. Rev. X 5, 011039 (2015).
[Crossref]

2014 (6)

F. J. Rodríguez-Fortuño, D. Puerto, A. Griol, L. Bellieres, J. Martí, and A. Martínez, “Sorting linearly polarized photons with a single scatterer,” Opt. Lett. 39, 1394–1397 (2014).
[Crossref]

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5, 3300 (2014).
[Crossref]

F. J. Rodríguez-Fortuño, I. Barber-Sanz, D. Puerto, A. Griol, and A. Martínez, “Resolving light handedness with an on-chip silicon microdisk,” ACS Photon. 1, 762–767 (2014).
[Crossref]

M. Khorasaninejad and K. B. Crozier, “Silicon nanofin grating as a miniature chirality-distinguishing beam-splitter,” Nat. Commun. 5, 5386 (2014).
[Crossref]

J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346, 67–71 (2014).
[Crossref]

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, “All-optical routing of single photons by a one-atom switch controlled by a single photon,” Science 345, 903–906 (2014).
[Crossref]

2013 (4)

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339, 1405–1407 (2013).
[Crossref]

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340, 328–330 (2013).
[Crossref]

D. Dai, L. Liu, S. Gao, D. Xu, and S. He, “Polarization management for silicon photonic integrated circuits,” Laser Photon. Rev. 7, 303–328 (2013).
[Crossref]

J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
[Crossref]

2012 (1)

K. F. Mak, K. He, J. Shan, and T. F. Heinz, “Control of valley polarization in monolayer MoS2 by optical helicity,” Nat. Nanotechnol. 7, 494–498 (2012).
[Crossref]

2011 (1)

2010 (1)

2008 (2)

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2, 748–753 (2008).
[Crossref]

O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319, 787–790 (2008).
[Crossref]

2007 (1)

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
[Crossref]

2001 (2)

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[Crossref]

H. Wei, J. Yu, and X. Zhang, “Compact 3-dB tapered multimode interference coupler in silicon-on-insulator,” Opt. Lett. 26, 878–880 (2001).
[Crossref]

Aiello, A.

A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9, 789–795 (2015).
[Crossref]

Alpeggiani, F.

S. Gong, F. Alpeggiani, B. Sciacca, E. C. Garnett, and L. Kuipers, “Nanoscale chiral valley-photon interface through optical spin-orbit coupling,” Science 359, 443–447 (2018).
[Crossref]

Antoniou, N.

J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
[Crossref]

Banzer, P.

A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9, 789–795 (2015).
[Crossref]

Barber-Sanz, I.

F. J. Rodríguez-Fortuño, I. Barber-Sanz, D. Puerto, A. Griol, and A. Martínez, “Resolving light handedness with an on-chip silicon microdisk,” ACS Photon. 1, 762–767 (2014).
[Crossref]

Bechler, O.

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, “All-optical routing of single photons by a one-atom switch controlled by a single photon,” Science 345, 903–906 (2014).
[Crossref]

Bekshaev, A. Y.

A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse spin and momentum in two-wave interference,” Phys. Rev. X 5, 011039 (2015).
[Crossref]

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5, 3300 (2014).
[Crossref]

Bellieres, L.

Bliokh, K. Y.

A. Y. Bekshaev, K. Y. Bliokh, and F. Nori, “Transverse spin and momentum in two-wave interference,” Phys. Rev. X 5, 011039 (2015).
[Crossref]

K. Y. Bliokh, D. Smirnova, and F. Nori, “Quantum spin Hall effect of light,” Science 348, 1448–1451 (2015).
[Crossref]

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin-orbit interactions of light,” Nat. Photonics 9, 796–808 (2015).
[Crossref]

K. Y. Bliokh, A. Y. Bekshaev, and F. Nori, “Extraordinary momentum and spin in evanescent waves,” Nat. Commun. 5, 3300 (2014).
[Crossref]

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2, 748–753 (2008).
[Crossref]

Bowers, J. E.

Capasso, F.

M. Khorasaninejad, W. T. Chen, A. Y. Zhu, J. Oh, R. C. Devlin, D. Rousso, and F. Capasso, “Multispectral chiral imaging with a metalens,” Nano Lett. 16, 4595–4600 (2016).
[Crossref]

J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
[Crossref]

Chen, R. T.

Chen, W. T.

M. Khorasaninejad, W. T. Chen, A. Y. Zhu, J. Oh, R. C. Devlin, D. Rousso, and F. Capasso, “Multispectral chiral imaging with a metalens,” Nano Lett. 16, 4595–4600 (2016).
[Crossref]

Clarke, E.

R. J. Coles, D. M. Price, J. E. Dixon, B. Royall, E. Clarke, P. Kok, M. S. Skolnick, A. M. Fox, and M. N. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7, 11183 (2016).
[Crossref]

Coles, R. J.

R. J. Coles, D. M. Price, J. E. Dixon, B. Royall, E. Clarke, P. Kok, M. S. Skolnick, A. M. Fox, and M. N. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7, 11183 (2016).
[Crossref]

Crozier, K. B.

M. Khorasaninejad and K. B. Crozier, “Silicon nanofin grating as a miniature chirality-distinguishing beam-splitter,” Nat. Commun. 5, 5386 (2014).
[Crossref]

Dai, D.

D. Dai, L. Liu, S. Gao, D. Xu, and S. He, “Polarization management for silicon photonic integrated circuits,” Laser Photon. Rev. 7, 303–328 (2013).
[Crossref]

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

Dayan, B.

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, “All-optical routing of single photons by a one-atom switch controlled by a single photon,” Science 345, 903–906 (2014).
[Crossref]

Devlin, R. C.

M. Khorasaninejad, W. T. Chen, A. Y. Zhu, J. Oh, R. C. Devlin, D. Rousso, and F. Capasso, “Multispectral chiral imaging with a metalens,” Nano Lett. 16, 4595–4600 (2016).
[Crossref]

Dixon, J. E.

R. J. Coles, D. M. Price, J. E. Dixon, B. Royall, E. Clarke, P. Kok, M. S. Skolnick, A. M. Fox, and M. N. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7, 11183 (2016).
[Crossref]

El-Ella, H.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

Fang, L.

L. Fang and J. Wang, “Intrinsic transverse spin angular momentum of fiber eigenmodes,” Phys. Rev. A 95, 053827 (2017).
[Crossref]

Feber, B. L.

B. L. Feber, N. Rotenberg, and L. Kuipers, “Nanophotonic control of circular dipole emission,” Nat. Commun. 6, 6695 (2015).
[Crossref]

Fleischhauer, A.

D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
[Crossref]

Fox, A. M.

R. J. Coles, D. M. Price, J. E. Dixon, B. Royall, E. Clarke, P. Kok, M. S. Skolnick, A. M. Fox, and M. N. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7, 11183 (2016).
[Crossref]

Gao, S.

D. Dai, L. Liu, S. Gao, D. Xu, and S. He, “Polarization management for silicon photonic integrated circuits,” Laser Photon. Rev. 7, 303–328 (2013).
[Crossref]

Garnett, E. C.

S. Gong, F. Alpeggiani, B. Sciacca, E. C. Garnett, and L. Kuipers, “Nanoscale chiral valley-photon interface through optical spin-orbit coupling,” Science 359, 443–447 (2018).
[Crossref]

Ge, R.

G. Li, A. S. Sheremet, R. Ge, T. C. H. Liew, and A. V. Kavokin, “Design for a nanoscale single-photon spin splitter for modes with orbital angular momentum,” Phys. Rev. Lett. 121, 053901 (2018).
[Crossref]

Ginzburg, P.

F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340, 328–330 (2013).
[Crossref]

Gong, S.

S. Gong, F. Alpeggiani, B. Sciacca, E. C. Garnett, and L. Kuipers, “Nanoscale chiral valley-photon interface through optical spin-orbit coupling,” Science 359, 443–447 (2018).
[Crossref]

Griol, A.

F. J. Rodríguez-Fortuño, I. Barber-Sanz, D. Puerto, A. Griol, and A. Martínez, “Resolving light handedness with an on-chip silicon microdisk,” ACS Photon. 1, 762–767 (2014).
[Crossref]

F. J. Rodríguez-Fortuño, D. Puerto, A. Griol, L. Bellieres, J. Martí, and A. Martínez, “Sorting linearly polarized photons with a single scatterer,” Opt. Lett. 39, 1394–1397 (2014).
[Crossref]

Guendelman, G.

I. Shomroni, S. Rosenblum, Y. Lovsky, O. Bechler, G. Guendelman, and B. Dayan, “All-optical routing of single photons by a one-atom switch controlled by a single photon,” Science 345, 903–906 (2014).
[Crossref]

Hansen, S. L.

I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
[Crossref]

Hansteen, F.

C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto, A. Itoh, and T. Rasing, “All-optical magnetic recording with circularly polarized light,” Phys. Rev. Lett. 99, 047601 (2007).
[Crossref]

Hasman, E.

K. Y. Bliokh, A. Niv, V. Kleiner, and E. Hasman, “Geometrodynamics of spinning light,” Nat. Photonics 2, 748–753 (2008).
[Crossref]

He, K.

K. F. Mak, K. He, J. Shan, and T. F. Heinz, “Control of valley polarization in monolayer MoS2 by optical helicity,” Nat. Nanotechnol. 7, 494–498 (2012).
[Crossref]

He, S.

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M. Khorasaninejad, W. T. Chen, A. Y. Zhu, J. Oh, R. C. Devlin, D. Rousso, and F. Capasso, “Multispectral chiral imaging with a metalens,” Nano Lett. 16, 4595–4600 (2016).
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J. Petersen, J. Volz, and A. Rauschenbeutel, “Chiral nanophotonic waveguide interface based on spin-orbit interaction of light,” Science 346, 67–71 (2014).
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M. Khorasaninejad, W. T. Chen, A. Y. Zhu, J. Oh, R. C. Devlin, D. Rousso, and F. Capasso, “Multispectral chiral imaging with a metalens,” Nano Lett. 16, 4595–4600 (2016).
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M. Scheucher, A. Hilico, E. Will, J. Volz, and A. Rauschenbeute, “Quantum optical circulator controlled by a single chirally coupled atom,” Science 354, 1577–1580 (2016).
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P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541, 473–480 (2017).
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S. Gong, F. Alpeggiani, B. Sciacca, E. C. Garnett, and L. Kuipers, “Nanoscale chiral valley-photon interface through optical spin-orbit coupling,” Science 359, 443–447 (2018).
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G. Li, A. S. Sheremet, R. Ge, T. C. H. Liew, and A. V. Kavokin, “Design for a nanoscale single-photon spin splitter for modes with orbital angular momentum,” Phys. Rev. Lett. 121, 053901 (2018).
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R. J. Coles, D. M. Price, J. E. Dixon, B. Royall, E. Clarke, P. Kok, M. S. Skolnick, A. M. Fox, and M. N. Makhonin, “Chirality of nanophotonic waveguide with embedded quantum emitter for unidirectional spin transfer,” Nat. Commun. 7, 11183 (2016).
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K. Y. Bliokh, D. Smirnova, and F. Nori, “Quantum spin Hall effect of light,” Science 348, 1448–1451 (2015).
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I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
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I. Söllner, S. Mahmoodian, S. L. Hansen, L. Midolo, A. Javadi, G. Kiršanskė, T. Pregnolato, H. El-Ella, E. H. Lee, J. D. Song, S. Stobbe, and P. Lodahl, “Deterministic photon-emitter coupling in chiral photonic circuits,” Nat. Nanotechnol. 10, 775–778 (2015).
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P. Lodahl, S. Mahmoodian, S. Stobbe, A. Rauschenbeutel, P. Schneeweiss, J. Volz, H. Pichler, and P. Zoller, “Chiral quantum optics,” Nature 541, 473–480 (2017).
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M. Scheucher, A. Hilico, E. Will, J. Volz, and A. Rauschenbeute, “Quantum optical circulator controlled by a single chirally coupled atom,” Science 354, 1577–1580 (2016).
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D. F. Phillips, A. Fleischhauer, A. Mair, R. L. Walsworth, and M. D. Lukin, “Storage of light in atomic vapor,” Phys. Rev. Lett. 86, 783–786 (2001).
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J. Lin, J. P. B. Mueller, Q. Wang, G. Yuan, N. Antoniou, X. Yuan, and F. Capasso, “Polarization-controlled tunable directional coupling of surface plasmon polaritons,” Science 340, 331–334 (2013).
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X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339, 1405–1407 (2013).
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Wen, S.

X. Ling, X. Zhou, K. Huang, Y. Liu, C. Qiu, H. Luo, and S. Wen, “Recent advances in the spin Hall effect of light,” Rep. Prog. Phys. 80, 066401 (2017).
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M. Scheucher, A. Hilico, E. Will, J. Volz, and A. Rauschenbeute, “Quantum optical circulator controlled by a single chirally coupled atom,” Science 354, 1577–1580 (2016).
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F. J. Rodríguez-Fortuño, G. Marino, P. Ginzburg, D. O’Connor, A. Martínez, G. A. Wurtz, and A. V. Zayats, “Near-field interference for the unidirectional excitation of electromagnetic guided modes,” Science 340, 328–330 (2013).
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D. Dai, L. Liu, S. Gao, D. Xu, and S. He, “Polarization management for silicon photonic integrated circuits,” Laser Photon. Rev. 7, 303–328 (2013).
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X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339, 1405–1407 (2013).
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Supplementary Material (1)

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Figures (5)

Fig. 1.
Fig. 1. Principle and design of chiral silicon photonic circuits. (a) Schematic illustration of chiral effect of light–matter interactions. The polarization handedness of incident light determines the chiral behavior of light–matter interactions. (b) 3D view of chiral silicon photonic circuits (polymer-assisted inversely tapered Y -branch silicon waveguide) for chiral coupling based on low-to-high-order mode conversion and interference. (c) Calculated effective refractive index versus the silicon waveguide width. In the adiabatic inverse taper structure with the waveguide width varying from 600 to 840 nm, the TE 0 mode remains unchanged, while the TM 0 mode evolves into the TE 1 mode due to mode hybridization.
Fig. 2.
Fig. 2. Results of numerical simulation. (a) Transverse mode pattern evolution at six positions [1, 2, 3, 4, 5, 6 in Fig. 1(b)] along the waveguide for both the x - and y -polarization component inputs. (b)–(d) Simulation results of chiral coupling in silicon photonic circuits when the incident polarization handedness is (b) RCP, (c) LCP, and (d) LP, respectively.
Fig. 3.
Fig. 3. Experimental setup and results for measurements of chiral coupling outputs. (a) Experimental schematic diagram with an inset of an optical microscope image. Pol, polarizer; HWP, half-wave plate; QWP, quarter-wave plate; OL, objective lens; L, lens. (b)–(k) Measured spin-dependent output from chiral silicon photonic circuits under different incident polarization handedness values with helicity (b), (g)  σ = 1 , (c), (h)  σ = 0.5 , (d), (i)  σ = 0, (e), (j)  σ = 0.5, and (f), (k)  σ = 1, respectively, at two wavelengths [ λ 1 : (b)–(f), λ 2 : (g)–(k)] with opposite directionality.
Fig. 4.
Fig. 4. Measured directionality of chiral coupling under different incident polarization handedness at two wavelengths ( λ 1 , λ 2 ) with opposite directionality. The top of the figure shows the incident polarization handedness that varies with rotation angle of the QWP. The measured results in the experiment (balls) are in good agreement with the predicated values by theory (dashed lines).
Fig. 5.
Fig. 5. Measured and simulated performance of chiral coupling in silicon photonic circuits versus wavelength. (a), (b), (d), (e) Normalized power from (a), (d) up and (b), (e) down output ports of the Y -branch waveguide. (c), (f) Directionality of chiral coupling in silicon photonic circuits. (a)–(c) LCP ( σ 1 ) incident light. (d)–(f), RCP ( σ + 1 ) incident light. Solid lines, experiment. Dashed lines, theory.

Equations (7)

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E = A [ e x + m · exp ( i δ ) · e y ] exp [ i ( k z ω t ) ] ,
σ = 2 · Im ( E x · E y * ) | E x | 2 + | E y | 2 = 2 m · sin δ 1 + m 2 .
I u = ξ + m 2 · ψ + 2 m · ζ · cos ( Δ β · z δ ) .
I d = ξ + m 2 · ψ 2 m · ζ · cos ( Δ β · z δ ) .
D = I u I d I u + I d = 2 m · ζ · cos ( Δ β · z δ ) ξ + m 2 · ψ .
D 2 m · sin δ 1 + m 2 = σ ,
[ cos α sin α ] = 1 2 ( cos α i sin α ) [ 1 i ] + 1 2 ( cos α + i sin α ) [    1 i ] .