Abstract

Gears are rotating machines, meshing with each other by teeth to transmit torque. Interestingly, the rotating directions of two meshing gears are opposite, clockwise and counterclockwise. Although this opposite handedness motion has been widely investigated in machinery science, the analogue behavior of light remains undiscovered. Here, we present a simple nanophotonic directional coupler structure which can generate two light beams with opposite handedness of polarization states—optical gears. Due to the abrupt phase shift effect and birefringence effect, the angular momentum (AM) states of photons vary with the propagation distance in two adjacent waveguides of the coupler. Thus, by the choice of coupling length, it is able to obtain two light beams with opposite handedness of polarization, confirming the appearance of optical gears. The full control in the handedness of output beams is achieved via tuning the relative phase between two orthogonal modes at the input port. Optical gears thus offer the possibility of exploring light-matter interactions in nanoscale, opening up new avenues in fields of integrated quantum computing and nanoscale bio-sensing of chiral molecules.

© 2017 Optical Society of America

Full Article  |  PDF Article
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References

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2016 (6)

H. Mühlenbernd, P. Georgi, N. Pholchai, L. Huang, G. Li, S. Zhang, and T. Zentgraf, “Amplitude- and Phase-Controlled Surface Plasmon Polariton Excitation with Metasurfaces,” ACS Photonics 3(1), 124–129 (2016).
[Crossref]

Y. Liang, F. Zhang, J. Gu, X. G. Huang, and S. Liu, “Integratable quarter-wave plates enable one-way angular momentum conversion,” Sci. Rep. 6(1), 24959 (2016).
[Crossref] [PubMed]

H. Liang, L. Zhang, S. Zhang, T. Cao, A. Alù, S. Ruan, and C.-W. Qiu, “Gate-Programmable Electro-Optical Addressing Array of Graphene-Coated Nanowires with Sub-10 nm Resolution,” ACS Photonics 3(10), 1847–1853 (2016).
[Crossref]

S. Mei, K. Huang, H. Liu, F. Qin, M. Q. Mehmood, Z. Xu, M. Hong, D. Zhang, J. Teng, A. Danner, and C.-W. Qiu, “On-chip discrimination of orbital angular momentum of light with plasmonic nanoslits,” Nanoscale 8(4), 2227–2233 (2016).
[Crossref] [PubMed]

F. Setzpfandt, A. S. Solntsev, J. Titchener, C. W. Wu, C. L. Xiong, R. Schiek, T. Pertsch, D. N. Neshev, and A. A. Sukhorukov, “Tunable generation of entangled photons in a nonlinear directional coupler,” Laser Photonics Rev. 10(1), 131–136 (2016).
[Crossref]

S. Wu, P. Qu, J. Liu, D. Lei, K. Zhang, S. Zhao, and Y. Zhu, “Giant circular dichroism and its reversal in solid and inverse plasmonic gammadion-shaped structures,” Opt. Express 24(24), 27763–27770 (2016).
[Crossref] [PubMed]

2015 (4)

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin–orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

C.-L. Wu, Y.-H. Lin, S.-P. Su, B.-J. Huang, C.-T. Tsai, H.-Y. Wang, Y.-C. Chi, C.-I. Wu, and G.-R. Lin, “Enhancing Optical Nonlinearity in a Nonstoichiometric SiN Waveguide for Cross-Wavelength All-Optical Data Processing,” ACS Photonics 2(8), 1141–1154 (2015).
[Crossref]

A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9(12), 789–795 (2015).
[Crossref]

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Optics. Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

2014 (7)

Y. Liang, H. W. Wu, B. J. Huang, and X. G. Huang, “Light beams with selective angular momentum generated by hybrid plasmonic waveguides,” Nanoscale 6(21), 12360–12365 (2014).
[Crossref] [PubMed]

J. S. Fakonas, H. Lee, Y. A. Kelaita, and H. A. Atwater, “Two-plasmon quantum interference,” Nat. Photonics 8(4), 317–320 (2014).
[Crossref]

E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
[Crossref]

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

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

T. Chen and S. He, “Frequency-tunable circular polarization beam splitter using a graphene-dielectric sub-wavelength film,” Opt. Express 22(16), 19748–19757 (2014).
[Crossref] [PubMed]

2013 (5)

M. Z. Alam, J. N. Caspers, J. S. Aitchison, and M. Mojahedi, “Compact low loss and broadband hybrid plasmonic directional coupler,” Opt. Express 21(13), 16029–16034 (2013).
[Crossref] [PubMed]

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [PubMed]

M. D. Turner, M. Saba, Q. M. Zhang, B. P. Cumming, G. E. Schroder-Turk, and M. Gu, “Miniature chiral beamsplitter based on gyroid photonic crystals,” Nat. Photonics 7(10), 801–805 (2013).
[Crossref]

Q. Tan, X. Huang, W. Zhou, and K. Yang, “A plasmonic based ultracompact polarization beam splitter on silicon-on-insulator waveguides,” Sci. Rep. 3(1), 2206 (2013).
[Crossref] [PubMed]

F. Ye, M. J. Burns, and M. J. Naughton, “Plasmonic halos--optical surface plasmon drumhead modes,” Nano Lett. 13(2), 519–523 (2013).
[Crossref] [PubMed]

2012 (1)

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[Crossref] [PubMed]

2011 (3)

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13(6), 064001 (2011).
[Crossref]

C. L. Zou, F. W. Sun, C. H. Dong, X. F. Ren, J. M. Cui, X. D. Chen, Z. F. Han, and G. C. Guo, “Broadband integrated polarization beam splitter with surface plasmon,” Opt. Lett. 36(18), 3630–3632 (2011).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

2010 (1)

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

2008 (2)

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).
[Crossref]

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[Crossref] [PubMed]

2006 (1)

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

2002 (1)

M. Bennett, M. F. Schatz, H. Rockwood, and K. Wiesenfeld, “Huygens’s clocks,” Proc. R. Soc. Lond. A 458(2019), 563–579 (2002).
[Crossref]

2001 (1)

1995 (1)

A. Yacoby, M. Heiblum, D. Mahalu, and H. Shtrikman, “Coherence and Phase Sensitive Measurements in a Quantum Dot,” Phys. Rev. Lett. 74(20), 4047–4050 (1995).
[Crossref] [PubMed]

1978 (1)

R. C. Alferness and R. V. Schmidt, “Tunable optical waveguide directional coupler filter,” Appl. Phys. Lett. 33(2), 161–163 (1978).
[Crossref]

1973 (1)

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9(9), 919–933 (1973).
[Crossref]

1935 (1)

H. Mueller, “Theory of the Photoelastic Effect of Cubic Crystals,” Phys. Rev. 47(12), 947–957 (1935).
[Crossref]

Aiello, A.

A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9(12), 789–795 (2015).
[Crossref]

Aieta, F.

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Aitchison, J. S.

Alam, M. Z.

Alferness, R. C.

R. C. Alferness and R. V. Schmidt, “Tunable optical waveguide directional coupler filter,” Appl. Phys. Lett. 33(2), 161–163 (1978).
[Crossref]

Allen, L.

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).
[Crossref]

Alù, A.

H. Liang, L. Zhang, S. Zhang, T. Cao, A. Alù, S. Ruan, and C.-W. Qiu, “Gate-Programmable Electro-Optical Addressing Array of Graphene-Coated Nanowires with Sub-10 nm Resolution,” ACS Photonics 3(10), 1847–1853 (2016).
[Crossref]

Andersen, K. N.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Atwater, H. A.

J. S. Fakonas, H. Lee, Y. A. Kelaita, and H. A. Atwater, “Two-plasmon quantum interference,” Nat. Photonics 8(4), 317–320 (2014).
[Crossref]

Banzer, P.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Optics. Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9(12), 789–795 (2015).
[Crossref]

Bauer, T.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Optics. Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

Bennett, M.

M. Bennett, M. F. Schatz, H. Rockwood, and K. Wiesenfeld, “Huygens’s clocks,” Proc. R. Soc. Lond. A 458(2019), 563–579 (2002).
[Crossref]

Bjarklev, A.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Bliokh, K. Y.

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin–orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

Borel, P. I.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Boyd, R. W.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Optics. Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
[Crossref]

Brongersma, M. L.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

Burns, M. J.

F. Ye, M. J. Burns, and M. J. Naughton, “Plasmonic halos--optical surface plasmon drumhead modes,” Nano Lett. 13(2), 519–523 (2013).
[Crossref] [PubMed]

Cao, T.

H. Liang, L. Zhang, S. Zhang, T. Cao, A. Alù, S. Ruan, and C.-W. Qiu, “Gate-Programmable Electro-Optical Addressing Array of Graphene-Coated Nanowires with Sub-10 nm Resolution,” ACS Photonics 3(10), 1847–1853 (2016).
[Crossref]

Capasso, F.

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Caspers, J. N.

Chen, T.

Chen, X. D.

Chi, Y.-C.

C.-L. Wu, Y.-H. Lin, S.-P. Su, B.-J. Huang, C.-T. Tsai, H.-Y. Wang, Y.-C. Chi, C.-I. Wu, and G.-R. Lin, “Enhancing Optical Nonlinearity in a Nonstoichiometric SiN Waveguide for Cross-Wavelength All-Optical Data Processing,” ACS Photonics 2(8), 1141–1154 (2015).
[Crossref]

Christodoulides, D. N.

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Cumming, B. P.

M. D. Turner, M. Saba, Q. M. Zhang, B. P. Cumming, G. E. Schroder-Turk, and M. Gu, “Miniature chiral beamsplitter based on gyroid photonic crystals,” Nat. Photonics 7(10), 801–805 (2013).
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E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
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El-Ganainy, R.

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J. S. Fakonas, H. Lee, Y. A. Kelaita, and H. A. Atwater, “Two-plasmon quantum interference,” Nat. Photonics 8(4), 317–320 (2014).
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D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
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R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
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S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).
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N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
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N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
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N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
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N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
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H. Mühlenbernd, P. Georgi, N. Pholchai, L. Huang, G. Li, S. Zhang, and T. Zentgraf, “Amplitude- and Phase-Controlled Surface Plasmon Polariton Excitation with Metasurfaces,” ACS Photonics 3(1), 124–129 (2016).
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Y. Liang, F. Zhang, J. Gu, X. G. Huang, and S. Liu, “Integratable quarter-wave plates enable one-way angular momentum conversion,” Sci. Rep. 6(1), 24959 (2016).
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M. D. Turner, M. Saba, Q. M. Zhang, B. P. Cumming, G. E. Schroder-Turk, and M. Gu, “Miniature chiral beamsplitter based on gyroid photonic crystals,” Nat. Photonics 7(10), 801–805 (2013).
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Han, Z. F.

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R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
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D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
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Heiblum, M.

A. Yacoby, M. Heiblum, D. Mahalu, and H. Shtrikman, “Coherence and Phase Sensitive Measurements in a Quantum Dot,” Phys. Rev. Lett. 74(20), 4047–4050 (1995).
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Y. Liang, H. W. Wu, B. J. Huang, and X. G. Huang, “Light beams with selective angular momentum generated by hybrid plasmonic waveguides,” Nanoscale 6(21), 12360–12365 (2014).
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C.-L. Wu, Y.-H. Lin, S.-P. Su, B.-J. Huang, C.-T. Tsai, H.-Y. Wang, Y.-C. Chi, C.-I. Wu, and G.-R. Lin, “Enhancing Optical Nonlinearity in a Nonstoichiometric SiN Waveguide for Cross-Wavelength All-Optical Data Processing,” ACS Photonics 2(8), 1141–1154 (2015).
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S. Mei, K. Huang, H. Liu, F. Qin, M. Q. Mehmood, Z. Xu, M. Hong, D. Zhang, J. Teng, A. Danner, and C.-W. Qiu, “On-chip discrimination of orbital angular momentum of light with plasmonic nanoslits,” Nanoscale 8(4), 2227–2233 (2016).
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H. Mühlenbernd, P. Georgi, N. Pholchai, L. Huang, G. Li, S. Zhang, and T. Zentgraf, “Amplitude- and Phase-Controlled Surface Plasmon Polariton Excitation with Metasurfaces,” ACS Photonics 3(1), 124–129 (2016).
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Q. Tan, X. Huang, W. Zhou, and K. Yang, “A plasmonic based ultracompact polarization beam splitter on silicon-on-insulator waveguides,” Sci. Rep. 3(1), 2206 (2013).
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Y. Liang, F. Zhang, J. Gu, X. G. Huang, and S. Liu, “Integratable quarter-wave plates enable one-way angular momentum conversion,” Sci. Rep. 6(1), 24959 (2016).
[Crossref] [PubMed]

Y. Liang, H. W. Wu, B. J. Huang, and X. G. Huang, “Light beams with selective angular momentum generated by hybrid plasmonic waveguides,” Nanoscale 6(21), 12360–12365 (2014).
[Crossref] [PubMed]

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R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

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T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Optics. Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
[Crossref]

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13(6), 064001 (2011).
[Crossref]

Kats, M. A.

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Kelaita, Y. A.

J. S. Fakonas, H. Lee, Y. A. Kelaita, and H. A. Atwater, “Two-plasmon quantum interference,” Nat. Photonics 8(4), 317–320 (2014).
[Crossref]

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

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C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

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R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

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Lavrinenko, A. V.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
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Lee, H.

J. S. Fakonas, H. Lee, Y. A. Kelaita, and H. A. Atwater, “Two-plasmon quantum interference,” Nat. Photonics 8(4), 317–320 (2014).
[Crossref]

Lei, D.

Leuchs, G.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Optics. Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9(12), 789–795 (2015).
[Crossref]

Li, G.

H. Mühlenbernd, P. Georgi, N. Pholchai, L. Huang, G. Li, S. Zhang, and T. Zentgraf, “Amplitude- and Phase-Controlled Surface Plasmon Polariton Excitation with Metasurfaces,” ACS Photonics 3(1), 124–129 (2016).
[Crossref]

Liang, H.

H. Liang, L. Zhang, S. Zhang, T. Cao, A. Alù, S. Ruan, and C.-W. Qiu, “Gate-Programmable Electro-Optical Addressing Array of Graphene-Coated Nanowires with Sub-10 nm Resolution,” ACS Photonics 3(10), 1847–1853 (2016).
[Crossref]

Liang, Y.

Y. Liang, F. Zhang, J. Gu, X. G. Huang, and S. Liu, “Integratable quarter-wave plates enable one-way angular momentum conversion,” Sci. Rep. 6(1), 24959 (2016).
[Crossref] [PubMed]

Y. Liang, H. W. Wu, B. J. Huang, and X. G. Huang, “Light beams with selective angular momentum generated by hybrid plasmonic waveguides,” Nanoscale 6(21), 12360–12365 (2014).
[Crossref] [PubMed]

Lin, D.

D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
[Crossref] [PubMed]

Lin, G.-R.

C.-L. Wu, Y.-H. Lin, S.-P. Su, B.-J. Huang, C.-T. Tsai, H.-Y. Wang, Y.-C. Chi, C.-I. Wu, and G.-R. Lin, “Enhancing Optical Nonlinearity in a Nonstoichiometric SiN Waveguide for Cross-Wavelength All-Optical Data Processing,” ACS Photonics 2(8), 1141–1154 (2015).
[Crossref]

Lin, Y.-H.

C.-L. Wu, Y.-H. Lin, S.-P. Su, B.-J. Huang, C.-T. Tsai, H.-Y. Wang, Y.-C. Chi, C.-I. Wu, and G.-R. Lin, “Enhancing Optical Nonlinearity in a Nonstoichiometric SiN Waveguide for Cross-Wavelength All-Optical Data Processing,” ACS Photonics 2(8), 1141–1154 (2015).
[Crossref]

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S. Mei, K. Huang, H. Liu, F. Qin, M. Q. Mehmood, Z. Xu, M. Hong, D. Zhang, J. Teng, A. Danner, and C.-W. Qiu, “On-chip discrimination of orbital angular momentum of light with plasmonic nanoslits,” Nanoscale 8(4), 2227–2233 (2016).
[Crossref] [PubMed]

Liu, J.

Liu, S.

Y. Liang, F. Zhang, J. Gu, X. G. Huang, and S. Liu, “Integratable quarter-wave plates enable one-way angular momentum conversion,” Sci. Rep. 6(1), 24959 (2016).
[Crossref] [PubMed]

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A. Yacoby, M. Heiblum, D. Mahalu, and H. Shtrikman, “Coherence and Phase Sensitive Measurements in a Quantum Dot,” Phys. Rev. Lett. 74(20), 4047–4050 (1995).
[Crossref] [PubMed]

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C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

Marrucci, L.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Optics. Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13(6), 064001 (2011).
[Crossref]

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S. Mei, K. Huang, H. Liu, F. Qin, M. Q. Mehmood, Z. Xu, M. Hong, D. Zhang, J. Teng, A. Danner, and C.-W. Qiu, “On-chip discrimination of orbital angular momentum of light with plasmonic nanoslits,” Nanoscale 8(4), 2227–2233 (2016).
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S. Mei, K. Huang, H. Liu, F. Qin, M. Q. Mehmood, Z. Xu, M. Hong, D. Zhang, J. Teng, A. Danner, and C.-W. Qiu, “On-chip discrimination of orbital angular momentum of light with plasmonic nanoslits,” Nanoscale 8(4), 2227–2233 (2016).
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Moulin, G.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
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H. Mühlenbernd, P. Georgi, N. Pholchai, L. Huang, G. Li, S. Zhang, and T. Zentgraf, “Amplitude- and Phase-Controlled Surface Plasmon Polariton Excitation with Metasurfaces,” ACS Photonics 3(1), 124–129 (2016).
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Nagali, E.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13(6), 064001 (2011).
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Neugebauer, M.

A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9(12), 789–795 (2015).
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Nori, F.

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin–orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
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A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
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Orlov, S.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Optics. Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
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R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
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S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).
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F. Setzpfandt, A. S. Solntsev, J. Titchener, C. W. Wu, C. L. Xiong, R. Schiek, T. Pertsch, D. N. Neshev, and A. A. Sukhorukov, “Tunable generation of entangled photons in a nonlinear directional coupler,” Laser Photonics Rev. 10(1), 131–136 (2016).
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R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
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H. Mühlenbernd, P. Georgi, N. Pholchai, L. Huang, G. Li, S. Zhang, and T. Zentgraf, “Amplitude- and Phase-Controlled Surface Plasmon Polariton Excitation with Metasurfaces,” ACS Photonics 3(1), 124–129 (2016).
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L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13(6), 064001 (2011).
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A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
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E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
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S. Mei, K. Huang, H. Liu, F. Qin, M. Q. Mehmood, Z. Xu, M. Hong, D. Zhang, J. Teng, A. Danner, and C.-W. Qiu, “On-chip discrimination of orbital angular momentum of light with plasmonic nanoslits,” Nanoscale 8(4), 2227–2233 (2016).
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Qiu, C.-W.

H. Liang, L. Zhang, S. Zhang, T. Cao, A. Alù, S. Ruan, and C.-W. Qiu, “Gate-Programmable Electro-Optical Addressing Array of Graphene-Coated Nanowires with Sub-10 nm Resolution,” ACS Photonics 3(10), 1847–1853 (2016).
[Crossref]

S. Mei, K. Huang, H. Liu, F. Qin, M. Q. Mehmood, Z. Xu, M. Hong, D. Zhang, J. Teng, A. Danner, and C.-W. Qiu, “On-chip discrimination of orbital angular momentum of light with plasmonic nanoslits,” Nanoscale 8(4), 2227–2233 (2016).
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Rarity, J. G.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
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K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin–orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
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Ruan, S.

H. Liang, L. Zhang, S. Zhang, T. Cao, A. Alù, S. Ruan, and C.-W. Qiu, “Gate-Programmable Electro-Optical Addressing Array of Graphene-Coated Nanowires with Sub-10 nm Resolution,” ACS Photonics 3(10), 1847–1853 (2016).
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Rubano, A.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Optics. Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
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Rüter, C. E.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

Saba, M.

M. D. Turner, M. Saba, Q. M. Zhang, B. P. Cumming, G. E. Schroder-Turk, and M. Gu, “Miniature chiral beamsplitter based on gyroid photonic crystals,” Nat. Photonics 7(10), 801–805 (2013).
[Crossref]

Santamato, E.

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Optics. Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13(6), 064001 (2011).
[Crossref]

Schatz, M. F.

M. Bennett, M. F. Schatz, H. Rockwood, and K. Wiesenfeld, “Huygens’s clocks,” Proc. R. Soc. Lond. A 458(2019), 563–579 (2002).
[Crossref]

Schiek, R.

F. Setzpfandt, A. S. Solntsev, J. Titchener, C. W. Wu, C. L. Xiong, R. Schiek, T. Pertsch, D. N. Neshev, and A. A. Sukhorukov, “Tunable generation of entangled photons in a nonlinear directional coupler,” Laser Photonics Rev. 10(1), 131–136 (2016).
[Crossref]

Schmidt, R. V.

R. C. Alferness and R. V. Schmidt, “Tunable optical waveguide directional coupler filter,” Appl. Phys. Lett. 33(2), 161–163 (1978).
[Crossref]

Schroder-Turk, G. E.

M. D. Turner, M. Saba, Q. M. Zhang, B. P. Cumming, G. E. Schroder-Turk, and M. Gu, “Miniature chiral beamsplitter based on gyroid photonic crystals,” Nat. Photonics 7(10), 801–805 (2013).
[Crossref]

Schulz, S. A.

E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
[Crossref]

Sciarrino, F.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13(6), 064001 (2011).
[Crossref]

Segev, M.

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

Setzpfandt, F.

F. Setzpfandt, A. S. Solntsev, J. Titchener, C. W. Wu, C. L. Xiong, R. Schiek, T. Pertsch, D. N. Neshev, and A. A. Sukhorukov, “Tunable generation of entangled photons in a nonlinear directional coupler,” Laser Photonics Rev. 10(1), 131–136 (2016).
[Crossref]

Shtrikman, H.

A. Yacoby, M. Heiblum, D. Mahalu, and H. Shtrikman, “Coherence and Phase Sensitive Measurements in a Quantum Dot,” Phys. Rev. Lett. 74(20), 4047–4050 (1995).
[Crossref] [PubMed]

Slussarenko, S.

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13(6), 064001 (2011).
[Crossref]

Solntsev, A. S.

F. Setzpfandt, A. S. Solntsev, J. Titchener, C. W. Wu, C. L. Xiong, R. Schiek, T. Pertsch, D. N. Neshev, and A. A. Sukhorukov, “Tunable generation of entangled photons in a nonlinear directional coupler,” Laser Photonics Rev. 10(1), 131–136 (2016).
[Crossref]

Su, S.-P.

C.-L. Wu, Y.-H. Lin, S.-P. Su, B.-J. Huang, C.-T. Tsai, H.-Y. Wang, Y.-C. Chi, C.-I. Wu, and G.-R. Lin, “Enhancing Optical Nonlinearity in a Nonstoichiometric SiN Waveguide for Cross-Wavelength All-Optical Data Processing,” ACS Photonics 2(8), 1141–1154 (2015).
[Crossref]

Sukhorukov, A. A.

F. Setzpfandt, A. S. Solntsev, J. Titchener, C. W. Wu, C. L. Xiong, R. Schiek, T. Pertsch, D. N. Neshev, and A. A. Sukhorukov, “Tunable generation of entangled photons in a nonlinear directional coupler,” Laser Photonics Rev. 10(1), 131–136 (2016).
[Crossref]

Sun, F. W.

Tan, Q.

Q. Tan, X. Huang, W. Zhou, and K. Yang, “A plasmonic based ultracompact polarization beam splitter on silicon-on-insulator waveguides,” Sci. Rep. 3(1), 2206 (2013).
[Crossref] [PubMed]

Teng, J.

S. Mei, K. Huang, H. Liu, F. Qin, M. Q. Mehmood, Z. Xu, M. Hong, D. Zhang, J. Teng, A. Danner, and C.-W. Qiu, “On-chip discrimination of orbital angular momentum of light with plasmonic nanoslits,” Nanoscale 8(4), 2227–2233 (2016).
[Crossref] [PubMed]

Tetienne, J. P.

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Titchener, J.

F. Setzpfandt, A. S. Solntsev, J. Titchener, C. W. Wu, C. L. Xiong, R. Schiek, T. Pertsch, D. N. Neshev, and A. A. Sukhorukov, “Tunable generation of entangled photons in a nonlinear directional coupler,” Laser Photonics Rev. 10(1), 131–136 (2016).
[Crossref]

Tsai, C.-T.

C.-L. Wu, Y.-H. Lin, S.-P. Su, B.-J. Huang, C.-T. Tsai, H.-Y. Wang, Y.-C. Chi, C.-I. Wu, and G.-R. Lin, “Enhancing Optical Nonlinearity in a Nonstoichiometric SiN Waveguide for Cross-Wavelength All-Optical Data Processing,” ACS Photonics 2(8), 1141–1154 (2015).
[Crossref]

Turner, M. D.

M. D. Turner, M. Saba, Q. M. Zhang, B. P. Cumming, G. E. Schroder-Turk, and M. Gu, “Miniature chiral beamsplitter based on gyroid photonic crystals,” Nat. Photonics 7(10), 801–805 (2013).
[Crossref]

Upham, J.

E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
[Crossref]

Wang, H.-Y.

C.-L. Wu, Y.-H. Lin, S.-P. Su, B.-J. Huang, C.-T. Tsai, H.-Y. Wang, Y.-C. Chi, C.-I. Wu, and G.-R. Lin, “Enhancing Optical Nonlinearity in a Nonstoichiometric SiN Waveguide for Cross-Wavelength All-Optical Data Processing,” ACS Photonics 2(8), 1141–1154 (2015).
[Crossref]

Wang, Y.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [PubMed]

Y. Wang, C.-K. Lee, and J. Kuang, “Phase jump in an optical directional coupler,” J. Opt. Soc. Am. B 18(11), 1554 (2001).
[Crossref]

Wiesenfeld, K.

M. Bennett, M. F. Schatz, H. Rockwood, and K. Wiesenfeld, “Huygens’s clocks,” Proc. R. Soc. Lond. A 458(2019), 563–579 (2002).
[Crossref]

Wu, C. W.

F. Setzpfandt, A. S. Solntsev, J. Titchener, C. W. Wu, C. L. Xiong, R. Schiek, T. Pertsch, D. N. Neshev, and A. A. Sukhorukov, “Tunable generation of entangled photons in a nonlinear directional coupler,” Laser Photonics Rev. 10(1), 131–136 (2016).
[Crossref]

Wu, C.-I.

C.-L. Wu, Y.-H. Lin, S.-P. Su, B.-J. Huang, C.-T. Tsai, H.-Y. Wang, Y.-C. Chi, C.-I. Wu, and G.-R. Lin, “Enhancing Optical Nonlinearity in a Nonstoichiometric SiN Waveguide for Cross-Wavelength All-Optical Data Processing,” ACS Photonics 2(8), 1141–1154 (2015).
[Crossref]

Wu, C.-L.

C.-L. Wu, Y.-H. Lin, S.-P. Su, B.-J. Huang, C.-T. Tsai, H.-Y. Wang, Y.-C. Chi, C.-I. Wu, and G.-R. Lin, “Enhancing Optical Nonlinearity in a Nonstoichiometric SiN Waveguide for Cross-Wavelength All-Optical Data Processing,” ACS Photonics 2(8), 1141–1154 (2015).
[Crossref]

Wu, H. W.

Y. Liang, H. W. Wu, B. J. Huang, and X. G. Huang, “Light beams with selective angular momentum generated by hybrid plasmonic waveguides,” Nanoscale 6(21), 12360–12365 (2014).
[Crossref] [PubMed]

Wu, S.

Xiong, C. L.

F. Setzpfandt, A. S. Solntsev, J. Titchener, C. W. Wu, C. L. Xiong, R. Schiek, T. Pertsch, D. N. Neshev, and A. A. Sukhorukov, “Tunable generation of entangled photons in a nonlinear directional coupler,” Laser Photonics Rev. 10(1), 131–136 (2016).
[Crossref]

Xu, Z.

S. Mei, K. Huang, H. Liu, F. Qin, M. Q. Mehmood, Z. Xu, M. Hong, D. Zhang, J. Teng, A. Danner, and C.-W. Qiu, “On-chip discrimination of orbital angular momentum of light with plasmonic nanoslits,” Nanoscale 8(4), 2227–2233 (2016).
[Crossref] [PubMed]

Yacoby, A.

A. Yacoby, M. Heiblum, D. Mahalu, and H. Shtrikman, “Coherence and Phase Sensitive Measurements in a Quantum Dot,” Phys. Rev. Lett. 74(20), 4047–4050 (1995).
[Crossref] [PubMed]

Yang, K.

Q. Tan, X. Huang, W. Zhou, and K. Yang, “A plasmonic based ultracompact polarization beam splitter on silicon-on-insulator waveguides,” Sci. Rep. 3(1), 2206 (2013).
[Crossref] [PubMed]

Yariv, A.

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9(9), 919–933 (1973).
[Crossref]

Ye, F.

F. Ye, M. J. Burns, and M. J. Naughton, “Plasmonic halos--optical surface plasmon drumhead modes,” Nano Lett. 13(2), 519–523 (2013).
[Crossref] [PubMed]

Ye, Z.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [PubMed]

Yin, X.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [PubMed]

Yu, N.

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

Yu, S.

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
[Crossref] [PubMed]

Zayats, A. V.

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin–orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

Zentgraf, T.

H. Mühlenbernd, P. Georgi, N. Pholchai, L. Huang, G. Li, S. Zhang, and T. Zentgraf, “Amplitude- and Phase-Controlled Surface Plasmon Polariton Excitation with Metasurfaces,” ACS Photonics 3(1), 124–129 (2016).
[Crossref]

Zhang, D.

S. Mei, K. Huang, H. Liu, F. Qin, M. Q. Mehmood, Z. Xu, M. Hong, D. Zhang, J. Teng, A. Danner, and C.-W. Qiu, “On-chip discrimination of orbital angular momentum of light with plasmonic nanoslits,” Nanoscale 8(4), 2227–2233 (2016).
[Crossref] [PubMed]

Zhang, F.

Y. Liang, F. Zhang, J. Gu, X. G. Huang, and S. Liu, “Integratable quarter-wave plates enable one-way angular momentum conversion,” Sci. Rep. 6(1), 24959 (2016).
[Crossref] [PubMed]

Zhang, K.

Zhang, L.

H. Liang, L. Zhang, S. Zhang, T. Cao, A. Alù, S. Ruan, and C.-W. Qiu, “Gate-Programmable Electro-Optical Addressing Array of Graphene-Coated Nanowires with Sub-10 nm Resolution,” ACS Photonics 3(10), 1847–1853 (2016).
[Crossref]

Zhang, Q. M.

M. D. Turner, M. Saba, Q. M. Zhang, B. P. Cumming, G. E. Schroder-Turk, and M. Gu, “Miniature chiral beamsplitter based on gyroid photonic crystals,” Nat. Photonics 7(10), 801–805 (2013).
[Crossref]

Zhang, S.

H. Liang, L. Zhang, S. Zhang, T. Cao, A. Alù, S. Ruan, and C.-W. Qiu, “Gate-Programmable Electro-Optical Addressing Array of Graphene-Coated Nanowires with Sub-10 nm Resolution,” ACS Photonics 3(10), 1847–1853 (2016).
[Crossref]

H. Mühlenbernd, P. Georgi, N. Pholchai, L. Huang, G. Li, S. Zhang, and T. Zentgraf, “Amplitude- and Phase-Controlled Surface Plasmon Polariton Excitation with Metasurfaces,” ACS Photonics 3(1), 124–129 (2016).
[Crossref]

Zhang, X.

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [PubMed]

Zhao, S.

Zhou, W.

Q. Tan, X. Huang, W. Zhou, and K. Yang, “A plasmonic based ultracompact polarization beam splitter on silicon-on-insulator waveguides,” Sci. Rep. 3(1), 2206 (2013).
[Crossref] [PubMed]

Zhu, Y.

Zou, C. L.

Zsigri, B.

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

ACS Photonics (3)

H. Mühlenbernd, P. Georgi, N. Pholchai, L. Huang, G. Li, S. Zhang, and T. Zentgraf, “Amplitude- and Phase-Controlled Surface Plasmon Polariton Excitation with Metasurfaces,” ACS Photonics 3(1), 124–129 (2016).
[Crossref]

C.-L. Wu, Y.-H. Lin, S.-P. Su, B.-J. Huang, C.-T. Tsai, H.-Y. Wang, Y.-C. Chi, C.-I. Wu, and G.-R. Lin, “Enhancing Optical Nonlinearity in a Nonstoichiometric SiN Waveguide for Cross-Wavelength All-Optical Data Processing,” ACS Photonics 2(8), 1141–1154 (2015).
[Crossref]

H. Liang, L. Zhang, S. Zhang, T. Cao, A. Alù, S. Ruan, and C.-W. Qiu, “Gate-Programmable Electro-Optical Addressing Array of Graphene-Coated Nanowires with Sub-10 nm Resolution,” ACS Photonics 3(10), 1847–1853 (2016).
[Crossref]

Appl. Phys. Lett. (1)

R. C. Alferness and R. V. Schmidt, “Tunable optical waveguide directional coupler filter,” Appl. Phys. Lett. 33(2), 161–163 (1978).
[Crossref]

IEEE J. Quantum Electron. (1)

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9(9), 919–933 (1973).
[Crossref]

J. Opt. (1)

L. Marrucci, E. Karimi, S. Slussarenko, B. Piccirillo, E. Santamato, E. Nagali, and F. Sciarrino, “Spin-to-orbital conversion of the angular momentum of light and its classical and quantum applications,” J. Opt. 13(6), 064001 (2011).
[Crossref]

J. Opt. Soc. Am. B (1)

Laser Photonics Rev. (2)

S. Franke-Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photonics Rev. 2(4), 299–313 (2008).
[Crossref]

F. Setzpfandt, A. S. Solntsev, J. Titchener, C. W. Wu, C. L. Xiong, R. Schiek, T. Pertsch, D. N. Neshev, and A. A. Sukhorukov, “Tunable generation of entangled photons in a nonlinear directional coupler,” Laser Photonics Rev. 10(1), 131–136 (2016).
[Crossref]

Light Sci. Appl. (1)

E. Karimi, S. A. Schulz, I. De Leon, H. Qassim, J. Upham, and R. W. Boyd, “Generating optical orbital angular momentum at visible wavelengths using a plasmonic metasurface,” Light Sci. Appl. 3(5), e167 (2014).
[Crossref]

Nano Lett. (2)

N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broadband, background-free quarter-wave plate based on plasmonic metasurfaces,” Nano Lett. 12(12), 6328–6333 (2012).
[Crossref] [PubMed]

F. Ye, M. J. Burns, and M. J. Naughton, “Plasmonic halos--optical surface plasmon drumhead modes,” Nano Lett. 13(2), 519–523 (2013).
[Crossref] [PubMed]

Nanoscale (2)

S. Mei, K. Huang, H. Liu, F. Qin, M. Q. Mehmood, Z. Xu, M. Hong, D. Zhang, J. Teng, A. Danner, and C.-W. Qiu, “On-chip discrimination of orbital angular momentum of light with plasmonic nanoslits,” Nanoscale 8(4), 2227–2233 (2016).
[Crossref] [PubMed]

Y. Liang, H. W. Wu, B. J. Huang, and X. G. Huang, “Light beams with selective angular momentum generated by hybrid plasmonic waveguides,” Nanoscale 6(21), 12360–12365 (2014).
[Crossref] [PubMed]

Nat. Commun. (1)

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

Nat. Mater. (1)

N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13(2), 139–150 (2014).
[Crossref] [PubMed]

Nat. Photonics (4)

J. S. Fakonas, H. Lee, Y. A. Kelaita, and H. A. Atwater, “Two-plasmon quantum interference,” Nat. Photonics 8(4), 317–320 (2014).
[Crossref]

M. D. Turner, M. Saba, Q. M. Zhang, B. P. Cumming, G. E. Schroder-Turk, and M. Gu, “Miniature chiral beamsplitter based on gyroid photonic crystals,” Nat. Photonics 7(10), 801–805 (2013).
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A. Aiello, P. Banzer, M. Neugebauer, and G. Leuchs, “From transverse angular momentum to photonic wheels,” Nat. Photonics 9(12), 789–795 (2015).
[Crossref]

K. Y. Bliokh, F. J. Rodríguez-Fortuño, F. Nori, and A. V. Zayats, “Spin–orbit interactions of light,” Nat. Photonics 9(12), 796–808 (2015).
[Crossref]

Nat. Phys. (1)

C. E. Rüter, K. G. Makris, R. El-Ganainy, D. N. Christodoulides, M. Segev, and D. Kip, “Observation of parity–time symmetry in optics,” Nat. Phys. 6(3), 192–195 (2010).
[Crossref]

Nature (1)

R. S. Jacobsen, K. N. Andersen, P. I. Borel, J. Fage-Pedersen, L. H. Frandsen, O. Hansen, M. Kristensen, A. V. Lavrinenko, G. Moulin, H. Ou, C. Peucheret, B. Zsigri, and A. Bjarklev, “Strained silicon as a new electro-optic material,” Nature 441(7090), 199–202 (2006).
[Crossref] [PubMed]

Opt. Express (3)

Opt. Lett. (1)

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H. Mueller, “Theory of the Photoelastic Effect of Cubic Crystals,” Phys. Rev. 47(12), 947–957 (1935).
[Crossref]

Phys. Rev. Lett. (1)

A. Yacoby, M. Heiblum, D. Mahalu, and H. Shtrikman, “Coherence and Phase Sensitive Measurements in a Quantum Dot,” Phys. Rev. Lett. 74(20), 4047–4050 (1995).
[Crossref] [PubMed]

Proc. R. Soc. Lond. A (1)

M. Bennett, M. F. Schatz, H. Rockwood, and K. Wiesenfeld, “Huygens’s clocks,” Proc. R. Soc. Lond. A 458(2019), 563–579 (2002).
[Crossref]

Sci. Rep. (2)

Y. Liang, F. Zhang, J. Gu, X. G. Huang, and S. Liu, “Integratable quarter-wave plates enable one-way angular momentum conversion,” Sci. Rep. 6(1), 24959 (2016).
[Crossref] [PubMed]

Q. Tan, X. Huang, W. Zhou, and K. Yang, “A plasmonic based ultracompact polarization beam splitter on silicon-on-insulator waveguides,” Sci. Rep. 3(1), 2206 (2013).
[Crossref] [PubMed]

Science (5)

T. Bauer, P. Banzer, E. Karimi, S. Orlov, A. Rubano, L. Marrucci, E. Santamato, R. W. Boyd, and G. Leuchs, “Optics. Observation of optical polarization Möbius strips,” Science 347(6225), 964–966 (2015).
[Crossref] [PubMed]

N. Yu, P. Genevet, M. A. Kats, F. Aieta, J. P. Tetienne, F. Capasso, and Z. Gaburro, “Light propagation with phase discontinuities: generalized laws of reflection and refraction,” Science 334(6054), 333–337 (2011).
[Crossref] [PubMed]

X. Yin, Z. Ye, J. Rho, Y. Wang, and X. Zhang, “Photonic spin Hall effect at metasurfaces,” Science 339(6126), 1405–1407 (2013).
[Crossref] [PubMed]

A. Politi, M. J. Cryan, J. G. Rarity, S. Yu, and J. L. O’Brien, “Silica-on-silicon waveguide quantum circuits,” Science 320(5876), 646–649 (2008).
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D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345(6194), 298–302 (2014).
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M. Born and E. Wolf, Principles of optics: electromagnetic theory of propagation, interference and diffraction of light (CUP Archive, 2000).

K. Okamoto, Fundamentals of optical waveguides (Academic: San Diego, 2006).

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Figures (6)

Fig. 1
Fig. 1 (a) The abrupt phase shift found in classical and quantum systems. (b) A π phase lag observed in the reflection of an interface between glass and air. (c) Schematic of the proposed structure with geometric details. The optical analogue of two meshing gears: the output beams have the opposite handedness of polarization states. The coordinate system used.
Fig. 2
Fig. 2 Schematic of the abrupt phase shift introduced in the coupling process. The complex amplitudes at the beginning position for each period (top). The relative phase evolution for each period, which is shown on a complex plane, and which includes the π phase shift information (bottom).
Fig. 3
Fig. 3 Amplitude and phase profiles for (a) a quasi-TM mode, and (b) a right handed quasi-circularly polarized mode, and their decomposed components (|Ex/y/z| and φx/y/z). The operating wavelength is 1.55 μm. The plots show the polarization states at the central points of 1-9 areas (shown with color arrows, and they projection in xy-plane are shown in black). The Si waveguide is surrounded by SiO2, which is not shown for clarity. (c) mode distributions of the even and odd modes for the TE- and -TM polarized modes in the coupling region. (d) Theoretical (lines) and stimulated (symbols) dependences of the phase on the propagation distance (z). Inserted figure shows mode distributions of the dominant components at the yz-plane (cross the WGs centers) for the quasi-TE and -TM polarized modes. (e) Theoretical (lines) and stimulated (symbols) dependences of the abrupt phase shift and power (|E|2) on z in WG1.
Fig. 4
Fig. 4 The theoretical results. The powers dependence on the propagation distance (z) for the quasi-TE and -TM polarized modes in (a) WG1 and (b) WG2. The relative phase between the quasi-TE and -TM polarized modes, respectively in (c) WG1 and (d) WG2. (e) the z-dependence of Δ ϕ ˜ 1 (z)Δ ϕ ˜ 2 (z) . (f) The relative phase between the quasi-TE and -TM polarized modes at the longitudinal positions z e (m) , where P 1,2_TE [ z e (m)]= P 1,2_TM [ z e (m)] in WG1 and WG2.
Fig. 5
Fig. 5 Evolution of polarization at waveguides central points along the propagation length (z) of the coupler. The left side shows the theoretical prediction while the right side shows the simulated electric field distribution at the corresponding cross sections
Fig. 6
Fig. 6 (a) The dependence of relative phase Δ ϕ 1/2 [ z e (4) ] of output modes on the initial relative phase Δ ϕ 0 . (b) Simulation results. The field distributions (|E| and |Ez|) and central points polarization of output modes at z e (4) are shown for different values of Δ ϕ 0 . The (c) gap and (d) wavelength dependence of z e (4) . Also plotted are the dependences of effective indices of the TE and TM modes (odd and even modes in the coupling region) on the gap and wavelength.

Equations (13)

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{ d a 1 (z) dz =i β 1 a 1 (z)+κ a 2 (z) d a 2 (z) dz =i β 2 a 2 (z)+κ a 1 (z) ,
[ a 1 (z) a 2 (z) ]=[ cos(κz) jsin(κz) jsin(κz) cos(κz) ][ a 1 (0) e i β 1 z a 2 (0) e i β 2 z ],
{ a 1 (z)=cos(κz) e i β 1 z a 2 (z)=jsin(κz) e i β 2 z .
{ a 1 (z)=cos(κzn z c ) e i( β 1 z+n π 2 ) a 2 (z)=sin(κzn z c ) e i[ β 2 z+(n+1) π 2 ] n=0, 2, 4 , { a 1 (z)=sin(κzn z c ) e i[ β 1 z+(n+1) π 2 ] a 2 (z)=cos(κzn z c ) e i( β 2 z+n π 2 ) n=1, 3, 5
ϕ 1 (z)= β ¯ z+π[ floor( z 2 z c + 1 2 ) ]+ ϕ 1 (0) (z>0),
ϕ 2 (z)= π 2 + β ¯ z+π[ floor( z 2 z c ) ]+ ϕ 1 (0) (z>0).
{ P 1 ( z ) = co s 2 ( κz ) P 2 ( z ) = si n 2 ( κz ) ,
ϕ 1A (z)= ϕ 1 (z) β ¯ z ϕ 1 (0) (z>0),
Δ ϕ 1/2 (z)= ϕ 1/2_TM (z) ϕ 1/2_TE (z).
Δ ϕ ˜ 1/2 (z)=mod[ ϕ 1/2_TM (z) ϕ 1/2_TE (z),2π ],
cos 2 ( κ TM z e )= cos 2 ( κ TE z e ).
z e (m)={ mπ κ TM + κ TE mπ κ TM κ TE m = 0,1,2,3...,
| Δ ϕ ˜ 1 [ z e ( m )]Δ ϕ ˜ 2 [ z e ( m )] |=π.

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