Abstract

While metasurfaces are now widely considered in free-space optics, their potential for coupling and tailoring guided waves is not fully explored. Here we transfer the Jones matrix method to target versatile on-chip coupling using metasurface-patterned photonic waveguides around the telecommunication wavelength of 1.55 μm, which can accommodate both propagation and Pancharatnam-Berry phase metasurfaces for guided waves. One can either encode two arbitrary and independent phase profiles to any pair of orthogonal polarizations or deploy complete control over both the phase and polarization of coupled modes. A set of design scenarios synergizing silicon nanoantennas and low-loss silicon-nitride waveguides are proposed, including directional couplers with mode-selectivity and polarization splitters with directionality ranging from 10 to 20 dB. Furthermore, our optimization method can be further extended to cover multiple working wavelengths. Exemplary on-chip color routers are also numerically demonstrated. This chip-integrated metasurface platform further translates the concept of a metasurface into photonic integrated circuits, serving as a positive paradigm for versatile and complete control over waveguide optical signals and motivating chip-scale applications such as polarization/wavelength demultiplexers, optical switches, and multifunctional mode converters.

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

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2018 (15)

G. Kovacevic, C. Phare, S. Y. Set, M. Lipson, and S. Yamashita, “Ultra-high-speed graphene optical modulator design based on tight field confinement in a slot waveguide,” Appl. Phys. Express 11, 065102 (2018).
[Crossref]

J. T. Kim and H. Choi, “Polarization control in graphene-based polymer waveguide polarizer,” Laser Photon. Rev. 12, 1800142 (2018).
[Crossref]

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mancinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenlowe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

P. Xie, Q. Sun, L. Wang, Y. Wen, X. Wang, G. Wang, C. Zeng, M. Liu, Z. Ge, and Z. Lu, “Impact of two-photon absorption and free-carrier effects on time lens based on four-wave mixing in silicon waveguides,” Appl. Phys. Express 11, 082204 (2018).
[Crossref]

B. Yao, S.-W. Huang, Y. Liu, A. K. Vinod, C. Choi, M. Hoff, Y. Li, M. Yu, Z. Feng, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Gate-tunable frequency combs in graphene-nitride microresonators,” Nature 558, 410–414 (2018).
[Crossref] [PubMed]

K. Y. Yang, D. Y. Oh, S. H. Lee, Q.-F. Yang, X. Yi, B. Shen, H. Wang, and K. Vahala, “Bridging ultrahigh-q devices and photonic circuits,” Nat. Photonics 12, 297–302 (2018).
[Crossref]

S. Molesky, Z. Lin, A. Y. Piggott, W. Jin, J. Vuckovic, and A. W. Rodriguez, “Inverse design in nanophotonics,” Nat. Photonics 12, 659–670 (2018).
[Crossref]

Y. Meng, F. Hu, Y. Shen, Y. Yang, Q. Xiao, X. Fu, and M. Gong, “Ultracompact graphene-assisted tunable waveguide couplers with high directivity and mode selectivity,” Sci. Rep. 8, 13362 (2018).
[Crossref]

Y. Guo, M. Pu, X. Li, X. Ma, S. Song, Z. Zhao, and X. Luo, “Chip-integrated geometric metasurface as a novel platform for directional coupling and polarization sorting by spin-orbit interaction,” IEEE J. Sel. Top. Quantum Electron. 24, 4700107 (2018).
[Crossref]

W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
[Crossref] [PubMed]

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref] [PubMed]

H. Zhang, X. Zhang, Q. Xu, Q. Wang, Y. Xu, M. Wei, Y. Li, J. Gu, Z. Tian, C. Ouyang, X. Zhang, C. Hu, J. Han, and W. Zhang, “Polarization-independent all-silicon dielectric metasurfaces in the terahertz regime,” Photonics Res. 6, 24–29 (2018).
[Crossref]

Y. Meng, S. Ye, Y. Shen, Q. Xiao, X. Fu, R. Lu, Y. Liu, and M. Gong, “Waveguide engineering of graphene optoelectronics – modulators and polarizers,” IEEE Photonics J. 10, 6600217 (2018).
[Crossref]

J. Shim, S.-H. Bae, W. Kong, D. Lee, K. Qiao, D. Nezich, Y. J. Park, R. Zhao, S. Sundaram, X. Li, H. Yeon, C. Choi, H. Kum, R. Yue, G. Zhou, Y. Ou, K. Lee, J. Moodera, X. Zhao, J.-H. Ahn, C. Hinkle, A. Ougazzaden, and J. Kim, “Controlled crack propagation for atomic precision handling of wafer-scale two-dimensional materials,” Science 362, 665–670 (2018).
[Crossref] [PubMed]

X. Piao, S. Yu, and N. Park, “Design of transverse spinning of light with globally unique handedness,” Phys. Rev. Lett. 120, 203901 (2018).
[Crossref] [PubMed]

2017 (10)

D. L. Sounas and A. Alu, “Non-reciprocal photonics based on time modulation,” Nat. Photonics 11, 774–783 (2017).
[Crossref]

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).
[Crossref]

J. P. B. Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: Independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118, 113901 (2017).
[Crossref]

R. Guo, M. Decker, F. Setzpfandt, X. Gai, D.-Y. Choi, R. Kiselev, A. Chipouline, I. Staude, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “High-bit rate ultra-compact light routing with mode-selective on-chip nanoantennas,” Sci. Adv. 3, e1700007 (2017).
[Crossref] [PubMed]

M. Khorasaninejad and F. Capasso, “Metalenses: Versatile multifunctional photonic components,” Science 358, 1146 (2017).
[Crossref]

P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4, 139–152 (2017).
[Crossref]

Z. Li, M.-H. Kim, C. Wang, Z. Han, S. Shrestha, A. C. Overvig, M. Lu, A. Stein, A. M. Agarwal, M. Loncar, and N. Yu, “Controlling propagation and coupling of waveguide modes using phase-gradient metasurfaces,” Nat. Nanotechnol. 12, 675–683 (2017).
[Crossref] [PubMed]

C. Wang, Z. Li, M.-H. Kim, X. Xiong, X.-F. Ren, G.-C. Guo, N. Yu, and M. Loncar, “Metasurface-assisted phase-matching-free second harmonic generation in lithium niobate waveguides,” Nat. Commun. 8, 2098 (2017).
[Crossref] [PubMed]

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, “Arbitrary spin-to-orbital angular momentum conversion of light,” Science 358, 896–901 (2017).
[Crossref] [PubMed]

A. Rahim, E. Ryckeboer, A. Z. Subramanian, S. Clemmen, B. Kuyken, A. Dhakal, A. Raza, A. Hermans, M. Muneeb, S. Dhoore, Y. Li, U. Dave, P. Bienstman, N. L. Thomas, G. Roelkens, D. V. Thourhout, P. Helin, S. Severi, X. Rottenberg, and R. Baets, “Expanding the silicon photonics portfolio with silicon nitride photonic integrated circuits,” J. Lightwave Technol. 35, 639–649 (2017).
[Crossref]

2015 (7)

F. Najafi, J. Mower, N. C. Harris, F. Bellei, A. Dane, C. Lee, X. Hu, P. Kharel, F. Marsili, S. Assefa, K. K. Berggren, and D. Englund, “On-chip detection of non-classical light by scalable integration of single-photon detectors,” Nat. Commun. 6, 5873 (2015).
[Crossref] [PubMed]

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1, e1500396 (2015).
[Crossref] [PubMed]

G. Zheng, H. Muhlenbernd, M. Kenney, G. Li, T. Zentgraf, and S. Zhang, “Metasurface holograms reaching 80% efficiency,” Nat. Nanotechnol. 10, 308–312 (2015).
[Crossref] [PubMed]

R. Guo, M. Decker, F. Setzpfandt, I. Staude, D. N. Neshev, and Y. S. Kivshar, “Plasmonic fano nanoantennas for on-chip separation of wavelength-encoded optical signals,” Nano Lett. 15, 3324–3328 (2015).
[Crossref] [PubMed]

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–943 (2015).
[Crossref] [PubMed]

G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. HanWong, E. Y. B. Pun, K. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14, 607–612 (2015).
[Crossref] [PubMed]

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

2014 (4)

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

R. Guo, M. Decker, I. Staude, D. N. Neshev, and Y. S. Kivshar, “Bidirectional waveguide coupling with plasmonic fano nanoantennas,” Appl. Phys. Lett. 105, 053114 (2014).
[Crossref]

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alu, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343, 160–163 (2014).
[Crossref] [PubMed]

Y.-D. Yang, Y. Li, Y.-Z. Huang, and A. W. Poon, “Silicon nitride three-mode division multiplexing and wavelength-division multiplexing using asymmetrical directional couplers and microring resonators,” Opt. Express 22, 22172–22183 (2014).
[Crossref] [PubMed]

2013 (3)

N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: Controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New cmos-compatible platforms based on silicon nitride and hydex for nonlinear optics,” Nat. Photonics 7, 597–607 (2013).
[Crossref]

P. T. Lin, V. Singh, H.-Y. G. Lin, T. Tiwald, L. C. Kimerling, and A. M. Agarwal, “Low-stress silicon nitride platform for mid-infrared broadband and monolithically integrated microphotonics,” Adv. Opt. Mater. 1, 732–739 (2013).
[Crossref]

2012 (3)

Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6, 3677–3694 (2012).
[Crossref] [PubMed]

S. Sun, Q. He, S. Xiao, Q. Xu, X. Li, and L. Zhou, “Gradient-index meta-surfaces as a bridge linking propagating waves and surface waves,” Nat. Mater. 11, 426–431 (2012).
[Crossref] [PubMed]

M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U. S. A. 109, 12364–12368 (2012).
[Crossref]

2011 (2)

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, 333–337 (2011).
[Crossref] [PubMed]

T. Shegai, S. Chen, V. D. Miljkovic, G. Zengin, P. Johansson, and M. Kall, “A bimetallic nanoantenna for directional colour routing,” Nat. Commun. 2, 481 (2011).
[Crossref] [PubMed]

2010 (2)

R. Soref, “Mid-infrared photonics in silicon and germanium,” Nat. Photonics 4, 495–497 (2010).
[Crossref]

B. Wu, A. Kumar, and S. Pamarthy, “High aspect ratio silicon etch: A review,” J. Appl. Phys. 108, 051101 (2010).
[Crossref]

2002 (1)

Acin, A.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mancinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenlowe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

Agarwal, A. M.

Z. Li, M.-H. Kim, C. Wang, Z. Han, S. Shrestha, A. C. Overvig, M. Lu, A. Stein, A. M. Agarwal, M. Loncar, and N. Yu, “Controlling propagation and coupling of waveguide modes using phase-gradient metasurfaces,” Nat. Nanotechnol. 12, 675–683 (2017).
[Crossref] [PubMed]

P. T. Lin, V. Singh, H.-Y. G. Lin, T. Tiwald, L. C. Kimerling, and A. M. Agarwal, “Low-stress silicon nitride platform for mid-infrared broadband and monolithically integrated microphotonics,” Adv. Opt. Mater. 1, 732–739 (2013).
[Crossref]

Ahn, J.-H.

J. Shim, S.-H. Bae, W. Kong, D. Lee, K. Qiao, D. Nezich, Y. J. Park, R. Zhao, S. Sundaram, X. Li, H. Yeon, C. Choi, H. Kum, R. Yue, G. Zhou, Y. Ou, K. Lee, J. Moodera, X. Zhao, J.-H. Ahn, C. Hinkle, A. Ougazzaden, and J. Kim, “Controlled crack propagation for atomic precision handling of wafer-scale two-dimensional materials,” Science 362, 665–670 (2018).
[Crossref] [PubMed]

Aieta, F.

P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4, 139–152 (2017).
[Crossref]

N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: Controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U. S. A. 109, 12364–12368 (2012).
[Crossref]

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, 333–337 (2011).
[Crossref] [PubMed]

Alu, A.

D. L. Sounas and A. Alu, “Non-reciprocal photonics based on time modulation,” Nat. Photonics 11, 774–783 (2017).
[Crossref]

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alu, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343, 160–163 (2014).
[Crossref] [PubMed]

Ambrosio, A.

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, “Arbitrary spin-to-orbital angular momentum conversion of light,” Science 358, 896–901 (2017).
[Crossref] [PubMed]

Aoust, G.

N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: Controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U. S. A. 109, 12364–12368 (2012).
[Crossref]

Arbabi, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–943 (2015).
[Crossref] [PubMed]

Assefa, S.

F. Najafi, J. Mower, N. C. Harris, F. Bellei, A. Dane, C. Lee, X. Hu, P. Kharel, F. Marsili, S. Assefa, K. K. Berggren, and D. Englund, “On-chip detection of non-classical light by scalable integration of single-photon detectors,” Nat. Commun. 6, 5873 (2015).
[Crossref] [PubMed]

Augusiak, R.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mancinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenlowe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

Bacco, D.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mancinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenlowe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

Bae, S.-H.

J. Shim, S.-H. Bae, W. Kong, D. Lee, K. Qiao, D. Nezich, Y. J. Park, R. Zhao, S. Sundaram, X. Li, H. Yeon, C. Choi, H. Kum, R. Yue, G. Zhou, Y. Ou, K. Lee, J. Moodera, X. Zhao, J.-H. Ahn, C. Hinkle, A. Ougazzaden, and J. Kim, “Controlled crack propagation for atomic precision handling of wafer-scale two-dimensional materials,” Science 362, 665–670 (2018).
[Crossref] [PubMed]

Baehr-Jones, T.

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).
[Crossref]

Baets, R.

Bagheri, M.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–943 (2015).
[Crossref] [PubMed]

Bao, Q.

Q. Bao and K. P. Loh, “Graphene photonics, plasmonics, and broadband optoelectronic devices,” ACS Nano 6, 3677–3694 (2012).
[Crossref] [PubMed]

Bellei, F.

F. Najafi, J. Mower, N. C. Harris, F. Bellei, A. Dane, C. Lee, X. Hu, P. Kharel, F. Marsili, S. Assefa, K. K. Berggren, and D. Englund, “On-chip detection of non-classical light by scalable integration of single-photon detectors,” Nat. Commun. 6, 5873 (2015).
[Crossref] [PubMed]

Berggren, K. K.

F. Najafi, J. Mower, N. C. Harris, F. Bellei, A. Dane, C. Lee, X. Hu, P. Kharel, F. Marsili, S. Assefa, K. K. Berggren, and D. Englund, “On-chip detection of non-classical light by scalable integration of single-photon detectors,” Nat. Commun. 6, 5873 (2015).
[Crossref] [PubMed]

Biener, G.

Bienstman, P.

Blanchard, R.

N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: Controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U. S. A. 109, 12364–12368 (2012).
[Crossref]

Bliokh, K. Y.

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

Bomzon, Z.

Bonneau, D.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mancinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenlowe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

Capasso, F.

W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
[Crossref] [PubMed]

P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4, 139–152 (2017).
[Crossref]

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, “Arbitrary spin-to-orbital angular momentum conversion of light,” Science 358, 896–901 (2017).
[Crossref] [PubMed]

M. Khorasaninejad and F. Capasso, “Metalenses: Versatile multifunctional photonic components,” Science 358, 1146 (2017).
[Crossref]

J. P. B. Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: Independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118, 113901 (2017).
[Crossref]

N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: Controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U. S. A. 109, 12364–12368 (2012).
[Crossref]

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, 333–337 (2011).
[Crossref] [PubMed]

Castaldi, G.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alu, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343, 160–163 (2014).
[Crossref] [PubMed]

Cheah, K.

G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. HanWong, E. Y. B. Pun, K. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14, 607–612 (2015).
[Crossref] [PubMed]

Chen, B. H.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref] [PubMed]

Chen, M.-K.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref] [PubMed]

Chen, S.

G. Li, S. Chen, N. Pholchai, B. Reineke, P. W. HanWong, E. Y. B. Pun, K. Cheah, T. Zentgraf, and S. Zhang, “Continuous control of the nonlinearity phase for harmonic generations,” Nat. Mater. 14, 607–612 (2015).
[Crossref] [PubMed]

T. Shegai, S. Chen, V. D. Miljkovic, G. Zengin, P. Johansson, and M. Kall, “A bimetallic nanoantenna for directional colour routing,” Nat. Commun. 2, 481 (2011).
[Crossref] [PubMed]

Chen, W. T.

W. T. Chen, A. Y. Zhu, V. Sanjeev, M. Khorasaninejad, Z. Shi, E. Lee, and F. Capasso, “A broadband achromatic metalens for focusing and imaging in the visible,” Nat. Nanotechnol. 13, 220–226 (2018).
[Crossref] [PubMed]

Chen, Y. H.

S. Wang, P. C. Wu, V.-C. Su, Y.-C. Lai, M.-K. Chen, H. Y. Kuo, B. H. Chen, Y. H. Chen, T.-T. Huang, J.-H. Wang, R.-M. Lin, C.-H. Kuan, T. Li, Z. Wang, S. Zhu, and D. P. Tsai, “A broadband achromatic metalens in the visible,” Nat. Nanotechnol. 13, 227–232 (2018).
[Crossref] [PubMed]

Chipouline, A.

R. Guo, M. Decker, F. Setzpfandt, X. Gai, D.-Y. Choi, R. Kiselev, A. Chipouline, I. Staude, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “High-bit rate ultra-compact light routing with mode-selective on-chip nanoantennas,” Sci. Adv. 3, e1700007 (2017).
[Crossref] [PubMed]

Choi, C.

B. Yao, S.-W. Huang, Y. Liu, A. K. Vinod, C. Choi, M. Hoff, Y. Li, M. Yu, Z. Feng, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Gate-tunable frequency combs in graphene-nitride microresonators,” Nature 558, 410–414 (2018).
[Crossref] [PubMed]

J. Shim, S.-H. Bae, W. Kong, D. Lee, K. Qiao, D. Nezich, Y. J. Park, R. Zhao, S. Sundaram, X. Li, H. Yeon, C. Choi, H. Kum, R. Yue, G. Zhou, Y. Ou, K. Lee, J. Moodera, X. Zhao, J.-H. Ahn, C. Hinkle, A. Ougazzaden, and J. Kim, “Controlled crack propagation for atomic precision handling of wafer-scale two-dimensional materials,” Science 362, 665–670 (2018).
[Crossref] [PubMed]

Choi, D.-Y.

R. Guo, M. Decker, F. Setzpfandt, X. Gai, D.-Y. Choi, R. Kiselev, A. Chipouline, I. Staude, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “High-bit rate ultra-compact light routing with mode-selective on-chip nanoantennas,” Sci. Adv. 3, e1700007 (2017).
[Crossref] [PubMed]

Choi, H.

J. T. Kim and H. Choi, “Polarization control in graphene-based polymer waveguide polarizer,” Laser Photon. Rev. 12, 1800142 (2018).
[Crossref]

Clemmen, S.

Crozier, K. B.

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

F. Najafi, J. Mower, N. C. Harris, F. Bellei, A. Dane, C. Lee, X. Hu, P. Kharel, F. Marsili, S. Assefa, K. K. Berggren, and D. Englund, “On-chip detection of non-classical light by scalable integration of single-photon detectors,” Nat. Commun. 6, 5873 (2015).
[Crossref] [PubMed]

Dave, U.

Decker, M.

R. Guo, M. Decker, F. Setzpfandt, X. Gai, D.-Y. Choi, R. Kiselev, A. Chipouline, I. Staude, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “High-bit rate ultra-compact light routing with mode-selective on-chip nanoantennas,” Sci. Adv. 3, e1700007 (2017).
[Crossref] [PubMed]

R. Guo, M. Decker, F. Setzpfandt, I. Staude, D. N. Neshev, and Y. S. Kivshar, “Plasmonic fano nanoantennas for on-chip separation of wavelength-encoded optical signals,” Nano Lett. 15, 3324–3328 (2015).
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R. Guo, M. Decker, I. Staude, D. N. Neshev, and Y. S. Kivshar, “Bidirectional waveguide coupling with plasmonic fano nanoantennas,” Appl. Phys. Lett. 105, 053114 (2014).
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Devlin, R.

Devlin, R. C.

R. C. Devlin, A. Ambrosio, N. A. Rubin, J. P. B. Mueller, and F. Capasso, “Arbitrary spin-to-orbital angular momentum conversion of light,” Science 358, 896–901 (2017).
[Crossref] [PubMed]

J. P. B. Mueller, N. A. Rubin, R. C. Devlin, B. Groever, and F. Capasso, “Metasurface polarization optics: Independent phase control of arbitrary orthogonal states of polarization,” Phys. Rev. Lett. 118, 113901 (2017).
[Crossref]

Dhakal, A.

Dhoore, S.

Ding, Y.

J. Wang, S. Paesani, Y. Ding, R. Santagati, P. Skrzypczyk, A. Salavrakos, J. Tura, R. Augusiak, L. Mancinska, D. Bacco, D. Bonneau, J. W. Silverstone, Q. Gong, A. Acin, K. Rottwitt, L. K. Oxenlowe, J. L. O’Brien, A. Laing, and M. G. Thompson, “Multidimensional quantum entanglement with large-scale integrated optics,” Science 360, 285–291 (2018).
[Crossref] [PubMed]

Duan, X.

B. Yao, S.-W. Huang, Y. Liu, A. K. Vinod, C. Choi, M. Hoff, Y. Li, M. Yu, Z. Feng, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Gate-tunable frequency combs in graphene-nitride microresonators,” Nature 558, 410–414 (2018).
[Crossref] [PubMed]

Engheta, N.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alu, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343, 160–163 (2014).
[Crossref] [PubMed]

Englund, D.

Y. Shen, N. C. Harris, S. Skirlo, M. Prabhu, T. Baehr-Jones, M. Hochberg, X. Sun, S. Zhao, H. Larochelle, D. Englund, and M. Soljacic, “Deep learning with coherent nanophotonic circuits,” Nat. Photonics 11, 441–446 (2017).
[Crossref]

F. Najafi, J. Mower, N. C. Harris, F. Bellei, A. Dane, C. Lee, X. Hu, P. Kharel, F. Marsili, S. Assefa, K. K. Berggren, and D. Englund, “On-chip detection of non-classical light by scalable integration of single-photon detectors,” Nat. Commun. 6, 5873 (2015).
[Crossref] [PubMed]

Faraon, A.

A. Arbabi, Y. Horie, M. Bagheri, and A. Faraon, “Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission,” Nat. Nanotechnol. 10, 937–943 (2015).
[Crossref] [PubMed]

Feng, Z.

B. Yao, S.-W. Huang, Y. Liu, A. K. Vinod, C. Choi, M. Hoff, Y. Li, M. Yu, Z. Feng, D.-L. Kwong, Y. Huang, Y. Rao, X. Duan, and C. W. Wong, “Gate-tunable frequency combs in graphene-nitride microresonators,” Nature 558, 410–414 (2018).
[Crossref] [PubMed]

Fu, X.

Y. Meng, F. Hu, Y. Shen, Y. Yang, Q. Xiao, X. Fu, and M. Gong, “Ultracompact graphene-assisted tunable waveguide couplers with high directivity and mode selectivity,” Sci. Rep. 8, 13362 (2018).
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Y. Meng, S. Ye, Y. Shen, Q. Xiao, X. Fu, R. Lu, Y. Liu, and M. Gong, “Waveguide engineering of graphene optoelectronics – modulators and polarizers,” IEEE Photonics J. 10, 6600217 (2018).
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Gaburro, Z.

N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: Controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U. S. A. 109, 12364–12368 (2012).
[Crossref]

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, 333–337 (2011).
[Crossref] [PubMed]

Gaeta, A. L.

D. J. Moss, R. Morandotti, A. L. Gaeta, and M. Lipson, “New cmos-compatible platforms based on silicon nitride and hydex for nonlinear optics,” Nat. Photonics 7, 597–607 (2013).
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Gai, X.

R. Guo, M. Decker, F. Setzpfandt, X. Gai, D.-Y. Choi, R. Kiselev, A. Chipouline, I. Staude, T. Pertsch, D. N. Neshev, and Y. S. Kivshar, “High-bit rate ultra-compact light routing with mode-selective on-chip nanoantennas,” Sci. Adv. 3, e1700007 (2017).
[Crossref] [PubMed]

Galdi, V.

A. Silva, F. Monticone, G. Castaldi, V. Galdi, A. Alu, and N. Engheta, “Performing mathematical operations with metamaterials,” Science 343, 160–163 (2014).
[Crossref] [PubMed]

Gao, P.

M. Pu, X. Li, X. Ma, Y. Wang, Z. Zhao, C. Wang, C. Hu, P. Gao, C. Huang, H. Ren, X. Li, F. Qin, J. Yang, M. Gu, M. Hong, and X. Luo, “Catenary optics for achromatic generation of perfect optical angular momentum,” Sci. Adv. 1, e1500396 (2015).
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Ge, Z.

P. Xie, Q. Sun, L. Wang, Y. Wen, X. Wang, G. Wang, C. Zeng, M. Liu, Z. Ge, and Z. Lu, “Impact of two-photon absorption and free-carrier effects on time lens based on four-wave mixing in silicon waveguides,” Appl. Phys. Express 11, 082204 (2018).
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Genevet, P.

P. Genevet, F. Capasso, F. Aieta, M. Khorasaninejad, and R. Devlin, “Recent advances in planar optics: from plasmonic to dielectric metasurfaces,” Optica 4, 139–152 (2017).
[Crossref]

N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: Controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U. S. A. 109, 12364–12368 (2012).
[Crossref]

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, 333–337 (2011).
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N. Yu, P. Genevet, F. Aieta, M. A. Kats, R. Blanchard, G. Aoust, J.-P. Tetienne, Z. Gaburro, and F. Capasso, “Flat optics: Controlling wavefronts with optical antenna metasurfaces,” IEEE J. Sel. Top. Quantum Electron. 19, 4700423 (2013).
[Crossref]

M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro, and F. Capasso, “Giant birefringence in optical antenna arrays with widely tailorable optical anisotropy,” Proc. Natl. Acad. Sci. U. S. A. 109, 12364–12368 (2012).
[Crossref]

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, 333–337 (2011).
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Yu, S.

X. Piao, S. Yu, and N. Park, “Design of transverse spinning of light with globally unique handedness,” Phys. Rev. Lett. 120, 203901 (2018).
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Yue, R.

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Figures (8)

Fig. 1
Fig. 1 (a) Schematic of an antenna unit. (b) and (c) Comparison of | E | distribution along the X O Z or Y O Z plane respectively for a Si antenna irradiated by linearly x- or y-polarized light. Antenna geometry: l x × l y × l z = 0.3 × 0.6 × 1 μm and θ = 0. (d) and (e) Phase retardation φx and transmittance | t x | of the x-polarized light respectively under different combinations of lx and ly. A linearly x-polarized plane wave normally irradiates the antenna (electric field vector aligned with antenna axis). (f) Corresponding complex amplitude transmission rate t x = | t x | exp   ( i φ x ) in the complex plane.
Fig. 2
Fig. 2 (a) Summary for the two operation scenarios, where the geometry of each pixel lx, ly and θ can be chosen freely. The red and orange color-highlighted phase and polarizations denote configurable parts, while the black orgrey colored phase and polarizations indicate given or not configurable factors. (b) Flow chart introduction to the whole design methodology.
Fig. 3
Fig. 3 Chip-integrated metasurface coupler (a) Device structure sketch. (b) Antenna parameters. (c) Incident polarizations. (d) and (e) Transmission rates to waveguide ports under | λ + and | λ illumination. (f) Coupling directivity γ = 10 × lg   ( T right / T left ) as a function of light wavelength. (g) | E | distribution at the left and right ports under the excitation of | λ + at λ = 1.55 μm. (h) and (i) Electric field component E x and E y along waveguide middle plane respectively with | λ + illumination.
Fig. 4
Fig. 4 Metasurface-integrated orthogonal polarization splitters for arbitrary elliptical polarizations. (a), (f) and (k) Device structures for polarization ellipse ε = 50 , 60° and 70° accordingly. (b), (g) and (l) Corresponding incident polarizations. (c), (h) and (m) | E | distribution at left and right waveguide port for λ = 1.55 μm at | λ + illumination. (d), (i) and (n) Waveguide transmission spectrum under | λ + excitation for (a), (f) and (k) respectively. (e), (j) and (o) Corresponding directivity spectrum.
Fig. 5
Fig. 5 Device structure sketch for linear polarizations. (b) Illustration for incident polarizations. (c) Distribution of electric field component E y and E z along waveguide middle plane at λ = 1.55 μm. (d) | E | distribution at left and right ports for λ = 1.55 μm. (e) Waveguide transmission spectrum. | λ + incident polarization is applied for (c), (d) and (e). (f) Device directivity spectrum. (g)-(l) Same for the device working at circular polarizations.
Fig. 6
Fig. 6 (a) Device structure sketch. (b) Incident polarization. (c) | E | distribution for the left and right port at λ = 1.55 μm. (d) Vector map for E at the right port ( λ = 1.55 μm). (e) and (f) Waveguide transmission and coupling directivity spectrum respectively. (g)-(l) Same for the directional coupler for fundamental TM mode (coupling to the left port). (m)-(r), Same for the TM mode coupler (coupling to the right port) with constraint condition l y 300 nm applied in optimization.
Fig. 7
Fig. 7 (a) and (g) Device structure for dual wavelength directional couplers working for both 1.35 and 1.55 μm. Incident polarization states are illustrated as (b) and (h) accordingly.(c) and (i) Waveguide transmission spectrum for devices in (a) and (g) respectively. (d) and (j) Corresponding directivity spectrum. (e) and (k) Distribution of E z at 1.35 and 1.55 μm. (f) and (l) | E | distribution at the left and right ports at dual working wavelengths for the two proposed devices accordingly.
Fig. 8
Fig. 8 (a) and (f) Device structure sketch working for linear polarizations | λ + shown in (b) and (g) accordingly. (c) and (h) Waveguide transmission spectrum for (a) and (f) respectively. (d) and (i) Corresponding directivity curve. (e) Electric field norm | E | distribution at waveguide ports for 1.35 and 1.55 μm of the device shown in (a). (j) Distribution of E z for (f) at 1.5 and 1.6 μm under | λ + excitation. (k) and (l) | E | distribution at waveguide ports for dual wavelength under the illumination of | λ + and | λ respectively.

Equations (10)

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J = [ j x x j x y j x y j y y ] = R ( θ ) [ e i φ x 0 0 e i φ y ] R ( θ )
n eff = λ 2 π Δ φ Λ sign ( Δ φ Λ )
J ( p , q ) | λ + = | κ +
[ ( κ 1 + ) * ( κ 2 + ) * λ 1   + λ 2   + ] [ j x x j x y ] = [ | ( κ + ) * , | λ + ] T [ j x x j x y ] = M [ j x x j x y ] = [ ( λ 1 + ) * κ 1 + ]
[ j x x , j x y ] T = M 1 [ λ 1 * , κ 1 ] T and j y y = j x x * exp  ( 2 i j x y )
η | E antenna ( x , y , z ) E wg * ( x , y , z ) d y d z | 2 ( | E antenna ( x , y , z ) | 2 d y d z ) ( | E wg ( x , y , z ) | 2 d y d z )
J ( p , q ) | λ + = e i φ + ( p , q ) | ( λ + ) * and J ( p , q ) | λ = e i φ ( p , q ) | ( λ ) *
J ( p , q ) = [ e i φ + ( p , q ) | ( λ + ) * , e i φ ( p , q ) | ( λ ) * ] [ | λ + , | λ ] 1
min     ( l x , l y ) { max  { | φ x design φ x simulation | , | φ y design φ y simulation | } }
min   ( l x , l y ) , φ 0 [ 0 , 2 π ] { m max  { | φ + design | λ = λ 1 φ + simulation | m b d a = λ 1 | , | φ + design | λ = λ 2 φ + simulation | λ = λ 2 | } }

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