Abstract

In the past decade, the research field that uses arrays of high-index-contrast near-wavelength dielectric structures on flat surfaces, known as high-contrast metastructures (HCMs) or metasurfaces, has emerged and expanded rapidly. Although HCMs and metasurfaces share great similarities in physical structures with photonic crystals (PhCs), i.e., periodic nanostructures, many differences exist in their design, analysis, operation conditions, and applications. In this paper, we provide a generalized theoretical understanding of the two subjects and show their intrinsic connections. We further discuss the simulation and design approaches, categorized by their functionalities and applications. We summarize the similarities and differences among HCMs, metasurfaces, and PhCs. New findings are presented regarding the physical connection between PhC band structures and 1D and 2D HCM scattering spectra under transverse and longitudinal tilt incidence. Novel designs using HCMs as holograms, spatial light modulators, and surface plasmonic couplers are discussed. Recent advances in HCMs, metasurfaces, and PhCs are reviewed and compared for applications such as broadband mirrors, waveguides, couplers, resonators, and reconfigurable optics.

© 2018 Optical Society of America

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2018 (1)

2017 (8)

2016 (17)

L. Wang, S. Kruk, H. Tang, T. Li, I. Kravchenko, D. N. Neshev, and Y. S. Kivshar, “Grayscale transparent metasurface holograms,” Optica 3, 1504–1505 (2016).
[Crossref]

J.-Y. Ou, E. Plum, J. Zhang, and N. I. Zheludev, “Giant nonlinearity of an optically reconfigurable plasmonic metamaterial,” Adv. Mater. 28, 729–733 (2016).
[Crossref]

N. I. Zheludev and E. Plum, “Reconfigurable nanomechanical photonic metamaterials,” Nat. Nanotechnol. 11, 16–22 (2016).
[Crossref]

J. Rensberg, S. Zhang, Y. Zhou, A. S. McLeod, C. Schwarz, M. Goldflam, M. Liu, J. Kerbusch, R. Nawrodt, S. Ramanathan, D. N. Basov, F. Capasso, C. Ronning, and M. A. Kats, “Active optical metasurfaces based on defect-engineered phase-transition materials,” Nano Lett. 16, 1050–1055 (2016).
[Crossref]

H.-S. Ee and R. Agarwal, “Tunable metasurface and flat optical zoom lens on a stretchable substrate,” Nano Lett. 16, 2818–2823 (2016).
[Crossref]

S. M. Kamali, E. Arbabi, A. Arbabi, Y. Horie, and A. Faraon, “Highly tunable elastic dielectric metasurface lenses,” Laser Photon. Rev. 10, 1002–1008 (2016).
[Crossref]

Y.-W. Huang, H. W. H. Lee, R. Sokhoyan, R. A. Pala, K. Thyagarajan, S. Han, D. P. Tsai, and H. A. Atwater, “Gate-tunable conducting oxide metasurfaces,” Nano Lett. 16, 5319–5325 (2016).
[Crossref]

P. P. Iyer, M. Pendharkar, and J. A. Schuller, “Electrically reconfigurable metasurfaces using heterojunction resonators,” Adv. Opt. Mater. 4, 1582–1588 (2016).
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E. Arbabi, A. Arbabi, S. M. Kamali, Y. Horie, and A. Faraon, “Multiwavelength polarization-insensitive lenses based on dielectric metasurfaces with meta-molecules,” Optica 3, 628–633 (2016).
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H. Zhang, L. Cao, and G. Jin, “Lighting effects rendering in three-dimensional computer-generated holographic display,” Opt. Commun. 370, 192–197 (2016).
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T. Sun, J. Kim, J. M. Yuk, A. Zettl, F. Wang, and C. Chang-Hasnain, “Surface-normal electro-optic spatial light modulator using graphene integrated on a high-contrast grating resonator,” Opt. Express 24, 26035–26043 (2016).
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N. M. Estakhri and A. Alù, “Recent progress in gradient metasurfaces,” J. Opt. Soc. Am. B 33, A21–A30 (2016).
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A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354, aag2472 (2016).
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P. Qiao, L. Zhu, and C. J. Chang-Hasnain, “High-efficiency aperiodic two-dimensional high-contrast-grating hologram,” Proc. SPIE 9757, 975708 (2016).
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E. Haglund, J. S. Gustavsson, J. Bengtsson, Å. Haglund, A. Larsson, D. Fattal, W. Sorin, and M. Tan, “Demonstration of post-growth wavelength setting of VCSELs using high-contrast gratings,” Opt. Express 24, 1999–2005 (2016).
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B. Pesala, W. Yang, and C. J. Chang-Hasnain, “Compact on-chip optical components based on multimode interference design using high-contrast grating hollow-core waveguides,” IEEE J. Sel. Top. Quantum Electron. 22, 279–287 (2016).
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T. Sun, S. Kan, G. Marriott, and C. Chang-Hasnain, “High-contrast grating resonators for label-free detection of disease biomarkers,” Sci. Rep. 6, 27482 (2016).
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2015 (9)

L. Zhu, J. Kapraun, J. Ferrara, and C. J. Chang-Hasnain, “Flexible photonic metastructures for tunable coloration,” Optica 2, 255–258 (2015).
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J. Ferrara, W. Yang, L. Zhu, P. Qiao, and C. J. Chang-Hasnain, “Heterogeneously integrated long-wavelength VCSEL using silicon high contrast grating on an SOI substrate,” Opt. Express 23, 2512–2523 (2015).
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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).
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W. Yang, S. A. Gerke, K. W. Ng, Y. Rao, C. Chase, and C. J. Chang-Hasnain, “Laser optomechanics,” Sci. Rep. 5, 13700 (2015).
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P. Qiao, L. Zhu, W. C. Chew, and C. J. Chang-Hasnain, “Theory and design of two-dimensional high-contrast-grating phased arrays,” Opt. Express 23, 24508–24524 (2015).
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T. Sun, W. Yang, and C. Chang-Hasnain, “Surface-normal coupled four-wave mixing in a high contrast gratings resonator,” Opt. Express 23, 29565–29572 (2015).
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Y. F. Yu, A. Y. Zhu, R. Paniagua-Domínguez, Y. H. Fu, B. Luk’yanchuk, and A. I. Kuznetsov, “High-transmission dielectric metasurface with 2π phase control at visible wavelengths,” Laser Photon. Rev. 9, 412–418 (2015).
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M. Khorasaninejad, F. Aieta, P. Kanhaiya, M. A. Kats, P. Genevet, D. Rousso, and F. Capasso, “Achromatic metasurface lens at telecommunication wavelengths,” Nano Lett. 15, 5358–5362 (2015).
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J. Valente, J.-Y. Ou, E. Plum, I. J. Youngs, and N. I. Zheludev, “A magneto-electro-optical effect in a plasmonic nanowire material,” Nat. Commun. 6, 7021 (2015).
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2014 (7)

K. Hirose, Y. Liang, Y. Kurosaka, A. Watanabe, T. Sugiyama, and S. Noda, “Watt-class high-power, high-beam-quality photonic-crystal lasers,” Nat. Photonics 8, 406–411 (2014).
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D. Lin, P. Fan, E. Hasman, and M. L. Brongersma, “Dielectric gradient metasurface optical elements,” Science 345, 298–302 (2014).
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C. L. Holloway, E. F. Kuester, and A. Dienstfrey, “A homogenization technique for obtaining generalized sheet transition conditions for an arbitrarily shaped coated wire grating,” Radio Sci. 49, 813–850 (2014).
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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, e167 (2014).
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R. Magnusson, “Wideband reflectors with zero-contrast gratings,” Opt. Lett. 39, 4337–4340 (2014).
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N. Yu and F. Capasso, “Flat optics with designer metasurfaces,” Nat. Mater. 13, 139–150 (2014).
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W. Yang, T. Sun, Y. Rao, M. Megens, T. Chan, B.-W. Yoo, D. A. Horsley, M. C. Wu, and C. J. Chang-Hasnain, “High speed optical phased array using high contrast grating all-pass filters,” Opt. Express 22, 20038–20044 (2014).
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2013 (8)

T. Tran, V. Karagodsky, Y. Rao, W. Yang, R. Chen, C. Chase, L. C. Chuang, and C. J. Chang-Hasnain, “Surface-normal second harmonic emission from AlGaAs high-contrast gratings,” Appl. Phys. Lett. 102, 021102 (2013).
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Y. Rao, W. Yang, C. Chase, M. C. Y. Huang, D. P. Worland, S. Khaleghi, M. R. Chitgarha, M. Ziyadi, A. E. Willner, and C. J. Chang-Hasnain, “Long-wavelength VCSEL using high-contrast grating,” IEEE J. Sel. Top. Quantum Electron. 19, 1701311 (2013).
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B.-W. Yoo, M. Megens, T. Chan, T. Sun, W. Yang, C. J. Chang-Hasnain, D. A. Horsley, and M. C. Wu, “Optical phased array using high contrast gratings for two dimensional beamforming and beamsteering,” Opt. Express 21, 12238–12248 (2013).
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K. Ikeda, K. Takeuchi, K. Takayose, I.-S. Chung, J. Mørk, and H. Kawaguchi, “Polarization-independent high-index contrast grating and its fabrication tolerances,” Appl. Opt. 52, 1049–1053 (2013).
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D. Fattal, Z. Peng, T. Tran, S. Vo, M. Fiorentino, J. Brug, and R. G. Beausoleil, “A multi-directional backlight for a wide-angle, glasses-free three-dimensional display,” Nature 495, 348–351 (2013).
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L. Huang, X. Chen, H. Mühlenbernd, H. Zhang, S. Chen, B. Bai, Q. Tan, G. Jin, K.-W. Cheah, C.-W. Qiu, J. Li, T. Zentgraf, and S. Zhang, “Three-dimensional optical holography using a plasmonic metasurface,” Nat. Commun. 4, 2808 (2013).

S. Chakravarty, W.-C. Lai, Y. Zou, H. A. Drabkin, R. M. Gemmill, G. R. Simon, S. H. Chin, and R. T. Chen, “Multiplexed specific label-free detection of NCI-H358 lung cancer cell line lysates with silicon based photonic crystal microcavity biosensors,” Biosens. Bioelectron. 43, 50–55 (2013).
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J. Sun, E. Timurdogan, A. Yaacobi, E. S. Hosseini, and M. R. Watts, “Large-scale nanophotonic phased array,” Nature 493, 195–199 (2013).
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2012 (12)

W. Zhou, G. Dang, M. Taysing-Lara, V. Karagodsky, T. Sun, and C. Chang-Hasnain, “Slow-light high contrast metastructure hollow-core waveguides,” Proc. SPIE 8270, 827009 (2012).
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T. Sun, W. Yang, V. Karagodsky, W. Zhou, and C. Chang-Hasnain, “Low-loss slow light inside high contrast grating waveguide,” Proc. SPIE 8270, 82700A (2012).
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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).
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B. Walther, C. Helgert, C. Rockstuhl, F. Setzpfandt, F. Eilenberger, E.-B. Kley, F. Lederer, A. Tünnermann, and T. Pertsch, “Spatial and spectral light shaping with metamaterials,” Adv. Mater. 24, 6300–6304 (2012).
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L. Huang, X. Chen, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, T. Zentgraf, and S. Zhang, “Dispersionless phase discontinuities for controlling light propagation,” Nano Lett. 12, 5750–5755 (2012).
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A. Liu, F. Fu, Y. Wang, B. Jiang, and W. Zheng, “Polarization-insensitive subwavelength grating reflector based on a semiconductor-insulator-metal structure,” Opt. Express 20, 14991–15000 (2012).
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C. Sciancalepore, B. B. Bakir, X. Letartre, J. Harduin, N. Olivier, C. Seassal, J. M. Fedeli, and P. Viktorovitch, “CMOS-compatible ultra-compact 1.55-μm emitting VCSELs using double photonic crystal mirrors,” IEEE Photon. Technol. Lett. 24, 455–457 (2012).
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H. Yang, D. Zhao, S. Chuwongin, J.-H. Seo, W. Yang, Y. Shuai, J. Berggren, M. Hammar, Z. Ma, and W. Zhou, “Transfer-printed stacked nanomembrane lasers on silicon,” Nat. Photonics 6, 615–620 (2012).
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N. Lawrence, J. Trevino, and L. D. Negro, “Aperiodic arrays of active nanopillars for radiation engineering,” J. Appl. Phys. 111, 113101 (2012).
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W. Yang, J. Ferrara, K. Grutter, A. Yeh, C. Chase, Y. Yue, A. E. Willner, M. C. Wu, and C. J. Chang-Hasnain, “Low loss hollow-core waveguide on a silicon substrate,” Nanophotonics 1, 23 (2012).
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C. J. Chang-Hasnain and W. Yang, “High-contrast gratings for integrated optoelectronics,” Adv. Opt. Photon. 4, 379–440 (2012).
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C. L. Holloway, E. F. Kuester, J. A. Gordon, J. O. Hara, J. Booth, and D. R. Smith, “An overview of the theory and applications of metasurfaces: the two-dimensional equivalents of metamaterials,” IEEE Antennas Propag. Mag. 54(2), 10–35 (2012).
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2011 (6)

D. Zhao, H. Yang, Z. Ma, and W. Zhou, “Polarization independent broadband reflectors based on cross-stacked gratings,” Opt. Express 19, 9050–9055 (2011).
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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, 333–337 (2011).
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N. Shitrit, I. Bretner, Y. Gorodetski, V. Kleiner, and E. Hasman, “Optical spin Hall effects in plasmonic chains,” Nano Lett. 11, 2038–2042 (2011).
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V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, “Matrix Fabry–Perot resonance mechanism in high-contrast gratings,” Opt. Lett. 36, 1704–1706 (2011).
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B. Ellis, M. A. Mayer, G. Shambat, T. Sarmiento, J. Harris, E. E. Haller, and J. Vuckovic, “Ultralow-threshold electrically pumped quantum-dot photonic-crystal nanocavity laser,” Nat. Photonics 5, 297–300 (2011).
[Crossref]

J. Y. Ou, E. Plum, L. Jiang, and N. I. Zheludev, “Reconfigurable photonic metamaterials,” Nano Lett. 11, 2142–2144 (2011).
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2010 (7)

Y. Kurosaka, S. Iwahashi, Y. Liang, K. Sakai, E. Miyai, W. Kunishi, D. Ohnishi, and S. Noda, “On-chip beam-steering photonic-crystal lasers,” Nat. Photonics 4, 447–450 (2010).
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K. Nozaki, T. Tanabe, A. Shinya, S. Matsuo, T. Sato, H. Taniyama, and M. Notomi, “Sub-femtojoule all-optical switching using a photonic-crystal nanocavity,” Nat. Photonics 4, 477–483 (2010).
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P. Viktorovitch, B. Ben Bakir, S. Boutami, J. L. Leclercq, X. Letartre, P. Rojo-Romeo, C. Seassal, M. Zussy, L. Di Cioccio, and J. M. Fedeli, “3D harnessing of light with 2.5D photonic crystals,” Laser Photon. Rev. 4, 401–413 (2010).
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V. Karagodsky, F. G. Sedgwick, and C. J. Chang-Hasnain, “Theoretical analysis of subwavelength high contrast grating reflectors,” Opt. Express 18, 16973–16988 (2010).
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F. Lu, F. G. Sedgwick, V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, “Planar high-numerical-aperture low-loss focusing reflectors and lenses using subwavelength high contrast gratings,” Opt. Express 18, 12606–12614 (2010).
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D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4, 466–470 (2010).
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I. S. Chung, V. Iakovlev, A. Sirbu, A. Mereuta, A. Caliman, E. Kapon, and J. Mork, “Broadband MEMS-tunable high-index-contrast subwavelength grating long-wavelength VCSEL,” IEEE J. Quantum Electron. 46, 1245–1253 (2010).
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2009 (4)

J. Valentine, J. Li, T. Zentgraf, G. Bartal, and X. Zhang, “An optical cloak made of dielectrics,” Nat. Mater. 8, 568–571 (2009).
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C. Chase, Y. Zhou, and C. J. Chang-Hasnain, “Size effect of high contrast gratings in VCSELs,” Opt. Express 17, 24002–24007 (2009).
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Y. Zhou, M. C. Y. Huang, C. Chase, V. Karagodsky, M. Moewe, B. Pesala, F. G. Sedgwick, and C. J. Chang-Hasnain, “High-index-contrast grating (HCG) and its applications in optoelectronic devices,” IEEE J. Sel. Top. Quantum Electron. 15, 1485–1499 (2009).
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E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
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2008 (4)

2007 (2)

S. Kubo, D. Mori, and T. Baba, “Low-group-velocity and low-dispersion slow light in photonic crystal waveguides,” Opt. Lett. 32, 2981–2983 (2007).
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T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76, 033407 (2007).
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2006 (4)

T. Dirk, L. Frederik Van, A. Melanie, B. Wim, T. Dries Van, B. Peter, and B. Roel, “Grating couplers for coupling between optical fibers and nanophotonic waveguides,” Jpn. J. Appl. Phys. 45, 6071–6077 (2006).
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J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
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T. Mori, Y. Yamayoshi, and H. Kawaguchi, “Low-switching-energy and high-repetition-frequency all-optical flip-flop operations of a polarization bistable vertical-cavity surface-emitting laser,” Appl. Phys. Lett. 88, 101102 (2006).
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T. Asano, B. S. Song, Y. Akahane, and S. Noda, “Ultrahigh-Q nanocavities in two-dimensional photonic crystal slabs,” IEEE J. Sel. Top. Quantum Electron. 12, 1123–1134 (2006).
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2005 (2)

2004 (4)

B. Wang, J. Jiang, and G. P. Nordin, “Compact slanted grating couplers,” Opt. Express 12, 3313–3326 (2004).
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S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004).
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T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz magnetic response from artificial materials,” Science 303, 1494–1496 (2004).
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C. F. R. Mateus, M. C. Y. Huang, C. Lu, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12–1.62  μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16, 1676–1678 (2004).
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2003 (6)

G. Zhao and Q. H. Liu, “The 2.5-D multidomain pseudospectral time-domain algorithm,” IEEE Trans. Antennas Propag. 51, 619–627 (2003).
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E. Hasman, V. Kleiner, G. Biener, and A. Niv, “Polarization dependent focusing lens by use of quantized Pancharatnam–Berry phase diffractive optics,” Appl. Phys. Lett. 82, 328–330 (2003).
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E. F. Kuester, M. A. Mohamed, M. Piket-May, and C. L. Holloway, “Averaged transition conditions for electromagnetic fields at a metafilm,” IEEE Trans. Antennas Propag. 51, 2641–2651 (2003).
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C. J. Chang-Hasnain, P.-C. Ku, J. Kim, and S.-L. Chuang, “Variable optical buffer using slow light in semiconductor nanostructures,” Proc. IEEE 9, 1884–1897 (2003).
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W. Yang, T. Sun, Y. Rao, M. Megens, T. Chan, B.-W. Yoo, D. A. Horsley, M. C. Wu, and C. J. Chang-Hasnain, “High speed optical phased array using high contrast grating all-pass filters,” Opt. Express 22, 20038–20044 (2014).
[Crossref]

J. Ferrara, W. Yang, L. Zhu, P. Qiao, and C. J. Chang-Hasnain, “Heterogeneously integrated long-wavelength VCSEL using silicon high contrast grating on an SOI substrate,” Opt. Express 23, 2512–2523 (2015).
[Crossref]

P. Qiao, L. Zhu, W. C. Chew, and C. J. Chang-Hasnain, “Theory and design of two-dimensional high-contrast-grating phased arrays,” Opt. Express 23, 24508–24524 (2015).
[Crossref]

T. Sun, W. Yang, and C. Chang-Hasnain, “Surface-normal coupled four-wave mixing in a high contrast gratings resonator,” Opt. Express 23, 29565–29572 (2015).
[Crossref]

B.-W. Yoo, M. Megens, T. Chan, T. Sun, W. Yang, C. J. Chang-Hasnain, D. A. Horsley, and M. C. Wu, “Optical phased array using high contrast gratings for two dimensional beamforming and beamsteering,” Opt. Express 21, 12238–12248 (2013).
[Crossref]

Y. Zhou, M. Moewe, J. Kern, M. C. Y. Huang, and C. J. Chang-Hasnain, “Surface-normal emission of a high-Q resonator using a subwavelength high-contrast grating,” Opt. Express 16, 17282–17287 (2008).
[Crossref]

C. Chase, Y. Zhou, and C. J. Chang-Hasnain, “Size effect of high contrast gratings in VCSELs,” Opt. Express 17, 24002–24007 (2009).
[Crossref]

F. Lu, F. G. Sedgwick, V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, “Planar high-numerical-aperture low-loss focusing reflectors and lenses using subwavelength high contrast gratings,” Opt. Express 18, 12606–12614 (2010).
[Crossref]

V. Karagodsky, F. G. Sedgwick, and C. J. Chang-Hasnain, “Theoretical analysis of subwavelength high contrast grating reflectors,” Opt. Express 18, 16973–16988 (2010).
[Crossref]

D. Zhao, H. Yang, Z. Ma, and W. Zhou, “Polarization independent broadband reflectors based on cross-stacked gratings,” Opt. Express 19, 9050–9055 (2011).
[Crossref]

R. C. Devlin, A. Ambrosio, D. Wintz, S. L. Oscurato, A. Y. Zhu, M. Khorasaninejad, J. Oh, P. Maddalena, and F. Capasso, “Spin-to-orbital angular momentum conversion in dielectric metasurfaces,” Opt. Express 25, 377–393 (2017).
[Crossref]

A. Liu, F. Fu, Y. Wang, B. Jiang, and W. Zheng, “Polarization-insensitive subwavelength grating reflector based on a semiconductor-insulator-metal structure,” Opt. Express 20, 14991–15000 (2012).
[Crossref]

K. Li, C. Chase, P. Qiao, and C. J. Chang-Hasnain, “Widely tunable 1060-nm VCSEL with high-contrast grating mirror,” Opt. Express 25, 11855–11866 (2017).
[Crossref]

L. Zhu, W. Yang, and C. Chang-Hasnain, “Very high efficiency optical coupler for silicon nanophotonic waveguide and single mode optical fiber,” Opt. Express 25, 18462–18473 (2017).
[Crossref]

Opt. Lett. (10)

P. Qiao, K. Li, K. T. Cook, and C. J. Chang-Hasnain, “MEMS-tunable VCSELs using 2D high-contrast gratings,” Opt. Lett. 42, 823–826 (2017).
[Crossref]

V. Karagodsky, C. Chase, and C. J. Chang-Hasnain, “Matrix Fabry–Perot resonance mechanism in high-contrast gratings,” Opt. Lett. 36, 1704–1706 (2011).
[Crossref]

R. Magnusson, “Wideband reflectors with zero-contrast gratings,” Opt. Lett. 39, 4337–4340 (2014).
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U. Levy, H.-C. Kim, C.-H. Tsai, and Y. Fainman, “Near-infrared demonstration of computer-generated holograms implemented by using subwavelength gratings with space-variant orientation,” Opt. Lett. 30, 2089–2091 (2005).
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V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, “Negative index of refraction in optical metamaterials,” Opt. Lett. 30, 3356–3358 (2005).
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S. Kubo, D. Mori, and T. Baba, “Low-group-velocity and low-dispersion slow light in photonic crystal waveguides,” Opt. Lett. 32, 2981–2983 (2007).
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D. M. Beggs, T. P. White, L. O’Faolain, and T. F. Krauss, “Ultracompact and low-power optical switch based on silicon photonic crystals,” Opt. Lett. 33, 147–149 (2008).
[Crossref]

Z. Bomzon, V. Kleiner, and E. Hasman, “Pancharatnam–Berry phase in space-variant polarization-state manipulations with subwavelength gratings,” Opt. Lett. 26, 1424–1426 (2001).
[Crossref]

Z. Bomzon, G. Biener, V. Kleiner, and E. Hasman, “Radially and azimuthally polarized beams generated by space-variant dielectric subwavelength gratings,” Opt. Lett. 27, 285–287 (2002).
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T. A. Birks, J. C. Knight, and P. St. J. Russell, “Endlessly single-mode photonic crystal fiber,” Opt. Lett. 22, 961–963 (1997).
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Phys. Rev. B (5)

S. G. Tikhodeev, A. L. Yablonskii, E. A. Muljarov, N. A. Gippius, and T. Ishihara, “Quasiguided modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002).
[Crossref]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “All-angle negative refraction without negative effective index,” Phys. Rev. B 65, 201104 (2002).
[Crossref]

E. Plum, J. Zhou, J. Dong, V. A. Fedotov, T. Koschny, C. M. Soukoulis, and N. I. Zheludev, “Metamaterial with negative index due to chirality,” Phys. Rev. B 79, 035407 (2009).
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S. Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
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T. Zentgraf, T. P. Meyrath, A. Seidel, S. Kaiser, H. Giessen, C. Rockstuhl, and F. Lederer, “Babinet’s principle for optical frequency metamaterials and nanoantennas,” Phys. Rev. B 76, 033407 (2007).
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Phys. Rev. Lett. (3)

A. Papakostas, A. Potts, D. M. Bagnall, S. L. Prosvirnin, H. J. Coles, and N. I. Zheludev, “Optical manifestations of planar chirality,” Phys. Rev. Lett. 90, 107404 (2003).
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Proc. IEEE (2)

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C. J. Chang-Hasnain, P.-C. Ku, J. Kim, and S.-L. Chuang, “Variable optical buffer using slow light in semiconductor nanostructures,” Proc. IEEE 9, 1884–1897 (2003).
[Crossref]

Proc. Phys. Soc. London (1)

R. W. Wood, “On a remarkable case of uneven distribution of light in a diffraction grating spectrum,” Proc. Phys. Soc. London 18, 269–275 (1902).
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Lord Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. London A 79, 399–416 (1907).
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Proc. SPIE (3)

P. Qiao, L. Zhu, and C. J. Chang-Hasnain, “High-efficiency aperiodic two-dimensional high-contrast-grating hologram,” Proc. SPIE 9757, 975708 (2016).
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T. Sun, W. Yang, V. Karagodsky, W. Zhou, and C. Chang-Hasnain, “Low-loss slow light inside high contrast grating waveguide,” Proc. SPIE 8270, 82700A (2012).
[Crossref]

W. Zhou, G. Dang, M. Taysing-Lara, V. Karagodsky, T. Sun, and C. Chang-Hasnain, “Slow-light high contrast metastructure hollow-core waveguides,” Proc. SPIE 8270, 827009 (2012).
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Radio Sci. (1)

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J. M. Dudley, G. Genty, and S. Coen, “Supercontinuum generation in photonic crystal fiber,” Rev. Mod. Phys. 78, 1135–1184 (2006).
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Sci. Rep. (2)

T. Sun, S. Kan, G. Marriott, and C. Chang-Hasnain, “High-contrast grating resonators for label-free detection of disease biomarkers,” Sci. Rep. 6, 27482 (2016).
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W. Yang, S. A. Gerke, K. W. Ng, Y. Rao, C. Chase, and C. J. Chang-Hasnain, “Laser optomechanics,” Sci. Rep. 5, 13700 (2015).
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Science (7)

A. I. Kuznetsov, A. E. Miroshnichenko, M. L. Brongersma, Y. S. Kivshar, and B. Luk’yanchuk, “Optically resonant dielectric nanostructures,” Science 354, aag2472 (2016).
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Figures (45)

Figure 1.
Figure 1. Schematics of (a) a 1D PhC and (b) a 1D high-contrast metastructure (also known as high-contrast gratings) with a finite thickness t g . Physical parameters include period Λ , thickness t g , bar width w , high-index material n b for bars, and low-index material n a for gaps between bars. The wave number for an incident plane wave is k 0 . The incidence direction is defined by the polar angle θ and the azimuth angle ϕ . The incidence plane is the shaded plane in (b), defined by the surface-normal and the incidence directions. For 1D HCMs, x is the periodic direction and y is the invariant direction. For normal incidence ( θ = 0 ) on 1D HCMs, TE and TM are defined as the electric fields being parallel and perpendicular to the grating bars. For oblique incidence ( θ 0 ), s polarization and p polarization refer to the electrical fields being perpendicular and parallel to the incidence plane, respectively.
Figure 2.
Figure 2. Four cases of oblique incidence with combinations of the tilt directions and polarizations. (a) and (b) are referred to as the transverse tilt with the tilt plane ( x z ) being perpendicular to grating bars. (c) and (d) are referred to as the longitudinal tilt with the tilt plane ( y z ) being parallel to grating bars. The incidence is s polarized for (a) and (d), and p polarized for (b) and (c).
Figure 3.
Figure 3. Dispersion curves (optical angular frequency ω versus propagation constant β ) for (a), (b)  E y -polarized (TE) modes, and (c), (d)  H y -polarized (TM) modes in a z -infinite waveguide array with periodicity in x . In (a) and (c), k x = 0 , corresponding to normal incidence. In (b) and (d), k x 0 and is matched with the θ 0 = 20 ° incidence. The red and blue lines indicate the dominant field components being even and odd in x , respectively. The two black dashed lines indicate the light line of the media of the high- and low-index material. Discrete modes exist below the second light line because of the waveguide array structure. At surface-normal incidence, only even order modes can be excited. n a = 1 , n b = 3.17 , and η = w / Λ = 55.56 % .
Figure 4.
Figure 4. Dual-mode analysis reveals the supermodes in a 1D-periodic HCM under normal incidence for TE- and TM-polarization incident light. (a), (b) FP resonance conditions. The red and blue curves indicate that the resonance conditions are reached for the fundamental mode and first higher order even mode. (c), (d) Reflectivity contours of the HCM showing checker-board patterns. (e), (f) Overlaps between resonance lines in (a), (b) and reflectivity contours in (c), (d), showing that the reflectivity contours are gridded by the resonance lines. (g) Field profiles R [ E y 0 ] and R [ E y 2 ] for the E y 0 - and E y 2 -dominant supermode resonances shown in (a). (h) Field profiles R [ H y 0 ] and R [ H y 2 ] for the H y 0 - and H y 2 -dominant supermode resonances in (b). The polarization is TE for (a), (c), (e), and (g), and TM for (b), (d), (f), and (h). Here η = 55.56 % for (a), (c), (e), and (g), and 73.68% for (b), (d), (f), and (h). ω Λ / 2 π c = 0.65 in (g) and (h). n a = 1 and n b = 3.17 .
Figure 5.
Figure 5. Tri-mode analysis reveals the supermodes in a 1D-periodic HCM under transverse-tilt incidence at θ = 20 ° and ϕ = 0 ° for s - and p -polarized waves. (a), (b) FP resonance conditions, (c), (d) reflectivity contours, as functions of the wavelength and the HCM thickness. (e), (f) Overlaps of the resonance lines and reflectivity contours, showing that the reflectivity contours are gridded by the resonance lines. The incidence is s polarized for (a), (c), (e), and (g), and p polarized for (b), (d), (f), and (h). The red and black dots in (a) indicate E y 0 - and E y 1 -dominant supermode resonances. The red and black dots in (b) indicate H y 0 - and H y 1 -dominant supermode resonances. The pink dots in (a) and (b) indicate resonant supermodes being a mixture of E y 0 and E y 2 , and a mixture of H y 0 and H y 2 , respectively. η = 55.56 % for (a), (c), (e), (g), and (h), and 73.68% for (b), (d), (f), (i), and (j). S -polarized eigenmode profiles (g) before and (h) after excluding the phase variation e i k 0 x x matched to the incidence. P -polarized eigenmode profiles (i) before and (j) after excluding the phase variation e i k 0 x x matched to the incidence. ω Λ / 2 π c = 0.65 in (g)–(j). n a = 1 and n b = 3.17 .
Figure 6.
Figure 6. Tri-mode analysis reveals the supermodes in 1D-periodic HCM under longitudinal-tilt ( ϕ = 90 ° ) incidence at θ = 20 ° for p - and s -polarized waves: (a), (b) FP resonance conditions, (c), (d) reflectivity contours, and (e), (f) overlaps between resonance lines and reflectivity contours as functions of the wavelength and the HCM thickness. The incidence is p polarized for (a), (c), (e), and (g), and s polarized for (b), (d), (f), and (h). The red and blue dots in (a) indicate E y 0 - and E x 1 -dominant supermode resonances. The red and blue dots in (b) indicate H y 0 - and H x 1 -dominant supermode resonances. The pink dots in (a) and (b) indicate the resonances of supermodes being a mixture of E y 0 and E y 2 , and a mixture of H y 0 and H y 2 , respectively. η = 55.56 % for (a), (c), (e), (g), and (h), and 73.68% for (b), (d), (f), (i), and (j). (g) Field profiles of the three eigenmodes contributing to the resonance conditions in (a), including two E y -dominant even modes, and one E x -dominant odd mode. (h) The E x -dominant odd mode in (g) has an even E y component, which couples with the p -polarized incidence. (i) Field profiles of the three eigenmodes contributing to the resonance conditions in (b), including two H y -dominant even modes, and one H x -dominant odd mode. (j) The H x -dominant odd mode in (i) has an even H y -component that couples with the s -polarized incidence. ω Λ / 2 π c = 0.65 in (g)–(j). n a = 1 and n b = 3.17 .
Figure 7.
Figure 7. Band structures of 1D PhC and HCM. (a) Band structure of a 1D PhC t g = calculated using the FDTD and PWE methods, shown by the red circles and black lines, respectively. (b) Transverse-tilt s -polarized band structure of a 1D-periodic HCM with a finite thickness t g = 0.5 Λ calculated using FDTD. (c) Transverse-tilt s -polarized angle-dependent reflectivity contour of the same structure, calculated using RCWA. (d) Overlap between (c) and the extracted photonic bands (red dots) from (b). n a = 1 , n b = 3.48 , and η = 0.6 .
Figure 8.
Figure 8. Brillouin zones of metastructures with 1D periodicity in the x direction with (a)  k y = 0 , and (b)  k y 0 . (c) and (d) correspond to the transverse-tilt p -polarized case. (e) and (f) correspond to the longitudinal-tilt s -polarized case. (g) and (h) correspond to the longitudinal-tilt p -polarized case. The red and blue plots are band structures and tilt reflectivity contours obtained from FDTD and RCWA, respectively. The HCM parameters are the same as in Fig. 7.
Figure 9.
Figure 9. Schematics of 2D-periodic HCMs. The refractive index for the building block is n b , and the surrounding index is n a . (a) An island-type 2D-periodic HCM with n a < n b . (b) A mesh-type 2D-periodic HCM with n a > n b .
Figure 10.
Figure 10. Comparisons between the HCM band structures, and their angle-dependent reflectivity contours. (a)–(d) Four combinations of the incidence plane and polarization. Band structures in (e), (f), (i), and (j) are calculated using FDTD. Reflectivity contours in (g), (h), (k), and (l) are calculated using RCWA. (e)–(h) correspond to the x z -incidence plane ( ϕ = 0 ° ). (i)–(l) correspond to the y z -incidence plane ( ϕ = 90 ° ). (e), (g), (i), and (k) correspond to s polarization with regard to their incidence planes. (f), (h), (j), and (l) correspond to p polarization with regard to their incidence planes. Parameters: η x = 73.33 % , η y = 66.67 % , t g = 0.4 Λ x = 0.4 Λ y , n a = 3.141 , and n b = 1 .
Figure 11.
Figure 11. (a) Fourier space showing the first Brillouin zone of 2D-periodic HCMs on a square lattice. (b) Dispersion curves of the three lowest order E x / H y -dominant eigenmodes. The light lines in the high- and low-index materials are shown as the pink dashed lines. The cut-off frequencies for the E H 20 and E H 22 modes are ω c 2 and ω c 4 , respectively. (c)–(e) Magnetic field profiles R [ H y ] for E H 00 , E H 20 , and E H 22 modes, respectively. The refractive indices are n a = 3.141 and n b = 1 . The periods are Λ x = Λ y = 750    nm . The length and width of the air holes are w x = 550    nm and w y = 500    nm . The incidence is surface normal and E x / H y polarized. ω Λ x / 2 π c = 0.7 in (c)–(e) [29].
Figure 12.
Figure 12. 2D-periodic mesh-type HCM under E x / H y -polarized normal incidence. (a) FP resonance conditions, (b) reflectivity contour, and (c) overlaps between resonance lines and the reflectivity contour as functions of the wavelength and the HCM thickness. Red and black dots in (a) indicate the resonant supermodes dominated by the E H 00 and E H 20 modes, respectively. Pink and blue dots in (a) both indicate resonant supermodes being a mixture of E H 00 and E H 22 modes. HCM parameters are the same as in Fig. 11 [29].
Figure 13.
Figure 13. FDTD simulated band diagram of a 2D HCM or a 2D PhC slab on a square lattice ( Λ x = Λ y = Λ ), indicating their operation regimes. The incidence light is E x / H y polarized. The left half is the Γ X band structure, corresponding to Figs. 10(b), 10(f), and 10(h). The right half is the Γ Y band structure, corresponding to Figs. 10(c), 10(i), and 10(k). The operation regimes for HCMs and PhCs are separated by the θ = 90 ° light lines (red lines), and are shaded in red and green, respectively. The HCM and diffraction regimes are separated by folded light lines from neighboring Brillouin zones. The HCM parameters are the same as in Fig. 11.
Figure 14.
Figure 14. Examples of HCM mirrors: (a) 1D high-contrast gratings [10]; (b) 1D zero-contrast gratings. Adapted from [54]. Copyright 2014 Optical Society of America. (c) Combination of lateral periodic structures with 1D high-contrast vertical structure, using multilayer membrane stacks. Adapted from [55]. Copyright Wiley-VCH Verlag GmbH & Co. KGaA.
Figure 15.
Figure 15. (a) Schematic of a proton-implanted tunable VCSEL using a MEMS-controlled 1D HCM mirror [13]. (b) Magnified view of the top mirror of an oxide-confined MEMS-tunable VCSEL using 2D HCM [29].
Figure 16.
Figure 16. (a) Reflectivity spectrum (black) of a 2D HCM showing 100% reflection at wavelengths of 1024 and 1093 nm, indicated by the blue dashed lines. When perfect reflection occurs, the transmission phase spectrum (red) has a π discontinuity. (b) Magnitudes and (c) phases of the transmission coefficients outcoupled from individual HCM modes, with E H 00 , E H 20 , E H 22 , and all the remaining evanescent modes shown in blue, red, orange, and purple, respectively. The 2D HCM dimensions are the same as in Fig. 11.
Figure 17.
Figure 17. (a) Schematic of an optically-pumped CMOS-compatible double-HCM VCSEL. Copyright 2012 IEEE. Adapted from [66]. (b) Schematic of an optically pumped silicon membrane reflector VCSEL fabricated by transfer printing. Adapted from [67]. Copyright 2012.
Figure 18.
Figure 18. (a) Cross-sectional and (b) tilted-view schematics of an individual pixel of an optical phased array. Each pixel is an HCM all-pass filter (APF) individually controlled by MEMS voltage. The device is fabricated on a GaAs-based epitaxial wafer. GaAs HCMs are suspended on a GaAs/AlGaAs DBR, forming the FP etalon. (c) SEM of the 8 × 8 optical phased array using MEMS HCM-APFs [25].
Figure 19.
Figure 19. (a) SEM of an in-plane 20-row 2D PhC mirror next to a ridge waveguide. (b) Schematics of a short-cavity ridge waveguide laser using 2D PhC mirrors [69].
Figure 20.
Figure 20. Examples of frequency selective surfaces. (a) Copper scatterers on a dielectric sheet as a dual-frequency reflector [78]. © 1979 IEEE. Reprinted, with permission, from Agrawal and Imbriale, IEEE Trans. Antennas Propag. 27, 466–473 (1979). (b) A periodic array of dielectric strips for total reflection or total transmission [79]. © 1989 IEEE. Reprinted, with permission, from Bertoni et al., IEEE Trans. Antennas Propag. 37, 78–83 (1989)
Figure 21.
Figure 21. (a) “Metafilm,” first coined in 2003, refers to a 2D distribution of electrically small scatterers, which are characterized by electrical and magnetic polarization densities. Copyright 2003 IEEE. Reprinted with permission from Kuester et al., IEEE Trans. Antennas Propag. 51, 2641–2651 (2003) [81]. (b) Generalized sheet transition conditions for characterizing metasurfaces. Holloway et al., Radio Sci. 49, 813–850 (2014) [82]. Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission. (c) Generalized laws of reflection and refraction at metasurfaces with interfacial phase gradients. Reprinted with permission from Yu et al., Science 334, 333–337 (2011) [83]. Reprinted with permission from AAAS. (d) A 2D metasurface consisting of orientation-varying dielectric gratings. Adapted from [59]. Copyright 2002 Optical Society of America. (e) and (f) 2D metasurfaces consisting of dimension-varying dielectric gratings. (e) Reprinted from [22]. Copyright 2010 Optical Society of America. (f) Reprinted by permission from Macmillan Publishers Ltd.: Fattal et al., Nat. Photonics 4, 466–470 (2010) [23]. Copyright 2010.
Figure 22.
Figure 22. Regions of operation for metasurfaces classified based on the effective wavelength and mode interference.
Figure 23.
Figure 23. Examples of building blocks on metasurfaces. Metallic nanostructures: (a) V-antennas (adapted from [83]); (b) H-antennas (adapted from [86]. Copyright 2012); (c) slot antennas (adapted from [87]. Copyright Wiley-VCH Verlag GmbH & Co. KGaA); and (d) nanorod antennas (adapted from [88]. Copyright 2012 American Chemical Society). Dielectric nanostructures: (e) nanoposts (adapted from [30]. Copyright 2015); (f) nanobeams (adapted from [89]); (g) double rectangular resonators (adapted from [90]. Copyright 2015 American Chemical Society); and (h) dielectric mesh [25].
Figure 24.
Figure 24. Two types of arrangement for building blocks on metasurfaces: (a) dimension-varying and (b) orientation-varying metastructures [31].
Figure 25.
Figure 25. Design strategy for dimension-varying metasurfaces. (a) Transmissivity contour as a function of the lateral dimensions ( w x and w y ) of the rectangular building blocks. (b) Transmission phase ϕ x x contour as a function of w x and w y . The dashed lines in (a) and (b) show the varying ranges of w x and w y that provide high transmission ( > 95 % ) and covers a full 2 π transmission phase range. (c) Transmissivity (blue) and phase (red) variations as functions of the lateral dimensions along the black dashed line in (a) and (b). Both the incidence and the calculated transmission are x polarized at λ = 633    nm . The HCM parameters are Λ = 510    nm , t g = 240    nm , n a = 1 , and n b = 3.85 .
Figure 26.
Figure 26. Design strategy for orientation-varying metasurfaces. (a) Cross-polarized transmissivity | t cross | 2 contour at λ = 1550    nm as a function of the lateral dimensions of the rectangular building blocks. The white star indicates the chosen design. (b) Transmissivity spectra (solid) and phase (dashed) spectra for x polarization (blue) and y polarization (red). At 1550 nm, the difference between ϕ x x and ϕ y y is π . (c) Co-polarized (red), cross-polarized (blue), and total transmissivity spectra (green) showing the broadband operation of orientation-varying metasurfaces. The 3 dB bandwidth for cross polarization is Δ λ / λ 0 = 12.9 % . The HCM parameters are Λ = 1.1    μm , t g = 1    μm , w x = 540    nm , w y = 250    nm , n a = 1 , and n b = 3.48 .
Figure 27.
Figure 27. Major applications for metasurfaces. (a) Reflection and refraction of light at anomalous angles [27]. (b) Focusing, diverging, and collimation of light [93]. (c) Shaping of the spatial beam profiles [95]. For example, generation of vortex beams. (d) Polarization control or conversion of light [96]. (e) 3D display and holography [87].
Figure 28.
Figure 28. (a) GS algorithm for generating the near-field phase distribution and the phase hologram from a target image. (b) Target image with pseudo-color representation of the image brightness. (c) FDTD simulation of the reconstructed image from the transmitted near field through an orientation-varying metasurface. The incidence is LHCP at λ = 1550    nm and the RHCP transmitted field is captured. Field intensity is represented via pseudo-coloration. The hologram is generated by the GS algorithm and the HCM design is the same as in Fig. 26.
Figure 29.
Figure 29. (a) Generation of a hologram by the point-source algorithm. (b) Reconstruction of the 3D object with the virtual object and image distances at u and v , respectively. Simulation of the transmitted near field through a metasurface being projected onto an image plane at distances of (c)  v = 4.722    mm , (d)  v = 4.873    mm , and (e)  v = 5    mm . The focal length is f = 2.795    mm . The distance between the metasurface and the lens is 2.8 mm. The virtual object distances are (c)  u = 6.848    mm , (d)  u = 6.554    mm , and (e)  u = 6.3    mm , with blue arrows indicating the focused parts of the virtual object.
Figure 30.
Figure 30. SEM, schematic and full-wave simulation of the multi-directional backlight technology for glass-free 3D display. Each unit cell contains a group of directional gratings to cover the 64 views within the field-of-view. Polarized and guided input light is scattered from the in-plane direction into the viewing angle using the first-order diffraction. Reprinted by permission from Macmillan Publishers Ltd.: Fattal et al., Nature 495, 348–351 (2013) [104] Copyright 2013.
Figure 31.
Figure 31. Schematics of laterally tunable 2D metasurfaces. Each period comprises a wave-shaped grating bar (s-bar) and a straight grating bar (l-bar). (a) No displacement of s-bars when tuning is off. (b) Displacement of s-bars in the + x direction when tuning is on.
Figure 32.
Figure 32. Performance of laterally tunable 2D metasurfaces. (a) Reflection spectra for x -polarized light with the tuning on (red) and off (black). (b) Reflection spectra for y -polarized light with the tuning on (blue) and off (green). Tuning on and off correspond to zero and 50 nm displacement, respectively. (c) and (d) Correspond to the field profiles R [ H y / H 0 ] across the middle z -plane ( z = t g / 2 ) under E x / H y -polarized incidence. (e) and (f) Correspond to the field profiles R [ H x / H 0 ] across the middle z -plane ( z = t g / 2 ) under E y / H x -polarized incidence. The incidence wavelength is λ = 633    nm . Here, Λ x = Λ y = 490    nm and t g = 380    nm . Widths of both bars are 81.7 nm. The index of the bars is 3.48.
Figure 33.
Figure 33. (a) Schematic of an HCM 3D HCW. In the lateral direction, the core and cladding are defined by different HCG parameters to provide lateral confinement. In between the core and cladding region is the chirped HCG to provide a graded index profile. The waveguide height is d . (b) The bottom panel shows the experimentally measured mode profile for the HCM 2D HCW with d = 9    μm [19].
Figure 34.
Figure 34. Compact optical components based on HCM hollow-core waveguide. (a) 3 dB MMI-based splitter. (b)  1 × 4 splitter. (c)  2 × 2 MMI coupler. (d) An optical switch where the output can be switched from Ch1 to Ch2 by changing the refractive index of the HCM in the MMI region. (e) and (f) show the FDTD simulation of the switch. The switching length is 60    μm , and the refractive index change is 7 × 10 3 at this switching region [20].
Figure 35.
Figure 35. (a) Schematic of an HCM vertical coupler. (b) Field profiles of vertical-to-in-plane coupling (bottom left) and in-plane-to-vertical coupling (bottom right) with corresponding coupling efficiency spectra (top left and top right) [21].
Figure 36.
Figure 36. (a) Schematic of an HCM-plasmonic sensor under normal x -polarized (TM) incidence. The refractive indices for the superstrate, substrate, spacer, and HCM are n super = 1.45 , n sub = 1.33 , and n spacer = 1.5 , and n HCM = 3.84 , respectively. The HCM dimensions are Λ = 549.35    nm , η = 62.4 % , and t g = 200    nm . The gold layer thickness is 50 nm, and the permittivity is interpolated from Ref. [110]. (b) In-plane propagation constants k x as functions of the wavelength for the SPP at the spacer–Au interface (blue), the SPP at the substrate–Au interface (green), and the (+1)-diffraction order from the HCM (red) with k x = 2 π / Λ . The total propagation constant k = n super ω / c in the superstrate is shown as the black line. (c) RCWA-calculated reflectivity contour as a function of the wavelength and the spacer thickness t s . Strong SPP resonance is expected along the coupling lines indicated by the green and blue arrows. Three designs indicated by the black circles are analyzed for field enhancement. The FDTD-calculated intensity distributions | E z / E inc | 2 for (d)  t s = 2260    nm , λ = 762.66    nm , (e)  t s = 400    nm , λ = 765.46    nm , and (f)  t s = 500    nm , λ = 848.39    nm show enhancement of 296, 297, and 173, respectively.
Figure 37.
Figure 37. Slow light in a PhC waveguide. (a) Scanning electron microscope image of a PhC waveguide. (b)  ω k diagram and the group index spectrum of a silicon PhC waveguide. (c) Scanning electron microscope image of a PhC waveguide designed to have zero GVD slow light. (d) The group index of the zero GVD PhC waveguide. All sub-figures adapted from [7].
Figure 38.
Figure 38. Optical switch based on a PhC waveguide. (a) Scanning electron microscope image of a directional coupler switch. Reprinted with permission from [113]. Copyright 2008 Optical Society of America. (b) Schematic of an all-optical switch based on a PhC waveguide and an H0 cavity. (c) Operating principle of all-optical switching. A pump carrier induces a wavelength shift in the resonant transmission spectrum of the signal. (b) and (c) Figures adapted from [114] Copyright 2010.
Figure 39.
Figure 39. Assortment of optical and scanning electron microscope imaging of PCF structures. (a) Single-mode solid core PCF. (b) Far-field pattern produced by (a) when excited by red and green laser light. (c) Birefringent PCF. (d) Small core PCF. (e) First photonic bandgap PCF. (f) Near field of the six-leaved blue mode that appears when (e) is excited by white light. (g) Hollow-core photonic bandgap fiber. (h) Near field of a red mode in a hollow-core PCF. (i) A hollow-core PCF with a Kagome cladding lattice, guiding white light. Reprinted with permission from Russell, Science 299, 358–362 (2003) [115]. Reprinted with permission from AAAS.
Figure 40.
Figure 40. (a) Schematic of a high- Q resonator with 15-period middle 1D HCM grating and two 5-period mix DBR gratings on each side as mirrors [17]. (b) Schematic of surface-normal coupled Si-based 1D HCM resonator [116]. (c) Schematic of surface-normal spatial light modulator using graphene on an HCM resonator [117]. (d) Reflection spectra of an HCM resonator as a biosensor immersed in liquids with various refractive indices [18]. Reproduced from [18] under the terms of the http://creativecommons.org/licenses/by/4.0/. (e) HCM resonator for enhancing the four-wave mixing of the normal incidence [116]. (f) Voltage-tunable reflectivity spectra of a graphene-integrated HCM resonator showing electro-optic spatial light modulation [117].
Figure 41.
Figure 41. PhC laser operating at the band edge. (a) Schematic of the PhC structure. Arrows indicate the growth direction of the first epitaxial and regrowth structures. (b) Coupling diagram shown in the reciprocal space of the square-lattice PhC. Out-of-plane coupling occurs due to first-order Bragg diffraction. (c) Left panel, band structure of the PhC laser measured well below threshold current; right panel, the lasing spectrum measured in the surface-normal direction by injecting current above threshold. They are all adapted from [119]. Copyright 2014.
Figure 42.
Figure 42. Electrically pumped point-defect-type PhC laser. (a) Schematic of the electrically pumped PhC laser made of GaAs with InAs quantum dots as the active layer. The width of the intrinsic region is narrow in the cavity region to direct current flow to the active region of the laser. (b) Modified three-hole defect PhC cavity design (top), and an FDTD simulation of the electrical field of the cavity mode (bottom). Reprinted by permission from Macmillan Publishers Ltd.: Ellis et al., Nat. Photonics 5, 297–300 (2011) [121]. Copyright 2011.
Figure 43.
Figure 43. Examples of mechanical and optical reconfigurable metastructures. (a) Tunable coloration using flexible HCMs under various stretching deformation ε [27]. (b) Stretchable HCM lens showing continuously tunable focal length [131]. (c) Optically actuated HCMs giving rise to a large optical nonlinearity [123]. (d) Optomechanical oscillation of the HCM suspended mirror on a VCSEL. Left, laser being turned off; right, laser being turned on with CW pump current. (d) Reproduced from [53] under the terms of the http://creativecommons.org/licenses/by/4.0/.
Figure 44.
Figure 44. Examples of thermal and electrical reconfigurable metastructures. (a) Thermal control of the structural deformation [125]. (b) Electrostatic actuation of the structural position [125]. (a) and (b) reprinted by permission from Macmillan Publishers Ltd.: Zheludev and Plum, Nat. Nanotech. 11, 16–22 (2016). (c) Gate voltage control of the permittivity of conducting oxides [127]. Reprinted with permission from Huang et al., Nano Lett. 16, 5319–5325 (2016). [127]. Copyright 2016 American Chemical Society. (d) Thermal control of the phase delay of an individual waveguide, and thus the emitting phase of the corresponding antenna [129]. Reprinted with permission from Sun et al., Nature 493, 195–199 (2013). (e) Thermal control of material phase transition [130]. The VO2 layer is laterally patterned into a metastructure, with alternative regions of different phase transition critical temperatures. By changing the temperature, alternative regions transition to the metallic phase, abolishing the polarization selectivity in light reflectivity. Reprinted with permission from Rensberg et al., Nano Lett. 16, 1050–1055 (2016) [130]. Copyright 2016 American Chemical Society.
Figure 45.
Figure 45. Periodic and quasi-periodic structures for manipulating light properties including: propagation direction, intensity, phase, angular momentum, and interaction with matter [7,10,17,22,29,83,89,96,115,120,134138].

Tables (3)

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Table 1. Description of Math Symbols

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Table 2. Comparison among Various Computation Methods for Periodic Structures

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Table 3. Capabilities of Various Computation Methods for Periodic Structures a

Equations (41)

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k 0 = x ^ k 0 x + y ^ k 0 y + z ^ k 0 z = n 0 ω c ( x ^ sin θ cos ϕ + y ^ sin θ sin ϕ + z ^ cos θ ) .
E t ( r ) = A 0 E t ( 0 ) ( x , y ) e i β 0 z + A 2 E t ( 2 ) ( x , y ) e i β 2 z = [ E t ( 0 ) E t ( 2 ) ] [ e i β 0 z 0 0 e i β 2 z ] [ A 0 A 2 ] .
M ¯ RT ( λ , t g ) = R ¯ II I e i β ¯ t g R ¯ II III e i β ¯ t g ,
M ¯ 2 × 2 RT ( λ , t g ) [ A 0 A 2 ] = | Ω | e i ϕ [ A 0 A 2 ] .
ϕ p , q = 2 m π , m = 0,1 , 2,3 .
M ¯ 3 × 3 RT ( λ , t g ) [ A 0 A 1 A 2 ] = | Ω | e i ϕ [ A 0 A 1 A 2 ] .
ϕ n = 2 m π , m = 0,1 , 2,3 .
sin θ n = sin θ 0 + n λ Λ , n = 0 , ± 1 , ± 2 , .
n t sin θ t n i sin θ i = λ 0 2 π d ϕ d x .
W 0 = ( t x x 0 0 t y y ) .
W ( ψ ) = ( cos ψ sin ψ sin ψ cos ψ ) W 0 ( cos ψ sin ψ sin ψ cos ψ ) .
E t L / R = W ( ψ ) E i L / R = t x x + t y y 2 E i L / R + t x x t y y 2 exp ( 2 i ψ ) E i R / L .
E ( x j , y j ) = i A i r i j exp ( i 2 π λ r i j + i ϕ i ) .
E t ( r ) = x ^ E x ( r ) + y ^ E y ( r ) = i L A i E t ( i ) ( x , y ) e i β i z H t ( r ) = x ^ H x ( r ) + y ^ H y ( r ) = i L A i H t ( i ) ( x , y ) e i β i z ,
[ E t ( r ) H t ( r ) ] = [ E t ( 1 ) E t ( L ) E t ( 1 ) E t ( L ) H t ( 1 ) H t ( L ) H t ( 1 ) H t ( L ) ] [ e i β ¯ z 0 ¯ 0 ¯ e i β ¯ z ] [ A 1 + A L + A 1 A L ] .
[ E t ( r ) H t ( r ) ] = [ E ¯ t ( x , y ) E ¯ t ( x , y ) H ¯ t ( x , y ) H ¯ t ( x , y ) ] [ A + ( z ) A ( z ) ] .
[ A + ( z ) A ( z ) ] = [ e i β ¯ z 0 ¯ 0 ¯ e i β ¯ z ] [ A + ( 0 ) A ( 0 ) ] = ϕ ¯ 2 L × 2 L [ A + ( 0 ) A ( 0 ) ] ,
[ E t , I ( z 0 ) H t , I ( z 0 ) ] = [ E t , II ( z 0 + ) H t , II ( z 0 + ) ] .
[ E ¯ t , I E ¯ t , I H ¯ t , I H ¯ t , I ] [ A + ( z 0 ) A ( z 0 ) ] = [ E ¯ t , II E ¯ t , II H ¯ t , II H ¯ t , II ] [ A + ( z 0 + ) A ( z 0 + ) ] .
G x = 2 m π Λ x , m = 0 , ± 1 , ± 2 , , ± g x , max G y = 2 n π Λ y , n = 0 , ± 1 , ± 2 , , ± g y , max .
E t ( i ) E ˜ t ( i ) = [ E ˜ x , G 1 ( i ) E ˜ x , G N ( i ) E ˜ y , G 1 ( i ) E ˜ y , G N ( i ) ] 2 N × 1 , H t ( i ) H ˜ t ( i ) = [ H ˜ x , G 1 ( i ) H ˜ x , G N ( i ) H ˜ y , G 1 ( i ) H ˜ y , G N ( i ) ] 2 N × 1 ,
[ A + ( z 0 + ) A ( z 0 + ) ] = [ E ˜ ¯ t , II E ˜ ¯ t , II H ˜ ¯ t , II H ˜ ¯ t , II ] 4 N × 4 N 1 [ E ˜ ¯ t , I E ˜ ¯ t , I H ˜ ¯ t , II H ˜ ¯ t , II ] 4 N × 4 N [ A + ( z 0 ) A ( z 0 ) ] = T ¯ 4 N × 4 N [ A + ( z 0 ) A ( z 0 ) ] ,
A in + = [ 1 0 0 ] 2 N × 1 ,
E ˜ t ( 1 ) = [ 0 1 0 0 0 ] 2 N × 1 ,
[ A trans + A ref ] = S ¯ total [ A in + 0 ] .
E ( i ) ( r ) = E ( i ) ( x , y ) e i β i z = e i β i z ( G E ˜ G ( i ) e i G · r ) e i k 0 x x + i k 0 y y .
× × E ( i ) = ω 2 c 2 ϵ 0 D ( i ) = ω 2 c 2 ϵ r ( r ) E ( i ) .
2 E x z 2 + 2 E z z x = ω 2 c 2 ϵ 0 D x + 2 E x y 2 2 E y x y , 2 E y z 2 + 2 E z z y = ω 2 c 2 ϵ 0 D y + 2 E y x 2 2 E x y x , ( 2 x 2 + 2 y 2 ) E z + ω 2 c 2 ϵ 0 D z = 2 E x z x + 2 E y z y .
D ˜ G ( i ) = G ϵ 0 ϵ G G E ˜ G ( i ) ,
ϵ G G = 1 S ϵ r ( r ) e i ( G G ) · r d x d y .
G Q G G E ˜ z , G ( i ) = β i [ ( k 0 x + G x ) E ˜ x , G ( i ) + ( k 0 y + G y ) E ˜ y , G ( i ) ] ,
Q G G = ( k 0 x + G x ) 2 ( k 0 y + G y ) 2 δ G G + ω 2 c 2 ϵ G G .
E ˜ z , G ( i ) = G Q G G 1 β i [ ( k 0 x + G x ) E ˜ x , G ( i ) + ( k 0 y + G y ) E ˜ y , G ( i ) ] .
[ A ¯ 11 A ¯ 12 A ¯ 21 A ¯ 22 ] [ E ˜ x , G 1 ( i ) E ˜ x , G N ( i ) E ˜ y , G 1 ( i ) E ˜ y , G N ( i ) ] = β i 2 [ B ¯ 11 B ¯ 12 B ¯ 21 B ¯ 22 ] [ E ˜ x , G 1 ( i ) E ˜ x , G N ( i ) E ˜ y , G 1 ( i ) E ˜ y , G N ( i ) ] ,
( A ¯ 11 ) G G = ( k 0 y + G y ) 2 δ G G + ω 2 c 2 ϵ G G , ( A ¯ 22 ) G G = ( k 0 x + G x ) 2 δ G G + ω 2 c 2 ϵ G G , ( A ¯ 12 ) G G = ( A ¯ 21 ) G G = ( k 0 x + G x ) ( k 0 y + G y ) δ G G , ( B ¯ 11 ) G G = δ G G ( k 0 x + G x ) Q G G 1 ( k 0 x + G x ) , ( B ¯ 22 ) G G = δ G G ( k 0 y + G y ) Q G G 1 ( k 0 y + G y ) , ( B ¯ 12 ) G G = ( k 0 x + G x ) Q G G 1 ( k 0 y + G y ) , ( B ¯ 21 ) G G = ( k 0 y + G y ) Q G G 1 ( k 0 x + G x )
E ˜ ¯ t = [ E ˜ t ( 1 ) E ˜ t ( L ) ] = [ E ˜ x , G 1 ( 1 ) E ˜ x , G 1 ( L ) E ˜ x , G N ( 1 ) E ˜ x , G 1 ( L ) E ˜ y , G 1 ( 1 ) E ˜ x , G 1 ( L ) E ˜ y , G N ( 1 ) E ˜ x , G 1 ( L ) ] 2 N × L ,
H ˜ ¯ t = 1 ω μ 0 [ B ¯ 21 B ¯ 22 B ¯ 11 B ¯ 12 ] E ˜ ¯ t · β ¯ ,
ϵ G G = ϵ a δ G G + ( ϵ b ϵ a ) sin [ ( G G ) w / 2 ] ( G G ) Λ / 2 .
ϵ G G = ϵ a δ G G + ( ϵ b ϵ a ) sin [ ( G x G x ) w x / 2 ] ( G x G x ) Λ x / 2 sin [ ( G y G y ) w y / 2 ] ( G y G y ) Λ y / 2 .
ϵ G G = { ϵ a + ( ϵ b ϵ a ) π r 2 Λ x Λ y for    G = G 2 ( ϵ b ϵ a ) J 1 ( | G G | r ) | G G | r π r 2 Λ x Λ y for    G G .
ϵ G G = { ϵ a + ( ϵ b ϵ a ) 2 π r 2 3 Λ 2 for    G = G 2 ( ϵ b ϵ a ) J 1 ( | G G | r ) | G G | r π r 2 3 Λ 2 ( 1 + e i ( G x G x ) Λ / 2 e i ( G y G y ) 3 Λ / 2 ) for    G G .

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