Abstract

We experimentally demonstrate a TiO2 double-groove grating coupler with two different groove widths on a SiO2 substrate in the visible region. Tolerance investigations based on Bloch-mode profiles in the grating and coupling strengths between the Bloch modes and diffraction orders reveal that the transmission performance is robust when one of the paired ridges is narrow enough (60 nm and less) considering a typical nanofabrication accuracy. Moreover, the ridge shape affects weakly the transmission performance due to the non-resonance operation of our dielectric device. Such tolerance investigations together with current nanofabrication technology enable us to accomplish a 70% efficiency for coupling the normal incident light into the + 1st order transmission diffraction satisfying the total internal reflection condition at a 640 nm wavelength of operation.

© 2014 Optical Society of America

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References

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2014 (1)

K. Ito, T. Matsui, and H. Iizuka, “Thermal emission control by evanescent wave coupling between guided mode of resonant grating and surface phonon polaritons on silicon carbide plate,” Appl. Phys. Lett. 104(5), 051127 (2014).
[Crossref]

2013 (4)

M. Oliva, D. Michaelis, F. Fuchs, A. Tunnermann, and U. D. Zeitner, “Highly efficient broadband blazed grating in resonance domain,” Appl. Phys. Lett. 102(20), 203114 (2013).
[Crossref]

K. Ito and H. Iizuka, “Highly efficient −1st-order reflection in Littrow mounted dielectric double-groove grating,” AIP Advances 3(6), 062119 (2013).
[Crossref]

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

C. Ribot, M.-S. L. Lee, S. Collin, S. Bansropun, P. Plouhinec, D. Thenot, S. Cassette, B. Loiseaux, and P. Lalanne, “Broadband and efficient diffraction,” Adv. Opt. Mater. 1(7), 489–493 (2013).
[Crossref]

2012 (2)

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3, 692 (2012).
[Crossref] [PubMed]

V. Karagodsky and C. J. Chang-Hasnain, “Physics of near-wavelength high contrast gratings,” Opt. Express 20(10), 10888–10895 (2012).
[Crossref] [PubMed]

2011 (1)

2010 (4)

V. Karagodsky, B. Pesala, C. Chase, W. Hofmann, F. Koyama, and C. J. Chang-Hasnain, “Monolithically integrated multi-wavelength VCSEL arrays using high-contrast gratings,” Opt. Express 18(2), 694–699 (2010).
[Crossref] [PubMed]

H. Iizuka, N. Engheta, H. Fujikawa, K. Sato, and Y. Takeda, “Role of propagating modes in a double-groove grating with a +1st-order diffraction angle larger than the substrate-air critical angle,” Opt. Lett. 35(23), 3973–3975 (2010).
[Crossref] [PubMed]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[Crossref]

H. Iizuka, N. Engheta, H. Fujikawa, K. Sato, and Y. Takeda, “Switching capability of double-sided grating with horizontal shift,” Appl. Phys. Lett. 97(5), 053108 (2010).
[Crossref]

2008 (1)

G. Roelkens, D. Vermeulen, D. Van Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J.-M. Fedeli, “High efficiency diffractive grating couplers for interfacing a single mode optical fiber with a nanophotonic silicon-on-insulator waveguide circuit,” Appl. Phys. Lett. 92(13), 131101 (2008).
[Crossref]

2007 (4)

2006 (1)

2005 (1)

2004 (3)

D. Taillaert, P. Bienstman, and R. Baets, “Compact efficient broadband grating coupler for silicon-on-insulator waveguides,” Opt. Lett. 29(23), 2749–2751 (2004).
[Crossref] [PubMed]

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12-1.62 μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16(7), 1676–1678 (2004).
[Crossref]

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[Crossref]

2000 (1)

1998 (2)

1996 (3)

1995 (1)

1992 (2)

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992).
[Crossref]

M. W. Farn, “Binary gratings with increased efficiency,” Appl. Opt. 31(22), 4453–4458 (1992).
[Crossref] [PubMed]

1982 (1)

P. Sheng, R. S. Stepleman, and P. N. Sanda, “Exact eigenfunctions for square-wave gratings: application to diffraction and surface-plasmon calculations,” Phys. Rev. B 26(6), 2907–2916 (1982).
[Crossref]

1981 (1)

Astilean, S.

Baets, R.

G. Roelkens, D. Vermeulen, D. Van Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J.-M. Fedeli, “High efficiency diffractive grating couplers for interfacing a single mode optical fiber with a nanophotonic silicon-on-insulator waveguide circuit,” Appl. Phys. Lett. 92(13), 131101 (2008).
[Crossref]

D. Taillaert, P. Bienstman, and R. Baets, “Compact efficient broadband grating coupler for silicon-on-insulator waveguides,” Opt. Lett. 29(23), 2749–2751 (2004).
[Crossref] [PubMed]

Bansropun, S.

C. Ribot, M.-S. L. Lee, S. Collin, S. Bansropun, P. Plouhinec, D. Thenot, S. Cassette, B. Loiseaux, and P. Lalanne, “Broadband and efficient diffraction,” Adv. Opt. Mater. 1(7), 489–493 (2013).
[Crossref]

Beausoleil, R. G.

Z. Peng, D. Fattal, A. Faraon, M. Fiorentino, J. Li, and R. G. Beausoleil, “Reflective silicon binary diffraction grating for visible wavelengths,” Opt. Lett. 36(8), 1515–1517 (2011).
[Crossref] [PubMed]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[Crossref]

Bienstman, P.

Brener, I.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Brision, S.

G. Roelkens, D. Vermeulen, D. Van Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J.-M. Fedeli, “High efficiency diffractive grating couplers for interfacing a single mode optical fiber with a nanophotonic silicon-on-insulator waveguide circuit,” Appl. Phys. Lett. 92(13), 131101 (2008).
[Crossref]

Brundrett, D. L.

Cambril, E.

Cassette, S.

C. Ribot, M.-S. L. Lee, S. Collin, S. Bansropun, P. Plouhinec, D. Thenot, S. Cassette, B. Loiseaux, and P. Lalanne, “Broadband and efficient diffraction,” Adv. Opt. Mater. 1(7), 489–493 (2013).
[Crossref]

Chang-Hasnain, C. J.

V. Karagodsky and C. J. Chang-Hasnain, “Physics of near-wavelength high contrast gratings,” Opt. Express 20(10), 10888–10895 (2012).
[Crossref] [PubMed]

V. Karagodsky, B. Pesala, C. Chase, W. Hofmann, F. Koyama, and C. J. Chang-Hasnain, “Monolithically integrated multi-wavelength VCSEL arrays using high-contrast gratings,” Opt. Express 18(2), 694–699 (2010).
[Crossref] [PubMed]

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007).
[Crossref]

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[Crossref]

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12-1.62 μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16(7), 1676–1678 (2004).
[Crossref]

Chase, C.

Chavel, P.

Chen, L.

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12-1.62 μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16(7), 1676–1678 (2004).
[Crossref]

Clausnitzer, T.

Collin, S.

C. Ribot, M.-S. L. Lee, S. Collin, S. Bansropun, P. Plouhinec, D. Thenot, S. Cassette, B. Loiseaux, and P. Lalanne, “Broadband and efficient diffraction,” Adv. Opt. Mater. 1(7), 489–493 (2013).
[Crossref]

Decker, M.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Deng, Y.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[Crossref]

Dominguez, J.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Engheta, N.

Fainman, Y.

Faraon, A.

Farn, M. W.

Fattal, D.

Z. Peng, D. Fattal, A. Faraon, M. Fiorentino, J. Li, and R. G. Beausoleil, “Reflective silicon binary diffraction grating for visible wavelengths,” Opt. Lett. 36(8), 1515–1517 (2011).
[Crossref] [PubMed]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[Crossref]

Fedeli, J.-M.

G. Roelkens, D. Vermeulen, D. Van Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J.-M. Fedeli, “High efficiency diffractive grating couplers for interfacing a single mode optical fiber with a nanophotonic silicon-on-insulator waveguide circuit,” Appl. Phys. Lett. 92(13), 131101 (2008).
[Crossref]

Feng, J.

Fiorentino, M.

Z. Peng, D. Fattal, A. Faraon, M. Fiorentino, J. Li, and R. G. Beausoleil, “Reflective silicon binary diffraction grating for visible wavelengths,” Opt. Lett. 36(8), 1515–1517 (2011).
[Crossref] [PubMed]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[Crossref]

Fofang, N. T.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Fuchs, F.

M. Oliva, D. Michaelis, F. Fuchs, A. Tunnermann, and U. D. Zeitner, “Highly efficient broadband blazed grating in resonance domain,” Appl. Phys. Lett. 102(20), 203114 (2013).
[Crossref]

Fujikawa, H.

Gautier, P.

G. Roelkens, D. Vermeulen, D. Van Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J.-M. Fedeli, “High efficiency diffractive grating couplers for interfacing a single mode optical fiber with a nanophotonic silicon-on-insulator waveguide circuit,” Appl. Phys. Lett. 92(13), 131101 (2008).
[Crossref]

Gaylord, T. K.

Glytsis, E. N.

Gonzales, E.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Grann, E. B.

Hofmann, W.

Huang, M. C. Y.

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007).
[Crossref]

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[Crossref]

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12-1.62 μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16(7), 1676–1678 (2004).
[Crossref]

Hugonin, J. P.

Iizuka, H.

K. Ito, T. Matsui, and H. Iizuka, “Thermal emission control by evanescent wave coupling between guided mode of resonant grating and surface phonon polaritons on silicon carbide plate,” Appl. Phys. Lett. 104(5), 051127 (2014).
[Crossref]

K. Ito and H. Iizuka, “Highly efficient −1st-order reflection in Littrow mounted dielectric double-groove grating,” AIP Advances 3(6), 062119 (2013).
[Crossref]

H. Iizuka, N. Engheta, H. Fujikawa, K. Sato, and Y. Takeda, “Switching capability of double-sided grating with horizontal shift,” Appl. Phys. Lett. 97(5), 053108 (2010).
[Crossref]

H. Iizuka, N. Engheta, H. Fujikawa, K. Sato, and Y. Takeda, “Role of propagating modes in a double-groove grating with a +1st-order diffraction angle larger than the substrate-air critical angle,” Opt. Lett. 35(23), 3973–3975 (2010).
[Crossref] [PubMed]

Ito, K.

K. Ito, T. Matsui, and H. Iizuka, “Thermal emission control by evanescent wave coupling between guided mode of resonant grating and surface phonon polaritons on silicon carbide plate,” Appl. Phys. Lett. 104(5), 051127 (2014).
[Crossref]

K. Ito and H. Iizuka, “Highly efficient −1st-order reflection in Littrow mounted dielectric double-groove grating,” AIP Advances 3(6), 062119 (2013).
[Crossref]

Kämpfe, T.

Karagodsky, V.

Kivshar, Y.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Kley, E.-B.

Koyama, F.

Lalanne, P.

Launois, H.

Lee, M. S. L.

Lee, M.-S. L.

C. Ribot, M.-S. L. Lee, S. Collin, S. Bansropun, P. Plouhinec, D. Thenot, S. Cassette, B. Loiseaux, and P. Lalanne, “Broadband and efficient diffraction,” Adv. Opt. Mater. 1(7), 489–493 (2013).
[Crossref]

Li, J.

Z. Peng, D. Fattal, A. Faraon, M. Fiorentino, J. Li, and R. G. Beausoleil, “Reflective silicon binary diffraction grating for visible wavelengths,” Opt. Lett. 36(8), 1515–1517 (2011).
[Crossref] [PubMed]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[Crossref]

Li, L.

Liu, S.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Loiseaux, B.

C. Ribot, M.-S. L. Lee, S. Collin, S. Bansropun, P. Plouhinec, D. Thenot, S. Cassette, B. Loiseaux, and P. Lalanne, “Broadband and efficient diffraction,” Adv. Opt. Mater. 1(7), 489–493 (2013).
[Crossref]

Luk, T. S.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Lyan, P.

G. Roelkens, D. Vermeulen, D. Van Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J.-M. Fedeli, “High efficiency diffractive grating couplers for interfacing a single mode optical fiber with a nanophotonic silicon-on-insulator waveguide circuit,” Appl. Phys. Lett. 92(13), 131101 (2008).
[Crossref]

Magnusson, R.

Mateus, C. F. R.

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12-1.62 μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16(7), 1676–1678 (2004).
[Crossref]

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[Crossref]

Matsui, T.

K. Ito, T. Matsui, and H. Iizuka, “Thermal emission control by evanescent wave coupling between guided mode of resonant grating and surface phonon polaritons on silicon carbide plate,” Appl. Phys. Lett. 104(5), 051127 (2014).
[Crossref]

Michaelis, D.

M. Oliva, D. Michaelis, F. Fuchs, A. Tunnermann, and U. D. Zeitner, “Highly efficient broadband blazed grating in resonance domain,” Appl. Phys. Lett. 102(20), 203114 (2013).
[Crossref]

Miroshnichenko, A. E.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Moharam, M. G.

Morris, G. M.

Neshev, D. N.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Neureuther, A. R.

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[Crossref]

Oliva, M.

M. Oliva, D. Michaelis, F. Fuchs, A. Tunnermann, and U. D. Zeitner, “Highly efficient broadband blazed grating in resonance domain,” Appl. Phys. Lett. 102(20), 203114 (2013).
[Crossref]

Parriaux, O.

Peng, Z.

Z. Peng, D. Fattal, A. Faraon, M. Fiorentino, J. Li, and R. G. Beausoleil, “Reflective silicon binary diffraction grating for visible wavelengths,” Opt. Lett. 36(8), 1515–1517 (2011).
[Crossref] [PubMed]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[Crossref]

Pesala, B.

Peschel, U.

Plouhinec, P.

C. Ribot, M.-S. L. Lee, S. Collin, S. Bansropun, P. Plouhinec, D. Thenot, S. Cassette, B. Loiseaux, and P. Lalanne, “Broadband and efficient diffraction,” Adv. Opt. Mater. 1(7), 489–493 (2013).
[Crossref]

Polman, A.

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3, 692 (2012).
[Crossref] [PubMed]

Pommet, D. A.

Ribot, C.

C. Ribot, M.-S. L. Lee, S. Collin, S. Bansropun, P. Plouhinec, D. Thenot, S. Cassette, B. Loiseaux, and P. Lalanne, “Broadband and efficient diffraction,” Adv. Opt. Mater. 1(7), 489–493 (2013).
[Crossref]

Rodier, J. C.

Roelkens, G.

G. Roelkens, D. Vermeulen, D. Van Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J.-M. Fedeli, “High efficiency diffractive grating couplers for interfacing a single mode optical fiber with a nanophotonic silicon-on-insulator waveguide circuit,” Appl. Phys. Lett. 92(13), 131101 (2008).
[Crossref]

Sanda, P. N.

P. Sheng, R. S. Stepleman, and P. N. Sanda, “Exact eigenfunctions for square-wave gratings: application to diffraction and surface-plasmon calculations,” Phys. Rev. B 26(6), 2907–2916 (1982).
[Crossref]

Sato, K.

Scherer, A.

Sheng, P.

P. Sheng, R. S. Stepleman, and P. N. Sanda, “Exact eigenfunctions for square-wave gratings: application to diffraction and surface-plasmon calculations,” Phys. Rev. B 26(6), 2907–2916 (1982).
[Crossref]

Shokooh-Saremi, M.

Spinelli, P.

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3, 692 (2012).
[Crossref] [PubMed]

Staude, I.

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Stepleman, R. S.

P. Sheng, R. S. Stepleman, and P. N. Sanda, “Exact eigenfunctions for square-wave gratings: application to diffraction and surface-plasmon calculations,” Phys. Rev. B 26(6), 2907–2916 (1982).
[Crossref]

Sun, P. C.

Suzuki, Y.

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12-1.62 μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16(7), 1676–1678 (2004).
[Crossref]

Taillaert, D.

Takeda, Y.

Thenot, D.

C. Ribot, M.-S. L. Lee, S. Collin, S. Bansropun, P. Plouhinec, D. Thenot, S. Cassette, B. Loiseaux, and P. Lalanne, “Broadband and efficient diffraction,” Adv. Opt. Mater. 1(7), 489–493 (2013).
[Crossref]

Tishchenko, A. V.

Tunnermann, A.

M. Oliva, D. Michaelis, F. Fuchs, A. Tunnermann, and U. D. Zeitner, “Highly efficient broadband blazed grating in resonance domain,” Appl. Phys. Lett. 102(20), 203114 (2013).
[Crossref]

Tünnermann, A.

Tyan, R. C.

Van Thourhout, D.

G. Roelkens, D. Vermeulen, D. Van Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J.-M. Fedeli, “High efficiency diffractive grating couplers for interfacing a single mode optical fiber with a nanophotonic silicon-on-insulator waveguide circuit,” Appl. Phys. Lett. 92(13), 131101 (2008).
[Crossref]

Vermeulen, D.

G. Roelkens, D. Vermeulen, D. Van Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J.-M. Fedeli, “High efficiency diffractive grating couplers for interfacing a single mode optical fiber with a nanophotonic silicon-on-insulator waveguide circuit,” Appl. Phys. Lett. 92(13), 131101 (2008).
[Crossref]

Verschuuren, M. A.

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3, 692 (2012).
[Crossref] [PubMed]

Wang, B.

Wang, S.

Wang, S. S.

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992).
[Crossref]

Zeitner, U. D.

M. Oliva, D. Michaelis, F. Fuchs, A. Tunnermann, and U. D. Zeitner, “Highly efficient broadband blazed grating in resonance domain,” Appl. Phys. Lett. 102(20), 203114 (2013).
[Crossref]

Zhou, C.

Zhou, Y.

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007).
[Crossref]

Zhou, Z.

ACS Nano (1)

I. Staude, A. E. Miroshnichenko, M. Decker, N. T. Fofang, S. Liu, E. Gonzales, J. Dominguez, T. S. Luk, D. N. Neshev, I. Brener, and Y. Kivshar, “Tailoring directional scattering through magnetic and electric resonances in subwavelength silicon nanodisks,” ACS Nano 7(9), 7824–7832 (2013).
[Crossref] [PubMed]

Adv. Opt. Mater. (1)

C. Ribot, M.-S. L. Lee, S. Collin, S. Bansropun, P. Plouhinec, D. Thenot, S. Cassette, B. Loiseaux, and P. Lalanne, “Broadband and efficient diffraction,” Adv. Opt. Mater. 1(7), 489–493 (2013).
[Crossref]

AIP Advances (1)

K. Ito and H. Iizuka, “Highly efficient −1st-order reflection in Littrow mounted dielectric double-groove grating,” AIP Advances 3(6), 062119 (2013).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (5)

G. Roelkens, D. Vermeulen, D. Van Thourhout, R. Baets, S. Brision, P. Lyan, P. Gautier, and J.-M. Fedeli, “High efficiency diffractive grating couplers for interfacing a single mode optical fiber with a nanophotonic silicon-on-insulator waveguide circuit,” Appl. Phys. Lett. 92(13), 131101 (2008).
[Crossref]

K. Ito, T. Matsui, and H. Iizuka, “Thermal emission control by evanescent wave coupling between guided mode of resonant grating and surface phonon polaritons on silicon carbide plate,” Appl. Phys. Lett. 104(5), 051127 (2014).
[Crossref]

M. Oliva, D. Michaelis, F. Fuchs, A. Tunnermann, and U. D. Zeitner, “Highly efficient broadband blazed grating in resonance domain,” Appl. Phys. Lett. 102(20), 203114 (2013).
[Crossref]

R. Magnusson and S. S. Wang, “New principle for optical filters,” Appl. Phys. Lett. 61(9), 1022–1024 (1992).
[Crossref]

H. Iizuka, N. Engheta, H. Fujikawa, K. Sato, and Y. Takeda, “Switching capability of double-sided grating with horizontal shift,” Appl. Phys. Lett. 97(5), 053108 (2010).
[Crossref]

IEEE Photon. Technol. Lett. (2)

C. F. R. Mateus, M. C. Y. Huang, L. Chen, C. J. Chang-Hasnain, and Y. Suzuki, “Broad-band mirror (1.12-1.62 μm) using a subwavelength grating,” IEEE Photon. Technol. Lett. 16(7), 1676–1678 (2004).
[Crossref]

C. F. R. Mateus, M. C. Y. Huang, Y. Deng, A. R. Neureuther, and C. J. Chang-Hasnain, “Ultrabroadband mirror using low-index cladded subwavelength grating,” IEEE Photon. Technol. Lett. 16(2), 518–520 (2004).
[Crossref]

J. Lightwave Technol. (1)

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (3)

Nat. Commun. (1)

P. Spinelli, M. A. Verschuuren, and A. Polman, “Broadband omnidirectional antireflection coating based on subwavelength surface Mie resonators,” Nat. Commun. 3, 692 (2012).
[Crossref] [PubMed]

Nat. Photonics (2)

M. C. Y. Huang, Y. Zhou, and C. J. Chang-Hasnain, “A surface-emitting laser incorporating a high-index-contrast subwavelength grating,” Nat. Photonics 1(2), 119–122 (2007).
[Crossref]

D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “Flat dielectric grating reflectors with focusing abilities,” Nat. Photonics 4(7), 466–470 (2010).
[Crossref]

Opt. Express (4)

Opt. Lett. (9)

B. Wang, C. Zhou, S. Wang, and J. Feng, “Polarizing beam splitter of a deep-etched fused-silica grating,” Opt. Lett. 32(10), 1299–1301 (2007).
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D. Taillaert, P. Bienstman, and R. Baets, “Compact efficient broadband grating coupler for silicon-on-insulator waveguides,” Opt. Lett. 29(23), 2749–2751 (2004).
[Crossref] [PubMed]

R. C. Tyan, P. C. Sun, A. Scherer, and Y. Fainman, “Polarizing beam splitter based on the anisotropic spectral reflectivity characteristic of form-birefringent multilayer gratings,” Opt. Lett. 21(10), 761–763 (1996).
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D. L. Brundrett, E. N. Glytsis, and T. K. Gaylord, “Normal-incidence guided-mode resonant grating filters: design and experimental demonstration,” Opt. Lett. 23(9), 700–702 (1998).
[Crossref] [PubMed]

P. Lalanne, S. Astilean, P. Chavel, E. Cambril, and H. Launois, “Blazed binary subwavelength gratings with efficiencies larger than those of conventional echelette gratings,” Opt. Lett. 23(14), 1081–1083 (1998).
[Crossref] [PubMed]

J. Feng and Z. Zhou, “Polarization beam splitter using a binary blazed grating coupler,” Opt. Lett. 32(12), 1662–1664 (2007).
[Crossref] [PubMed]

Z. Peng, D. Fattal, A. Faraon, M. Fiorentino, J. Li, and R. G. Beausoleil, “Reflective silicon binary diffraction grating for visible wavelengths,” Opt. Lett. 36(8), 1515–1517 (2011).
[Crossref] [PubMed]

M. S. L. Lee, P. Lalanne, J. C. Rodier, and E. Cambril, “Wide-field-angle behavior of blazed-binary gratings in the resonance domain,” Opt. Lett. 25(23), 1690–1692 (2000).
[Crossref] [PubMed]

H. Iizuka, N. Engheta, H. Fujikawa, K. Sato, and Y. Takeda, “Role of propagating modes in a double-groove grating with a +1st-order diffraction angle larger than the substrate-air critical angle,” Opt. Lett. 35(23), 3973–3975 (2010).
[Crossref] [PubMed]

Phys. Rev. B (1)

P. Sheng, R. S. Stepleman, and P. N. Sanda, “Exact eigenfunctions for square-wave gratings: application to diffraction and surface-plasmon calculations,” Phys. Rev. B 26(6), 2907–2916 (1982).
[Crossref]

Other (2)

M. Neviere and E. Popov, Light Propagation in Periodic Media: Differential Theory and Design (Marcel Dekker, New York, 2003).

H. Kim, J. Park, and B. Lee, Fourier modal method and its applications in computational nanophotonics, (CRC Press, New York, 2012).

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Figures (6)

Fig. 1
Fig. 1 Geometry of a double-groove grating coupler. (a) Numerical model of a unit cell consisting of rectangular ridges. (dimensions; w1 = 60 nm, w2 = 140 nm, d = 180 nm, h = 230 nm, p = 580 nm, refractive indices; nTiO2 = 2.435, nSiO2 = 1.457) (b) Scanning electron microscopy (SEM) image of a device under test.
Fig. 2
Fig. 2 Experimental setup for the measurement of diffraction efficiencies of the grating in Fig. 1(b). Abbreviations stand for L: light source, P: polarizer, M: mirror, PS: prism stage, S: sample, OL: objective lens, A: analyzer, IL: imaging lens, F: fiber, and SM: spectrometer.
Fig. 3
Fig. 3 Transmission efficiency, as a function of wavelength, for the + 1st diffraction order. (symbols: experimental result, blue solid line: numerical result of the rectangular-ridge model in Fig. 1(a), pink dashed line: numerical result of the curved-ridge model in the inset, where the gray and white regions in the ridges represent TiO2 and SiO2 materials, respectively).
Fig. 4
Fig. 4 Transmission efficiencies of the + 1st diffraction order in the numerical model in Fig. 1(a). Three parameters, the wide ridge width w2, the ridge distance d, and the ridge height h are varied within ± 20 nm from the dimensions in the caption of Fig. 1 for each plot of the narrow ridge width w1. The number of the plots is 81(w1) × 41(w2) × 41(d) × 41(h).
Fig. 5
Fig. 5 Profiles of three propagating Bloch modes in the double-groove grating of Fig. 1(a). Each Bloch mode has large amplitude in (a) the wide ridge (g = 0), (b) the narrow ridge (g = 1), and (c) the wide groove (g = 2), respectively. The pink curves are obtained using Eq. (1) with the parameters in the caption of Fig. 1. Other curves represent Bloch modes with ± 20 nm variations of the three parameters, the wide ridge width w2, the ridge distance d, and the ridge height h while the narrow ridge width w1 = 60 nm is fixed. The number of curves in each figure is 3(w2) × 3(d) × 3(h). The refractive indices for the pink curves are ng = 0 = 2.04 in (a), ng = 1 = 1.49 in (b), and ng = 2 = 0.73 in (c), respectively.
Fig. 6
Fig. 6 Coupling coefficients of the three propagating Bloch modes, [ C + + [ X ] C in Eq. (2)], for the + 1st order of transmission diffraction. Coupling coefficients of Bloch modes g = 0 (green squares), g = 1 (blue diamonds), and g = 2 (black crosses) correspond to the Bloch-mode profiles of Figs. 5(a), 5(b), and 5(c), respectively. The summations of the three coupling coefficients are represented by black triangles and correspond to transmission coefficients to the + 1st order of diffraction from their contributions. The pink symbols are obtained with the parameters in the caption of Fig. 1.

Equations (2)

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{ [ K x ] [ K x ] ε } E y = ( i k z / k 0 ) 2 E y ,  
    T = [ W ] { C + + [ X ] C } ,

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