Abstract

This paper describes the derivation of surface plasmon polariton modes associated with the generalized three-dimensional rotation of liquid crystal molecules on a metal film. The calculated dispersion relation was verified by coupling laser light into surface plasmon polariton waves in a one-dimensional grating device. The grating-assisted plasmon coupling condition was consistent with the formulated kspp value. This provides a general rule for the design of liquid-crystal tunable plasmonic devices.

© 2015 Optical Society of America

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References

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    [Crossref]
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    [Crossref] [PubMed]
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2015 (3)

L. Ferrari, C. H. Wu, D. Lepage, X. Zhang, and Z. W. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
[Crossref]

D. Franklin, Y. Chen, A. Vazquez-Guardado, S. Modak, J. Boroumand, D. Xu, S.-T. Wu, and D. Chanda, “Polarization-independent actively tunable colour generation on imprinted plasmonic surfaces,” Nat. Commun. 6, 7337 (2015).
[Crossref] [PubMed]

H. Zhou, X. Zhang, D. Kong, Y. Wang, and Y. Song, “Complete dispersion relations of surface plasmon polaritons at a metal and birefringent dielectric interface,” Appl. Phys. Express 8(6), 062003 (2015).
[Crossref]

2014 (3)

A. Piccardi, A. Alberucci, N. Kravets, O. Buchnev, and G. Assanto, “Power-controlled transition from standard to negative refraction in reorientational soft matter,” Nat. Commun. 5, 5533 (2014).
[Crossref] [PubMed]

G. Si, Y. Zhao, E. S. P. Leong, and Y. J. Liu, “Liquid-Crystal-Enabled Active Plasmonics: A Review,” Materials (Basel) 7(2), 1296–1317 (2014).
[Crossref]

B. Stein, E. Devaux, C. Genet, and T. W. Ebbesen, “Plasmonic crystal enhanced refractive index sensing,” Appl. Phys. Lett. 104(25), 251111 (2014).
[Crossref]

2013 (6)

M. A. Razumova and I. M. Dmitruk, “Splitting of Plasmon Frequency in Spherical Metal Nanoparticles in Anisotropic Medium,” Plasmonics 8(4), 1699–1706 (2013).
[Crossref]

A. Babu, C. Bhagyaraj, J. Jacob, G. Mathew, and V. Mathew, “Surface plasmon propagation in a metal strip waveguide with biaxial substrate,” Opt. Quantum Electron. 45(6), 481–490 (2013).
[Crossref]

K. V. Sreekanth and T. Yu, “Long range surface plasmons in a symmetric graphene system with anisotropic dielectrics,” J. Opt. 15(5), 055002 (2013).
[Crossref]

R. Luo, Y. Gu, X. K. Li, L. J. Wang, I. C. Khoo, and Q. H. Gong, “Mode recombination and alternation of surface plasmons in anisotropic mediums,” Appl. Phys. Lett. 102(1), 011117 (2013).
[Crossref]

X. Li, Y. Gu, R. Luo, L. Wang, and Q. Gong, “Effects of dielectric anisotropy on surface plasmon polaritons in three-layer plasmonic nanostructures,” Plasmonics 8(2), 1043–1049 (2013).
[Crossref]

H.-H. Liu and H.-C. Chang, “Leaky surface plasmon polariton modes at an interface between metal and uniaxially anisotropic materials,” IEEE Photonics J. 5(6), 4800806 (2013).
[Crossref]

2012 (3)

W.-S. Chang, J. B. Lassiter, P. Swanglap, H. Sobhani, S. Khatua, P. Nordlander, N. J. Halas, and S. Link, “A Plasmonic Fano Switch,” Nano Lett. 12(9), 4977–4982 (2012).
[Crossref] [PubMed]

Y. Zhao, Q. Hao, Y. Ma, M. Lu, B. Zhang, M. Lapsley, I.-C. Khoo, and T. J. Huang, “Light-driven tunable dual-band plasmonic absorber using liquid-crystal-coated asymmetric nanodisk array,” Appl. Phys. Lett. 100(5), 053119 (2012).
[Crossref]

Y. J. Liu, G. Y. Si, E. S. P. Leong, N. Xiang, A. J. Danner, and J. H. Teng, “Light-Driven Plasmonic Color Filters by Overlaying Photoresponsive Liquid Crystals on Gold Annular Aperture Arrays,” Adv. Mater. 24(23), OP131–OP135 (2012).
[Crossref] [PubMed]

2011 (2)

Y. Takeichi, Y. Kimoto, M. Fujii, and S. Hayashi, “Anisotropic propagation of surface plasmon polaritons induced by para-sexiphenyl nanowire films,” Phys. Rev. B 84(8), 085417 (2011).
[Crossref]

X. L. Wang, P. Wang, J. X. Chen, Y. H. Lu, H. Ming, and Q. W. Zhan, “Theoretical and experimental studies of surface plasmons excited at metal-uniaxial dielectric interface,” Appl. Phys. Lett. 98(2), 021113 (2011).
[Crossref]

2010 (3)

M. R. Shcherbakov, M. I. Dobynde, T. V. Dolgova, D. P. Tsai, and A. A. Fedyanin, “Full Poincare sphere coverage with plasmonic nanoslit metamaterials at Fano resonance,” Phys. Rev. B 82(19), 193402 (2010).
[Crossref]

L. Feng, Z. W. Liu, V. Lomakin, and Y. Fainman, “Form birefringence metal and its plasmonic anisotropy,” Appl. Phys. Lett. 96(4), 041112 (2010).
[Crossref]

Y. J. Hung, M. H. Shih, J. H. Liou, and J. Y. Tai, “Polarity-variable birefringence on hyperlens structure,” Opt. Express 18(26), 27606–27612 (2010).
[Crossref] [PubMed]

2009 (1)

M. Ojima, N. Numata, Y. Ogawa, K. Murata, H. Kubo, A. Fujii, and M. Ozaki, “Electric field tuning of plasmonic absorption of metallic grating with twisted nematic liquid crystal,” Appl. Phys. Express 2(8), 086001 (2009).
[Crossref]

2008 (3)

J. Elser and V. A. Podolskiy, “Scattering-free plasmonic optics with anisotropic metamaterials,” Phys. Rev. Lett. 100(6), 066402 (2008).
[Crossref] [PubMed]

R. Li, C. Cheng, F. F. Ren, J. Chen, Y. X. Fan, J. P. Ding, and H. T. Wang, “Hybridized surface plasmon polaritons at an interface between a metal and a uniaxial crystal,” Appl. Phys. Lett. 92(14), 141115 (2008).
[Crossref]

B. K. Singh and A. C. Hillier, “Surface plasmon resonance enhanced transmission of light through gold-coated diffraction gratings,” Anal. Chem. 80(10), 3803–3810 (2008).
[Crossref] [PubMed]

2007 (3)

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007).
[Crossref] [PubMed]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

A. A. Krokhin, A. Neogi, and D. McNeil, “Long-range propagation of surface plasmons in a thin metallic film deposited on an anisotropic photonic crystal,” Phys. Rev. B 75(23), 235420 (2007).
[Crossref]

2006 (1)

1991 (1)

J. Lekner, “Reflection and refraction by uniaxial crystals,” J. Phys. Condens. Matter 3(32), 6121–6133 (1991).
[Crossref]

1986 (1)

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B Condens. Matter 33(8), 5186–5201 (1986).
[Crossref] [PubMed]

Alberucci, A.

A. Piccardi, A. Alberucci, N. Kravets, O. Buchnev, and G. Assanto, “Power-controlled transition from standard to negative refraction in reorientational soft matter,” Nat. Commun. 5, 5533 (2014).
[Crossref] [PubMed]

Alekseyev, L. V.

Assanto, G.

A. Piccardi, A. Alberucci, N. Kravets, O. Buchnev, and G. Assanto, “Power-controlled transition from standard to negative refraction in reorientational soft matter,” Nat. Commun. 5, 5533 (2014).
[Crossref] [PubMed]

Babu, A.

A. Babu, C. Bhagyaraj, J. Jacob, G. Mathew, and V. Mathew, “Surface plasmon propagation in a metal strip waveguide with biaxial substrate,” Opt. Quantum Electron. 45(6), 481–490 (2013).
[Crossref]

Bhagyaraj, C.

A. Babu, C. Bhagyaraj, J. Jacob, G. Mathew, and V. Mathew, “Surface plasmon propagation in a metal strip waveguide with biaxial substrate,” Opt. Quantum Electron. 45(6), 481–490 (2013).
[Crossref]

Boroumand, J.

D. Franklin, Y. Chen, A. Vazquez-Guardado, S. Modak, J. Boroumand, D. Xu, S.-T. Wu, and D. Chanda, “Polarization-independent actively tunable colour generation on imprinted plasmonic surfaces,” Nat. Commun. 6, 7337 (2015).
[Crossref] [PubMed]

Buchnev, O.

A. Piccardi, A. Alberucci, N. Kravets, O. Buchnev, and G. Assanto, “Power-controlled transition from standard to negative refraction in reorientational soft matter,” Nat. Commun. 5, 5533 (2014).
[Crossref] [PubMed]

Burke, J. J.

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B Condens. Matter 33(8), 5186–5201 (1986).
[Crossref] [PubMed]

Chanda, D.

D. Franklin, Y. Chen, A. Vazquez-Guardado, S. Modak, J. Boroumand, D. Xu, S.-T. Wu, and D. Chanda, “Polarization-independent actively tunable colour generation on imprinted plasmonic surfaces,” Nat. Commun. 6, 7337 (2015).
[Crossref] [PubMed]

Chang, H.-C.

H.-H. Liu and H.-C. Chang, “Leaky surface plasmon polariton modes at an interface between metal and uniaxially anisotropic materials,” IEEE Photonics J. 5(6), 4800806 (2013).
[Crossref]

Chang, W.-S.

W.-S. Chang, J. B. Lassiter, P. Swanglap, H. Sobhani, S. Khatua, P. Nordlander, N. J. Halas, and S. Link, “A Plasmonic Fano Switch,” Nano Lett. 12(9), 4977–4982 (2012).
[Crossref] [PubMed]

Chen, J.

R. Li, C. Cheng, F. F. Ren, J. Chen, Y. X. Fan, J. P. Ding, and H. T. Wang, “Hybridized surface plasmon polaritons at an interface between a metal and a uniaxial crystal,” Appl. Phys. Lett. 92(14), 141115 (2008).
[Crossref]

Chen, J. X.

X. L. Wang, P. Wang, J. X. Chen, Y. H. Lu, H. Ming, and Q. W. Zhan, “Theoretical and experimental studies of surface plasmons excited at metal-uniaxial dielectric interface,” Appl. Phys. Lett. 98(2), 021113 (2011).
[Crossref]

Chen, Y.

D. Franklin, Y. Chen, A. Vazquez-Guardado, S. Modak, J. Boroumand, D. Xu, S.-T. Wu, and D. Chanda, “Polarization-independent actively tunable colour generation on imprinted plasmonic surfaces,” Nat. Commun. 6, 7337 (2015).
[Crossref] [PubMed]

Cheng, C.

R. Li, C. Cheng, F. F. Ren, J. Chen, Y. X. Fan, J. P. Ding, and H. T. Wang, “Hybridized surface plasmon polaritons at an interface between a metal and a uniaxial crystal,” Appl. Phys. Lett. 92(14), 141115 (2008).
[Crossref]

Danner, A. J.

Y. J. Liu, G. Y. Si, E. S. P. Leong, N. Xiang, A. J. Danner, and J. H. Teng, “Light-Driven Plasmonic Color Filters by Overlaying Photoresponsive Liquid Crystals on Gold Annular Aperture Arrays,” Adv. Mater. 24(23), OP131–OP135 (2012).
[Crossref] [PubMed]

Davis, C. C.

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007).
[Crossref] [PubMed]

Devaux, E.

B. Stein, E. Devaux, C. Genet, and T. W. Ebbesen, “Plasmonic crystal enhanced refractive index sensing,” Appl. Phys. Lett. 104(25), 251111 (2014).
[Crossref]

Ding, J. P.

R. Li, C. Cheng, F. F. Ren, J. Chen, Y. X. Fan, J. P. Ding, and H. T. Wang, “Hybridized surface plasmon polaritons at an interface between a metal and a uniaxial crystal,” Appl. Phys. Lett. 92(14), 141115 (2008).
[Crossref]

Dmitruk, I. M.

M. A. Razumova and I. M. Dmitruk, “Splitting of Plasmon Frequency in Spherical Metal Nanoparticles in Anisotropic Medium,” Plasmonics 8(4), 1699–1706 (2013).
[Crossref]

Dobynde, M. I.

M. R. Shcherbakov, M. I. Dobynde, T. V. Dolgova, D. P. Tsai, and A. A. Fedyanin, “Full Poincare sphere coverage with plasmonic nanoslit metamaterials at Fano resonance,” Phys. Rev. B 82(19), 193402 (2010).
[Crossref]

Dolgova, T. V.

M. R. Shcherbakov, M. I. Dobynde, T. V. Dolgova, D. P. Tsai, and A. A. Fedyanin, “Full Poincare sphere coverage with plasmonic nanoslit metamaterials at Fano resonance,” Phys. Rev. B 82(19), 193402 (2010).
[Crossref]

Ebbesen, T. W.

B. Stein, E. Devaux, C. Genet, and T. W. Ebbesen, “Plasmonic crystal enhanced refractive index sensing,” Appl. Phys. Lett. 104(25), 251111 (2014).
[Crossref]

Elser, J.

J. Elser and V. A. Podolskiy, “Scattering-free plasmonic optics with anisotropic metamaterials,” Phys. Rev. Lett. 100(6), 066402 (2008).
[Crossref] [PubMed]

Fainman, Y.

L. Feng, Z. W. Liu, V. Lomakin, and Y. Fainman, “Form birefringence metal and its plasmonic anisotropy,” Appl. Phys. Lett. 96(4), 041112 (2010).
[Crossref]

Fan, Y. X.

R. Li, C. Cheng, F. F. Ren, J. Chen, Y. X. Fan, J. P. Ding, and H. T. Wang, “Hybridized surface plasmon polaritons at an interface between a metal and a uniaxial crystal,” Appl. Phys. Lett. 92(14), 141115 (2008).
[Crossref]

Fedyanin, A. A.

M. R. Shcherbakov, M. I. Dobynde, T. V. Dolgova, D. P. Tsai, and A. A. Fedyanin, “Full Poincare sphere coverage with plasmonic nanoslit metamaterials at Fano resonance,” Phys. Rev. B 82(19), 193402 (2010).
[Crossref]

Feng, L.

L. Feng, Z. W. Liu, V. Lomakin, and Y. Fainman, “Form birefringence metal and its plasmonic anisotropy,” Appl. Phys. Lett. 96(4), 041112 (2010).
[Crossref]

Ferrari, L.

L. Ferrari, C. H. Wu, D. Lepage, X. Zhang, and Z. W. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
[Crossref]

Franklin, D.

D. Franklin, Y. Chen, A. Vazquez-Guardado, S. Modak, J. Boroumand, D. Xu, S.-T. Wu, and D. Chanda, “Polarization-independent actively tunable colour generation on imprinted plasmonic surfaces,” Nat. Commun. 6, 7337 (2015).
[Crossref] [PubMed]

Fujii, A.

M. Ojima, N. Numata, Y. Ogawa, K. Murata, H. Kubo, A. Fujii, and M. Ozaki, “Electric field tuning of plasmonic absorption of metallic grating with twisted nematic liquid crystal,” Appl. Phys. Express 2(8), 086001 (2009).
[Crossref]

Fujii, M.

Y. Takeichi, Y. Kimoto, M. Fujii, and S. Hayashi, “Anisotropic propagation of surface plasmon polaritons induced by para-sexiphenyl nanowire films,” Phys. Rev. B 84(8), 085417 (2011).
[Crossref]

Genet, C.

B. Stein, E. Devaux, C. Genet, and T. W. Ebbesen, “Plasmonic crystal enhanced refractive index sensing,” Appl. Phys. Lett. 104(25), 251111 (2014).
[Crossref]

Gong, Q.

X. Li, Y. Gu, R. Luo, L. Wang, and Q. Gong, “Effects of dielectric anisotropy on surface plasmon polaritons in three-layer plasmonic nanostructures,” Plasmonics 8(2), 1043–1049 (2013).
[Crossref]

Gong, Q. H.

R. Luo, Y. Gu, X. K. Li, L. J. Wang, I. C. Khoo, and Q. H. Gong, “Mode recombination and alternation of surface plasmons in anisotropic mediums,” Appl. Phys. Lett. 102(1), 011117 (2013).
[Crossref]

Gu, Y.

R. Luo, Y. Gu, X. K. Li, L. J. Wang, I. C. Khoo, and Q. H. Gong, “Mode recombination and alternation of surface plasmons in anisotropic mediums,” Appl. Phys. Lett. 102(1), 011117 (2013).
[Crossref]

X. Li, Y. Gu, R. Luo, L. Wang, and Q. Gong, “Effects of dielectric anisotropy on surface plasmon polaritons in three-layer plasmonic nanostructures,” Plasmonics 8(2), 1043–1049 (2013).
[Crossref]

Halas, N. J.

W.-S. Chang, J. B. Lassiter, P. Swanglap, H. Sobhani, S. Khatua, P. Nordlander, N. J. Halas, and S. Link, “A Plasmonic Fano Switch,” Nano Lett. 12(9), 4977–4982 (2012).
[Crossref] [PubMed]

Hao, Q.

Y. Zhao, Q. Hao, Y. Ma, M. Lu, B. Zhang, M. Lapsley, I.-C. Khoo, and T. J. Huang, “Light-driven tunable dual-band plasmonic absorber using liquid-crystal-coated asymmetric nanodisk array,” Appl. Phys. Lett. 100(5), 053119 (2012).
[Crossref]

Hayashi, S.

Y. Takeichi, Y. Kimoto, M. Fujii, and S. Hayashi, “Anisotropic propagation of surface plasmon polaritons induced by para-sexiphenyl nanowire films,” Phys. Rev. B 84(8), 085417 (2011).
[Crossref]

Hillier, A. C.

B. K. Singh and A. C. Hillier, “Surface plasmon resonance enhanced transmission of light through gold-coated diffraction gratings,” Anal. Chem. 80(10), 3803–3810 (2008).
[Crossref] [PubMed]

Huang, T. J.

Y. Zhao, Q. Hao, Y. Ma, M. Lu, B. Zhang, M. Lapsley, I.-C. Khoo, and T. J. Huang, “Light-driven tunable dual-band plasmonic absorber using liquid-crystal-coated asymmetric nanodisk array,” Appl. Phys. Lett. 100(5), 053119 (2012).
[Crossref]

Hung, Y. J.

Y. J. Hung, M. H. Shih, J. H. Liou, and J. Y. Tai, “Polarity-variable birefringence on hyperlens structure,” Opt. Express 18(26), 27606–27612 (2010).
[Crossref] [PubMed]

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007).
[Crossref] [PubMed]

Jacob, J.

A. Babu, C. Bhagyaraj, J. Jacob, G. Mathew, and V. Mathew, “Surface plasmon propagation in a metal strip waveguide with biaxial substrate,” Opt. Quantum Electron. 45(6), 481–490 (2013).
[Crossref]

Jacob, Z.

Khatua, S.

W.-S. Chang, J. B. Lassiter, P. Swanglap, H. Sobhani, S. Khatua, P. Nordlander, N. J. Halas, and S. Link, “A Plasmonic Fano Switch,” Nano Lett. 12(9), 4977–4982 (2012).
[Crossref] [PubMed]

Khoo, I. C.

R. Luo, Y. Gu, X. K. Li, L. J. Wang, I. C. Khoo, and Q. H. Gong, “Mode recombination and alternation of surface plasmons in anisotropic mediums,” Appl. Phys. Lett. 102(1), 011117 (2013).
[Crossref]

Khoo, I.-C.

Y. Zhao, Q. Hao, Y. Ma, M. Lu, B. Zhang, M. Lapsley, I.-C. Khoo, and T. J. Huang, “Light-driven tunable dual-band plasmonic absorber using liquid-crystal-coated asymmetric nanodisk array,” Appl. Phys. Lett. 100(5), 053119 (2012).
[Crossref]

Kimoto, Y.

Y. Takeichi, Y. Kimoto, M. Fujii, and S. Hayashi, “Anisotropic propagation of surface plasmon polaritons induced by para-sexiphenyl nanowire films,” Phys. Rev. B 84(8), 085417 (2011).
[Crossref]

Kong, D.

H. Zhou, X. Zhang, D. Kong, Y. Wang, and Y. Song, “Complete dispersion relations of surface plasmon polaritons at a metal and birefringent dielectric interface,” Appl. Phys. Express 8(6), 062003 (2015).
[Crossref]

Kravets, N.

A. Piccardi, A. Alberucci, N. Kravets, O. Buchnev, and G. Assanto, “Power-controlled transition from standard to negative refraction in reorientational soft matter,” Nat. Commun. 5, 5533 (2014).
[Crossref] [PubMed]

Krokhin, A. A.

A. A. Krokhin, A. Neogi, and D. McNeil, “Long-range propagation of surface plasmons in a thin metallic film deposited on an anisotropic photonic crystal,” Phys. Rev. B 75(23), 235420 (2007).
[Crossref]

Kubo, H.

M. Ojima, N. Numata, Y. Ogawa, K. Murata, H. Kubo, A. Fujii, and M. Ozaki, “Electric field tuning of plasmonic absorption of metallic grating with twisted nematic liquid crystal,” Appl. Phys. Express 2(8), 086001 (2009).
[Crossref]

Lapsley, M.

Y. Zhao, Q. Hao, Y. Ma, M. Lu, B. Zhang, M. Lapsley, I.-C. Khoo, and T. J. Huang, “Light-driven tunable dual-band plasmonic absorber using liquid-crystal-coated asymmetric nanodisk array,” Appl. Phys. Lett. 100(5), 053119 (2012).
[Crossref]

Lassiter, J. B.

W.-S. Chang, J. B. Lassiter, P. Swanglap, H. Sobhani, S. Khatua, P. Nordlander, N. J. Halas, and S. Link, “A Plasmonic Fano Switch,” Nano Lett. 12(9), 4977–4982 (2012).
[Crossref] [PubMed]

Lee, H.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Lekner, J.

J. Lekner, “Reflection and refraction by uniaxial crystals,” J. Phys. Condens. Matter 3(32), 6121–6133 (1991).
[Crossref]

Leong, E. S. P.

G. Si, Y. Zhao, E. S. P. Leong, and Y. J. Liu, “Liquid-Crystal-Enabled Active Plasmonics: A Review,” Materials (Basel) 7(2), 1296–1317 (2014).
[Crossref]

Y. J. Liu, G. Y. Si, E. S. P. Leong, N. Xiang, A. J. Danner, and J. H. Teng, “Light-Driven Plasmonic Color Filters by Overlaying Photoresponsive Liquid Crystals on Gold Annular Aperture Arrays,” Adv. Mater. 24(23), OP131–OP135 (2012).
[Crossref] [PubMed]

Lepage, D.

L. Ferrari, C. H. Wu, D. Lepage, X. Zhang, and Z. W. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
[Crossref]

Li, R.

R. Li, C. Cheng, F. F. Ren, J. Chen, Y. X. Fan, J. P. Ding, and H. T. Wang, “Hybridized surface plasmon polaritons at an interface between a metal and a uniaxial crystal,” Appl. Phys. Lett. 92(14), 141115 (2008).
[Crossref]

Li, X.

X. Li, Y. Gu, R. Luo, L. Wang, and Q. Gong, “Effects of dielectric anisotropy on surface plasmon polaritons in three-layer plasmonic nanostructures,” Plasmonics 8(2), 1043–1049 (2013).
[Crossref]

Li, X. K.

R. Luo, Y. Gu, X. K. Li, L. J. Wang, I. C. Khoo, and Q. H. Gong, “Mode recombination and alternation of surface plasmons in anisotropic mediums,” Appl. Phys. Lett. 102(1), 011117 (2013).
[Crossref]

Link, S.

W.-S. Chang, J. B. Lassiter, P. Swanglap, H. Sobhani, S. Khatua, P. Nordlander, N. J. Halas, and S. Link, “A Plasmonic Fano Switch,” Nano Lett. 12(9), 4977–4982 (2012).
[Crossref] [PubMed]

Liou, J. H.

Liu, H.-H.

H.-H. Liu and H.-C. Chang, “Leaky surface plasmon polariton modes at an interface between metal and uniaxially anisotropic materials,” IEEE Photonics J. 5(6), 4800806 (2013).
[Crossref]

Liu, Y. J.

G. Si, Y. Zhao, E. S. P. Leong, and Y. J. Liu, “Liquid-Crystal-Enabled Active Plasmonics: A Review,” Materials (Basel) 7(2), 1296–1317 (2014).
[Crossref]

Y. J. Liu, G. Y. Si, E. S. P. Leong, N. Xiang, A. J. Danner, and J. H. Teng, “Light-Driven Plasmonic Color Filters by Overlaying Photoresponsive Liquid Crystals on Gold Annular Aperture Arrays,” Adv. Mater. 24(23), OP131–OP135 (2012).
[Crossref] [PubMed]

Liu, Z.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Liu, Z. W.

L. Ferrari, C. H. Wu, D. Lepage, X. Zhang, and Z. W. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
[Crossref]

L. Feng, Z. W. Liu, V. Lomakin, and Y. Fainman, “Form birefringence metal and its plasmonic anisotropy,” Appl. Phys. Lett. 96(4), 041112 (2010).
[Crossref]

Lomakin, V.

L. Feng, Z. W. Liu, V. Lomakin, and Y. Fainman, “Form birefringence metal and its plasmonic anisotropy,” Appl. Phys. Lett. 96(4), 041112 (2010).
[Crossref]

Lu, M.

Y. Zhao, Q. Hao, Y. Ma, M. Lu, B. Zhang, M. Lapsley, I.-C. Khoo, and T. J. Huang, “Light-driven tunable dual-band plasmonic absorber using liquid-crystal-coated asymmetric nanodisk array,” Appl. Phys. Lett. 100(5), 053119 (2012).
[Crossref]

Lu, Y. H.

X. L. Wang, P. Wang, J. X. Chen, Y. H. Lu, H. Ming, and Q. W. Zhan, “Theoretical and experimental studies of surface plasmons excited at metal-uniaxial dielectric interface,” Appl. Phys. Lett. 98(2), 021113 (2011).
[Crossref]

Luo, R.

X. Li, Y. Gu, R. Luo, L. Wang, and Q. Gong, “Effects of dielectric anisotropy on surface plasmon polaritons in three-layer plasmonic nanostructures,” Plasmonics 8(2), 1043–1049 (2013).
[Crossref]

R. Luo, Y. Gu, X. K. Li, L. J. Wang, I. C. Khoo, and Q. H. Gong, “Mode recombination and alternation of surface plasmons in anisotropic mediums,” Appl. Phys. Lett. 102(1), 011117 (2013).
[Crossref]

Ma, Y.

Y. Zhao, Q. Hao, Y. Ma, M. Lu, B. Zhang, M. Lapsley, I.-C. Khoo, and T. J. Huang, “Light-driven tunable dual-band plasmonic absorber using liquid-crystal-coated asymmetric nanodisk array,” Appl. Phys. Lett. 100(5), 053119 (2012).
[Crossref]

Mathew, G.

A. Babu, C. Bhagyaraj, J. Jacob, G. Mathew, and V. Mathew, “Surface plasmon propagation in a metal strip waveguide with biaxial substrate,” Opt. Quantum Electron. 45(6), 481–490 (2013).
[Crossref]

Mathew, V.

A. Babu, C. Bhagyaraj, J. Jacob, G. Mathew, and V. Mathew, “Surface plasmon propagation in a metal strip waveguide with biaxial substrate,” Opt. Quantum Electron. 45(6), 481–490 (2013).
[Crossref]

McNeil, D.

A. A. Krokhin, A. Neogi, and D. McNeil, “Long-range propagation of surface plasmons in a thin metallic film deposited on an anisotropic photonic crystal,” Phys. Rev. B 75(23), 235420 (2007).
[Crossref]

Ming, H.

X. L. Wang, P. Wang, J. X. Chen, Y. H. Lu, H. Ming, and Q. W. Zhan, “Theoretical and experimental studies of surface plasmons excited at metal-uniaxial dielectric interface,” Appl. Phys. Lett. 98(2), 021113 (2011).
[Crossref]

Modak, S.

D. Franklin, Y. Chen, A. Vazquez-Guardado, S. Modak, J. Boroumand, D. Xu, S.-T. Wu, and D. Chanda, “Polarization-independent actively tunable colour generation on imprinted plasmonic surfaces,” Nat. Commun. 6, 7337 (2015).
[Crossref] [PubMed]

Murata, K.

M. Ojima, N. Numata, Y. Ogawa, K. Murata, H. Kubo, A. Fujii, and M. Ozaki, “Electric field tuning of plasmonic absorption of metallic grating with twisted nematic liquid crystal,” Appl. Phys. Express 2(8), 086001 (2009).
[Crossref]

Narimanov, E.

Neogi, A.

A. A. Krokhin, A. Neogi, and D. McNeil, “Long-range propagation of surface plasmons in a thin metallic film deposited on an anisotropic photonic crystal,” Phys. Rev. B 75(23), 235420 (2007).
[Crossref]

Nordlander, P.

W.-S. Chang, J. B. Lassiter, P. Swanglap, H. Sobhani, S. Khatua, P. Nordlander, N. J. Halas, and S. Link, “A Plasmonic Fano Switch,” Nano Lett. 12(9), 4977–4982 (2012).
[Crossref] [PubMed]

Numata, N.

M. Ojima, N. Numata, Y. Ogawa, K. Murata, H. Kubo, A. Fujii, and M. Ozaki, “Electric field tuning of plasmonic absorption of metallic grating with twisted nematic liquid crystal,” Appl. Phys. Express 2(8), 086001 (2009).
[Crossref]

Ogawa, Y.

M. Ojima, N. Numata, Y. Ogawa, K. Murata, H. Kubo, A. Fujii, and M. Ozaki, “Electric field tuning of plasmonic absorption of metallic grating with twisted nematic liquid crystal,” Appl. Phys. Express 2(8), 086001 (2009).
[Crossref]

Ojima, M.

M. Ojima, N. Numata, Y. Ogawa, K. Murata, H. Kubo, A. Fujii, and M. Ozaki, “Electric field tuning of plasmonic absorption of metallic grating with twisted nematic liquid crystal,” Appl. Phys. Express 2(8), 086001 (2009).
[Crossref]

Ozaki, M.

M. Ojima, N. Numata, Y. Ogawa, K. Murata, H. Kubo, A. Fujii, and M. Ozaki, “Electric field tuning of plasmonic absorption of metallic grating with twisted nematic liquid crystal,” Appl. Phys. Express 2(8), 086001 (2009).
[Crossref]

Piccardi, A.

A. Piccardi, A. Alberucci, N. Kravets, O. Buchnev, and G. Assanto, “Power-controlled transition from standard to negative refraction in reorientational soft matter,” Nat. Commun. 5, 5533 (2014).
[Crossref] [PubMed]

Podolskiy, V. A.

J. Elser and V. A. Podolskiy, “Scattering-free plasmonic optics with anisotropic metamaterials,” Phys. Rev. Lett. 100(6), 066402 (2008).
[Crossref] [PubMed]

Razumova, M. A.

M. A. Razumova and I. M. Dmitruk, “Splitting of Plasmon Frequency in Spherical Metal Nanoparticles in Anisotropic Medium,” Plasmonics 8(4), 1699–1706 (2013).
[Crossref]

Ren, F. F.

R. Li, C. Cheng, F. F. Ren, J. Chen, Y. X. Fan, J. P. Ding, and H. T. Wang, “Hybridized surface plasmon polaritons at an interface between a metal and a uniaxial crystal,” Appl. Phys. Lett. 92(14), 141115 (2008).
[Crossref]

Shcherbakov, M. R.

M. R. Shcherbakov, M. I. Dobynde, T. V. Dolgova, D. P. Tsai, and A. A. Fedyanin, “Full Poincare sphere coverage with plasmonic nanoslit metamaterials at Fano resonance,” Phys. Rev. B 82(19), 193402 (2010).
[Crossref]

Shih, M. H.

Si, G.

G. Si, Y. Zhao, E. S. P. Leong, and Y. J. Liu, “Liquid-Crystal-Enabled Active Plasmonics: A Review,” Materials (Basel) 7(2), 1296–1317 (2014).
[Crossref]

Si, G. Y.

Y. J. Liu, G. Y. Si, E. S. P. Leong, N. Xiang, A. J. Danner, and J. H. Teng, “Light-Driven Plasmonic Color Filters by Overlaying Photoresponsive Liquid Crystals on Gold Annular Aperture Arrays,” Adv. Mater. 24(23), OP131–OP135 (2012).
[Crossref] [PubMed]

Singh, B. K.

B. K. Singh and A. C. Hillier, “Surface plasmon resonance enhanced transmission of light through gold-coated diffraction gratings,” Anal. Chem. 80(10), 3803–3810 (2008).
[Crossref] [PubMed]

Smolyaninov, I. I.

I. I. Smolyaninov, Y. J. Hung, and C. C. Davis, “Magnifying superlens in the visible frequency range,” Science 315(5819), 1699–1701 (2007).
[Crossref] [PubMed]

Sobhani, H.

W.-S. Chang, J. B. Lassiter, P. Swanglap, H. Sobhani, S. Khatua, P. Nordlander, N. J. Halas, and S. Link, “A Plasmonic Fano Switch,” Nano Lett. 12(9), 4977–4982 (2012).
[Crossref] [PubMed]

Song, Y.

H. Zhou, X. Zhang, D. Kong, Y. Wang, and Y. Song, “Complete dispersion relations of surface plasmon polaritons at a metal and birefringent dielectric interface,” Appl. Phys. Express 8(6), 062003 (2015).
[Crossref]

Sreekanth, K. V.

K. V. Sreekanth and T. Yu, “Long range surface plasmons in a symmetric graphene system with anisotropic dielectrics,” J. Opt. 15(5), 055002 (2013).
[Crossref]

Stegeman, G. I.

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B Condens. Matter 33(8), 5186–5201 (1986).
[Crossref] [PubMed]

Stein, B.

B. Stein, E. Devaux, C. Genet, and T. W. Ebbesen, “Plasmonic crystal enhanced refractive index sensing,” Appl. Phys. Lett. 104(25), 251111 (2014).
[Crossref]

Sun, C.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Swanglap, P.

W.-S. Chang, J. B. Lassiter, P. Swanglap, H. Sobhani, S. Khatua, P. Nordlander, N. J. Halas, and S. Link, “A Plasmonic Fano Switch,” Nano Lett. 12(9), 4977–4982 (2012).
[Crossref] [PubMed]

Tai, J. Y.

Takeichi, Y.

Y. Takeichi, Y. Kimoto, M. Fujii, and S. Hayashi, “Anisotropic propagation of surface plasmon polaritons induced by para-sexiphenyl nanowire films,” Phys. Rev. B 84(8), 085417 (2011).
[Crossref]

Tamir, T.

J. J. Burke, G. I. Stegeman, and T. Tamir, “Surface-polariton-like waves guided by thin, lossy metal films,” Phys. Rev. B Condens. Matter 33(8), 5186–5201 (1986).
[Crossref] [PubMed]

Teng, J. H.

Y. J. Liu, G. Y. Si, E. S. P. Leong, N. Xiang, A. J. Danner, and J. H. Teng, “Light-Driven Plasmonic Color Filters by Overlaying Photoresponsive Liquid Crystals on Gold Annular Aperture Arrays,” Adv. Mater. 24(23), OP131–OP135 (2012).
[Crossref] [PubMed]

Tsai, D. P.

M. R. Shcherbakov, M. I. Dobynde, T. V. Dolgova, D. P. Tsai, and A. A. Fedyanin, “Full Poincare sphere coverage with plasmonic nanoslit metamaterials at Fano resonance,” Phys. Rev. B 82(19), 193402 (2010).
[Crossref]

Vazquez-Guardado, A.

D. Franklin, Y. Chen, A. Vazquez-Guardado, S. Modak, J. Boroumand, D. Xu, S.-T. Wu, and D. Chanda, “Polarization-independent actively tunable colour generation on imprinted plasmonic surfaces,” Nat. Commun. 6, 7337 (2015).
[Crossref] [PubMed]

Wang, H. T.

R. Li, C. Cheng, F. F. Ren, J. Chen, Y. X. Fan, J. P. Ding, and H. T. Wang, “Hybridized surface plasmon polaritons at an interface between a metal and a uniaxial crystal,” Appl. Phys. Lett. 92(14), 141115 (2008).
[Crossref]

Wang, L.

X. Li, Y. Gu, R. Luo, L. Wang, and Q. Gong, “Effects of dielectric anisotropy on surface plasmon polaritons in three-layer plasmonic nanostructures,” Plasmonics 8(2), 1043–1049 (2013).
[Crossref]

Wang, L. J.

R. Luo, Y. Gu, X. K. Li, L. J. Wang, I. C. Khoo, and Q. H. Gong, “Mode recombination and alternation of surface plasmons in anisotropic mediums,” Appl. Phys. Lett. 102(1), 011117 (2013).
[Crossref]

Wang, P.

X. L. Wang, P. Wang, J. X. Chen, Y. H. Lu, H. Ming, and Q. W. Zhan, “Theoretical and experimental studies of surface plasmons excited at metal-uniaxial dielectric interface,” Appl. Phys. Lett. 98(2), 021113 (2011).
[Crossref]

Wang, X. L.

X. L. Wang, P. Wang, J. X. Chen, Y. H. Lu, H. Ming, and Q. W. Zhan, “Theoretical and experimental studies of surface plasmons excited at metal-uniaxial dielectric interface,” Appl. Phys. Lett. 98(2), 021113 (2011).
[Crossref]

Wang, Y.

H. Zhou, X. Zhang, D. Kong, Y. Wang, and Y. Song, “Complete dispersion relations of surface plasmon polaritons at a metal and birefringent dielectric interface,” Appl. Phys. Express 8(6), 062003 (2015).
[Crossref]

Wu, C. H.

L. Ferrari, C. H. Wu, D. Lepage, X. Zhang, and Z. W. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
[Crossref]

Wu, S.-T.

D. Franklin, Y. Chen, A. Vazquez-Guardado, S. Modak, J. Boroumand, D. Xu, S.-T. Wu, and D. Chanda, “Polarization-independent actively tunable colour generation on imprinted plasmonic surfaces,” Nat. Commun. 6, 7337 (2015).
[Crossref] [PubMed]

Xiang, N.

Y. J. Liu, G. Y. Si, E. S. P. Leong, N. Xiang, A. J. Danner, and J. H. Teng, “Light-Driven Plasmonic Color Filters by Overlaying Photoresponsive Liquid Crystals on Gold Annular Aperture Arrays,” Adv. Mater. 24(23), OP131–OP135 (2012).
[Crossref] [PubMed]

Xiong, Y.

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Xu, D.

D. Franklin, Y. Chen, A. Vazquez-Guardado, S. Modak, J. Boroumand, D. Xu, S.-T. Wu, and D. Chanda, “Polarization-independent actively tunable colour generation on imprinted plasmonic surfaces,” Nat. Commun. 6, 7337 (2015).
[Crossref] [PubMed]

Yu, T.

K. V. Sreekanth and T. Yu, “Long range surface plasmons in a symmetric graphene system with anisotropic dielectrics,” J. Opt. 15(5), 055002 (2013).
[Crossref]

Zhan, Q. W.

X. L. Wang, P. Wang, J. X. Chen, Y. H. Lu, H. Ming, and Q. W. Zhan, “Theoretical and experimental studies of surface plasmons excited at metal-uniaxial dielectric interface,” Appl. Phys. Lett. 98(2), 021113 (2011).
[Crossref]

Zhang, B.

Y. Zhao, Q. Hao, Y. Ma, M. Lu, B. Zhang, M. Lapsley, I.-C. Khoo, and T. J. Huang, “Light-driven tunable dual-band plasmonic absorber using liquid-crystal-coated asymmetric nanodisk array,” Appl. Phys. Lett. 100(5), 053119 (2012).
[Crossref]

Zhang, X.

H. Zhou, X. Zhang, D. Kong, Y. Wang, and Y. Song, “Complete dispersion relations of surface plasmon polaritons at a metal and birefringent dielectric interface,” Appl. Phys. Express 8(6), 062003 (2015).
[Crossref]

L. Ferrari, C. H. Wu, D. Lepage, X. Zhang, and Z. W. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
[Crossref]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref] [PubMed]

Zhao, Y.

G. Si, Y. Zhao, E. S. P. Leong, and Y. J. Liu, “Liquid-Crystal-Enabled Active Plasmonics: A Review,” Materials (Basel) 7(2), 1296–1317 (2014).
[Crossref]

Y. Zhao, Q. Hao, Y. Ma, M. Lu, B. Zhang, M. Lapsley, I.-C. Khoo, and T. J. Huang, “Light-driven tunable dual-band plasmonic absorber using liquid-crystal-coated asymmetric nanodisk array,” Appl. Phys. Lett. 100(5), 053119 (2012).
[Crossref]

Zhou, H.

H. Zhou, X. Zhang, D. Kong, Y. Wang, and Y. Song, “Complete dispersion relations of surface plasmon polaritons at a metal and birefringent dielectric interface,” Appl. Phys. Express 8(6), 062003 (2015).
[Crossref]

Adv. Mater. (1)

Y. J. Liu, G. Y. Si, E. S. P. Leong, N. Xiang, A. J. Danner, and J. H. Teng, “Light-Driven Plasmonic Color Filters by Overlaying Photoresponsive Liquid Crystals on Gold Annular Aperture Arrays,” Adv. Mater. 24(23), OP131–OP135 (2012).
[Crossref] [PubMed]

Anal. Chem. (1)

B. K. Singh and A. C. Hillier, “Surface plasmon resonance enhanced transmission of light through gold-coated diffraction gratings,” Anal. Chem. 80(10), 3803–3810 (2008).
[Crossref] [PubMed]

Appl. Phys. Express (2)

M. Ojima, N. Numata, Y. Ogawa, K. Murata, H. Kubo, A. Fujii, and M. Ozaki, “Electric field tuning of plasmonic absorption of metallic grating with twisted nematic liquid crystal,” Appl. Phys. Express 2(8), 086001 (2009).
[Crossref]

H. Zhou, X. Zhang, D. Kong, Y. Wang, and Y. Song, “Complete dispersion relations of surface plasmon polaritons at a metal and birefringent dielectric interface,” Appl. Phys. Express 8(6), 062003 (2015).
[Crossref]

Appl. Phys. Lett. (6)

R. Li, C. Cheng, F. F. Ren, J. Chen, Y. X. Fan, J. P. Ding, and H. T. Wang, “Hybridized surface plasmon polaritons at an interface between a metal and a uniaxial crystal,” Appl. Phys. Lett. 92(14), 141115 (2008).
[Crossref]

X. L. Wang, P. Wang, J. X. Chen, Y. H. Lu, H. Ming, and Q. W. Zhan, “Theoretical and experimental studies of surface plasmons excited at metal-uniaxial dielectric interface,” Appl. Phys. Lett. 98(2), 021113 (2011).
[Crossref]

B. Stein, E. Devaux, C. Genet, and T. W. Ebbesen, “Plasmonic crystal enhanced refractive index sensing,” Appl. Phys. Lett. 104(25), 251111 (2014).
[Crossref]

L. Feng, Z. W. Liu, V. Lomakin, and Y. Fainman, “Form birefringence metal and its plasmonic anisotropy,” Appl. Phys. Lett. 96(4), 041112 (2010).
[Crossref]

R. Luo, Y. Gu, X. K. Li, L. J. Wang, I. C. Khoo, and Q. H. Gong, “Mode recombination and alternation of surface plasmons in anisotropic mediums,” Appl. Phys. Lett. 102(1), 011117 (2013).
[Crossref]

Y. Zhao, Q. Hao, Y. Ma, M. Lu, B. Zhang, M. Lapsley, I.-C. Khoo, and T. J. Huang, “Light-driven tunable dual-band plasmonic absorber using liquid-crystal-coated asymmetric nanodisk array,” Appl. Phys. Lett. 100(5), 053119 (2012).
[Crossref]

IEEE Photonics J. (1)

H.-H. Liu and H.-C. Chang, “Leaky surface plasmon polariton modes at an interface between metal and uniaxially anisotropic materials,” IEEE Photonics J. 5(6), 4800806 (2013).
[Crossref]

J. Opt. (1)

K. V. Sreekanth and T. Yu, “Long range surface plasmons in a symmetric graphene system with anisotropic dielectrics,” J. Opt. 15(5), 055002 (2013).
[Crossref]

J. Phys. Condens. Matter (1)

J. Lekner, “Reflection and refraction by uniaxial crystals,” J. Phys. Condens. Matter 3(32), 6121–6133 (1991).
[Crossref]

Materials (Basel) (1)

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Figures (8)

Fig. 1
Fig. 1 (a) XYZ -global coordinate, and X”Y”Z”-LC coordinate; (b) k-vector indicating the eigen mode (SPP mode) propagation direction. The optical axis of the LC lies along the X” axis.
Fig. 2
Fig. 2 Structure of LC-metal-isotropic medium
Fig. 3
Fig. 3 Eigen values resolved using Eq. (16)
Fig. 4
Fig. 4 LC cell with metallic grating structure. 532nm light is incident in TM polarization. When LC is in @ON state, the OA of the LC lies perpendicular to the metal surface, regardless of whether it is over the edge or the flat area of the grating.
Fig. 5
Fig. 5 (a) Prism coupling setup- grating stripe is along y-direction. (b) Definition of incident light direction, where “pr” refers to prism.
Fig. 6
Fig. 6 Large transmission through grating region: (a) pitches ranging from 350 to 450nm (an increase in θ pr resulted in smaller pitches in the transmissive region, which indicates that the momentum matching integer m must be negative); (b) collected under NA = 0.5; (c)~(f) collected under NA = 0.3
Fig. 7
Fig. 7 T-1 transmission with m = −1 showing simulations at two incidence angles. In the case of a fixed incidence angle, T-1@ nLC = 1.52 is higher than T-1@nLC = 1.75. The fact that this differs from the results obtained in experiments means that SPP mode coupling must be involved. The arrow indicates the cutoff pitch when using an objective lens with NA = (0.3). No difficulties in the collection of light were encountered in cases of transmission through pitches exceeding the cutoff pitch.
Fig. 8
Fig. 8 (a) k composite for gratings of each pitch when m = −2 order; (b) k composite when m = −3 order. The two horizontal lines indicate k spp values derived using the formulae in this study, in the case where LC is @ON and @OFF. The k spp values at 1.67*ko and 1.80*ko are associated with an anti-symmetrical Ex field whereas 2.85*ko and 3.10*ko are associated with a symmetrical Ex field.

Equations (17)

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[ X Y Z ]=[ cosθcosϕ cosθsinϕ sinθ sinϕ cosϕ 0 sinθcosϕ sinθsinϕ cosθ ][ X Y Z ]=R(θ,ϕ)[ X Y Z ]
k x 2 k 0 2 + k y 2 k 0 2 + k z 2 k 0 2 = n o 2
E o =[ E x E y E z ] =[ 0 k z k y ]
k x 2 n o 2 k 0 2 + k y 2 n e 2 k 0 2 + k z 2 n e 2 k 0 2 =1
E e =[ E x E y E z ] = 1 k x ( k 2 n o 2 k 0 2 ) [ k x 2 n o 2 k 0 2 k x k y k x k z ]
k zo = n o 2 k 0 2 k x 2
k ze = ( n o 2 n e 2 )cosθsinθcosϕ k x + n o 2 n e 2 ( n e 2 sin 2 θ+ n o 2 cos 2 θ ) k 0 2 [ n o 2 n e 2 ( sin 2 θ sin 2 ϕ+ cos 2 ϕ )+ n o 4 cos 2 θ sin 2 ϕ ] k x 2 n e 2 sin 2 θ+ n o 2 cos 2 θ
k={ (β,0,i q LC ) z>d/2 (β,0,±i q m ) -d/2<z<d/2 (β,0,i q d ) z<d/2
E={ E 0 e i( βxωt ) q LC z ,z>d/2 E 0 e i( βxωt )± q m z ,d/2<z<d/2 E 0 e i( βxωt )+ q d z ,z<d/2
E O = M 1 [ i q o k 0 sinϕcosθ β k 0 sinθi q o k 0 cosθcosϕ β k 0 sinϕcosθ ] e i(βxωt) q o z
E e = M 2 [ q o 2 k 0 2 cosθcosϕ+i q e β k 0 2 sinθ ε o sinϕcosθ i q e β k 0 2 cosθcosϕ q e 2 + ε o k 0 2 k 0 2 sinθ ] e i(βxωt) q e z
E m TE± =  M 3|4 [ 0 1 0 ] e i( βxωt ) q m z
E m TM± =  M 5|6 [ i q m k 0 0 β k 0 ] e i( βxωt ) q m z  
E d TE = M 7 [ 0 1 0 ] e i( βxωt )+ q d z
E d TM = M 8 [ i q d k 0 0 β k 0 ] e i( βxωt )+ q d z
olight elight TE m + TE m TM m + TM m TE d TM d E x d 2 E y d 2 H x d 2 H y d 2 E x   d 2 E y   d 2 H x   d 2 H y   d 2 [ i q o sinϕcosθ k 0 e q o d 2 q o 2 cosθcosϕ+i q e βsinθ k 0 2 e q e d 2 0 0 i q m k 0 e q m d 2 i q m k 0 e q m d 2 0 0 βsinθi q o cosθcosϕ k 0 e q o d 2 ε o sinϕcosθ e q e d 2 e q m d 2 e q m d 2 0 0 0 0 q o 2 cosθcosϕi q o βsinθ k 0 2 e q o d 2 i q e ε o sinϕcosθ k 0 e q e d 2 i q m k 0 e q m d 2 i q m k 0 e q m d 2 0 0 0 0 ε o sinϕcosθ e q o d 2 β ε o sinθi q e ε o cosθcosϕ k 0 e q e d 2 0 0 ε m e q m d 2 ε m e q m d 2 0 0 0 0 0 0 i q m k 0 e q m d 2 i q m k 0 e q m d 2 0 i q d k 0 e q d d 2 0 0 e q m d 2 e q m d 2 0 0 e q d d 2 0 0 0 i q m k 0 e q m d 2 i q m k 0 e q m d 2 0 0 i q d k 0 e q d d 2 0 0 0 0 0 ε m e q m d 2 ε m e q m d 2 0 ε d e q d d 2 ][ M 1 M 2 M 3 M 4 M 5 M 6 M 7 M 8 ]=0
k composite 2 = ( n prism k 0 sin θ pr cos ϕ pr ) 2 + ( n prism k 0 sin θ pr sin ϕ pr ±m 2π Λ ) 2

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