Tunable Fano resonance in photonic crystal slabs

Junfeng Song; Remo Proietti Zaccaria; M. B. Yu; X. W. Sun

doi:10.1364/OE.14.008812

Tunable Fano resonance in photonic crystal slabs

Junfeng Song, Remo Proietti Zaccaria, M. B. Yu, and X. W. Sun

Optics Express
Vol. 14,
Issue 19,
pp. 8812-8826
(2006)
•https://doi.org/10.1364/OE.14.008812

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Junfeng Song, Remo Proietti Zaccaria, M. B. Yu, and X. W. Sun, "Tunable Fano resonance in photonic crystal slabs," Opt. Express 14, 8812-8826 (2006)

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Abstract

A three dimensional analysis of a special class of anisotropic materials is presented. We introduce an extension of the Scattering Matrix Method (SMM) to investigate the behavior of anisotropic Photonic Crystal Slabs (PhCS) subject to external radiation. We show how the Fano effect can play a fundamental role in the realization of tunable optical devices. Moreover, we show how to utilize electron injection, electric field and temperature as parameters to control the Fano resonance shift in both isotropic and anisotropic materials as Si and Potassium Titanium Oxide Phosphate (KTP). We will see that because Fano modes are sensitive and controllable, a broad range of applications can be considered.

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Jakob S. Jensen and Ole Sigmund, “Systematic design of photonic crystal structures using topology optimization: Low-loss waveguide bends,” Appl. Phys. Lett. 84, 2021–2023 (2004).
[Crossref]
Akihiko Shinya, Satoshi Mitsugi, Eiichi Kuramochi, and Masaya Notomi “Ultrasmall multi-channel resonant-tunneling filter using mode gap of width-tuned photonic crystal waveguide,” Opt. Express 13, 4202–4209 (2005).
[Crossref] [PubMed]
L. H. Frandsen, P. I. Borel, Y. X. Zhuang, A. Harpøth, M. Thorhauge, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Ultralow-loss 3-dB photonic crystal waveguide splitter,” Opt. Lett. 29, 1623–1625 (2004).
[Crossref] [PubMed]
X. Checoury, P. Boucaud, J-M. Lourtioz, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, G. H. Duan, D. Mulin, S. Bonnefont, O. Gauthier-Lafaye, J. Valentin, F. Lozes, and A. Talneau, “Distributed feedback regime of photonic crystal waveguide lasers at 1.5 mm,” Appl. Phys. Lett. 85, 5502–5504 (2004).
[Crossref]
Yongqiang Jiang, Wei Jiang, Lanlan Gu, Xiaonan Chen, and Ray T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett. 87, 221105–221107 (2005).
[Crossref]
Shanhui Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
[Crossref]
S. G. Tikhodeew, A. L. Yablonskii, E. A. Muljarow, N. A. Gippius, and Teruya Ishihara, “Quasiguide modes and optical properties of photonic crystal slabs,” Phys. Rev. B 66, 045102 (2002).
[Crossref]
Steven G. Johnson, Shanhui Fan, Pierre R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[Crossref]
K. B. Crozier, Virginie Lousse, Onur Kilic, Sora Kim, Shanhui Fan, and Olav Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelength,” Phys. Rev. B 73, 115126 (2006).
[Crossref]
Vasily N. Astratov, Ian S. Culshaw, R. Mark Stevenson, David M. Whittaker, Maurce S. Skolnick, Thomax F. Krauss, and Richard M. De La Rue, “Resonant coupling of near-infrared radiation to photonic band structure waveguide,” J. Lightwave Technol. 17, 2050–2057 (1999).
[Crossref]
V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M.S. Skolnick, T.F. Krauss, and R. M. De La Rue, “Heavy photon dispersions in photonic crystal waveguides,” Appl. Phys. Lett. 77, 178–180 (2000).
[Crossref]
A. Rosenberg, Michael W. Carter, J. A. Casey, Mijin Kim, Ronald T. Holm, Richard L. Henry, Charles R. Eddy, V. A. Shamamian, K. Bussmann Shouyuan Shi, and Dennis W. Prather, “Guided resonances in symmetrical GaN photonic crystal slabs observed in the visible spectrum,” Opt. Express 13, 6564–6571 (2005).
[Crossref] [PubMed]
Andrey E. Miroshnichenko and Yuri S. Kivshar, “Sharp bends in photonic crystal waveguides as nonlinear Fano resonators,” Opt. Express 13, 3969–3976 (2005),.
[Crossref] [PubMed]
David Yuk Kei Ko and J. C. Inkson, “Matrix method for tunneling in heterostructures: Resonant tunneling in multilayer systems,” Phys. Rev. B 38, 9945–9951 (1988).
[Crossref]
D. M. Whittaker and I. S. Culshaw, “Scattering-matrix treatment of patterned multilayer photonic structures,” Phys. Rev. B 60, 2610–2618 (1999).
[Crossref]
Maciej Dems, Rafal Kotynski, and Krassinir Panajotov, “Plane wave admittance method-a novel approach for determining the electromagnetic modes in photonic structures,” Opt. Express 13, 3196–3207 (2005).
[Crossref] [PubMed]
R. A. Soref and B. R. Bennett “Electro-optical Effects in Silicon,” IEEE J. Quantum Electron. 23, 123–129 (1987).
[Crossref]
A. Irace, G. Breglio, and A. Cutolo, “All-silicon optoelectronic modulator with 1 GHz switching capability,” Electron. Lett. 39, 232–233 (2003).
[Crossref]
R.W. Wood, “Anomalous Diffraction Gratings,” Phys. Rev. 48, 928–936 (1935).
[Crossref]
U. Fano, “The Theory of Anomalous Diffraction Gratings and of Quasi-Stationary Waves on Metallic Surfaces (Sommerfield’s Waves),” J. Opt. Soc. Am. 31, 213–222 (1941).
[Crossref]
U. Fano, “Effect of Configuration Interaction on Intensity and Phase Shifts,” Phys. Rev. 124, 1866–1878 (1961).
[Crossref]
A. Hessel and A.A. Oliner, “A New Theory of Wood’s Anomalies on Optical Gratings,” Appl. Opt. 4, 1275–1297 (1965).
[Crossref]
T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]
E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100–16108 (2000).
[Crossref]
M.G. Banaee, A.R. Cowan, and J.F. Young, “Third-order nonlinear influence on specular reflectivity of two-dimensional waveguide-based photonic crystals,” J. Opt. Soc. Am. B 19, 2224 (2002).
[Crossref]
M. Sarrazin, J.P. Vigneron, and J.M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with bidimensional array of subwavelength holes,” Phys. Rev. B 67, 085415 (2003).
[Crossref]
J.M. Steele, C.E. Moran, A. Lee, C.M. Aguirre, and N.J. Halas, “Metallodielectric gratings with subwavelength slots: Optical properties,” Phys. Rev. B 68, 205103 (2003).
[Crossref]
W.L. Barnes, W.A. Murray, J. Dintinger, E. Devaux, and T.W. Ebbesen, “Surface Plasmon Polaritons and Their Role in the Enhanced Transmission of Light through Periodic Arrays of Subwavelength Holes in a Metal Film,” Phys. Rev. Lett. 92, 107401 (2004).
[Crossref] [PubMed]
W.V. Lousse and J.P. Vigneron, “Use of Fano resonances for bistable optical transfer through photonic crystal film,” Phys. Rev. B 69, 155106 (2004).
[Crossref]
H.J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12, 3629–3651 (2004).
[Crossref] [PubMed]
A.E. Miroshnichenko and Y.S. Kivshar, “Engineering Fano resonances in discrete arrays,” Phys. Rev. E 72, 056611 (2005).
[Crossref]
E. Moreno, L. Martin-Moreno, and F.J. Garcia-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A: Pure Appl. Opt. 8, S94–S97 (2006).
[Crossref]
R. Gomez-Medina, M. Laroche, and J.J. Saenz, “Extraordinary optical reflection from sub-wavelength cylinder arrays,” Opt. Express 14, 3730–3737 (2006).
[Crossref] [PubMed]
B. Boulanger, J.P. Feve, and Y. Guillien, “Thermo-optical effect and saturation of nonlinear absorption induced by gray tracking in a 532-nm pumped KTP optical parametric oscillator,” Opt. Lett. 25, 484–486 (2000).
[Crossref]

2006 (3)

K. B. Crozier, Virginie Lousse, Onur Kilic, Sora Kim, Shanhui Fan, and Olav Solgaard, “Air-bridged photonic crystal slabs at visible and near-infrared wavelength,” Phys. Rev. B 73, 115126 (2006).
[Crossref]

E. Moreno, L. Martin-Moreno, and F.J. Garcia-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A: Pure Appl. Opt. 8, S94–S97 (2006).
[Crossref]

R. Gomez-Medina, M. Laroche, and J.J. Saenz, “Extraordinary optical reflection from sub-wavelength cylinder arrays,” Opt. Express 14, 3730–3737 (2006).
[Crossref] [PubMed]

2005 (6)

A.E. Miroshnichenko and Y.S. Kivshar, “Engineering Fano resonances in discrete arrays,” Phys. Rev. E 72, 056611 (2005).
[Crossref]

Maciej Dems, Rafal Kotynski, and Krassinir Panajotov, “Plane wave admittance method-a novel approach for determining the electromagnetic modes in photonic structures,” Opt. Express 13, 3196–3207 (2005).
[Crossref] [PubMed]

Andrey E. Miroshnichenko and Yuri S. Kivshar, “Sharp bends in photonic crystal waveguides as nonlinear Fano resonators,” Opt. Express 13, 3969–3976 (2005),.
[Crossref] [PubMed]

Akihiko Shinya, Satoshi Mitsugi, Eiichi Kuramochi, and Masaya Notomi “Ultrasmall multi-channel resonant-tunneling filter using mode gap of width-tuned photonic crystal waveguide,” Opt. Express 13, 4202–4209 (2005).
[Crossref] [PubMed]

A. Rosenberg, Michael W. Carter, J. A. Casey, Mijin Kim, Ronald T. Holm, Richard L. Henry, Charles R. Eddy, V. A. Shamamian, K. Bussmann Shouyuan Shi, and Dennis W. Prather, “Guided resonances in symmetrical GaN photonic crystal slabs observed in the visible spectrum,” Opt. Express 13, 6564–6571 (2005).
[Crossref] [PubMed]

Yongqiang Jiang, Wei Jiang, Lanlan Gu, Xiaonan Chen, and Ray T. Chen, “80-micron interaction length silicon photonic crystal waveguide modulator,” Appl. Phys. Lett. 87, 221105–221107 (2005).
[Crossref]

2004 (6)

Jakob S. Jensen and Ole Sigmund, “Systematic design of photonic crystal structures using topology optimization: Low-loss waveguide bends,” Appl. Phys. Lett. 84, 2021–2023 (2004).
[Crossref]

X. Checoury, P. Boucaud, J-M. Lourtioz, F. Pommereau, C. Cuisin, E. Derouin, O. Drisse, L. Legouezigou, F. Lelarge, F. Poingt, G. H. Duan, D. Mulin, S. Bonnefont, O. Gauthier-Lafaye, J. Valentin, F. Lozes, and A. Talneau, “Distributed feedback regime of photonic crystal waveguide lasers at 1.5 mm,” Appl. Phys. Lett. 85, 5502–5504 (2004).
[Crossref]

L. H. Frandsen, P. I. Borel, Y. X. Zhuang, A. Harpøth, M. Thorhauge, M. Kristensen, W. Bogaerts, P. Dumon, R. Baets, V. Wiaux, J. Wouters, and S. Beckx, “Ultralow-loss 3-dB photonic crystal waveguide splitter,” Opt. Lett. 29, 1623–1625 (2004).
[Crossref] [PubMed]

H.J. Lezec and T. Thio, “Diffracted evanescent wave model for enhanced and suppressed optical transmission through subwavelength hole arrays,” Opt. Express 12, 3629–3651 (2004).
[Crossref] [PubMed]

W.L. Barnes, W.A. Murray, J. Dintinger, E. Devaux, and T.W. Ebbesen, “Surface Plasmon Polaritons and Their Role in the Enhanced Transmission of Light through Periodic Arrays of Subwavelength Holes in a Metal Film,” Phys. Rev. Lett. 92, 107401 (2004).
[Crossref] [PubMed]

W.V. Lousse and J.P. Vigneron, “Use of Fano resonances for bistable optical transfer through photonic crystal film,” Phys. Rev. B 69, 155106 (2004).
[Crossref]

2003 (3)

M. Sarrazin, J.P. Vigneron, and J.M. Vigoureux, “Role of Wood anomalies in optical properties of thin metallic films with bidimensional array of subwavelength holes,” Phys. Rev. B 67, 085415 (2003).
[Crossref]

J.M. Steele, C.E. Moran, A. Lee, C.M. Aguirre, and N.J. Halas, “Metallodielectric gratings with subwavelength slots: Optical properties,” Phys. Rev. B 68, 205103 (2003).
[Crossref]

A. Irace, G. Breglio, and A. Cutolo, “All-silicon optoelectronic modulator with 1 GHz switching capability,” Electron. Lett. 39, 232–233 (2003).
[Crossref]

2002 (3)

Shanhui Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
[Crossref]

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

M.G. Banaee, A.R. Cowan, and J.F. Young, “Third-order nonlinear influence on specular reflectivity of two-dimensional waveguide-based photonic crystals,” J. Opt. Soc. Am. B 19, 2224 (2002).
[Crossref]

2000 (3)

V. N. Astratov, R. M. Stevenson, I. S. Culshaw, D. M. Whittaker, M.S. Skolnick, T.F. Krauss, and R. M. De La Rue, “Heavy photon dispersions in photonic crystal waveguides,” Appl. Phys. Lett. 77, 178–180 (2000).
[Crossref]

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100–16108 (2000).
[Crossref]

B. Boulanger, J.P. Feve, and Y. Guillien, “Thermo-optical effect and saturation of nonlinear absorption induced by gray tracking in a 532-nm pumped KTP optical parametric oscillator,” Opt. Lett. 25, 484–486 (2000).
[Crossref]

1999 (3)

Vasily N. Astratov, Ian S. Culshaw, R. Mark Stevenson, David M. Whittaker, Maurce S. Skolnick, Thomax F. Krauss, and Richard M. De La Rue, “Resonant coupling of near-infrared radiation to photonic band structure waveguide,” J. Lightwave Technol. 17, 2050–2057 (1999).
[Crossref]

D. M. Whittaker and I. S. Culshaw, “Scattering-matrix treatment of patterned multilayer photonic structures,” Phys. Rev. B 60, 2610–2618 (1999).
[Crossref]

Steven G. Johnson, Shanhui Fan, Pierre R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[Crossref]

1998 (1)

T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

1988 (1)

David Yuk Kei Ko and J. C. Inkson, “Matrix method for tunneling in heterostructures: Resonant tunneling in multilayer systems,” Phys. Rev. B 38, 9945–9951 (1988).
[Crossref]

1987 (1)

R. A. Soref and B. R. Bennett “Electro-optical Effects in Silicon,” IEEE J. Quantum Electron. 23, 123–129 (1987).
[Crossref]

1965 (1)

A. Hessel and A.A. Oliner, “A New Theory of Wood’s Anomalies on Optical Gratings,” Appl. Opt. 4, 1275–1297 (1965).
[Crossref]

1961 (1)

U. Fano, “Effect of Configuration Interaction on Intensity and Phase Shifts,” Phys. Rev. 124, 1866–1878 (1961).
[Crossref]

1941 (1)

U. Fano, “The Theory of Anomalous Diffraction Gratings and of Quasi-Stationary Waves on Metallic Surfaces (Sommerfield’s Waves),” J. Opt. Soc. Am. 31, 213–222 (1941).
[Crossref]

1935 (1)

R.W. Wood, “Anomalous Diffraction Gratings,” Phys. Rev. 48, 928–936 (1935).
[Crossref]

Aguirre, C.M.

J.M. Steele, C.E. Moran, A. Lee, C.M. Aguirre, and N.J. Halas, “Metallodielectric gratings with subwavelength slots: Optical properties,” Phys. Rev. B 68, 205103 (2003).
[Crossref]

Astratov, V. N.

Astratov, Vasily N.

Baets, R.

Banaee, M.G.

Barnes, W.L.

Beckx, S.

Bennett, B. R.

R. A. Soref and B. R. Bennett “Electro-optical Effects in Silicon,” IEEE J. Quantum Electron. 23, 123–129 (1987).
[Crossref]

Bogaerts, W.

Bonnefont, S.

Borel, P. I.

Boucaud, P.

Boulanger, B.

Breglio, G.

A. Irace, G. Breglio, and A. Cutolo, “All-silicon optoelectronic modulator with 1 GHz switching capability,” Electron. Lett. 39, 232–233 (2003).
[Crossref]

Bussmann Shouyuan Shi, K.

Carter, Michael W.

Casey, J. A.

Checoury, X.

Chen, Ray T.

Chen, Xiaonan

Cowan, A.R.

Crozier, K. B.

Cuisin, C.

Culshaw, I. S.

D. M. Whittaker and I. S. Culshaw, “Scattering-matrix treatment of patterned multilayer photonic structures,” Phys. Rev. B 60, 2610–2618 (1999).
[Crossref]

Culshaw, Ian S.

Cutolo, A.

A. Irace, G. Breglio, and A. Cutolo, “All-silicon optoelectronic modulator with 1 GHz switching capability,” Electron. Lett. 39, 232–233 (2003).
[Crossref]

De La Rue, R. M.

De La Rue, Richard M.

Dems, Maciej

Derouin, E.

Devaux, E.

Dintinger, J.

Drisse, O.

Duan, G. H.

Dumon, P.

Ebbesen, T.W.

T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

Eddy, Charles R.

Enoch, S.

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100–16108 (2000).
[Crossref]

Fan, Shanhui

Shanhui Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
[Crossref]

Steven G. Johnson, Shanhui Fan, Pierre R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[Crossref]

Fano, U.

U. Fano, “Effect of Configuration Interaction on Intensity and Phase Shifts,” Phys. Rev. 124, 1866–1878 (1961).
[Crossref]

U. Fano, “The Theory of Anomalous Diffraction Gratings and of Quasi-Stationary Waves on Metallic Surfaces (Sommerfield’s Waves),” J. Opt. Soc. Am. 31, 213–222 (1941).
[Crossref]

Feve, J.P.

Frandsen, L. H.

Garcia-Vidal, F.J.

E. Moreno, L. Martin-Moreno, and F.J. Garcia-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A: Pure Appl. Opt. 8, S94–S97 (2006).
[Crossref]

Gauthier-Lafaye, O.

Ghaemi, H.F.

T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

Gippius, N. A.

Gomez-Medina, R.

R. Gomez-Medina, M. Laroche, and J.J. Saenz, “Extraordinary optical reflection from sub-wavelength cylinder arrays,” Opt. Express 14, 3730–3737 (2006).
[Crossref] [PubMed]

Gu, Lanlan

Guillien, Y.

Halas, N.J.

J.M. Steele, C.E. Moran, A. Lee, C.M. Aguirre, and N.J. Halas, “Metallodielectric gratings with subwavelength slots: Optical properties,” Phys. Rev. B 68, 205103 (2003).
[Crossref]

Harpøth, A.

Henry, Richard L.

Hessel, A.

A. Hessel and A.A. Oliner, “A New Theory of Wood’s Anomalies on Optical Gratings,” Appl. Opt. 4, 1275–1297 (1965).
[Crossref]

Holm, Ronald T.

Inkson, J. C.

David Yuk Kei Ko and J. C. Inkson, “Matrix method for tunneling in heterostructures: Resonant tunneling in multilayer systems,” Phys. Rev. B 38, 9945–9951 (1988).
[Crossref]

Irace, A.

A. Irace, G. Breglio, and A. Cutolo, “All-silicon optoelectronic modulator with 1 GHz switching capability,” Electron. Lett. 39, 232–233 (2003).
[Crossref]

Ishihara, Teruya

Jensen, Jakob S.

Jakob S. Jensen and Ole Sigmund, “Systematic design of photonic crystal structures using topology optimization: Low-loss waveguide bends,” Appl. Phys. Lett. 84, 2021–2023 (2004).
[Crossref]

Jiang, Wei

Jiang, Yongqiang

Joannopoulos, J. D.

Shanhui Fan and J. D. Joannopoulos, “Analysis of guided resonances in photonic crystal slabs,” Phys. Rev. B 65, 235112 (2002).
[Crossref]

Steven G. Johnson, Shanhui Fan, Pierre R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[Crossref]

Johnson, Steven G.

Steven G. Johnson, Shanhui Fan, Pierre R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[Crossref]

Kilic, Onur

Kim, Mijin

Kim, Sora

Kivshar, Y.S.

A.E. Miroshnichenko and Y.S. Kivshar, “Engineering Fano resonances in discrete arrays,” Phys. Rev. E 72, 056611 (2005).
[Crossref]

Kivshar, Yuri S.

Andrey E. Miroshnichenko and Yuri S. Kivshar, “Sharp bends in photonic crystal waveguides as nonlinear Fano resonators,” Opt. Express 13, 3969–3976 (2005),.
[Crossref] [PubMed]

Kolodziejski, L. A.

Steven G. Johnson, Shanhui Fan, Pierre R. Villeneuve, J. D. Joannopoulos, and L. A. Kolodziejski, “Guided modes in photonic crystal slabs,” Phys. Rev. B 60, 5751–5758 (1999).
[Crossref]

Kotynski, Rafal

Krauss, T.F.

Krauss, Thomax F.

Kristensen, M.

Kuramochi, Eiichi

Laroche, M.

R. Gomez-Medina, M. Laroche, and J.J. Saenz, “Extraordinary optical reflection from sub-wavelength cylinder arrays,” Opt. Express 14, 3730–3737 (2006).
[Crossref] [PubMed]

Lee, A.

J.M. Steele, C.E. Moran, A. Lee, C.M. Aguirre, and N.J. Halas, “Metallodielectric gratings with subwavelength slots: Optical properties,” Phys. Rev. B 68, 205103 (2003).
[Crossref]

Legouezigou, L.

Lelarge, F.

Lezec, H.J.

T.W. Ebbesen, H.J. Lezec, H.F. Ghaemi, T. Thio, and P.A. Wolff, “Extraordinary optical transmission through sub-wavelength hole arrays,” Nature 391, 667–669 (1998).
[Crossref]

Lourtioz, J-M.

Lousse, Virginie

Lousse, W.V.

W.V. Lousse and J.P. Vigneron, “Use of Fano resonances for bistable optical transfer through photonic crystal film,” Phys. Rev. B 69, 155106 (2004).
[Crossref]

Lozes, F.

Mark Stevenson, R.

Martin-Moreno, L.

E. Moreno, L. Martin-Moreno, and F.J. Garcia-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A: Pure Appl. Opt. 8, S94–S97 (2006).
[Crossref]

Miroshnichenko, A.E.

A.E. Miroshnichenko and Y.S. Kivshar, “Engineering Fano resonances in discrete arrays,” Phys. Rev. E 72, 056611 (2005).
[Crossref]

Miroshnichenko, Andrey E.

Andrey E. Miroshnichenko and Yuri S. Kivshar, “Sharp bends in photonic crystal waveguides as nonlinear Fano resonators,” Opt. Express 13, 3969–3976 (2005),.
[Crossref] [PubMed]

Mitsugi, Satoshi

Moran, C.E.

J.M. Steele, C.E. Moran, A. Lee, C.M. Aguirre, and N.J. Halas, “Metallodielectric gratings with subwavelength slots: Optical properties,” Phys. Rev. B 68, 205103 (2003).
[Crossref]

Moreno, E.

E. Moreno, L. Martin-Moreno, and F.J. Garcia-Vidal, “Extraordinary optical transmission without plasmons: the s-polarization case,” J. Opt. A: Pure Appl. Opt. 8, S94–S97 (2006).
[Crossref]

Mulin, D.

Muljarow, E. A.

Murray, W.A.

Nevière, M.

E. Popov, M. Nevière, S. Enoch, and R. Reinisch, “Theory of light transmission through subwavelength periodic hole arrays,” Phys. Rev. B 62, 16100–16108 (2000).
[Crossref]

Notomi, Masaya

Oliner, A.A.

A. Hessel and A.A. Oliner, “A New Theory of Wood’s Anomalies on Optical Gratings,” Appl. Opt. 4, 1275–1297 (1965).
[Crossref]

Panajotov, Krassinir

Poingt, F.

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Fig. 1.

Photonic crystal slab structure consisting of a square lattice of holes embedded into a uniform material.

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Fig. 2.

Three Fano’s resonances at 1.9871a, 2.0658a and 2.0841a are shown. In particular, the top graph shows the variation of transmission in the wavelength region from 1.9a to 2.2a. The bottom graph shows the energy P calculated in a unit cell of PhCS. The energy peaks correspond to wavelength values roughly in between T=0 and T=1.

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Fig. 3.

(a), (b) and (c) show the Sz distribution for each Fano resonance of Fig (2). The patterns cover four unit cells, which have a hole just in the center. (d) Distribution of the Poynting vector at the plane y/a=0.5, z≥0.

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Fig. 4.

(a) Transmission spectrum of the incident light for s (top) and p (bottom) polarization. The incoming angle θ is from 0° to 80°, where zero means a beam parallel to the z axis. Narrow Fano resonances form several characteristic lines. (b) Relation between n_eff and incident light angle. Light is along ΓX direction. The dashed line denotes the X point, beyond which the mirror effect for neff is shown.

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Fig. 5.

(a) Transmission and reflection spectra calculated at θ=0. The sharp lines show Fano resonances. The reduction of Si refractive index shifts the resonance lines to shorter wavelengths. (b) Transmission and reflection variation spectra. ΔT and ΔR are defined as T(n₀+Δn)-T(n₀) and R(n₀+Δn)-R(n₀). At Fano wavelengths strong changes of T and R are possible. Variation range of Si index is from 0 to -0.01. The range of wavelength is from 1.97a to 2.12a.

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Fig. 6.

(a) Sketch of 0^th and 1^st order scattered light directions. Incident light, 0^th, and 1^st order scattered light are denoted by heavy, dot and thin line, respectively. (b) Power flux spectrum of 0^th and 1^st order transmitted light. Dot and solid lines represent 0^th and 1^st order transmitted light, respectively. (c) Power flux ratio between 1^st and 0^th order transmitted light. (d) and (e) describe the reflection case. Figs. (b), (c), (d) and (e) consist of five graphs each, corresponding to variations of Si refractive index in the interval [-0.001, -0.009].

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Fig. 7.

Transmission (top) and reflection (bottom) spectra for different incident polarizations. ϕ is the angle between electric field angle and x axis.

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Fig. 8.

(a) and (b) show transmission spectra at varies temperatures for E‖y and E‖x, respectively. The differences are due to the anisotropic nature of KTP. Each graph consists of ten curves. Temperature is increased from 20°C to 200°C with constant steps of 20°C. The dot line shows the relation between Fano resonance wavelengths and temperature.

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Fig. 9.

Fano resonant wavelength λ_f versus temperature. The graph shows linear dependence of $λ_{f}^{2}$ with T², namely linear relation between λ_f and temperature. In abscissa is plotted T²-400 to be consistent with Eq. 18.

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Equations (39)

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\nabla \times E = i ω B, \nabla \times H = - i ω D, \nabla \cdot B = 0, \nabla \cdot D = 0

- \frac{\partial}{\partial z} E_{∥} + (\begin{matrix} \frac{\partial}{\partial y} \\ \frac{\partial}{\partial x} \end{matrix}) e_{z} = - i ω μ_{0} (\begin{matrix} μ_{xx} & - μ_{xy} \\ - μ_{yx} & μ_{yy} \end{matrix}) H_{∥} + i ω μ_{0} (\begin{matrix} μ_{xz} \\ - μ_{yz} \end{matrix}) h_{z}

(\frac{\partial}{\partial x} - \frac{\partial}{\partial y}) E_{∥} = i ω μ_{0} (\begin{matrix} - μ_{zx} & μ_{zy} \end{matrix}) H_{∥} + i ω μ_{0} μ_{zz} h_{z}

- \frac{\partial}{\partial z} H_{∥} + (\begin{matrix} - \frac{\partial}{\partial x} \\ \frac{\partial}{\partial y} \end{matrix}) h_{z} = - i ω ε_{0} (\begin{matrix} ε_{yy} & ε_{yx} \\ ε_{xy} & ε_{xx} \end{matrix}) H_{∥} - i ω ε_{0} (\begin{matrix} ε_{yz} \\ ε_{xz} \end{matrix}) e_{z}

(\begin{matrix} \frac{\partial}{\partial y} & \frac{\partial}{\partial x} \end{matrix}) H_{∥} = - i ω ε_{0} (\begin{matrix} ε_{zy} & ε_{zx} \end{matrix}) E_{∥} - i ω ε_{0} ε_{zz} e_{z}

\frac{\partial}{\partial z} H_{∥} + i F^{(1)} H_{∥} = \frac{{ik}_{0}}{ω μ_{0}} [F^{(0)} E_{∥}]

\frac{\partial}{\partial z} E_{∥} + i T^{(1)} E_{∥} = \frac{i ω μ_{0}}{k_{0}} [T^{(0)} H_{∥}]

{\hat{F}}^{(1)} = - (\begin{matrix} - \frac{\partial}{\partial x} \\ \frac{\partial}{\partial y} \end{matrix}) μ_{zz}^{- 1} (\begin{matrix} - μ_{zx} & μ_{zy} \end{matrix}) - (\begin{matrix} ε_{yz} \\ ε_{xz} \end{matrix}) ε_{zz}^{- 1} (\begin{matrix} \frac{\partial}{\partial y} & \frac{\partial}{\partial x} \end{matrix})

{\hat{F}}^{(0)} = (\begin{matrix} ε_{yy} & ε_{yx} \\ ε_{xy} & ε_{xx} \end{matrix}) - (\begin{matrix} ε_{yz} \\ ε_{xz} \end{matrix}) ε_{zz}^{- 1} (\begin{matrix} ε_{zy} & ε_{zx} \end{matrix}) - (\begin{matrix} - \frac{\partial}{\partial x} \\ \frac{\partial}{\partial y} \end{matrix}) μ_{zz}^{- 1} (\begin{matrix} \frac{\partial}{\partial x} & - \frac{\partial}{\partial y} \end{matrix})

{\hat{T}}^{(1)} = (\begin{matrix} μ_{xz} \\ - μ_{yz} \end{matrix}) μ_{zz}^{- 1} (\begin{matrix} \frac{\partial}{\partial x} & - \frac{\partial}{\partial y} \end{matrix}) - (\begin{matrix} \frac{\partial}{\partial y} \\ \frac{\partial}{\partial x} \end{matrix}) ε_{zz}^{- 1} (\begin{matrix} ε_{zy} & ε_{zx} \end{matrix})

{\hat{T}}^{(0)} = (\begin{matrix} μ_{xx} & {- μ}_{xy} \\ {- μ}_{yx} & μ_{yy} \end{matrix}) + (\begin{matrix} μ_{xz} \\ {- μ}_{yz} \end{matrix}) μ_{zz}^{- 1} (\begin{matrix} {- μ}_{zx} & μ_{zy} \end{matrix}) - (\begin{matrix} - \frac{\partial}{\partial y} \\ \frac{\partial}{\partial x} \end{matrix}) ε_{zz}^{- 1} (\begin{matrix} \frac{\partial}{\partial y} & \frac{\partial}{\partial x} \end{matrix})

H_{∥} (r) = \sum_{G} ∣ k + G 〉 H_{∥} (G) \exp (i β z)

E_{∥} (r) = \sum_{G} ∣ k + G 〉 E_{∥} (G) \exp (i β z)

ε (r) = \sum_{G} V_{G} \exp [i (k + G) \cdot r]

μ (r) = \sum_{G} U_{G} \exp [i (k + G) \cdot r]

V_{G' - G} = 〈 k + G' ∣ ε (r) ∣ k + G 〉 = V_{G', G}

U_{G' - G} = 〈 k + G' ∣ μ (r) ∣ k + G 〉 = U_{G', G}

〈 k + G' ∣ PQ ∣ k + G 〉 = \sum_{G'} P_{G', G ″} \cdot Q_{G', G}

F^{(1)} = (\begin{matrix} diag (k_{x} + G_{x}) \\ - diag (k_{y} + G_{y}) \end{matrix}) U_{zz}^{- 1} (\begin{matrix} - U_{zx} & U_{zy} \end{matrix}) + (\begin{matrix} V_{yz} \\ V_{xz} \end{matrix}) V_{zz}^{- 1} (\begin{matrix} diag (k_{y} + G_{y}) & diag (k_{x} + G_{x}) \end{matrix})

F^{(0)} = (\begin{matrix} V_{yy} & V_{yx} \\ V_{xy} & V_{xx} \end{matrix}) - (\begin{matrix} V_{yz} \\ V_{xz} \end{matrix}) V_{zz}^{- 1} (\begin{matrix} V_{zy} & V_{zx} \end{matrix}) -

(\begin{matrix} diag (k_{x} + G_{x}) \\ - diag (k_{y} + G_{y}) \end{matrix}) U_{zz}^{- 1} (\begin{matrix} diag (k_{x} + G_{x}) & - diag (k_{y} + G_{y}) \end{matrix})

T^{(1)} = (\begin{matrix} U_{xz} \\ {- U}_{yz} \end{matrix}) U_{zz}^{- 1} (\begin{matrix} diag (k_{x} + G_{x}) & - diag (k_{y} + G_{y}) \end{matrix}) + (\begin{matrix} diag (k_{y} + G_{y}) \\ diag (k_{x} + G_{x}) \end{matrix}) V_{zz}^{- 1} (\begin{matrix} V_{zy} & V_{zx} \end{matrix})

T^{(0)} = (\begin{matrix} U_{xx} & {- U}_{xy} \\ {- U}_{yx} & U_{yy} \end{matrix}) + (\begin{matrix} U_{xz} \\ {- U}_{yz} \end{matrix}) U_{zz}^{- 1} (\begin{matrix} {- U}_{zx} & U_{zy} \end{matrix}) -

(\begin{matrix} diag (k_{y} + G_{y}) \\ diag (k_{x} + G_{x}) \end{matrix}) V_{zz}^{- 1} (\begin{matrix} diag (k_{y} + G_{y}) & diag (k_{x} + G_{x}) \end{matrix})

H_{∥} (G) β^{2} + [F^{(1)} + F^{(0)} T^{(1)} {(F^{(0)})}^{- 1}] H_{∥} (G) β + [F^{(0)} T^{(1)} {(F^{(0)})}^{- 1} F^{(1)} - F^{(0)} T^{(0)}] H_{∥} (G) = O

E_{∥} (G) β^{2} + [T^{(1)} + T^{(0)} F^{(1)} {(T^{(0)})}^{- 1}] E_{∥} (G) β + [T^{(0)} F^{(1)} {(T^{(0)})}^{- 1} T^{(1)} - T^{(0)} F^{(0)}] E_{∥} (G) = O

H_{∥} (G) β^{2} - F^{(0)} T^{(0)} H_{∥} (G) = O

E_{∥} (G) β^{2} - T^{(0)} F^{(0)} E_{∥} (G) = O

F^{(0)} = (\begin{matrix} V & O \\ O & V \end{matrix}) - (\begin{matrix} diag (k_{x} + G_{x}) \\ - diag (k_{y} + G_{y}) \end{matrix}) U^{- 1} (diag (k_{x} + G_{x}) - diag (k_{y} + G_{y}))

T^{(0)} = (\begin{matrix} U & O \\ O & U \end{matrix}) - (\begin{matrix} diag (k_{y} + G_{y}) \\ diag (k_{x} + G_{x}) \end{matrix}) V^{- 1} (diag (k_{y} + G_{y}) diag (k_{x} + G_{x}))

F^{(0)} = (\begin{matrix} V_{yy} & V_{yx} \\ V_{xy} & V_{xx} \end{matrix}) - (\begin{matrix} diag (k_{x} + G_{x}) \\ - diag (k_{y} + G_{y}) \end{matrix}) U_{zz}^{- 1} (diag (k_{x} + G_{x}) - diag (k_{y} + G_{y}))

T^{(0)} = (\begin{matrix} U_{xx} & {- U}_{xy} \\ {- U}_{yx} & U_{yy} \end{matrix}) - (\begin{matrix} diag (k_{y} + G_{y}) \\ diag (k_{x} + G_{x}) \end{matrix}) V_{zz}^{- 1} (diag (k_{y} + G_{y}) diag (k_{x} + G_{x}))

H_{∥} (r) = \sum_{G, j} ∣ k + G 〉 [H_{∥, j}^{(+)} (G) a_{j} \exp (i β_{j}^{(+)} z) + H_{∥, j}^{(-)} (G) b_{j} \exp (i β_{j}^{(-)} z)]

E_{∥} (r) = \sum_{G, j} ∣ k + G 〉 [E_{∥, j}^{(+)} (G) a_{j} \exp (i β_{j}^{(+)} z) + E_{∥, j}^{(-)} (G) b_{j} \exp (i β_{j}^{(-)} z)]

(\begin{matrix} E_{∥}^{(+)} (G) & - {E'}_{∥}^{(-)} (G) \\ H_{∥}^{(+)} (G) & - {H'}_{∥}^{(-)} (G) \end{matrix}) (\begin{matrix} a \\ b' \end{matrix}) = (\begin{matrix} - E_{∥}^{(-)} (G) & {E'}_{∥}^{(+)} (G) \\ - H_{∥}^{(-)} (G) & {H'}_{∥}^{(+)} (G) \end{matrix}) (\begin{matrix} b \\ a' \end{matrix})

S (\begin{matrix} a \\ b' \end{matrix}) = (\begin{matrix} b \\ a' \end{matrix}),

S = {(\begin{matrix} - E_{∥}^{(-)} (G) & {E'}_{∥}^{(+)} (G) \\ - H_{∥}^{(-)} (G) & {H'}_{∥}^{(+)} (G) \end{matrix})}^{- 1} (\begin{matrix} E_{∥}^{(+)} (G) & {- E'}_{∥}^{(-)} (G) \\ H_{∥}^{(+)} (G) & {- H'}_{∥}^{(-)} (G) \end{matrix})

P = \int_{cell} \frac{1}{2} (D^{*} \cdot E + B^{*} \cdot H) dV

n_{i}^{2} (λ, T) = a_{i} + β_{i} (T^{2} - 400) + \frac{b_{i} + δ_{i} (T^{2} - 400)}{λ^{2} - c_{i} + ϕ_{i} (T^{2} - 400)} - λ^{2} [d_{i} + ρ_{i} (T^{2} - 400)]