Abstract

Propagation of electromagnetic waves in a one-dimensional photonic crystal with a twin-defect—a periodicity break where one half of the photonic structure is a mirror image of the other one—is studied using a transfer-matrix method. This work is done in the general framework of photonic structures composed of isotropic materials exhibiting both dielectric and magnetic properties. Both polarizations of electromagnetic waves impinging at oblique incidence on the structure are considered. We derive analytical expressions for the frequency of defect modes and for the enhancement of the electromagnetic field inside the defect. In particular, we discuss possibilities of tuning of defect levels for a photonic crystal structure with a two-layer elementary cell.

© 2004 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef]
  3. H. Míguez, C. López, F. Meseguer, A. Blanco, L. Vázquez, R. Mayoral, M. Ocaña, V. Fornés, and A. Mifsud, “Photonic crystal properties of packed submicrometric SiO2 spheres,” Appl. Phys. Lett. 71, 1148–1150 (1997).
    [CrossRef]
  4. A. de Lustrac, F. Gadot, S. Cabaret, J.-M. Lourtioz, T. Brillat, A. Priou, and E. Akmansoy, “Experimental demonstration of electrically controllable photonic crystals at centimeter wavelengths,” Appl. Phys. Lett. 75, 1625–1627 1999).
    [CrossRef]
  5. A. Chelnokov, S. Rowson, J. M. Lourtioz, L. Duvillaret, and J. L. Coutaz, “Light controllable defect modes in three-dimensional photonic crystal,” Electron. Lett. 34, 1965–1967 (1998).
    [CrossRef]
  6. H.-Y. Lee and T. Yao, “Design and evaluation of omnidirectional one-dimensional photonic crystals,” J. Appl. Phys. 93, 819–830 (2003).
    [CrossRef]
  7. M. Okano, A. Chutinan, and S. Noda, “Analysis and design of single-defect cavities in a three-dimensional photonic crystal,” Phys. Rev. B 66, 165211 (2002).
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    [CrossRef]
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    [CrossRef]
  14. C.-S. Kee, J.-E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, “Essential parameter in the formation of photonic band gaps,” Phys. Rev. E 59, 4695–4698 (1999).
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  22. B. Shi, Z. M. Jiang, X. F. Zhou, and X. Wang, “A two-dimensional nonlinear photonic crystal for strong second harmonic generation,” J. Appl. Phys. 91, 6769–6771 (2002).
    [CrossRef]

2003

H.-Y. Lee and T. Yao, “Design and evaluation of omnidirectional one-dimensional photonic crystals,” J. Appl. Phys. 93, 819–830 (2003).
[CrossRef]

2002

M. Okano, A. Chutinan, and S. Noda, “Analysis and design of single-defect cavities in a three-dimensional photonic crystal,” Phys. Rev. B 66, 165211 (2002).
[CrossRef]

B. Shi, Z. M. Jiang, X. F. Zhou, and X. Wang, “A two-dimensional nonlinear photonic crystal for strong second harmonic generation,” J. Appl. Phys. 91, 6769–6771 (2002).
[CrossRef]

2001

T. Aoki, M. W. Takeda, J. W. Haus, Z. Yuan, M. Tani, K. Sakai, N. Kawai, and K. Inoue, “Terahertz time-domain study of a pseudo-simple-cubic photonic lattice,” Phys. Rev. B 64, 045106 (2001).
[CrossRef]

1999

N. Tsurumachi, S. Yamashita, N. Muroi, T. Fuji, T. Hattori, and H. Nakatsuka, “Enhancement of nonlinear optical effect in one-dimensional photonic crystal structures,” Jpn. J. Appl. Phys., Part 1 38, 6302–6308 (1999).
[CrossRef]

A. de Lustrac, F. Gadot, S. Cabaret, J.-M. Lourtioz, T. Brillat, A. Priou, and E. Akmansoy, “Experimental demonstration of electrically controllable photonic crystals at centimeter wavelengths,” Appl. Phys. Lett. 75, 1625–1627 1999).
[CrossRef]

C.-S. Kee, J.-E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, “Essential parameter in the formation of photonic band gaps,” Phys. Rev. E 59, 4695–4698 (1999).
[CrossRef]

1998

A. Chelnokov, S. Rowson, J. M. Lourtioz, L. Duvillaret, and J. L. Coutaz, “Light controllable defect modes in three-dimensional photonic crystal,” Electron. Lett. 34, 1965–1967 (1998).
[CrossRef]

J. N. Winn, Y. Fink, S. Fan, and J. D. Joannopoulos, “Omnidirectional reflection from a one-dimensional photonic crystal,” Opt. Lett. 23, 1573–1575 (1998).
[CrossRef]

Y. C. Tsai, K. W. K. Shung, and S. C. Gou, “Impurity modes in one-dimensional photonic crystals—analytic approach,” J. Mod. Opt. 45, 2147–2157 (1998).

A. Figotin and V. Gorentsveig, “Localized electromagnetic waves in a layered periodic dielectric medium with a defect,” Phys. Rev. B 58, 180–188 (1998).
[CrossRef]

1997

M. M. Sigalas, C. M. Soukoulis, R. Biwas, and K. M. Ho, “Effect of the magnetic permeability on photonic band gaps,” Phys. Rev. B 56, 959–962 (1997).
[CrossRef]

T. Hattori, N. Tsurumachi, and H. Nakatsuka, “Analysis of optical nonlinearity by defect states in one-dimensional photonic crystals,” J. Opt. Soc. Am. B 14, 348–355 (1997).
[CrossRef]

A. Chelnokov, S. Rowson, J. M. Lourtioz, L. Duvillaret, and J. L. Coutaz, “Terahertz characterisation of mechanically machined 3D photonic crystal,” Electron. Lett. 33, 1981–1983 (1997).
[CrossRef]

H. Míguez, C. López, F. Meseguer, A. Blanco, L. Vázquez, R. Mayoral, M. Ocaña, V. Fornés, and A. Mifsud, “Photonic crystal properties of packed submicrometric SiO2 spheres,” Appl. Phys. Lett. 71, 1148–1150 (1997).
[CrossRef]

K. Sakoda and H. Shiroma, “Numerical method for localized defect modes in photonic lattices,” Phys. Rev. B 56, 4830–4835 (1997).
[CrossRef]

1996

H. Miyazaki, Y. Jimba, C. Y. Kim, and T. Watanabe, “Defects and photonic wells in one-dimensional photonic lattices,” J. Phys. Soc. Jpn. 65, 3842–3852 (1996).
[CrossRef]

E. Özbay and B. Temelkuran, “Reflection properties and defect formation in photonic crystals,” Appl. Phys. Lett. 69, 743–745 (1996).
[CrossRef]

1993

1987

E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987).
[CrossRef] [PubMed]

Akmansoy, E.

A. de Lustrac, F. Gadot, S. Cabaret, J.-M. Lourtioz, T. Brillat, A. Priou, and E. Akmansoy, “Experimental demonstration of electrically controllable photonic crystals at centimeter wavelengths,” Appl. Phys. Lett. 75, 1625–1627 1999).
[CrossRef]

Aoki, T.

T. Aoki, M. W. Takeda, J. W. Haus, Z. Yuan, M. Tani, K. Sakai, N. Kawai, and K. Inoue, “Terahertz time-domain study of a pseudo-simple-cubic photonic lattice,” Phys. Rev. B 64, 045106 (2001).
[CrossRef]

Biwas, R.

M. M. Sigalas, C. M. Soukoulis, R. Biwas, and K. M. Ho, “Effect of the magnetic permeability on photonic band gaps,” Phys. Rev. B 56, 959–962 (1997).
[CrossRef]

Blanco, A.

H. Míguez, C. López, F. Meseguer, A. Blanco, L. Vázquez, R. Mayoral, M. Ocaña, V. Fornés, and A. Mifsud, “Photonic crystal properties of packed submicrometric SiO2 spheres,” Appl. Phys. Lett. 71, 1148–1150 (1997).
[CrossRef]

Brillat, T.

A. de Lustrac, F. Gadot, S. Cabaret, J.-M. Lourtioz, T. Brillat, A. Priou, and E. Akmansoy, “Experimental demonstration of electrically controllable photonic crystals at centimeter wavelengths,” Appl. Phys. Lett. 75, 1625–1627 1999).
[CrossRef]

Cabaret, S.

A. de Lustrac, F. Gadot, S. Cabaret, J.-M. Lourtioz, T. Brillat, A. Priou, and E. Akmansoy, “Experimental demonstration of electrically controllable photonic crystals at centimeter wavelengths,” Appl. Phys. Lett. 75, 1625–1627 1999).
[CrossRef]

Chelnokov, A.

A. Chelnokov, S. Rowson, J. M. Lourtioz, L. Duvillaret, and J. L. Coutaz, “Light controllable defect modes in three-dimensional photonic crystal,” Electron. Lett. 34, 1965–1967 (1998).
[CrossRef]

A. Chelnokov, S. Rowson, J. M. Lourtioz, L. Duvillaret, and J. L. Coutaz, “Terahertz characterisation of mechanically machined 3D photonic crystal,” Electron. Lett. 33, 1981–1983 (1997).
[CrossRef]

Chutinan, A.

M. Okano, A. Chutinan, and S. Noda, “Analysis and design of single-defect cavities in a three-dimensional photonic crystal,” Phys. Rev. B 66, 165211 (2002).
[CrossRef]

Coutaz, J. L.

A. Chelnokov, S. Rowson, J. M. Lourtioz, L. Duvillaret, and J. L. Coutaz, “Light controllable defect modes in three-dimensional photonic crystal,” Electron. Lett. 34, 1965–1967 (1998).
[CrossRef]

A. Chelnokov, S. Rowson, J. M. Lourtioz, L. Duvillaret, and J. L. Coutaz, “Terahertz characterisation of mechanically machined 3D photonic crystal,” Electron. Lett. 33, 1981–1983 (1997).
[CrossRef]

Dalichaouch, R.

de Lustrac, A.

A. de Lustrac, F. Gadot, S. Cabaret, J.-M. Lourtioz, T. Brillat, A. Priou, and E. Akmansoy, “Experimental demonstration of electrically controllable photonic crystals at centimeter wavelengths,” Appl. Phys. Lett. 75, 1625–1627 1999).
[CrossRef]

Duvillaret, L.

A. Chelnokov, S. Rowson, J. M. Lourtioz, L. Duvillaret, and J. L. Coutaz, “Light controllable defect modes in three-dimensional photonic crystal,” Electron. Lett. 34, 1965–1967 (1998).
[CrossRef]

A. Chelnokov, S. Rowson, J. M. Lourtioz, L. Duvillaret, and J. L. Coutaz, “Terahertz characterisation of mechanically machined 3D photonic crystal,” Electron. Lett. 33, 1981–1983 (1997).
[CrossRef]

Fan, S.

Figotin, A.

A. Figotin and V. Gorentsveig, “Localized electromagnetic waves in a layered periodic dielectric medium with a defect,” Phys. Rev. B 58, 180–188 (1998).
[CrossRef]

Fink, Y.

Fornés, V.

H. Míguez, C. López, F. Meseguer, A. Blanco, L. Vázquez, R. Mayoral, M. Ocaña, V. Fornés, and A. Mifsud, “Photonic crystal properties of packed submicrometric SiO2 spheres,” Appl. Phys. Lett. 71, 1148–1150 (1997).
[CrossRef]

Fuji, T.

N. Tsurumachi, S. Yamashita, N. Muroi, T. Fuji, T. Hattori, and H. Nakatsuka, “Enhancement of nonlinear optical effect in one-dimensional photonic crystal structures,” Jpn. J. Appl. Phys., Part 1 38, 6302–6308 (1999).
[CrossRef]

Gadot, F.

A. de Lustrac, F. Gadot, S. Cabaret, J.-M. Lourtioz, T. Brillat, A. Priou, and E. Akmansoy, “Experimental demonstration of electrically controllable photonic crystals at centimeter wavelengths,” Appl. Phys. Lett. 75, 1625–1627 1999).
[CrossRef]

Gorentsveig, V.

A. Figotin and V. Gorentsveig, “Localized electromagnetic waves in a layered periodic dielectric medium with a defect,” Phys. Rev. B 58, 180–188 (1998).
[CrossRef]

Gou, S. C.

Y. C. Tsai, K. W. K. Shung, and S. C. Gou, “Impurity modes in one-dimensional photonic crystals—analytic approach,” J. Mod. Opt. 45, 2147–2157 (1998).

Hattori, T.

N. Tsurumachi, S. Yamashita, N. Muroi, T. Fuji, T. Hattori, and H. Nakatsuka, “Enhancement of nonlinear optical effect in one-dimensional photonic crystal structures,” Jpn. J. Appl. Phys., Part 1 38, 6302–6308 (1999).
[CrossRef]

T. Hattori, N. Tsurumachi, and H. Nakatsuka, “Analysis of optical nonlinearity by defect states in one-dimensional photonic crystals,” J. Opt. Soc. Am. B 14, 348–355 (1997).
[CrossRef]

Haus, J. W.

T. Aoki, M. W. Takeda, J. W. Haus, Z. Yuan, M. Tani, K. Sakai, N. Kawai, and K. Inoue, “Terahertz time-domain study of a pseudo-simple-cubic photonic lattice,” Phys. Rev. B 64, 045106 (2001).
[CrossRef]

Ho, K. M.

M. M. Sigalas, C. M. Soukoulis, R. Biwas, and K. M. Ho, “Effect of the magnetic permeability on photonic band gaps,” Phys. Rev. B 56, 959–962 (1997).
[CrossRef]

Inoue, K.

T. Aoki, M. W. Takeda, J. W. Haus, Z. Yuan, M. Tani, K. Sakai, N. Kawai, and K. Inoue, “Terahertz time-domain study of a pseudo-simple-cubic photonic lattice,” Phys. Rev. B 64, 045106 (2001).
[CrossRef]

Jiang, Z. M.

B. Shi, Z. M. Jiang, X. F. Zhou, and X. Wang, “A two-dimensional nonlinear photonic crystal for strong second harmonic generation,” J. Appl. Phys. 91, 6769–6771 (2002).
[CrossRef]

Jimba, Y.

H. Miyazaki, Y. Jimba, C. Y. Kim, and T. Watanabe, “Defects and photonic wells in one-dimensional photonic lattices,” J. Phys. Soc. Jpn. 65, 3842–3852 (1996).
[CrossRef]

Joannopoulos, J. D.

Kawai, N.

T. Aoki, M. W. Takeda, J. W. Haus, Z. Yuan, M. Tani, K. Sakai, N. Kawai, and K. Inoue, “Terahertz time-domain study of a pseudo-simple-cubic photonic lattice,” Phys. Rev. B 64, 045106 (2001).
[CrossRef]

Kee, C.-S.

C.-S. Kee, J.-E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, “Essential parameter in the formation of photonic band gaps,” Phys. Rev. E 59, 4695–4698 (1999).
[CrossRef]

Kim, C. Y.

H. Miyazaki, Y. Jimba, C. Y. Kim, and T. Watanabe, “Defects and photonic wells in one-dimensional photonic lattices,” J. Phys. Soc. Jpn. 65, 3842–3852 (1996).
[CrossRef]

Kim, J.-E.

C.-S. Kee, J.-E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, “Essential parameter in the formation of photonic band gaps,” Phys. Rev. E 59, 4695–4698 (1999).
[CrossRef]

Kim, S. J.

C.-S. Kee, J.-E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, “Essential parameter in the formation of photonic band gaps,” Phys. Rev. E 59, 4695–4698 (1999).
[CrossRef]

Kroll, N.

Kwon, Y. S.

C.-S. Kee, J.-E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, “Essential parameter in the formation of photonic band gaps,” Phys. Rev. E 59, 4695–4698 (1999).
[CrossRef]

Lee, H.-Y.

H.-Y. Lee and T. Yao, “Design and evaluation of omnidirectional one-dimensional photonic crystals,” J. Appl. Phys. 93, 819–830 (2003).
[CrossRef]

Lim, H.

C.-S. Kee, J.-E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, “Essential parameter in the formation of photonic band gaps,” Phys. Rev. E 59, 4695–4698 (1999).
[CrossRef]

López, C.

H. Míguez, C. López, F. Meseguer, A. Blanco, L. Vázquez, R. Mayoral, M. Ocaña, V. Fornés, and A. Mifsud, “Photonic crystal properties of packed submicrometric SiO2 spheres,” Appl. Phys. Lett. 71, 1148–1150 (1997).
[CrossRef]

Lourtioz, J. M.

A. Chelnokov, S. Rowson, J. M. Lourtioz, L. Duvillaret, and J. L. Coutaz, “Light controllable defect modes in three-dimensional photonic crystal,” Electron. Lett. 34, 1965–1967 (1998).
[CrossRef]

A. Chelnokov, S. Rowson, J. M. Lourtioz, L. Duvillaret, and J. L. Coutaz, “Terahertz characterisation of mechanically machined 3D photonic crystal,” Electron. Lett. 33, 1981–1983 (1997).
[CrossRef]

Lourtioz, J.-M.

A. de Lustrac, F. Gadot, S. Cabaret, J.-M. Lourtioz, T. Brillat, A. Priou, and E. Akmansoy, “Experimental demonstration of electrically controllable photonic crystals at centimeter wavelengths,” Appl. Phys. Lett. 75, 1625–1627 1999).
[CrossRef]

Mayoral, R.

H. Míguez, C. López, F. Meseguer, A. Blanco, L. Vázquez, R. Mayoral, M. Ocaña, V. Fornés, and A. Mifsud, “Photonic crystal properties of packed submicrometric SiO2 spheres,” Appl. Phys. Lett. 71, 1148–1150 (1997).
[CrossRef]

McCall, S. L.

Meseguer, F.

H. Míguez, C. López, F. Meseguer, A. Blanco, L. Vázquez, R. Mayoral, M. Ocaña, V. Fornés, and A. Mifsud, “Photonic crystal properties of packed submicrometric SiO2 spheres,” Appl. Phys. Lett. 71, 1148–1150 (1997).
[CrossRef]

Mifsud, A.

H. Míguez, C. López, F. Meseguer, A. Blanco, L. Vázquez, R. Mayoral, M. Ocaña, V. Fornés, and A. Mifsud, “Photonic crystal properties of packed submicrometric SiO2 spheres,” Appl. Phys. Lett. 71, 1148–1150 (1997).
[CrossRef]

Míguez, H.

H. Míguez, C. López, F. Meseguer, A. Blanco, L. Vázquez, R. Mayoral, M. Ocaña, V. Fornés, and A. Mifsud, “Photonic crystal properties of packed submicrometric SiO2 spheres,” Appl. Phys. Lett. 71, 1148–1150 (1997).
[CrossRef]

Miyazaki, H.

H. Miyazaki, Y. Jimba, C. Y. Kim, and T. Watanabe, “Defects and photonic wells in one-dimensional photonic lattices,” J. Phys. Soc. Jpn. 65, 3842–3852 (1996).
[CrossRef]

Muroi, N.

N. Tsurumachi, S. Yamashita, N. Muroi, T. Fuji, T. Hattori, and H. Nakatsuka, “Enhancement of nonlinear optical effect in one-dimensional photonic crystal structures,” Jpn. J. Appl. Phys., Part 1 38, 6302–6308 (1999).
[CrossRef]

Myung, N. H.

C.-S. Kee, J.-E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, “Essential parameter in the formation of photonic band gaps,” Phys. Rev. E 59, 4695–4698 (1999).
[CrossRef]

Nakatsuka, H.

N. Tsurumachi, S. Yamashita, N. Muroi, T. Fuji, T. Hattori, and H. Nakatsuka, “Enhancement of nonlinear optical effect in one-dimensional photonic crystal structures,” Jpn. J. Appl. Phys., Part 1 38, 6302–6308 (1999).
[CrossRef]

T. Hattori, N. Tsurumachi, and H. Nakatsuka, “Analysis of optical nonlinearity by defect states in one-dimensional photonic crystals,” J. Opt. Soc. Am. B 14, 348–355 (1997).
[CrossRef]

Noda, S.

M. Okano, A. Chutinan, and S. Noda, “Analysis and design of single-defect cavities in a three-dimensional photonic crystal,” Phys. Rev. B 66, 165211 (2002).
[CrossRef]

Ocaña, M.

H. Míguez, C. López, F. Meseguer, A. Blanco, L. Vázquez, R. Mayoral, M. Ocaña, V. Fornés, and A. Mifsud, “Photonic crystal properties of packed submicrometric SiO2 spheres,” Appl. Phys. Lett. 71, 1148–1150 (1997).
[CrossRef]

Okano, M.

M. Okano, A. Chutinan, and S. Noda, “Analysis and design of single-defect cavities in a three-dimensional photonic crystal,” Phys. Rev. B 66, 165211 (2002).
[CrossRef]

Özbay, E.

E. Özbay and B. Temelkuran, “Reflection properties and defect formation in photonic crystals,” Appl. Phys. Lett. 69, 743–745 (1996).
[CrossRef]

Park, H. Y.

C.-S. Kee, J.-E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, “Essential parameter in the formation of photonic band gaps,” Phys. Rev. E 59, 4695–4698 (1999).
[CrossRef]

Platzman, P. M.

Priou, A.

A. de Lustrac, F. Gadot, S. Cabaret, J.-M. Lourtioz, T. Brillat, A. Priou, and E. Akmansoy, “Experimental demonstration of electrically controllable photonic crystals at centimeter wavelengths,” Appl. Phys. Lett. 75, 1625–1627 1999).
[CrossRef]

Rowson, S.

A. Chelnokov, S. Rowson, J. M. Lourtioz, L. Duvillaret, and J. L. Coutaz, “Light controllable defect modes in three-dimensional photonic crystal,” Electron. Lett. 34, 1965–1967 (1998).
[CrossRef]

A. Chelnokov, S. Rowson, J. M. Lourtioz, L. Duvillaret, and J. L. Coutaz, “Terahertz characterisation of mechanically machined 3D photonic crystal,” Electron. Lett. 33, 1981–1983 (1997).
[CrossRef]

Sakai, K.

T. Aoki, M. W. Takeda, J. W. Haus, Z. Yuan, M. Tani, K. Sakai, N. Kawai, and K. Inoue, “Terahertz time-domain study of a pseudo-simple-cubic photonic lattice,” Phys. Rev. B 64, 045106 (2001).
[CrossRef]

Sakoda, K.

K. Sakoda and H. Shiroma, “Numerical method for localized defect modes in photonic lattices,” Phys. Rev. B 56, 4830–4835 (1997).
[CrossRef]

Schultz, S.

Shi, B.

B. Shi, Z. M. Jiang, X. F. Zhou, and X. Wang, “A two-dimensional nonlinear photonic crystal for strong second harmonic generation,” J. Appl. Phys. 91, 6769–6771 (2002).
[CrossRef]

Shin, S. Y.

C.-S. Kee, J.-E. Kim, H. Y. Park, S. J. Kim, H. C. Song, Y. S. Kwon, N. H. Myung, S. Y. Shin, and H. Lim, “Essential parameter in the formation of photonic band gaps,” Phys. Rev. E 59, 4695–4698 (1999).
[CrossRef]

Shiroma, H.

K. Sakoda and H. Shiroma, “Numerical method for localized defect modes in photonic lattices,” Phys. Rev. B 56, 4830–4835 (1997).
[CrossRef]

Shung, K. W. K.

Y. C. Tsai, K. W. K. Shung, and S. C. Gou, “Impurity modes in one-dimensional photonic crystals—analytic approach,” J. Mod. Opt. 45, 2147–2157 (1998).

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T. Aoki, M. W. Takeda, J. W. Haus, Z. Yuan, M. Tani, K. Sakai, N. Kawai, and K. Inoue, “Terahertz time-domain study of a pseudo-simple-cubic photonic lattice,” Phys. Rev. B 64, 045106 (2001).
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N. Tsurumachi, S. Yamashita, N. Muroi, T. Fuji, T. Hattori, and H. Nakatsuka, “Enhancement of nonlinear optical effect in one-dimensional photonic crystal structures,” Jpn. J. Appl. Phys., Part 1 38, 6302–6308 (1999).
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T. Aoki, M. W. Takeda, J. W. Haus, Z. Yuan, M. Tani, K. Sakai, N. Kawai, and K. Inoue, “Terahertz time-domain study of a pseudo-simple-cubic photonic lattice,” Phys. Rev. B 64, 045106 (2001).
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J. Opt. Soc. Am. B

J. Phys. Soc. Jpn.

H. Miyazaki, Y. Jimba, C. Y. Kim, and T. Watanabe, “Defects and photonic wells in one-dimensional photonic lattices,” J. Phys. Soc. Jpn. 65, 3842–3852 (1996).
[CrossRef]

Jpn. J. Appl. Phys., Part 1

N. Tsurumachi, S. Yamashita, N. Muroi, T. Fuji, T. Hattori, and H. Nakatsuka, “Enhancement of nonlinear optical effect in one-dimensional photonic crystal structures,” Jpn. J. Appl. Phys., Part 1 38, 6302–6308 (1999).
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Opt. Lett.

Phys. Rev. B

T. Aoki, M. W. Takeda, J. W. Haus, Z. Yuan, M. Tani, K. Sakai, N. Kawai, and K. Inoue, “Terahertz time-domain study of a pseudo-simple-cubic photonic lattice,” Phys. Rev. B 64, 045106 (2001).
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[CrossRef]

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[CrossRef]

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[CrossRef]

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Other

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, Cambridge, 1999), Sect. 1.6, pp. 54–74.

H. Němec, P. Kužel, F. Garet, and L. Duvillaret, “Time-domain terahertz study of defect formation in one-dimensional photonic crystals,” Appl. Opt. (to be published).

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Figures (5)

Fig. 1
Fig. 1

Schematic of parameters of the transfer matrix method.

Fig. 2
Fig. 2

Structure and corresponding transfer matrices: F… L, arbitrary sequence of layers starting with F and ending with L.

Fig. 3
Fig. 3

(a) Dimensionless frequency [in units of c/(2ltot); ltot=nFdF+nLdL] of defect modes, (b) their relative tunability by optical thickness, and (c) enhancement of the electric field in the middle of the defect versus optical thickness of the defect. Dashed lines in (a) indicate band edges; thicker curves, even-parity modes; and thinner curves, odd-parity modes. The calculations were made with θ=0° and ZD=0.0025 (dotted curves), ZD=0.25 (solid curves), and ZD=25 (dashed–dotted curves). Parameters of the PC are nFdF=nLdL=ltot/2, ZF=1/3.4, and ZL=ZA=1. The number of periods in (c) is N=10. For clarity, only modes with m=2 are plotted in (b) and (c).

Fig. 4
Fig. 4

(a) Dimensionless frequency of defect modes and (b) their relative tunability by impedance versus impedance of the defect. Long-dashed lines-indicate band edges; Dashed–dotted curve, middle of the gap; dotted curve, asymptotic limits of defect levels when ZD 0 (m=2) or ZD (m=3). The calculations were performed with nDdD=1.824ltot and θ=0°; other parameters are the same as in Fig. 3.

Fig. 5
Fig. 5

Dimensionless frequency of a defect mode as a function of angle of incidence θ on the PC. Dashed curves, band edges; dotted and solid curves, nDdD=0.735ltot and nDdD=ltot, respectively. For both polarizations ZD=0.25 and nA=1. Other parameters are the same as in Fig. 3.

Equations (22)

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EF(zj+1)EB(zj+1)=Tj,j+1EF(zj)EB(zj).
Tj,j+1=T11T12T21T22=wj,j+12(1+xj,j+1)exp(-ikz,jdj)(1-xj,j+1)exp(+ikz,jdj)(1-xj,j+1)exp(-ikz,jdj)(1+xj,j+1)exp(+ikz,jdj),
TEpolarization:wj,j+1=1,
xj,j+1=Zj+1Zjcos θjcos θj+1,
TMpolarization:wj,j+1=cos θjcos θj+1,
xj,j+1=Zj+1Zjcos θj+1cos θj.
T22=T11*,T12=T21*.
EiEr=Q11Q21*Q21Q11*Et0,
M=A·SN·Δ,
P=M·(M*)-1=A·SN·Δ·(Δ*)-1·(S*)-N·(A*)-1.
EiEr=SNEt0,
SN=1texp(-iτ)r exp[-i(ρ-τ)]r exp[i(ρ-τ)]exp(iτ),
[exp i(ρ-2τ)]=-Δ21±Δ11*Δ11±Δ21*.
2τ-ρ2 arg(Δ11+Δ21*)+π[2π],
2 arg(Δ11-Δ21*)[2π],
kz,DdD=mπ+2φ,φ=arctan(tan κ/xD,L),κ=ρ(f)-2τ(f)+π2,
dDfdfddD=-11+{(cxD,L/πnDdD cos θD)[d(ρ-2τ)/df][1/((xD,L2-1)cos(ρ-2τ)-(xD,L2+1))]}.
Efwd±Ebck=1M11±M21*Ein
Efwd±EbckEin=4wL,At1exp(-iτ)(Δ11±Δ21*)(1+xL,A)+exp(iτ)(Δ21±Δ11*)(1-xL,A).
Efwd±EbckEin=2texp(iτ)Δ11±Δ21*.
1Δ11+Δ21*=1wD,L1xD,Lcoskz,DdD2-ixD,L1sinkz,DdD2-1.
f=m-2 fcπxD,Lκ(fc)c2nDdD-2cπxD,Lκ(fc),

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