Abstract

Optical asymmetry with regard to transmission has been numerically explored in one-dimensional (1D) plasmonic crystal slabs (PlCSs) with the help of a genetic algorithm (GA). Optically deep asymmetric PlCSs are not obtained in one-layer systems and can be achieved in unit cell structures composed of more than two layers. The optical asymmetry is classified into two types. One is ascribed to anisotropic diffraction efficiency, and the other comes from collective oscillations of particle plasmons in each metallic nanorod and can induce nearly perfect absorption over a broad band. In both asymmetry types, the degree of freedom in depth is crucial to manipulate the linear optical responses of PlCSs. On the basis of the GA search, a simple design for optically asymmetric 1D PlCS is extracted, which provides a standard for broadband plasmonic absorbers in both photon energy and incident angles.

© 2009 Optical Society of America

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2008

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376-380 (2008).
[CrossRef] [PubMed]

M. Iwanaga, “Ultracompact waveplates: approach from metamaterials,” Appl. Phys. Lett. 92, 153102 (2008).
[CrossRef]

P. Y. Chen, C. H. Chen, H. Wang, J. H. Tsai, and W. X. Ni, “Synthesis design of artificial magnetic metamaterials using a genetic algorithm,” Opt. Express 16, 12806-12818 (2008).
[CrossRef] [PubMed]

T. V. Teperik, F. J. G. de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2, 299-301 (2008).
[CrossRef]

A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett. 8, 2171-2175 (2008).
[CrossRef] [PubMed]

2007

M. Iwanaga, A. S. Vengurlekar, T. Hatano, and T. Ishihara, “Reciprocal transmittances and reflectances: an elementary proof,” Am. J. Phys. 75, 899-902 (2007).
[CrossRef]

J. Goh, I. Fushman, D. Englund, and J. Vučković, “Genetic optimization of photonic bandgap structures,” Opt. Express 15, 8218-8230 (2007).
[CrossRef] [PubMed]

A. V. Kildishev, U. K. Chettiar, Z. Liu, V. M. Shalaev, D.-H. Kwon, Z. Bayraktar, and D. H. Werner, “Stochastic optimization of low-loss optical negative-index metamaterial,” J. Opt. Soc. Am. B 24, A34-A39 (2007).
[CrossRef]

M. Iwanaga, “Effective optical constants in stratified metal-dielectric metamaterial,” Opt. Lett. 32, 1314-1316 (2007).
[CrossRef] [PubMed]

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
[CrossRef]

2006

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B. Gralak, “Photonic crystal lens: from negative refraction and negative index to negative permittivity and permeability,” Phys. Rev. Lett. 97, 073905 (2006).
[CrossRef] [PubMed]

A. Håkansson, H. T. Miyazaki, and J. Sánchez-Dehesa, “Inverse design for full control of spontaneous emission using light emitting scattering optical elements,” Phys. Rev. Lett. 96, 153902 (2006).
[CrossRef] [PubMed]

2005

C. Y. Kao, S. Osher, and E. Yablonovitch, “Maximizing band gaps in two-dimensional photonic crystals by using level set methods,” Appl. Phys. B 81, 235-244 (2005).
[CrossRef]

2004

R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67, 717-754 (2004).
[CrossRef]

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Efficient light absorption in metal-semiconductor-metal nanostructures,” Appl. Phys. Lett. 85, 194-196 (2004).
[CrossRef]

A. Christ, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical properties of planar metallic photonic crystal structures: experiment and theory,” Phys. Rev. B 70, 125113 (2004).
[CrossRef]

2003

L. Shen, Z. Ye, and S. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B 68, 035109 (2003).
[CrossRef]

Y. Chen, R. Yu, W. Li, O. Nohadani, S. Haas, and A. F. J. Levi, “Adaptive design of nanoscale dielectric structures for photonics,” J. Appl. Phys. 94, 6065-6068 (2003).
[CrossRef]

2002

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

2001

T. Ito and K. Sakoda, “Photonic bands of metallic systems. II. features of surface plasmon polaritons,” Phys. Rev. B 64, 045117 (2001).
[CrossRef]

2000

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696-10705 (2000).
[CrossRef]

1998

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

1996

1988

D. Y. K. Ko and J. C. Inkson, “Matrix method for tunneling in heterostructures: resonant tunneling in multilayer systems,” Phys. Rev. B 38, 9945-9951 (1988).
[CrossRef]

1976

M. C. Hutley and D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431-436 (1976).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Abdelsalam, M.

T. V. Teperik, F. J. G. de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2, 299-301 (2008).
[CrossRef]

Alekseyev, L.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
[CrossRef]

Bartal, G.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376-380 (2008).
[CrossRef] [PubMed]

Bartlett, P. N.

T. V. Teperik, F. J. G. de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2, 299-301 (2008).
[CrossRef]

Baumberg, J. J.

T. V. Teperik, F. J. G. de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2, 299-301 (2008).
[CrossRef]

Bayraktar, Z.

Borisov, A. G.

T. V. Teperik, F. J. G. de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2, 299-301 (2008).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), p. 446.

Chen, C. H.

Chen, P. Y.

Chen, Y.

Y. Chen, R. Yu, W. Li, O. Nohadani, S. Haas, and A. F. J. Levi, “Adaptive design of nanoscale dielectric structures for photonics,” J. Appl. Phys. 94, 6065-6068 (2003).
[CrossRef]

Chettiar, U. K.

Christ, A.

A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett. 8, 2171-2175 (2008).
[CrossRef] [PubMed]

A. Christ, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical properties of planar metallic photonic crystal structures: experiment and theory,” Phys. Rev. B 70, 125113 (2004).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Collin, S.

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Efficient light absorption in metal-semiconductor-metal nanostructures,” Appl. Phys. Lett. 85, 194-196 (2004).
[CrossRef]

de Abajo, F. J. G.

T. V. Teperik, F. J. G. de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2, 299-301 (2008).
[CrossRef]

Decoopman, T.

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B. Gralak, “Photonic crystal lens: from negative refraction and negative index to negative permittivity and permeability,” Phys. Rev. Lett. 97, 073905 (2006).
[CrossRef] [PubMed]

Ekinci, Y.

A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett. 8, 2171-2175 (2008).
[CrossRef] [PubMed]

Englund, D.

Enoch, S.

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B. Gralak, “Photonic crystal lens: from negative refraction and negative index to negative permittivity and permeability,” Phys. Rev. Lett. 97, 073905 (2006).
[CrossRef] [PubMed]

Franz, K. J.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
[CrossRef]

Fushman, I.

Genov, D. A.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376-380 (2008).
[CrossRef] [PubMed]

Giessen, H.

A. Christ, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical properties of planar metallic photonic crystal structures: experiment and theory,” Phys. Rev. B 70, 125113 (2004).
[CrossRef]

Gippius, N. A.

A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett. 8, 2171-2175 (2008).
[CrossRef] [PubMed]

A. Christ, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical properties of planar metallic photonic crystal structures: experiment and theory,” Phys. Rev. B 70, 125113 (2004).
[CrossRef]

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

Gmachl, C.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
[CrossRef]

Goh, J.

Goldberg, D. E.

D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, 1989).

Gralak, B.

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B. Gralak, “Photonic crystal lens: from negative refraction and negative index to negative permittivity and permeability,” Phys. Rev. Lett. 97, 073905 (2006).
[CrossRef] [PubMed]

Haas, S.

Y. Chen, R. Yu, W. Li, O. Nohadani, S. Haas, and A. F. J. Levi, “Adaptive design of nanoscale dielectric structures for photonics,” J. Appl. Phys. 94, 6065-6068 (2003).
[CrossRef]

Håkansson, A.

A. Håkansson, H. T. Miyazaki, and J. Sánchez-Dehesa, “Inverse design for full control of spontaneous emission using light emitting scattering optical elements,” Phys. Rev. Lett. 96, 153902 (2006).
[CrossRef] [PubMed]

Hatano, T.

M. Iwanaga, A. S. Vengurlekar, T. Hatano, and T. Ishihara, “Reciprocal transmittances and reflectances: an elementary proof,” Am. J. Phys. 75, 899-902 (2007).
[CrossRef]

He, S.

L. Shen, Z. Ye, and S. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B 68, 035109 (2003).
[CrossRef]

Hoffman, A. J.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
[CrossRef]

Holland, J. H.

J. H. Holland, Adaptation in Natural and Artificial Systems (MIT Press, 1992).

Howard, S. S.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
[CrossRef]

Hutley, M. C.

M. C. Hutley and D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431-436 (1976).
[CrossRef]

Inkson, J. C.

D. Y. K. Ko and J. C. Inkson, “Matrix method for tunneling in heterostructures: resonant tunneling in multilayer systems,” Phys. Rev. B 38, 9945-9951 (1988).
[CrossRef]

Ishihara, T.

M. Iwanaga, A. S. Vengurlekar, T. Hatano, and T. Ishihara, “Reciprocal transmittances and reflectances: an elementary proof,” Am. J. Phys. 75, 899-902 (2007).
[CrossRef]

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

Ito, T.

T. Ito and K. Sakoda, “Photonic bands of metallic systems. II. features of surface plasmon polaritons,” Phys. Rev. B 64, 045117 (2001).
[CrossRef]

Iwanaga, M.

M. Iwanaga, “Ultracompact waveplates: approach from metamaterials,” Appl. Phys. Lett. 92, 153102 (2008).
[CrossRef]

M. Iwanaga, A. S. Vengurlekar, T. Hatano, and T. Ishihara, “Reciprocal transmittances and reflectances: an elementary proof,” Am. J. Phys. 75, 899-902 (2007).
[CrossRef]

M. Iwanaga, “Effective optical constants in stratified metal-dielectric metamaterial,” Opt. Lett. 32, 1314-1316 (2007).
[CrossRef] [PubMed]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Kao, C. Y.

C. Y. Kao, S. Osher, and E. Yablonovitch, “Maximizing band gaps in two-dimensional photonic crystals by using level set methods,” Appl. Phys. B 81, 235-244 (2005).
[CrossRef]

Kawakami, S.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Kawashima, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Kildishev, A. V.

Ko, D. Y. K.

D. Y. K. Ko and J. C. Inkson, “Matrix method for tunneling in heterostructures: resonant tunneling in multilayer systems,” Phys. Rev. B 38, 9945-9951 (1988).
[CrossRef]

Kosaka, H.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Kuhl, J.

A. Christ, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical properties of planar metallic photonic crystal structures: experiment and theory,” Phys. Rev. B 70, 125113 (2004).
[CrossRef]

Kwon, D.-H.

Levi, A. F. J.

Y. Chen, R. Yu, W. Li, O. Nohadani, S. Haas, and A. F. J. Levi, “Adaptive design of nanoscale dielectric structures for photonics,” J. Appl. Phys. 94, 6065-6068 (2003).
[CrossRef]

Li, L.

Li, W.

Y. Chen, R. Yu, W. Li, O. Nohadani, S. Haas, and A. F. J. Levi, “Adaptive design of nanoscale dielectric structures for photonics,” J. Appl. Phys. 94, 6065-6068 (2003).
[CrossRef]

Liu, Z.

Martin, O. J. F.

A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett. 8, 2171-2175 (2008).
[CrossRef] [PubMed]

Maystre, D.

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B. Gralak, “Photonic crystal lens: from negative refraction and negative index to negative permittivity and permeability,” Phys. Rev. Lett. 97, 073905 (2006).
[CrossRef] [PubMed]

M. C. Hutley and D. Maystre, “The total absorption of light by a diffraction grating,” Opt. Commun. 19, 431-436 (1976).
[CrossRef]

Miyazaki, H. T.

A. Håkansson, H. T. Miyazaki, and J. Sánchez-Dehesa, “Inverse design for full control of spontaneous emission using light emitting scattering optical elements,” Phys. Rev. Lett. 96, 153902 (2006).
[CrossRef] [PubMed]

Muljarov, E. A.

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

Narimanov, E. E.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
[CrossRef]

Ni, W. X.

Nohadani, O.

Y. Chen, R. Yu, W. Li, O. Nohadani, S. Haas, and A. F. J. Levi, “Adaptive design of nanoscale dielectric structures for photonics,” J. Appl. Phys. 94, 6065-6068 (2003).
[CrossRef]

Notomi, M.

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696-10705 (2000).
[CrossRef]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Osher, S.

C. Y. Kao, S. Osher, and E. Yablonovitch, “Maximizing band gaps in two-dimensional photonic crystals by using level set methods,” Appl. Phys. B 81, 235-244 (2005).
[CrossRef]

Pardo, F.

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Efficient light absorption in metal-semiconductor-metal nanostructures,” Appl. Phys. Lett. 85, 194-196 (2004).
[CrossRef]

Pelouard, J.-L.

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Efficient light absorption in metal-semiconductor-metal nanostructures,” Appl. Phys. Lett. 85, 194-196 (2004).
[CrossRef]

Podolskiy, V. A.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
[CrossRef]

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R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67, 717-754 (2004).
[CrossRef]

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T. Ito and K. Sakoda, “Photonic bands of metallic systems. II. features of surface plasmon polaritons,” Phys. Rev. B 64, 045117 (2001).
[CrossRef]

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A. Håkansson, H. T. Miyazaki, and J. Sánchez-Dehesa, “Inverse design for full control of spontaneous emission using light emitting scattering optical elements,” Phys. Rev. Lett. 96, 153902 (2006).
[CrossRef] [PubMed]

Sato, T.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

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L. Shen, Z. Ye, and S. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B 68, 035109 (2003).
[CrossRef]

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A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
[CrossRef]

Sugawara, Y.

T. V. Teperik, F. J. G. de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2, 299-301 (2008).
[CrossRef]

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H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Tayeb, G.

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B. Gralak, “Photonic crystal lens: from negative refraction and negative index to negative permittivity and permeability,” Phys. Rev. Lett. 97, 073905 (2006).
[CrossRef] [PubMed]

Teissier, R.

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Efficient light absorption in metal-semiconductor-metal nanostructures,” Appl. Phys. Lett. 85, 194-196 (2004).
[CrossRef]

Teperik, T. V.

T. V. Teperik, F. J. G. de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2, 299-301 (2008).
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A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett. 8, 2171-2175 (2008).
[CrossRef] [PubMed]

A. Christ, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical properties of planar metallic photonic crystal structures: experiment and theory,” Phys. Rev. B 70, 125113 (2004).
[CrossRef]

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

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H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, “Superprism phenomena in photonic crystals,” Phys. Rev. B 58, R10096-R10099 (1998).
[CrossRef]

Tsai, J. H.

Ulin-Avila, E.

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[CrossRef] [PubMed]

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J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376-380 (2008).
[CrossRef] [PubMed]

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[CrossRef]

Vuckovic, J.

Wang, H.

Wasserman, D.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
[CrossRef]

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Wolf, E.

M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge U. Press, 1999), p. 446.

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C. Y. Kao, S. Osher, and E. Yablonovitch, “Maximizing band gaps in two-dimensional photonic crystals by using level set methods,” Appl. Phys. B 81, 235-244 (2005).
[CrossRef]

Yablonskii, A. L.

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

Ye, Z.

L. Shen, Z. Ye, and S. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B 68, 035109 (2003).
[CrossRef]

Yu, R.

Y. Chen, R. Yu, W. Li, O. Nohadani, S. Haas, and A. F. J. Levi, “Adaptive design of nanoscale dielectric structures for photonics,” J. Appl. Phys. 94, 6065-6068 (2003).
[CrossRef]

Zentgraf, T.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376-380 (2008).
[CrossRef] [PubMed]

A. Christ, T. Zentgraf, J. Kuhl, S. G. Tikhodeev, N. A. Gippius, and H. Giessen, “Optical properties of planar metallic photonic crystal structures: experiment and theory,” Phys. Rev. B 70, 125113 (2004).
[CrossRef]

Zhang, S.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376-380 (2008).
[CrossRef] [PubMed]

Zhang, X.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376-380 (2008).
[CrossRef] [PubMed]

Am. J. Phys.

M. Iwanaga, A. S. Vengurlekar, T. Hatano, and T. Ishihara, “Reciprocal transmittances and reflectances: an elementary proof,” Am. J. Phys. 75, 899-902 (2007).
[CrossRef]

Appl. Phys. B

C. Y. Kao, S. Osher, and E. Yablonovitch, “Maximizing band gaps in two-dimensional photonic crystals by using level set methods,” Appl. Phys. B 81, 235-244 (2005).
[CrossRef]

Appl. Phys. Lett.

M. Iwanaga, “Ultracompact waveplates: approach from metamaterials,” Appl. Phys. Lett. 92, 153102 (2008).
[CrossRef]

S. Collin, F. Pardo, R. Teissier, and J.-L. Pelouard, “Efficient light absorption in metal-semiconductor-metal nanostructures,” Appl. Phys. Lett. 85, 194-196 (2004).
[CrossRef]

J. Appl. Phys.

Y. Chen, R. Yu, W. Li, O. Nohadani, S. Haas, and A. F. J. Levi, “Adaptive design of nanoscale dielectric structures for photonics,” J. Appl. Phys. 94, 6065-6068 (2003).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Nano Lett.

A. Christ, O. J. F. Martin, Y. Ekinci, N. A. Gippius, and S. G. Tikhodeev, “Symmetry breaking in a plasmonic metamaterial at optical wavelength,” Nano Lett. 8, 2171-2175 (2008).
[CrossRef] [PubMed]

Nat. Photonics

T. V. Teperik, F. J. G. de Abajo, A. G. Borisov, M. Abdelsalam, P. N. Bartlett, Y. Sugawara, and J. J. Baumberg, “Omnidirectional absorption in nanostructured metal surfaces,” Nat. Photonics 2, 299-301 (2008).
[CrossRef]

Nature

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455, 376-380 (2008).
[CrossRef] [PubMed]

Nature Mater.

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nature Mater. 6, 946-950 (2007).
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[CrossRef]

M. Notomi, “Theory of light propagation in strongly modulated photonic crystals: refractionlike behavior in the vicinity of the photonic band gap,” Phys. Rev. B 62, 10696-10705 (2000).
[CrossRef]

T. Ito and K. Sakoda, “Photonic bands of metallic systems. II. features of surface plasmon polaritons,” Phys. Rev. B 64, 045117 (2001).
[CrossRef]

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[CrossRef]

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

L. Shen, Z. Ye, and S. He, “Design of two-dimensional photonic crystals with large absolute band gaps using a genetic algorithm,” Phys. Rev. B 68, 035109 (2003).
[CrossRef]

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[CrossRef]

Phys. Rev. Lett.

A. Håkansson, H. T. Miyazaki, and J. Sánchez-Dehesa, “Inverse design for full control of spontaneous emission using light emitting scattering optical elements,” Phys. Rev. Lett. 96, 153902 (2006).
[CrossRef] [PubMed]

T. Decoopman, G. Tayeb, S. Enoch, D. Maystre, and B. Gralak, “Photonic crystal lens: from negative refraction and negative index to negative permittivity and permeability,” Phys. Rev. Lett. 97, 073905 (2006).
[CrossRef] [PubMed]

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R. J. Potton, “Reciprocity in optics,” Rep. Prog. Phys. 67, 717-754 (2004).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

(a) Schematic drawing of the x z section of 1D PlCS and optical configuration. The unit cell of 1D PlCS is defined in the area between the vertical dashed lines. The 1D PlCS is periodic along the x axis and infinitely long along the y axis. In accordance with the coordinates, the diffraction channels T n and R n are labeled. (b) and (c) are reciprocal concerning reflection R 0 with each other. (d) A structurally asymmetric 1D PlCS. (e) Optical spectra of (d) at 1.3 eV , dependent on incident angles under p polarization. Reflectance ( R ) , transmittance ( T ) , total diffraction efficiency ( D ) , and absorption ( A ) are displayed with dotted red, solid blue, dashed-dotted green, and dashed gray lines, respectively. Note that A is close to zero.

Fig. 2
Fig. 2

Scheme of SGA. Each unit cell (or chromosome) in the N th generation is evaluated by fitness σ, and then a tentative set of unit cells are reproduced in proportion to their fitness. Random pairing is executed. Each pair does crossover by exchanging a part of each unit cell. The part is the area between orange vertical lines. The next ( N + 1 ) th generation is finally produced. Succeeding generations are produced similarly.

Fig. 3
Fig. 3

Configuration of unit cell and a typical result of SGA search. (a) Actual configuration in the SGA search. The unit cell is located on an infinitely thick substrate and periodically arrayed along the x axis. The unit cell is infinitely long along the y axis. (b) Average (red open circles) and the maximum (blue closed circles) of σ at each generation, which has a population of 600. The photon energy was set to be 1.65 eV , and incident angles were ± 30 ° .

Fig. 4
Fig. 4

(a) An optically asymmetric two-layer 1D PlCS of σ = 0.19 and (b) the optical spectra at 2.0 eV , in which the notation is similar to Fig. 1e. (c) Highly asymmetric two-layer unit cell of σ = 0.56 , searched by SGA and (d) the optical spectra at 2.0 eV .

Fig. 5
Fig. 5

Optically highly asymmetric three-layer 1D PlCSs found by SGA, and the linear optical spectra: (a) unit cell of σ = 0.68 , (b) optical spectra of (a) at 2.0 eV , dependent on incident angles. The notation of optical spectra is similar to Fig. 1e. Similarly, (c) unit cell of σ = 0.76 , and (d) the optical spectra of (c). (e) unit cell of σ = 0.53 , and (f) the optical spectra of (e). (g) unit cell of σ = 0.74 , and (h) the optical spectra of (g).

Fig. 6
Fig. 6

Optically highly asymmetric four-layer 1D PlCS, which is designed by hand on the basis of the results of SGA search. (a) Unit structures. (b) Optical spectra at 2.0 eV ; the notation is similar to Fig. 1e. (c) and (d) Snapshots of H y distributions at 40° and 40 ° , respectively. The scale is determined by the definition such that the magnitude of incident electric field E in is equal to unity. Arrows indicate the direction of incident wave vectors.

Fig. 7
Fig. 7

(a) Structurally asymmetric 1D PlCS designed to compare with Fig. 6a. (b) Optical spectra at 2.0 eV ; the notation is similar to Fig. 1e.

Equations (2)

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σ 0 = T ( θ ) T ( θ ) T ( θ ) + T ( θ ) ,
σ = T ( θ ) T ( θ ) [ 1 R ( θ ) ] .

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