Abstract

In this paper we theoretically study refraction effects in the 2D square-like Archimedean photonic crystals (32, 4, 3, 4) and (4, 82) made of dielectric rods in air. In addition, we investigated a band isotropy and band gap structure in these lattices. We compared the square and square-like structures as well, their refraction characteristics, zone structures and the level of band and band gap isotropy (bandwidth and band gap dependence on the wave vector). We found that square-like structures can have some advantages over the square ones regarding the completeness of the gap, its isotropy and the gap width. Also, due to the same square primitive unit cell and the first Brillouin zone, the square and square-like lattices have similar optical response in lower bands.

© 2008 Optical Society of America

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2008 (1)

R. Gaji?, ?. Jovanovi?, K. Hingerl, R. Meisels, and F. Kuchar, "2D photonic crystals on the archimedean lattices tribute to Johannes Kepler (1571-1630)," Opt. Mater. 30, 1065 (2008).
[CrossRef]

2007 (3)

R. Gaji?, R. Meisels, F. Kuchar, ?. Jovanovi?, and K. Hingerl, "Negative refraction and left-handedness in 2D Archimedean lattice photonic crystals," Mater. Sci. Forum 555, 83-88 (2007)
[CrossRef]

K. Ueda, T. Dotera, and T. Gemma, "Photonic band structure calculations of two-dimensional Archimedean tiling patterns," Phys. Rev. B 75, 195122 (2007).
[CrossRef]

L. Moretti and V. Mocella, "Two-dimensional photonic aperiodic crystals based on Thue-Morse sequence," Opt. Express 15, 15314 (2007).
[CrossRef] [PubMed]

2006 (4)

C. Rockstuhl, U. Peschel, and F. Lederer, "Correlation between single-cylinder properties and bandgap formation in photonic structures," Opt. Lett. 31, 1741 (2006).
[CrossRef] [PubMed]

R. Meisels, R. Gajic, F. Kuchar, and K. Hingerl, "Negative refraction and flat-lens focusing in a 2D square-lattice photonic crystal at microwave and millimeter wave frequencies," Opt. Express 14, 6766-6777 (2006).
[CrossRef] [PubMed]

A. David, T. Fujii, E. Matioli, R. Sharma, S. Nakamura, and H. Benisty", GaN light-emitting diodes with Archimedean lattice photonic crystals," Appl. Phys. Lett. 88, 073510 (2006).
[CrossRef]

R. Gajic, R. Meisels, F. Kuchar, and K. Hingerl, "All-angle left-handed negative refraction in Kagomé and honeycomb lattice photonic crystals," Phys. Rev. B 73, 165310 (2006)
[CrossRef]

2005 (2)

S. Foteinopoulou and C. M. Soukoulis, "Electromagnetic wave propagation in two-dimensional photonic crystals: A study of anomalous refractive effects," Phys. Rev. B 72, 165112 (2005).
[CrossRef]

R. Gajic, R. Meisels, F. Kuchar, and K. Hingerl, "Refraction and rightness in photonic crystals," Opt. Express 13, 8596-8605 (2005).
[CrossRef] [PubMed]

2004 (1)

J. B. Pendry and D. R. Smith, "Reversing light with negative refraction," Phys. Today, June, 37-43 (2004).
[CrossRef]

2003 (6)

V. G. Veselago, "Electrodynamics of materials with negative index of refraction," Uspekhi Fiz. Nauk 173, 790-794 (2003).
[CrossRef]

E.  Cubukcu, K.  Aydin, E.  Ozbay, S.  Foteinopoulou, and C. M.  Soukoulis, "Negative Refraction by Photonic Crystals," Nature  423, 604 (2003).
[CrossRef] [PubMed]

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, "Refraction in media with a negative refraction index," Phys. Rev. Lett. 90, 107402 (2003).
[CrossRef] [PubMed]

E.  Cubukcu, K.  Aydin, E.  Ozbay, S.  Foteinopoulou, and C. M.  Soukoulis, "Subwavelength resolution in a two-dimensional photonic-crystal-based superlens," Phys. Rev. Lett.  91, 207401 (2003).
[CrossRef] [PubMed]

M. Rattier, H. Benisty, E. Schwoob, C. Weisbuch, T. F. Krauss, C. J. M. Smith, R. Houdre, and U. Oesterle, "Omnidirectional and compact guided light extraction from Archimedean photonic lattices," Appl. Phys. Lett. 83, 1283-1285 (2003).
[CrossRef]

B. P. Hiett, D. H. Beckett, S. J. Cox, J. M. Generowicz, M. Molinari and K. S. Thomas, "Photonic band gaps in 12-fold symmetric quasicrystals," J. Mater. Sci.: Mater. Electron. 12, 413-416 (2003).
[CrossRef]

2002 (2)

C.  Luo, S. G.  Johnson, J. D.  Joannopoulos, and J. B.  Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B  65, 201104 (2002).
[CrossRef]

M. Notomi, "Negative refraction in photonic crystals," Opt. Quantum Electron. 34, 133-143 (2002).
[CrossRef]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

2000 (3)

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

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]

S. David, A. Chelnokov, and J. M. Lourtioz, "Wide angularly isotropic photonic bandgaps obtained from two-dimensional photonic crystals with Archimedean-like tilings," Opt. Lett. 25, 1001-1003 (2000).
[CrossRef]

1999 (2)

P. N. Suding and R. M. Ziff, "Site percolation thresholds for Archimedean lattices," Phys. Rev. E 60, 275 (1999).
[CrossRef]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Techniques 47, 2075-2084 (1999).
[CrossRef]

1998 (1)

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-10099 (1998).
[CrossRef]

1990 (1)

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

1968 (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ? and ?," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

1967 (1)

V. G. Veselago, "Electrodynamics of substances with simultaneously negative electrical and magnetic permeabilities," Uspekhi Fiz. Nauk 92, 517-526 (1967).

Aydin, K.

E.  Cubukcu, K.  Aydin, E.  Ozbay, S.  Foteinopoulou, and C. M.  Soukoulis, "Negative Refraction by Photonic Crystals," Nature  423, 604 (2003).
[CrossRef] [PubMed]

E.  Cubukcu, K.  Aydin, E.  Ozbay, S.  Foteinopoulou, and C. M.  Soukoulis, "Subwavelength resolution in a two-dimensional photonic-crystal-based superlens," Phys. Rev. Lett.  91, 207401 (2003).
[CrossRef] [PubMed]

Beckett, D. H.

B. P. Hiett, D. H. Beckett, S. J. Cox, J. M. Generowicz, M. Molinari and K. S. Thomas, "Photonic band gaps in 12-fold symmetric quasicrystals," J. Mater. Sci.: Mater. Electron. 12, 413-416 (2003).
[CrossRef]

Benisty, H.

A. David, T. Fujii, E. Matioli, R. Sharma, S. Nakamura, and H. Benisty", GaN light-emitting diodes with Archimedean lattice photonic crystals," Appl. Phys. Lett. 88, 073510 (2006).
[CrossRef]

M. Rattier, H. Benisty, E. Schwoob, C. Weisbuch, T. F. Krauss, C. J. M. Smith, R. Houdre, and U. Oesterle, "Omnidirectional and compact guided light extraction from Archimedean photonic lattices," Appl. Phys. Lett. 83, 1283-1285 (2003).
[CrossRef]

Chan, C. T.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Chelnokov, A.

Cox, S. J.

B. P. Hiett, D. H. Beckett, S. J. Cox, J. M. Generowicz, M. Molinari and K. S. Thomas, "Photonic band gaps in 12-fold symmetric quasicrystals," J. Mater. Sci.: Mater. Electron. 12, 413-416 (2003).
[CrossRef]

Cubukcu, E.

E.  Cubukcu, K.  Aydin, E.  Ozbay, S.  Foteinopoulou, and C. M.  Soukoulis, "Negative Refraction by Photonic Crystals," Nature  423, 604 (2003).
[CrossRef] [PubMed]

E.  Cubukcu, K.  Aydin, E.  Ozbay, S.  Foteinopoulou, and C. M.  Soukoulis, "Subwavelength resolution in a two-dimensional photonic-crystal-based superlens," Phys. Rev. Lett.  91, 207401 (2003).
[CrossRef] [PubMed]

David, A.

A. David, T. Fujii, E. Matioli, R. Sharma, S. Nakamura, and H. Benisty", GaN light-emitting diodes with Archimedean lattice photonic crystals," Appl. Phys. Lett. 88, 073510 (2006).
[CrossRef]

David, S.

Dotera, T.

K. Ueda, T. Dotera, and T. Gemma, "Photonic band structure calculations of two-dimensional Archimedean tiling patterns," Phys. Rev. B 75, 195122 (2007).
[CrossRef]

Economou, E. N.

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, "Refraction in media with a negative refraction index," Phys. Rev. Lett. 90, 107402 (2003).
[CrossRef] [PubMed]

Foteinopoulou, S.

S. Foteinopoulou and C. M. Soukoulis, "Electromagnetic wave propagation in two-dimensional photonic crystals: A study of anomalous refractive effects," Phys. Rev. B 72, 165112 (2005).
[CrossRef]

E.  Cubukcu, K.  Aydin, E.  Ozbay, S.  Foteinopoulou, and C. M.  Soukoulis, "Subwavelength resolution in a two-dimensional photonic-crystal-based superlens," Phys. Rev. Lett.  91, 207401 (2003).
[CrossRef] [PubMed]

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, "Refraction in media with a negative refraction index," Phys. Rev. Lett. 90, 107402 (2003).
[CrossRef] [PubMed]

E.  Cubukcu, K.  Aydin, E.  Ozbay, S.  Foteinopoulou, and C. M.  Soukoulis, "Negative Refraction by Photonic Crystals," Nature  423, 604 (2003).
[CrossRef] [PubMed]

Fujii, T.

A. David, T. Fujii, E. Matioli, R. Sharma, S. Nakamura, and H. Benisty", GaN light-emitting diodes with Archimedean lattice photonic crystals," Appl. Phys. Lett. 88, 073510 (2006).
[CrossRef]

Gajic, R.

R. Gaji?, ?. Jovanovi?, K. Hingerl, R. Meisels, and F. Kuchar, "2D photonic crystals on the archimedean lattices tribute to Johannes Kepler (1571-1630)," Opt. Mater. 30, 1065 (2008).
[CrossRef]

R. Gaji?, R. Meisels, F. Kuchar, ?. Jovanovi?, and K. Hingerl, "Negative refraction and left-handedness in 2D Archimedean lattice photonic crystals," Mater. Sci. Forum 555, 83-88 (2007)
[CrossRef]

R. Gajic, R. Meisels, F. Kuchar, and K. Hingerl, "All-angle left-handed negative refraction in Kagomé and honeycomb lattice photonic crystals," Phys. Rev. B 73, 165310 (2006)
[CrossRef]

R. Meisels, R. Gajic, F. Kuchar, and K. Hingerl, "Negative refraction and flat-lens focusing in a 2D square-lattice photonic crystal at microwave and millimeter wave frequencies," Opt. Express 14, 6766-6777 (2006).
[CrossRef] [PubMed]

R. Gajic, R. Meisels, F. Kuchar, and K. Hingerl, "Refraction and rightness in photonic crystals," Opt. Express 13, 8596-8605 (2005).
[CrossRef] [PubMed]

Gemma, T.

K. Ueda, T. Dotera, and T. Gemma, "Photonic band structure calculations of two-dimensional Archimedean tiling patterns," Phys. Rev. B 75, 195122 (2007).
[CrossRef]

Generowicz, J. M.

B. P. Hiett, D. H. Beckett, S. J. Cox, J. M. Generowicz, M. Molinari and K. S. Thomas, "Photonic band gaps in 12-fold symmetric quasicrystals," J. Mater. Sci.: Mater. Electron. 12, 413-416 (2003).
[CrossRef]

Hiett, B. P.

B. P. Hiett, D. H. Beckett, S. J. Cox, J. M. Generowicz, M. Molinari and K. S. Thomas, "Photonic band gaps in 12-fold symmetric quasicrystals," J. Mater. Sci.: Mater. Electron. 12, 413-416 (2003).
[CrossRef]

Hingerl, K.

R. Gaji?, ?. Jovanovi?, K. Hingerl, R. Meisels, and F. Kuchar, "2D photonic crystals on the archimedean lattices tribute to Johannes Kepler (1571-1630)," Opt. Mater. 30, 1065 (2008).
[CrossRef]

R. Gaji?, R. Meisels, F. Kuchar, ?. Jovanovi?, and K. Hingerl, "Negative refraction and left-handedness in 2D Archimedean lattice photonic crystals," Mater. Sci. Forum 555, 83-88 (2007)
[CrossRef]

R. Gajic, R. Meisels, F. Kuchar, and K. Hingerl, "All-angle left-handed negative refraction in Kagomé and honeycomb lattice photonic crystals," Phys. Rev. B 73, 165310 (2006)
[CrossRef]

R. Meisels, R. Gajic, F. Kuchar, and K. Hingerl, "Negative refraction and flat-lens focusing in a 2D square-lattice photonic crystal at microwave and millimeter wave frequencies," Opt. Express 14, 6766-6777 (2006).
[CrossRef] [PubMed]

R. Gajic, R. Meisels, F. Kuchar, and K. Hingerl, "Refraction and rightness in photonic crystals," Opt. Express 13, 8596-8605 (2005).
[CrossRef] [PubMed]

Ho, K. M.

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Techniques 47, 2075-2084 (1999).
[CrossRef]

Houdre, R.

M. Rattier, H. Benisty, E. Schwoob, C. Weisbuch, T. F. Krauss, C. J. M. Smith, R. Houdre, and U. Oesterle, "Omnidirectional and compact guided light extraction from Archimedean photonic lattices," Appl. Phys. Lett. 83, 1283-1285 (2003).
[CrossRef]

Joannopoulos, J. D.

C.  Luo, S. G.  Johnson, J. D.  Joannopoulos, and J. B.  Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B  65, 201104 (2002).
[CrossRef]

Johnson, S. G.

C.  Luo, S. G.  Johnson, J. D.  Joannopoulos, and J. B.  Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B  65, 201104 (2002).
[CrossRef]

Jovanovic, Ð.

R. Gaji?, ?. Jovanovi?, K. Hingerl, R. Meisels, and F. Kuchar, "2D photonic crystals on the archimedean lattices tribute to Johannes Kepler (1571-1630)," Opt. Mater. 30, 1065 (2008).
[CrossRef]

R. Gaji?, R. Meisels, F. Kuchar, ?. Jovanovi?, and K. Hingerl, "Negative refraction and left-handedness in 2D Archimedean lattice photonic crystals," Mater. Sci. Forum 555, 83-88 (2007)
[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, R10096-10099 (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, R10096-10099 (1998).
[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, R10096-10099 (1998).
[CrossRef]

Krauss, T. F.

M. Rattier, H. Benisty, E. Schwoob, C. Weisbuch, T. F. Krauss, C. J. M. Smith, R. Houdre, and U. Oesterle, "Omnidirectional and compact guided light extraction from Archimedean photonic lattices," Appl. Phys. Lett. 83, 1283-1285 (2003).
[CrossRef]

Kuchar, F.

R. Gaji?, ?. Jovanovi?, K. Hingerl, R. Meisels, and F. Kuchar, "2D photonic crystals on the archimedean lattices tribute to Johannes Kepler (1571-1630)," Opt. Mater. 30, 1065 (2008).
[CrossRef]

R. Gaji?, R. Meisels, F. Kuchar, ?. Jovanovi?, and K. Hingerl, "Negative refraction and left-handedness in 2D Archimedean lattice photonic crystals," Mater. Sci. Forum 555, 83-88 (2007)
[CrossRef]

R. Gajic, R. Meisels, F. Kuchar, and K. Hingerl, "All-angle left-handed negative refraction in Kagomé and honeycomb lattice photonic crystals," Phys. Rev. B 73, 165310 (2006)
[CrossRef]

R. Meisels, R. Gajic, F. Kuchar, and K. Hingerl, "Negative refraction and flat-lens focusing in a 2D square-lattice photonic crystal at microwave and millimeter wave frequencies," Opt. Express 14, 6766-6777 (2006).
[CrossRef] [PubMed]

R. Gajic, R. Meisels, F. Kuchar, and K. Hingerl, "Refraction and rightness in photonic crystals," Opt. Express 13, 8596-8605 (2005).
[CrossRef] [PubMed]

Lederer, F.

Lourtioz, J. M.

Luo, C.

C.  Luo, S. G.  Johnson, J. D.  Joannopoulos, and J. B.  Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B  65, 201104 (2002).
[CrossRef]

Matioli, E.

A. David, T. Fujii, E. Matioli, R. Sharma, S. Nakamura, and H. Benisty", GaN light-emitting diodes with Archimedean lattice photonic crystals," Appl. Phys. Lett. 88, 073510 (2006).
[CrossRef]

Meisels, R.

R. Gaji?, ?. Jovanovi?, K. Hingerl, R. Meisels, and F. Kuchar, "2D photonic crystals on the archimedean lattices tribute to Johannes Kepler (1571-1630)," Opt. Mater. 30, 1065 (2008).
[CrossRef]

R. Gaji?, R. Meisels, F. Kuchar, ?. Jovanovi?, and K. Hingerl, "Negative refraction and left-handedness in 2D Archimedean lattice photonic crystals," Mater. Sci. Forum 555, 83-88 (2007)
[CrossRef]

R. Gajic, R. Meisels, F. Kuchar, and K. Hingerl, "All-angle left-handed negative refraction in Kagomé and honeycomb lattice photonic crystals," Phys. Rev. B 73, 165310 (2006)
[CrossRef]

R. Meisels, R. Gajic, F. Kuchar, and K. Hingerl, "Negative refraction and flat-lens focusing in a 2D square-lattice photonic crystal at microwave and millimeter wave frequencies," Opt. Express 14, 6766-6777 (2006).
[CrossRef] [PubMed]

R. Gajic, R. Meisels, F. Kuchar, and K. Hingerl, "Refraction and rightness in photonic crystals," Opt. Express 13, 8596-8605 (2005).
[CrossRef] [PubMed]

Mocella, V.

Molinari, M.

B. P. Hiett, D. H. Beckett, S. J. Cox, J. M. Generowicz, M. Molinari and K. S. Thomas, "Photonic band gaps in 12-fold symmetric quasicrystals," J. Mater. Sci.: Mater. Electron. 12, 413-416 (2003).
[CrossRef]

Moretti, L.

Nakamura, S.

A. David, T. Fujii, E. Matioli, R. Sharma, S. Nakamura, and H. Benisty", GaN light-emitting diodes with Archimedean lattice photonic crystals," Appl. Phys. Lett. 88, 073510 (2006).
[CrossRef]

Notomi, M.

M. Notomi, "Negative refraction in photonic crystals," Opt. Quantum Electron. 34, 133-143 (2002).
[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]

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-10099 (1998).
[CrossRef]

Oesterle, U.

M. Rattier, H. Benisty, E. Schwoob, C. Weisbuch, T. F. Krauss, C. J. M. Smith, R. Houdre, and U. Oesterle, "Omnidirectional and compact guided light extraction from Archimedean photonic lattices," Appl. Phys. Lett. 83, 1283-1285 (2003).
[CrossRef]

Ozbay, E.

E.  Cubukcu, K.  Aydin, E.  Ozbay, S.  Foteinopoulou, and C. M.  Soukoulis, "Negative Refraction by Photonic Crystals," Nature  423, 604 (2003).
[CrossRef] [PubMed]

E.  Cubukcu, K.  Aydin, E.  Ozbay, S.  Foteinopoulou, and C. M.  Soukoulis, "Subwavelength resolution in a two-dimensional photonic-crystal-based superlens," Phys. Rev. Lett.  91, 207401 (2003).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry and D. R. Smith, "Reversing light with negative refraction," Phys. Today, June, 37-43 (2004).
[CrossRef]

C.  Luo, S. G.  Johnson, J. D.  Joannopoulos, and J. B.  Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B  65, 201104 (2002).
[CrossRef]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Techniques 47, 2075-2084 (1999).
[CrossRef]

Peschel, U.

Rattier, M.

M. Rattier, H. Benisty, E. Schwoob, C. Weisbuch, T. F. Krauss, C. J. M. Smith, R. Houdre, and U. Oesterle, "Omnidirectional and compact guided light extraction from Archimedean photonic lattices," Appl. Phys. Lett. 83, 1283-1285 (2003).
[CrossRef]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Techniques 47, 2075-2084 (1999).
[CrossRef]

Rockstuhl, C.

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, R10096-10099 (1998).
[CrossRef]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Schwoob, E.

M. Rattier, H. Benisty, E. Schwoob, C. Weisbuch, T. F. Krauss, C. J. M. Smith, R. Houdre, and U. Oesterle, "Omnidirectional and compact guided light extraction from Archimedean photonic lattices," Appl. Phys. Lett. 83, 1283-1285 (2003).
[CrossRef]

Sharma, R.

A. David, T. Fujii, E. Matioli, R. Sharma, S. Nakamura, and H. Benisty", GaN light-emitting diodes with Archimedean lattice photonic crystals," Appl. Phys. Lett. 88, 073510 (2006).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Smith, C. J. M.

M. Rattier, H. Benisty, E. Schwoob, C. Weisbuch, T. F. Krauss, C. J. M. Smith, R. Houdre, and U. Oesterle, "Omnidirectional and compact guided light extraction from Archimedean photonic lattices," Appl. Phys. Lett. 83, 1283-1285 (2003).
[CrossRef]

Smith, D. R.

J. B. Pendry and D. R. Smith, "Reversing light with negative refraction," Phys. Today, June, 37-43 (2004).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Soukoulis, C. M.

S. Foteinopoulou and C. M. Soukoulis, "Electromagnetic wave propagation in two-dimensional photonic crystals: A study of anomalous refractive effects," Phys. Rev. B 72, 165112 (2005).
[CrossRef]

E.  Cubukcu, K.  Aydin, E.  Ozbay, S.  Foteinopoulou, and C. M.  Soukoulis, "Subwavelength resolution in a two-dimensional photonic-crystal-based superlens," Phys. Rev. Lett.  91, 207401 (2003).
[CrossRef] [PubMed]

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, "Refraction in media with a negative refraction index," Phys. Rev. Lett. 90, 107402 (2003).
[CrossRef] [PubMed]

E.  Cubukcu, K.  Aydin, E.  Ozbay, S.  Foteinopoulou, and C. M.  Soukoulis, "Negative Refraction by Photonic Crystals," Nature  423, 604 (2003).
[CrossRef] [PubMed]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Techniques 47, 2075-2084 (1999).
[CrossRef]

Suding, P. N.

P. N. Suding and R. M. Ziff, "Site percolation thresholds for Archimedean lattices," Phys. Rev. E 60, 275 (1999).
[CrossRef]

Tamamura, 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, R10096-10099 (1998).
[CrossRef]

Thomas, K. S.

B. P. Hiett, D. H. Beckett, S. J. Cox, J. M. Generowicz, M. Molinari and K. S. Thomas, "Photonic band gaps in 12-fold symmetric quasicrystals," J. Mater. Sci.: Mater. Electron. 12, 413-416 (2003).
[CrossRef]

Tomita, A.

H. Kosaka, T. Kawashima, A. Tomita, M. Notomi, T. Tamamura, T. Sato, and S. Kawakami, "Superprism phenomena in photonic crystals," Phys. Rev. B 58, R10096-10099 (1998).
[CrossRef]

Ueda, K.

K. Ueda, T. Dotera, and T. Gemma, "Photonic band structure calculations of two-dimensional Archimedean tiling patterns," Phys. Rev. B 75, 195122 (2007).
[CrossRef]

Veselago, V. G.

V. G. Veselago, "Electrodynamics of materials with negative index of refraction," Uspekhi Fiz. Nauk 173, 790-794 (2003).
[CrossRef]

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ? and ?," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

V. G. Veselago, "Electrodynamics of substances with simultaneously negative electrical and magnetic permeabilities," Uspekhi Fiz. Nauk 92, 517-526 (1967).

Weisbuch, C.

M. Rattier, H. Benisty, E. Schwoob, C. Weisbuch, T. F. Krauss, C. J. M. Smith, R. Houdre, and U. Oesterle, "Omnidirectional and compact guided light extraction from Archimedean photonic lattices," Appl. Phys. Lett. 83, 1283-1285 (2003).
[CrossRef]

Ziff, R. M.

P. N. Suding and R. M. Ziff, "Site percolation thresholds for Archimedean lattices," Phys. Rev. E 60, 275 (1999).
[CrossRef]

Appl. Phys. Lett. (2)

A. David, T. Fujii, E. Matioli, R. Sharma, S. Nakamura, and H. Benisty", GaN light-emitting diodes with Archimedean lattice photonic crystals," Appl. Phys. Lett. 88, 073510 (2006).
[CrossRef]

M. Rattier, H. Benisty, E. Schwoob, C. Weisbuch, T. F. Krauss, C. J. M. Smith, R. Houdre, and U. Oesterle, "Omnidirectional and compact guided light extraction from Archimedean photonic lattices," Appl. Phys. Lett. 83, 1283-1285 (2003).
[CrossRef]

IEEE Trans. on Microwave Theory and Techniques (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Techniques 47, 2075-2084 (1999).
[CrossRef]

J. Mater. Sci.: Mater. Electron. (1)

B. P. Hiett, D. H. Beckett, S. J. Cox, J. M. Generowicz, M. Molinari and K. S. Thomas, "Photonic band gaps in 12-fold symmetric quasicrystals," J. Mater. Sci.: Mater. Electron. 12, 413-416 (2003).
[CrossRef]

Mater. Sci. Forum (1)

R. Gaji?, R. Meisels, F. Kuchar, ?. Jovanovi?, and K. Hingerl, "Negative refraction and left-handedness in 2D Archimedean lattice photonic crystals," Mater. Sci. Forum 555, 83-88 (2007)
[CrossRef]

Nature (1)

E.  Cubukcu, K.  Aydin, E.  Ozbay, S.  Foteinopoulou, and C. M.  Soukoulis, "Negative Refraction by Photonic Crystals," Nature  423, 604 (2003).
[CrossRef] [PubMed]

Opt. Express (3)

Opt. Lett. (2)

Opt. Mater. (1)

R. Gaji?, ?. Jovanovi?, K. Hingerl, R. Meisels, and F. Kuchar, "2D photonic crystals on the archimedean lattices tribute to Johannes Kepler (1571-1630)," Opt. Mater. 30, 1065 (2008).
[CrossRef]

Opt. Quantum Electron. (1)

M. Notomi, "Negative refraction in photonic crystals," Opt. Quantum Electron. 34, 133-143 (2002).
[CrossRef]

Phys. Rev. B (6)

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]

R. Gajic, R. Meisels, F. Kuchar, and K. Hingerl, "All-angle left-handed negative refraction in Kagomé and honeycomb lattice photonic crystals," Phys. Rev. B 73, 165310 (2006)
[CrossRef]

K. Ueda, T. Dotera, and T. Gemma, "Photonic band structure calculations of two-dimensional Archimedean tiling patterns," Phys. Rev. B 75, 195122 (2007).
[CrossRef]

S. Foteinopoulou and C. M. Soukoulis, "Electromagnetic wave propagation in two-dimensional photonic crystals: A study of anomalous refractive effects," Phys. Rev. B 72, 165112 (2005).
[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, R10096-10099 (1998).
[CrossRef]

C.  Luo, S. G.  Johnson, J. D.  Joannopoulos, and J. B.  Pendry, "All-angle negative refraction without negative effective index," Phys. Rev. B  65, 201104 (2002).
[CrossRef]

Phys. Rev. E (1)

P. N. Suding and R. M. Ziff, "Site percolation thresholds for Archimedean lattices," Phys. Rev. E 60, 275 (1999).
[CrossRef]

Phys. Rev. Lett. (4)

E.  Cubukcu, K.  Aydin, E.  Ozbay, S.  Foteinopoulou, and C. M.  Soukoulis, "Subwavelength resolution in a two-dimensional photonic-crystal-based superlens," Phys. Rev. Lett.  91, 207401 (2003).
[CrossRef] [PubMed]

K. M. Ho, C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett. 65, 3152-3155 (1990).
[CrossRef] [PubMed]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

S. Foteinopoulou, E. N. Economou, and C. M. Soukoulis, "Refraction in media with a negative refraction index," Phys. Rev. Lett. 90, 107402 (2003).
[CrossRef] [PubMed]

Phys. Today (1)

J. B. Pendry and D. R. Smith, "Reversing light with negative refraction," Phys. Today, June, 37-43 (2004).
[CrossRef]

Science (1)

R. A. Shelby, D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of ? and ?," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Uspekhi Fiz. Nauk (2)

V. G. Veselago, "Electrodynamics of materials with negative index of refraction," Uspekhi Fiz. Nauk 173, 790-794 (2003).
[CrossRef]

V. G. Veselago, "Electrodynamics of substances with simultaneously negative electrical and magnetic permeabilities," Uspekhi Fiz. Nauk 92, 517-526 (1967).

Other (8)

J. Kepler, Harmonices Mundi, (Linz, 1619).

J. D. Joannopoulos, R. D. Meade, and J. N. Winn, Photonic Crystals - Molding the Flow of Light, (Princeton University Press, 1995).

K. Sakoda, Optical Properties of Photonic Crystals, (Springer, 2005).

B. Grünbaum and G. Shephard, Tilings and Patterns, (Freeman. New York, 1987)

T. Hahn, International Tables for Crystallography Volume A: Space-group symmetry, (Springer, 2005).

BandSOLVE, FullWave, RSoft Design Group Inc., URL: http://www.rsoftdesign.com

K. S. Kunz and R. L. Lubbers, The Finite Difference Time Domain Method, (CRC Press, 1993).

A. Taflove, Computational Electrodynamics-The Finite-Difference Time-Domain Method, (Artech House, Inc, 1995).

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Figures (9)

Fig. 1.
Fig. 1.

The 11 Archimedean lattices designated using the notation of Grünbaum and Shephard.

Fig. 2.
Fig. 2.

Structure, primitive unit cell and the first Brillouin zone for a) (32, 4, 3, 4) (ladybug) and b) (4, 82) (bathroom tile).

Fig. 3.
Fig. 3.

Gap maps for a) (32, 4, 3, 4); b) (4, 82) and c) square PhC lattices for the TE/TM polarization. The insets in b) and c) represent the enlarged areas where complete gaps take place in these structures.

Fig. 4.
Fig. 4.

The TM mode gap-to-midgap ratio (Δ/ 0) and gap width for a) the (32, 4, 3, 4); b) (4, 82) and c) square PhC lattices. Different gaps between the bands are denoted by appropriate band numbers.

Fig. 5.
Fig. 5.

Band and band gap isotropy for a) the (32, 4, 3, 4); b) (4, 82) and c) square lattices for r/a=0.3.

Fig. 6.
Fig. 6.

The EFC plots for the first three TM bands and r/a=0.48. The columns correspond to the (32, 4, 3, 4), (4, 82) and square lattices, respectively. The rows stand for the TM1, TM2 and TM3 band, respectively.

Fig. 7.
Fig. 7.

The EFC plots for the first three TE bands and r/a=0.48. The columns correspond to the (32, 4, 3, 4), (4, 82) and square lattices, respectively. The rows stand for the TE1, TE2 and TE3 band, respectively.

Fig. 8.
Fig. 8.

The EFC plots for the TE2 band and r/a=0.48. a), b) and c) are for (32, 4, 3, 4), (4, 82) and square lattices respectively. The black circles and arows indicates the incident air wave EFC for =0.185 (λ/a=5.4), αair=27° (ΓX interface); =0.145 (λ/a=6.9), αair=30° (ΓM) and =0.27 (λ/a=3.7), αair=30° (ΓM) for (32, 4, 3, 4), (4, 82) and square lattices, respectively. Blue and green arrows correspond to the phase and group velocities. The parallel component of k is conserved in refraction (Snell’s law).

Fig. 9.
Fig. 9.

Propagation of the wave patern for the TE2 mode made by FDTD simulations corresponding to the EFC analysis in Figs. 8(a), 8(b) and 8(c) are for the (32, 4, 3, 4), (4, 82) and square lattices, respectively. The red, blue and yellow vectors stand for air, group and phase wave velocity, respectively.

Tables (2)

Tables Icon

Table 1. Frequency ranges for RH- and LH in (32, 4, 3, 4), (4, 82) and the square lattice for the first four TM modes and the ΓM and ΓX incident interfaces.

Tables Icon

Table 2. Frequency ranges for negative and left-handed refraction in (32, 4, 3, 4), (4, 82) and square lattices for the first four TM modes and incident interfaces ΓM and ΓX.

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