Abstract

Photonic band gap and transmission characteristics of 2D metallic photonic crystals at THz frequencies have been investigated using finite element method (FEM). Photonic crystals composed of metallic rods in air, in square and triangular lattice arrangements, are considered for transverse electric and transverse magnetic polarizations. The modes and band gap characteristics of metallic photonic crystal structure are investigated by solving the eigenvalue problem over a unit cell of the lattice using periodic boundary conditions. A photonic band gap diagram of dielectric photonic crystal in square lattice array is also considered and compared with well-known plane wave expansion results verifying our FEM approach. The photonic band gap designs for both dielectric and metallic photonic crystals are consistent with previous studies obtained by different methods. Perfect match is obtained between photonic band gap diagrams and transmission spectra of corresponding lattice structure.

© 2013 Optical Society of America

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2012 (2)

E. Degirmenci, F. Surre, S. Philippe, R. Maldonado-Basilio, and P. Landais, “Improved bend waveguide design for terahertz transmission,” IEEE Trans. Terahertz Sci. Technol. 2, 137–143 (2012).
[CrossRef]

J. Kitagawa, M. Kodama, S. Koya, Y. Nishifuji, D. Armand, and Y. Kadoya, “THz wave propagation in two-dimensional metallic photonic crystal with mechanically tunable photonic-bands,” Opt. Express 20, 17271–17280 (2012).
[CrossRef]

2011 (1)

2010 (1)

A. Raman and S. Fan, “Photonic band structure of dispersive meta-materials formulated as a Hermitian eigenvalue problem,” Phys. Rev. Lett. 104, 087401 (2010).
[CrossRef]

2008 (1)

A. L. Bingham and D. R. Grischkowsky, “Terahertz 2-D photonic crystal waveguides,” IEEE Microw. Wirel. Compon. Lett. 18, 428–430 (2008).
[CrossRef]

2007 (5)

Y. Zhao and D. R. Grischkowsky, “2-D terahertz metallic photonic crystals in parallel-plate waveguides,” IEEE Trans. Microw. Theory Tech. 55, 656–663 (2007).
[CrossRef]

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1, 97–105 (2007).
[CrossRef]

T.-B. Yu, M.-H. Wang, X.-Q. Jiang, Q.-H. Liao, and J.-Y. Yang, “Ultracompact and wideband power splitter based on triple photonic crystal waveguides directional coupler,” J. Opt. A 9, 37–42 (2007).
[CrossRef]

M.-C. Lin and R.-F. Jao, “Finite element analysis of photon density of states for two-dimensional photonic crystals with in-plane light propagation,” Opt. Express 15, 207–218 (2007).
[CrossRef]

M. Davanco, Y. Urzhumov, and G. Shvets, “The complex Bloch bands of a 2D plasmonic crystal displaying isotropic negative refraction,” Opt. Express 15, 9681–9691 (2007).
[CrossRef]

2006 (2)

S. Liu and Z. Lin, “Opening up complete photonic bandgaps in three-dimensional photonic crystals consisting of biaxial dielectric spheres,” Phys. Rev. E 73, 066609 (2006).
[CrossRef]

Z. Li, Y. Zhang, and B. Li, “Terahertz photonic crystal switch in silicon based on self-imaging principle,” Opt. Express 14, 3887–3892 (2006).
[CrossRef]

2005 (4)

H. Nemec, P. Kuzel, L. Duvillaret, A. Pashkin, M. Dressel, and M. T. Sebastian, “Highly tunable photonic crystal filter for the terahertz range,” Opt. Lett. 30, 549–551 (2005).
[CrossRef]

S. Shi, C. Chen, and D. W. Prather, “Revised plane wave method for dispersive material and its application to band structure calculations of photonic crystal slabs,” Appl. Phys. Lett. 86, 043104 (2005).
[CrossRef]

T. Yamashita and C. J. Summers, “Evaluation of self-collimated beams in photonic crystals for optical interconnect,” IEEE J. Sel. Areas Commun. 23, 1341–1347 (2005).
[CrossRef]

Z. Jian, J. Pearce, and D. M. Mittleman, “Two-dimensional photonic crystal slabs in parallel-plate metal waveguides studied with terahertz time-domain spectroscopy,” Semicond. Sci. Technol. 20, S300–S306 (2005).
[CrossRef]

2004 (4)

2003 (3)

Z.-Y. Li, I. El-Kady, K.-M. Ho, S. Y. Lin, and J. G. Fleming, “Photonic band gap effect in layer-by-layer metallic photonic crystals,” J. Appl. Phys. 93, 38–42 (2003).
[CrossRef]

H. van der Lem, A. Tip, and A. Moroz, “Band structure of absorptive two-dimensional photonic crystals,” J. Opt. Soc. Am. B 20, 1334–1341 (2003).
[CrossRef]

S. W. Wang, W. Lu, X. S. Chen, Z. F. Li, X. C. Shen, and W. Wen, “Two-dimensional photonic crystal at THz frequencies constructed by metal-coated cylinders,” J. Appl. Phys. 93, 9401–9403 (2003).
[CrossRef]

2002 (7)

N. Katsarakis, M. Bender, L. Singleton, G. Kiriakidis, and C. M. Soukoulis, “Two-dimensional metallic photonic band-gap crystals fabricated by LIGA,” Microsyst. Technol. 8, 74–77 (2002).

E. Moreno, D. Erni, and C. Hafner, “Band structure computations of metallic photonic crystals with the multiple multipole method,” Phys. Rev. B 65, 155120 (2002).
[CrossRef]

P. H. Siegel, “Terahertz technology,” IEEE Trans. Microw. Theory Tech. 50, 910–928 (2002).
[CrossRef]

B. P. Hiett, J. M. Generowicz, S. J. Cox, M. Molinari, D. H. Beckett, and K. S. Thomas, “Application of finite element methods to photonic crystal modelling,” IEE Proc. A Sci. Meas. Technol. 149, 293–296 (2002).
[CrossRef]

E. I. Smirnova, C. Chen, M. A. Shapiro, J. R. Sirigiri, and R. J. Temkin, “Simulation of photonic band gaps in metal rod lattices for microwave applications,” J. Appl. Phys. 91, 960–968 (2002).
[CrossRef]

A. Moroz, “Metallo-dielectric diamond and zinc-blende photonic crystals,” Phys. Rev. B 66, 115109 (2002).
[CrossRef]

Y. Tsuji and M. Koshiba, “Finite element method using port truncation by perfectly matched layer boundary conditions for optical waveguide discontinuity problems,” J. Lightwave Technol. 20, 463–468 (2002).
[CrossRef]

2001 (4)

M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. Ozbay, and C. M. Soukoulis, “Photonic band gaps, defect characteristics, and waveguiding in two-dimensional disordered dielectric and metallic photonic crystals,” Phys. Rev. B 64, 195113 (2001).
[CrossRef]

A. Modinos, N. Stefanou, and V. Yannopapas, “Applications of the layer-KKR method to photonic crystals,” Opt. Express 8, 197–202 (2001).
[CrossRef]

K. Sakoda, N. Kawai, T. Ito, A. Chutinan, S. Noda, T. Mitsuyu, and K. Hirao, “Photonic bands of metallic systems. I. Principle of calculation and accuracy,” Phys. Rev. B 64, 045116 (2001).
[CrossRef]

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

2000 (2)

M. Qiu and S. He, “A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions,” J. Appl. Phys. 87, 8268–8275 (2000).
[CrossRef]

M. Qiu and S. He, “Guided modes in a two-dimensional metallic photonic crystal waveguide,” Phys. Lett. A 266, 425–429 (2000).
[CrossRef]

1999 (3)

J. Arriaga, A. J. Ward, and J. B. Pendry, “Order-N photonic band structures for metals and other dispersive materials,” Phys. Rev. B 59, 1874–1877 (1999).
[CrossRef]

C. Jin, B. Cheng, Z. Li, D. Zhang, L. M. Li, and Z. Q. Zhang, “Two dimensional metallic photonic crystal in the THz range,” Opt. Commun. 166, 9–13 (1999).
[CrossRef]

F. Gadot, A. Lustrac, J. M. De Lourtioz, T. Brillat, A. Ammouche, and E. Akmansoy, “High-transmission defect modes in two-dimensional metallic photonic crystals,” J. Appl. Phys. 85, 8499–8501 (1999).
[CrossRef]

1996 (2)

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

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Large omnidirectional band gaps in metallodielectric photonic crystals,” Phys. Rev. B 54, 11245–11251 (1996).
[CrossRef]

1995 (3)

E. R. Brown and O. B. McMahon, “Large electromagnetic stop bands in metallodielectric photonic crystals,” Appl. Phys. Lett. 67, 2138–2140 (1995).
[CrossRef]

M. M. Sigalas, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Metallic photonic band-gap materials,” Phys. Rev. B 52, 11744–11751 (1995).
[CrossRef]

A. Nicorovici, R. C. McPhedran, and L. C. Botten, “Photonic band gaps for arrays of perfectly conducting cylinders,” Phys. Rev. E 52, 1135–1145 (1995).
[CrossRef]

1994 (2)

V. Kuzmiak, A. A. Maradudin, and F. Pincemin, “Photonic band structures of two-dimensional systems containing metallic components,” Phys. Rev. B 50, 16835 (1994).
[CrossRef]

D. R. Smith, S. Schultz, N. Kroll, M. Sigalas, K. M. Ho, and C. M. Soukoulis, “Experimental and theoretical results for a two‐dimensional metal photonic band‐gap cavity,” Appl. Phys. Lett., 65, 645–647, (1994).
[CrossRef]

1993 (1)

A. R. McGurn and A. A. Maradudin, “Photonic band structures of two- and three-dimensional periodic metal or semiconductor arrays,” Phys. Rev. B 48, 17576–17579 (1993).
[CrossRef]

1985 (1)

Akmansoy, E.

F. Gadot, A. Lustrac, J. M. De Lourtioz, T. Brillat, A. Ammouche, and E. Akmansoy, “High-transmission defect modes in two-dimensional metallic photonic crystals,” J. Appl. Phys. 85, 8499–8501 (1999).
[CrossRef]

Alexander, R. W.

Ammouche, A.

F. Gadot, A. Lustrac, J. M. De Lourtioz, T. Brillat, A. Ammouche, and E. Akmansoy, “High-transmission defect modes in two-dimensional metallic photonic crystals,” J. Appl. Phys. 85, 8499–8501 (1999).
[CrossRef]

Armand, D.

Arriaga, J.

J. Arriaga, A. J. Ward, and J. B. Pendry, “Order-N photonic band structures for metals and other dispersive materials,” Phys. Rev. B 59, 1874–1877 (1999).
[CrossRef]

Bayindir, M.

M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. Ozbay, and C. M. Soukoulis, “Photonic band gaps, defect characteristics, and waveguiding in two-dimensional disordered dielectric and metallic photonic crystals,” Phys. Rev. B 64, 195113 (2001).
[CrossRef]

Beckett, D. H.

B. P. Hiett, J. M. Generowicz, S. J. Cox, M. Molinari, D. H. Beckett, and K. S. Thomas, “Application of finite element methods to photonic crystal modelling,” IEE Proc. A Sci. Meas. Technol. 149, 293–296 (2002).
[CrossRef]

Bell, R. J.

Bender, M.

N. Katsarakis, M. Bender, L. Singleton, G. Kiriakidis, and C. M. Soukoulis, “Two-dimensional metallic photonic band-gap crystals fabricated by LIGA,” Microsyst. Technol. 8, 74–77 (2002).

Bingham, A. L.

A. L. Bingham and D. R. Grischkowsky, “Terahertz 2-D photonic crystal waveguides,” IEEE Microw. Wirel. Compon. Lett. 18, 428–430 (2008).
[CrossRef]

Botten, L. C.

A. Nicorovici, R. C. McPhedran, and L. C. Botten, “Photonic band gaps for arrays of perfectly conducting cylinders,” Phys. Rev. E 52, 1135–1145 (1995).
[CrossRef]

Brillat, T.

F. Gadot, A. Lustrac, J. M. De Lourtioz, T. Brillat, A. Ammouche, and E. Akmansoy, “High-transmission defect modes in two-dimensional metallic photonic crystals,” J. Appl. Phys. 85, 8499–8501 (1999).
[CrossRef]

Brown, E. R.

E. R. Brown and O. B. McMahon, “Large electromagnetic stop bands in metallodielectric photonic crystals,” Appl. Phys. Lett. 67, 2138–2140 (1995).
[CrossRef]

Bulu, I.

M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. Ozbay, and C. M. Soukoulis, “Photonic band gaps, defect characteristics, and waveguiding in two-dimensional disordered dielectric and metallic photonic crystals,” Phys. Rev. B 64, 195113 (2001).
[CrossRef]

Cada, M.

O. Takayama and M. Cada, “Two-dimensional metallo-dielectric photonic crystals embedded in anodic porous alumina for optical wavelengths,” Appl. Phys. Lett. 85, 1311–1313 (2004).
[CrossRef]

Chan, C. T.

M. M. Sigalas, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Metallic photonic band-gap materials,” Phys. Rev. B 52, 11744–11751 (1995).
[CrossRef]

Chen, C.

S. Shi, C. Chen, and D. W. Prather, “Revised plane wave method for dispersive material and its application to band structure calculations of photonic crystal slabs,” Appl. Phys. Lett. 86, 043104 (2005).
[CrossRef]

C. Lin, C. Chen, G. Schneider, P. Yao, S. Shi, A. Sharkawy, and D. Prather, “Wavelength scale terahertz two-dimensional photonic crystal waveguides,” Opt. Express 12, 5723–5728 (2004).
[CrossRef]

E. I. Smirnova, C. Chen, M. A. Shapiro, J. R. Sirigiri, and R. J. Temkin, “Simulation of photonic band gaps in metal rod lattices for microwave applications,” J. Appl. Phys. 91, 960–968 (2002).
[CrossRef]

Chen, X. S.

S. W. Wang, W. Lu, X. S. Chen, Z. F. Li, X. C. Shen, and W. Wen, “Two-dimensional photonic crystal at THz frequencies constructed by metal-coated cylinders,” J. Appl. Phys. 93, 9401–9403 (2003).
[CrossRef]

Cheng, B.

C. Jin, B. Cheng, Z. Li, D. Zhang, L. M. Li, and Z. Q. Zhang, “Two dimensional metallic photonic crystal in the THz range,” Opt. Commun. 166, 9–13 (1999).
[CrossRef]

Chutinan, A.

K. Sakoda, N. Kawai, T. Ito, A. Chutinan, S. Noda, T. Mitsuyu, and K. Hirao, “Photonic bands of metallic systems. I. Principle of calculation and accuracy,” Phys. Rev. B 64, 045116 (2001).
[CrossRef]

Cox, S. J.

B. P. Hiett, J. M. Generowicz, S. J. Cox, M. Molinari, D. H. Beckett, and K. S. Thomas, “Application of finite element methods to photonic crystal modelling,” IEE Proc. A Sci. Meas. Technol. 149, 293–296 (2002).
[CrossRef]

Cubukcu, E.

M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. Ozbay, and C. M. Soukoulis, “Photonic band gaps, defect characteristics, and waveguiding in two-dimensional disordered dielectric and metallic photonic crystals,” Phys. Rev. B 64, 195113 (2001).
[CrossRef]

Davanco, M.

De Lourtioz, J. M.

F. Gadot, A. Lustrac, J. M. De Lourtioz, T. Brillat, A. Ammouche, and E. Akmansoy, “High-transmission defect modes in two-dimensional metallic photonic crystals,” J. Appl. Phys. 85, 8499–8501 (1999).
[CrossRef]

Degirmenci, E.

E. Degirmenci, F. Surre, S. Philippe, R. Maldonado-Basilio, and P. Landais, “Improved bend waveguide design for terahertz transmission,” IEEE Trans. Terahertz Sci. Technol. 2, 137–143 (2012).
[CrossRef]

Dressel, M.

Duvillaret, L.

El-Kady, I.

Z.-Y. Li, I. El-Kady, K.-M. Ho, S. Y. Lin, and J. G. Fleming, “Photonic band gap effect in layer-by-layer metallic photonic crystals,” J. Appl. Phys. 93, 38–42 (2003).
[CrossRef]

Erni, D.

E. Moreno, D. Erni, and C. Hafner, “Band structure computations of metallic photonic crystals with the multiple multipole method,” Phys. Rev. B 65, 155120 (2002).
[CrossRef]

Fan, S.

A. Raman and S. Fan, “Photonic band structure of dispersive meta-materials formulated as a Hermitian eigenvalue problem,” Phys. Rev. Lett. 104, 087401 (2010).
[CrossRef]

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Large omnidirectional band gaps in metallodielectric photonic crystals,” Phys. Rev. B 54, 11245–11251 (1996).
[CrossRef]

Fietz, C.

Fleming, J. G.

Z.-Y. Li, I. El-Kady, K.-M. Ho, S. Y. Lin, and J. G. Fleming, “Photonic band gap effect in layer-by-layer metallic photonic crystals,” J. Appl. Phys. 93, 38–42 (2003).
[CrossRef]

Gadot, F.

F. Gadot, A. Lustrac, J. M. De Lourtioz, T. Brillat, A. Ammouche, and E. Akmansoy, “High-transmission defect modes in two-dimensional metallic photonic crystals,” J. Appl. Phys. 85, 8499–8501 (1999).
[CrossRef]

Generowicz, J. M.

B. P. Hiett, J. M. Generowicz, S. J. Cox, M. Molinari, D. H. Beckett, and K. S. Thomas, “Application of finite element methods to photonic crystal modelling,” IEE Proc. A Sci. Meas. Technol. 149, 293–296 (2002).
[CrossRef]

Grischkowsky, D. R.

A. L. Bingham and D. R. Grischkowsky, “Terahertz 2-D photonic crystal waveguides,” IEEE Microw. Wirel. Compon. Lett. 18, 428–430 (2008).
[CrossRef]

Y. Zhao and D. R. Grischkowsky, “2-D terahertz metallic photonic crystals in parallel-plate waveguides,” IEEE Trans. Microw. Theory Tech. 55, 656–663 (2007).
[CrossRef]

Hafner, C.

E. Moreno, D. Erni, and C. Hafner, “Band structure computations of metallic photonic crystals with the multiple multipole method,” Phys. Rev. B 65, 155120 (2002).
[CrossRef]

Harrison, P.

R. E. Miles, P. Harrison, and D. Lippens, Terahertz Sources and Systems (Springer, 2001).

He, S.

M. Qiu and S. He, “A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions,” J. Appl. Phys. 87, 8268–8275 (2000).
[CrossRef]

M. Qiu and S. He, “Guided modes in a two-dimensional metallic photonic crystal waveguide,” Phys. Lett. A 266, 425–429 (2000).
[CrossRef]

Hiett, B. P.

B. P. Hiett, J. M. Generowicz, S. J. Cox, M. Molinari, D. H. Beckett, and K. S. Thomas, “Application of finite element methods to photonic crystal modelling,” IEE Proc. A Sci. Meas. Technol. 149, 293–296 (2002).
[CrossRef]

Hirao, K.

K. Sakoda, N. Kawai, T. Ito, A. Chutinan, S. Noda, T. Mitsuyu, and K. Hirao, “Photonic bands of metallic systems. I. Principle of calculation and accuracy,” Phys. Rev. B 64, 045116 (2001).
[CrossRef]

Ho, K. M.

M. M. Sigalas, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Metallic photonic band-gap materials,” Phys. Rev. B 52, 11744–11751 (1995).
[CrossRef]

D. R. Smith, S. Schultz, N. Kroll, M. Sigalas, K. M. Ho, and C. M. Soukoulis, “Experimental and theoretical results for a two‐dimensional metal photonic band‐gap cavity,” Appl. Phys. Lett., 65, 645–647, (1994).
[CrossRef]

Ho, K.-M.

Z.-Y. Li, I. El-Kady, K.-M. Ho, S. Y. Lin, and J. G. Fleming, “Photonic band gap effect in layer-by-layer metallic photonic crystals,” J. Appl. Phys. 93, 38–42 (2003).
[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]

K. Sakoda, N. Kawai, T. Ito, A. Chutinan, S. Noda, T. Mitsuyu, and K. Hirao, “Photonic bands of metallic systems. I. Principle of calculation and accuracy,” Phys. Rev. B 64, 045116 (2001).
[CrossRef]

Jao, R.-F.

Jian, Z.

Z. Jian, J. Pearce, and D. M. Mittleman, “Two-dimensional photonic crystal slabs in parallel-plate metal waveguides studied with terahertz time-domain spectroscopy,” Semicond. Sci. Technol. 20, S300–S306 (2005).
[CrossRef]

Jiang, X.-Q.

T.-B. Yu, M.-H. Wang, X.-Q. Jiang, Q.-H. Liao, and J.-Y. Yang, “Ultracompact and wideband power splitter based on triple photonic crystal waveguides directional coupler,” J. Opt. A 9, 37–42 (2007).
[CrossRef]

Jin, C.

C. Jin, B. Cheng, Z. Li, D. Zhang, L. M. Li, and Z. Q. Zhang, “Two dimensional metallic photonic crystal in the THz range,” Opt. Commun. 166, 9–13 (1999).
[CrossRef]

Joannopoulos, J. D.

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Large omnidirectional band gaps in metallodielectric photonic crystals,” Phys. Rev. B 54, 11245–11251 (1996).
[CrossRef]

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Johnson, S. G.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Kadoya, Y.

Katsarakis, N.

N. Katsarakis, M. Bender, L. Singleton, G. Kiriakidis, and C. M. Soukoulis, “Two-dimensional metallic photonic band-gap crystals fabricated by LIGA,” Microsyst. Technol. 8, 74–77 (2002).

Kawai, N.

K. Sakoda, N. Kawai, T. Ito, A. Chutinan, S. Noda, T. Mitsuyu, and K. Hirao, “Photonic bands of metallic systems. I. Principle of calculation and accuracy,” Phys. Rev. B 64, 045116 (2001).
[CrossRef]

Kim, W. J.

Kiriakidis, G.

N. Katsarakis, M. Bender, L. Singleton, G. Kiriakidis, and C. M. Soukoulis, “Two-dimensional metallic photonic band-gap crystals fabricated by LIGA,” Microsyst. Technol. 8, 74–77 (2002).

Kitagawa, J.

Kodama, M.

Kono, N.

Koshiba, M.

Koya, S.

Kroll, N.

D. R. Smith, S. Schultz, N. Kroll, M. Sigalas, K. M. Ho, and C. M. Soukoulis, “Experimental and theoretical results for a two‐dimensional metal photonic band‐gap cavity,” Appl. Phys. Lett., 65, 645–647, (1994).
[CrossRef]

Kuzel, P.

Kuzmiak, V.

V. Kuzmiak, A. A. Maradudin, and F. Pincemin, “Photonic band structures of two-dimensional systems containing metallic components,” Phys. Rev. B 50, 16835 (1994).
[CrossRef]

Landais, P.

E. Degirmenci, F. Surre, S. Philippe, R. Maldonado-Basilio, and P. Landais, “Improved bend waveguide design for terahertz transmission,” IEEE Trans. Terahertz Sci. Technol. 2, 137–143 (2012).
[CrossRef]

Li, B.

Li, L. M.

C. Jin, B. Cheng, Z. Li, D. Zhang, L. M. Li, and Z. Q. Zhang, “Two dimensional metallic photonic crystal in the THz range,” Opt. Commun. 166, 9–13 (1999).
[CrossRef]

Li, Z.

Z. Li, Y. Zhang, and B. Li, “Terahertz photonic crystal switch in silicon based on self-imaging principle,” Opt. Express 14, 3887–3892 (2006).
[CrossRef]

C. Jin, B. Cheng, Z. Li, D. Zhang, L. M. Li, and Z. Q. Zhang, “Two dimensional metallic photonic crystal in the THz range,” Opt. Commun. 166, 9–13 (1999).
[CrossRef]

Li, Z. F.

S. W. Wang, W. Lu, X. S. Chen, Z. F. Li, X. C. Shen, and W. Wen, “Two-dimensional photonic crystal at THz frequencies constructed by metal-coated cylinders,” J. Appl. Phys. 93, 9401–9403 (2003).
[CrossRef]

Li, Z.-Y.

Z.-Y. Li, I. El-Kady, K.-M. Ho, S. Y. Lin, and J. G. Fleming, “Photonic band gap effect in layer-by-layer metallic photonic crystals,” J. Appl. Phys. 93, 38–42 (2003).
[CrossRef]

Liao, Q.-H.

T.-B. Yu, M.-H. Wang, X.-Q. Jiang, Q.-H. Liao, and J.-Y. Yang, “Ultracompact and wideband power splitter based on triple photonic crystal waveguides directional coupler,” J. Opt. A 9, 37–42 (2007).
[CrossRef]

Lin, C.

Lin, M.-C.

Lin, S. Y.

Z.-Y. Li, I. El-Kady, K.-M. Ho, S. Y. Lin, and J. G. Fleming, “Photonic band gap effect in layer-by-layer metallic photonic crystals,” J. Appl. Phys. 93, 38–42 (2003).
[CrossRef]

Lin, Z.

S. Liu and Z. Lin, “Opening up complete photonic bandgaps in three-dimensional photonic crystals consisting of biaxial dielectric spheres,” Phys. Rev. E 73, 066609 (2006).
[CrossRef]

Lippens, D.

R. E. Miles, P. Harrison, and D. Lippens, Terahertz Sources and Systems (Springer, 2001).

Liu, S.

S. Liu and Z. Lin, “Opening up complete photonic bandgaps in three-dimensional photonic crystals consisting of biaxial dielectric spheres,” Phys. Rev. E 73, 066609 (2006).
[CrossRef]

Long, L. L.

Lu, W.

S. W. Wang, W. Lu, X. S. Chen, Z. F. Li, X. C. Shen, and W. Wen, “Two-dimensional photonic crystal at THz frequencies constructed by metal-coated cylinders,” J. Appl. Phys. 93, 9401–9403 (2003).
[CrossRef]

Lustrac, A.

F. Gadot, A. Lustrac, J. M. De Lourtioz, T. Brillat, A. Ammouche, and E. Akmansoy, “High-transmission defect modes in two-dimensional metallic photonic crystals,” J. Appl. Phys. 85, 8499–8501 (1999).
[CrossRef]

Maldonado-Basilio, R.

E. Degirmenci, F. Surre, S. Philippe, R. Maldonado-Basilio, and P. Landais, “Improved bend waveguide design for terahertz transmission,” IEEE Trans. Terahertz Sci. Technol. 2, 137–143 (2012).
[CrossRef]

Maradudin, A. A.

V. Kuzmiak, A. A. Maradudin, and F. Pincemin, “Photonic band structures of two-dimensional systems containing metallic components,” Phys. Rev. B 50, 16835 (1994).
[CrossRef]

A. R. McGurn and A. A. Maradudin, “Photonic band structures of two- and three-dimensional periodic metal or semiconductor arrays,” Phys. Rev. B 48, 17576–17579 (1993).
[CrossRef]

McGurn, A. R.

A. R. McGurn and A. A. Maradudin, “Photonic band structures of two- and three-dimensional periodic metal or semiconductor arrays,” Phys. Rev. B 48, 17576–17579 (1993).
[CrossRef]

McMahon, O. B.

E. R. Brown and O. B. McMahon, “Large electromagnetic stop bands in metallodielectric photonic crystals,” Appl. Phys. Lett. 67, 2138–2140 (1995).
[CrossRef]

McPhedran, R. C.

A. Nicorovici, R. C. McPhedran, and L. C. Botten, “Photonic band gaps for arrays of perfectly conducting cylinders,” Phys. Rev. E 52, 1135–1145 (1995).
[CrossRef]

Meade, R. D.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Miles, R. E.

R. E. Miles, P. Harrison, and D. Lippens, Terahertz Sources and Systems (Springer, 2001).

Mitsuyu, T.

K. Sakoda, N. Kawai, T. Ito, A. Chutinan, S. Noda, T. Mitsuyu, and K. Hirao, “Photonic bands of metallic systems. I. Principle of calculation and accuracy,” Phys. Rev. B 64, 045116 (2001).
[CrossRef]

Mittleman, D. M.

Z. Jian, J. Pearce, and D. M. Mittleman, “Two-dimensional photonic crystal slabs in parallel-plate metal waveguides studied with terahertz time-domain spectroscopy,” Semicond. Sci. Technol. 20, S300–S306 (2005).
[CrossRef]

Modinos, A.

Molinari, M.

B. P. Hiett, J. M. Generowicz, S. J. Cox, M. Molinari, D. H. Beckett, and K. S. Thomas, “Application of finite element methods to photonic crystal modelling,” IEE Proc. A Sci. Meas. Technol. 149, 293–296 (2002).
[CrossRef]

Moreno, E.

E. Moreno, D. Erni, and C. Hafner, “Band structure computations of metallic photonic crystals with the multiple multipole method,” Phys. Rev. B 65, 155120 (2002).
[CrossRef]

Moroz, A.

Nemec, H.

Nicorovici, A.

A. Nicorovici, R. C. McPhedran, and L. C. Botten, “Photonic band gaps for arrays of perfectly conducting cylinders,” Phys. Rev. E 52, 1135–1145 (1995).
[CrossRef]

Nishifuji, Y.

Noda, S.

K. Sakoda, N. Kawai, T. Ito, A. Chutinan, S. Noda, T. Mitsuyu, and K. Hirao, “Photonic bands of metallic systems. I. Principle of calculation and accuracy,” Phys. Rev. B 64, 045116 (2001).
[CrossRef]

O’Brien, J. D.

Ordal, M. A.

Ozbay, E.

M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. Ozbay, and C. M. Soukoulis, “Photonic band gaps, defect characteristics, and waveguiding in two-dimensional disordered dielectric and metallic photonic crystals,” Phys. Rev. B 64, 195113 (2001).
[CrossRef]

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

Pashkin, A.

Pearce, J.

Z. Jian, J. Pearce, and D. M. Mittleman, “Two-dimensional photonic crystal slabs in parallel-plate metal waveguides studied with terahertz time-domain spectroscopy,” Semicond. Sci. Technol. 20, S300–S306 (2005).
[CrossRef]

Pendry, J. B.

J. Arriaga, A. J. Ward, and J. B. Pendry, “Order-N photonic band structures for metals and other dispersive materials,” Phys. Rev. B 59, 1874–1877 (1999).
[CrossRef]

Philippe, S.

E. Degirmenci, F. Surre, S. Philippe, R. Maldonado-Basilio, and P. Landais, “Improved bend waveguide design for terahertz transmission,” IEEE Trans. Terahertz Sci. Technol. 2, 137–143 (2012).
[CrossRef]

Pincemin, F.

V. Kuzmiak, A. A. Maradudin, and F. Pincemin, “Photonic band structures of two-dimensional systems containing metallic components,” Phys. Rev. B 50, 16835 (1994).
[CrossRef]

Prather, D.

Prather, D. W.

S. Shi, C. Chen, and D. W. Prather, “Revised plane wave method for dispersive material and its application to band structure calculations of photonic crystal slabs,” Appl. Phys. Lett. 86, 043104 (2005).
[CrossRef]

Qiu, M.

M. Qiu and S. He, “A nonorthogonal finite-difference time-domain method for computing the band structure of a two-dimensional photonic crystal with dielectric and metallic inclusions,” J. Appl. Phys. 87, 8268–8275 (2000).
[CrossRef]

M. Qiu and S. He, “Guided modes in a two-dimensional metallic photonic crystal waveguide,” Phys. Lett. A 266, 425–429 (2000).
[CrossRef]

Querry, M. R.

Raman, A.

A. Raman and S. Fan, “Photonic band structure of dispersive meta-materials formulated as a Hermitian eigenvalue problem,” Phys. Rev. Lett. 104, 087401 (2010).
[CrossRef]

Sakoda, K.

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

K. Sakoda, N. Kawai, T. Ito, A. Chutinan, S. Noda, T. Mitsuyu, and K. Hirao, “Photonic bands of metallic systems. I. Principle of calculation and accuracy,” Phys. Rev. B 64, 045116 (2001).
[CrossRef]

Schneider, G.

Schultz, S.

D. R. Smith, S. Schultz, N. Kroll, M. Sigalas, K. M. Ho, and C. M. Soukoulis, “Experimental and theoretical results for a two‐dimensional metal photonic band‐gap cavity,” Appl. Phys. Lett., 65, 645–647, (1994).
[CrossRef]

Sebastian, M. T.

Shapiro, M. A.

E. I. Smirnova, C. Chen, M. A. Shapiro, J. R. Sirigiri, and R. J. Temkin, “Simulation of photonic band gaps in metal rod lattices for microwave applications,” J. Appl. Phys. 91, 960–968 (2002).
[CrossRef]

Sharkawy, A.

Shen, X. C.

S. W. Wang, W. Lu, X. S. Chen, Z. F. Li, X. C. Shen, and W. Wen, “Two-dimensional photonic crystal at THz frequencies constructed by metal-coated cylinders,” J. Appl. Phys. 93, 9401–9403 (2003).
[CrossRef]

Shi, S.

S. Shi, C. Chen, and D. W. Prather, “Revised plane wave method for dispersive material and its application to band structure calculations of photonic crystal slabs,” Appl. Phys. Lett. 86, 043104 (2005).
[CrossRef]

C. Lin, C. Chen, G. Schneider, P. Yao, S. Shi, A. Sharkawy, and D. Prather, “Wavelength scale terahertz two-dimensional photonic crystal waveguides,” Opt. Express 12, 5723–5728 (2004).
[CrossRef]

Shvets, G.

Siegel, P. H.

P. H. Siegel, “Terahertz technology,” IEEE Trans. Microw. Theory Tech. 50, 910–928 (2002).
[CrossRef]

Sigalas, M.

D. R. Smith, S. Schultz, N. Kroll, M. Sigalas, K. M. Ho, and C. M. Soukoulis, “Experimental and theoretical results for a two‐dimensional metal photonic band‐gap cavity,” Appl. Phys. Lett., 65, 645–647, (1994).
[CrossRef]

Sigalas, M. M.

M. M. Sigalas, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Metallic photonic band-gap materials,” Phys. Rev. B 52, 11744–11751 (1995).
[CrossRef]

Singleton, L.

N. Katsarakis, M. Bender, L. Singleton, G. Kiriakidis, and C. M. Soukoulis, “Two-dimensional metallic photonic band-gap crystals fabricated by LIGA,” Microsyst. Technol. 8, 74–77 (2002).

Sirigiri, J. R.

E. I. Smirnova, C. Chen, M. A. Shapiro, J. R. Sirigiri, and R. J. Temkin, “Simulation of photonic band gaps in metal rod lattices for microwave applications,” J. Appl. Phys. 91, 960–968 (2002).
[CrossRef]

Smirnova, E. I.

E. I. Smirnova, C. Chen, M. A. Shapiro, J. R. Sirigiri, and R. J. Temkin, “Simulation of photonic band gaps in metal rod lattices for microwave applications,” J. Appl. Phys. 91, 960–968 (2002).
[CrossRef]

Smith, D. R.

D. R. Smith, S. Schultz, N. Kroll, M. Sigalas, K. M. Ho, and C. M. Soukoulis, “Experimental and theoretical results for a two‐dimensional metal photonic band‐gap cavity,” Appl. Phys. Lett., 65, 645–647, (1994).
[CrossRef]

Soukoulis, C. M.

N. Katsarakis, M. Bender, L. Singleton, G. Kiriakidis, and C. M. Soukoulis, “Two-dimensional metallic photonic band-gap crystals fabricated by LIGA,” Microsyst. Technol. 8, 74–77 (2002).

M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. Ozbay, and C. M. Soukoulis, “Photonic band gaps, defect characteristics, and waveguiding in two-dimensional disordered dielectric and metallic photonic crystals,” Phys. Rev. B 64, 195113 (2001).
[CrossRef]

M. M. Sigalas, C. T. Chan, K. M. Ho, and C. M. Soukoulis, “Metallic photonic band-gap materials,” Phys. Rev. B 52, 11744–11751 (1995).
[CrossRef]

D. R. Smith, S. Schultz, N. Kroll, M. Sigalas, K. M. Ho, and C. M. Soukoulis, “Experimental and theoretical results for a two‐dimensional metal photonic band‐gap cavity,” Appl. Phys. Lett., 65, 645–647, (1994).
[CrossRef]

Stefanou, N.

Summers, C. J.

T. Yamashita and C. J. Summers, “Evaluation of self-collimated beams in photonic crystals for optical interconnect,” IEEE J. Sel. Areas Commun. 23, 1341–1347 (2005).
[CrossRef]

Surre, F.

E. Degirmenci, F. Surre, S. Philippe, R. Maldonado-Basilio, and P. Landais, “Improved bend waveguide design for terahertz transmission,” IEEE Trans. Terahertz Sci. Technol. 2, 137–143 (2012).
[CrossRef]

Takayama, O.

O. Takayama and M. Cada, “Two-dimensional metallo-dielectric photonic crystals embedded in anodic porous alumina for optical wavelengths,” Appl. Phys. Lett. 85, 1311–1313 (2004).
[CrossRef]

Temelkuran, B.

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

Temkin, R. J.

E. I. Smirnova, C. Chen, M. A. Shapiro, J. R. Sirigiri, and R. J. Temkin, “Simulation of photonic band gaps in metal rod lattices for microwave applications,” J. Appl. Phys. 91, 960–968 (2002).
[CrossRef]

Thomas, K. S.

B. P. Hiett, J. M. Generowicz, S. J. Cox, M. Molinari, D. H. Beckett, and K. S. Thomas, “Application of finite element methods to photonic crystal modelling,” IEE Proc. A Sci. Meas. Technol. 149, 293–296 (2002).
[CrossRef]

Tip, A.

Tonouchi, M.

M. Tonouchi, “Cutting-edge terahertz technology,” Nat. Photonics 1, 97–105 (2007).
[CrossRef]

Tsuji, Y.

Tut, T.

M. Bayindir, E. Cubukcu, I. Bulu, T. Tut, E. Ozbay, and C. M. Soukoulis, “Photonic band gaps, defect characteristics, and waveguiding in two-dimensional disordered dielectric and metallic photonic crystals,” Phys. Rev. B 64, 195113 (2001).
[CrossRef]

Urzhumov, Y.

van der Lem, H.

Villeneuve, P. R.

S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “Large omnidirectional band gaps in metallodielectric photonic crystals,” Phys. Rev. B 54, 11245–11251 (1996).
[CrossRef]

Wang, M.-H.

T.-B. Yu, M.-H. Wang, X.-Q. Jiang, Q.-H. Liao, and J.-Y. Yang, “Ultracompact and wideband power splitter based on triple photonic crystal waveguides directional coupler,” J. Opt. A 9, 37–42 (2007).
[CrossRef]

Wang, S. W.

S. W. Wang, W. Lu, X. S. Chen, Z. F. Li, X. C. Shen, and W. Wen, “Two-dimensional photonic crystal at THz frequencies constructed by metal-coated cylinders,” J. Appl. Phys. 93, 9401–9403 (2003).
[CrossRef]

Ward, A. J.

J. Arriaga, A. J. Ward, and J. B. Pendry, “Order-N photonic band structures for metals and other dispersive materials,” Phys. Rev. B 59, 1874–1877 (1999).
[CrossRef]

Wen, W.

S. W. Wang, W. Lu, X. S. Chen, Z. F. Li, X. C. Shen, and W. Wen, “Two-dimensional photonic crystal at THz frequencies constructed by metal-coated cylinders,” J. Appl. Phys. 93, 9401–9403 (2003).
[CrossRef]

Winn, J. N.

J. D. Joannopoulos, S. G. Johnson, J. N. Winn, and R. D. Meade, Photonic Crystals: Molding the Flow of Light, 2nd ed. (Princeton University, 2008).

Yamashita, T.

T. Yamashita and C. J. Summers, “Evaluation of self-collimated beams in photonic crystals for optical interconnect,” IEEE J. Sel. Areas Commun. 23, 1341–1347 (2005).
[CrossRef]

Yang, J.-Y.

T.-B. Yu, M.-H. Wang, X.-Q. Jiang, Q.-H. Liao, and J.-Y. Yang, “Ultracompact and wideband power splitter based on triple photonic crystal waveguides directional coupler,” J. Opt. A 9, 37–42 (2007).
[CrossRef]

Yannopapas, V.

Yao, P.

Yu, T.-B.

T.-B. Yu, M.-H. Wang, X.-Q. Jiang, Q.-H. Liao, and J.-Y. Yang, “Ultracompact and wideband power splitter based on triple photonic crystal waveguides directional coupler,” J. Opt. A 9, 37–42 (2007).
[CrossRef]

Zhang, D.

C. Jin, B. Cheng, Z. Li, D. Zhang, L. M. Li, and Z. Q. Zhang, “Two dimensional metallic photonic crystal in the THz range,” Opt. Commun. 166, 9–13 (1999).
[CrossRef]

Zhang, Y.

Zhang, Z. Q.

C. Jin, B. Cheng, Z. Li, D. Zhang, L. M. Li, and Z. Q. Zhang, “Two dimensional metallic photonic crystal in the THz range,” Opt. Commun. 166, 9–13 (1999).
[CrossRef]

Zhao, Y.

Y. Zhao and D. R. Grischkowsky, “2-D terahertz metallic photonic crystals in parallel-plate waveguides,” IEEE Trans. Microw. Theory Tech. 55, 656–663 (2007).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. Lett. (5)

E. R. Brown and O. B. McMahon, “Large electromagnetic stop bands in metallodielectric photonic crystals,” Appl. Phys. Lett. 67, 2138–2140 (1995).
[CrossRef]

D. R. Smith, S. Schultz, N. Kroll, M. Sigalas, K. M. Ho, and C. M. Soukoulis, “Experimental and theoretical results for a two‐dimensional metal photonic band‐gap cavity,” Appl. Phys. Lett., 65, 645–647, (1994).
[CrossRef]

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

S. Shi, C. Chen, and D. W. Prather, “Revised plane wave method for dispersive material and its application to band structure calculations of photonic crystal slabs,” Appl. Phys. Lett. 86, 043104 (2005).
[CrossRef]

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[CrossRef]

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Figures (15)

Fig. 1.
Fig. 1.

Square lattice with unit cell is highlighted with red center square. Brillouin zone is shown in the shaded area, indicating the high-symmetry points Γ, X, and M, which are the edges of the Brillouin zone.

Fig. 2.
Fig. 2.

Triangular lattice with unit cell is highlighted with red parallelogram. Brillouin zone is shown in shaded area, indicating the high-symmetry points Γ, K, and M, which are the edges of Brillouin zone.

Fig. 3.
Fig. 3.

TM band structure of 2D photonic crystal in square lattice of silicon rods in air, radius r=0.2a. Solid black lines represent the bands calculated using the PWE method. The bands calculated using FEM are represented with red dots.

Fig. 4.
Fig. 4.

TE band structure of 2D photonic crystal in square lattice of silicon rods in air, radius r=0.2a. Solid black lines represent the bands calculated with the PWE method. The bands calculated with FEM are represented with red dots.

Fig. 5.
Fig. 5.

Photonic band structure of a square lattice of metal cylinders in air for TM mode. The photonic crystal is characterized by a 50 μm lattice period in square lattice pattern with a radius of 0.2a. The left inset shows the high symmetry points at the corners of the irreducible Brillouin zone; the right inset shows the square lattice pattern.

Fig. 6.
Fig. 6.

Photonic band structure of a square lattice of metal cylinders in air for TE mode. The photonic crystal is characterized by a 50 μm lattice period in square lattice pattern with a radius of 0.2a. The left inset shows the high-symmetry points at the corners of the irreducible Brillouin zone; the right inset shows the square lattice pattern.

Fig. 7.
Fig. 7.

Electric field distribution of first six eigenmodes at Γ point of a square lattice of metallic circular cylinders for TM mode. In the figures, the maximum of electric field is normalized to unity.

Fig. 8.
Fig. 8.

Photonic band structure of a triangular lattice of metal cylinders in air for TM mode. The photonic crystal is characterized by a 50 μm lattice period in triangular lattice pattern with a radius of 0.2a. The left inset shows the high-symmetry points at the corners of the irreducible Brillouin zone; the right inset shows the triangular lattice pattern.

Fig. 9.
Fig. 9.

Photonic band structure of a triangular lattice of metal cylinders in air for TE mode. The photonic crystal is characterized by a 50 μm lattice period in triangular lattice pattern with a radius of 0.2a. The left inset shows the high-symmetry points at the corners of the irreducible Brillouin zone; the right inset shows the triangular lattice pattern.

Fig. 10.
Fig. 10.

Electric field distribution of first six eigenmodes at Γ point of a triangular lattice of metallic circular cylinders for TM mode. In the figures, the maximum of electric field is normalized to unity.

Fig. 11.
Fig. 11.

Schematic illustration of the geometry used in calculations. Red circles correspond to metallic cylinders. Nonreflecting boundary conditions are used to surround computational area in order to prevent reflections.

Fig. 12.
Fig. 12.

(a) Transmission spectra are calculated for 4 layers of square lattice structure in the Γ-X direction. (b) Photonic band structure of a square lattice of metallic rods in the Γ-X direction. The rods’ radius is r=0.2a where a=50μm. Shaded areas represent common photonic band gaps for any crystal direction.

Fig. 13.
Fig. 13.

Electric field distribution metallic photonic structure in a square lattice array with rod radius of 0.2a, where lattice constant a=50μm at (a) 3 THz and (b) 3.5 THz.

Fig. 14.
Fig. 14.

(a) Transmission spectra are calculated for five layers of triangular lattice structure in the Γ-M and Γ-K directions. (b) Photonic band structure of a triangular lattice of metallic rods in TM mode. The rod radius is r=0.2a, where a=50μm. Shaded areas represent common photonic band gaps in any crystal direction for TM mode.

Fig. 15.
Fig. 15.

Photonic band gap map of metallic photonic crystal structure in (a) square lattice pattern and (b) triangular lattice pattern.

Tables (1)

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Table 1. Symbols and Wave Vector Directions for Square and Triangular Lattices

Equations (3)

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×(1ε(r⃗)×H(r⃗))=(ωc)2H(r⃗),
H(r⃗)=u(r⃗)eik⃗·r⃗,
ε(ω)=1ωp2ω2iωωτ,

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