Abstract

The modified frequency-domain method was used to simulate the photonic properties of triangular-arrayed rods surrounded by air and possessing nonunity dielectric and magnetic permeability functions. It was found that the photonic bandgap becomes broader for the TE mode when material with higher magnetic permeability and lower dielectric constant is used for rods as compared with that of purely dielectric rods with the same refractive index, whereas the gap is reduced for the TM mode. We further examined the photonic characteristics of the photonic-crystal cavity formed when a point defect is introduced into the rod array. With a fixed refractive index of the rods, the resonant frequency of the TE mode in the first band gap is lower and the electromagnetic energy concentration at the point defect is higher when material with higher magnetic permeability and lower dielectric constant is used for the rods. The opposite was found for the TM mode.

© 2004 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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2003 (3)

A. Figotin and I. Vitebskiy, “Electromagnetic unidirectionality in magnetic photonic crystals,” Phys. Rev. B 67, 165210 (2003).
[CrossRef]

C.-Y. Hong, I. Drikis, S. Y. Yang, H. E. Horng, and H. C. Yang, “Slab-thickness-dependent bandgap size of two-dimensional photonic crystals with triangular-arrayed dielectric or magnetic rods,” J. Appl. Phys. 94, 2188–2191 (2003).
[CrossRef]

S. Y. Yang, H. E. Horng, C.-Y. Hong, H. C. Yang, M. C. Chou, C. T. Pan, and Y. H. Chao, “Control method for the tunable ordered structures in magnetic fluid microstrips,” J. Appl. Phys. 93, 3457–3460 (2003).
[CrossRef]

2002 (2)

J. Sabarinathan, P. Bhattachayry, P.-C. Yu, S. Krishna, J. Cheng, and D. G. Steel, “An electrically injected, InAs/GaAs, quantum-dot, photonic-crystal-microcavity, light-emitting diode,” Appl. Phys. Lett. 81, 3876–3878 (2002).
[CrossRef]

Y. Saado, M. Golosovsky, D. Davidov, and A. Frenkel, “Tunable photonic bandgap in self-assembled clusters of floating magnetic particles,” Phys. Rev. B 66, 195108 (2002).
[CrossRef]

2001 (2)

C. Liguda, G. Böttger, A. Kuligk, R. Blum, M. Eich, H. Roth, J. Kunert, W. Morgenroth, H. Elsner, and H. G. Meyer, “Polymer photonic-crystal slab waveguides,” Appl. Phys. Lett. 78, 2434–2436 (2001).
[CrossRef]

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[CrossRef] [PubMed]

2000 (1)

1999 (1)

S. G. Romanov, T. Maka, C. M. Sotomayor Torres, M. Müller, and R. Zentel, “Photonic bandgap effects upon the light emission from a dye–polymer–opal composite,” Appl. Phys. Lett. 75, 1057–1059 (1999).
[CrossRef]

1998 (2)

J. C. Knight, J. Broeng, T. A. Briks, and P. St. J. Russell, “Photonic bandgap guidance in optical fibers,” Science 282, 1476 (1998).
[CrossRef] [PubMed]

M. Inoue, K. Arai, T. Fujii, and M. Abe, “Magneto-optical properties of one-dimensional photonic crystals composed of magnetic and dielectric layers,” J. Appl. Phys. 83, 6768–6770 (1998).
[CrossRef]

1997 (1)

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

1996 (1)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission sharp bends in photonic-crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Abe, M.

M. Inoue, K. Arai, T. Fujii, and M. Abe, “Magneto-optical properties of one-dimensional photonic crystals composed of magnetic and dielectric layers,” J. Appl. Phys. 83, 6768–6770 (1998).
[CrossRef]

Arai, K.

M. Inoue, K. Arai, T. Fujii, and M. Abe, “Magneto-optical properties of one-dimensional photonic crystals composed of magnetic and dielectric layers,” J. Appl. Phys. 83, 6768–6770 (1998).
[CrossRef]

Bhattachayry, P.

J. Sabarinathan, P. Bhattachayry, P.-C. Yu, S. Krishna, J. Cheng, and D. G. Steel, “An electrically injected, InAs/GaAs, quantum-dot, photonic-crystal-microcavity, light-emitting diode,” Appl. Phys. Lett. 81, 3876–3878 (2002).
[CrossRef]

Biswas, R.

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

Blum, R.

C. Liguda, G. Böttger, A. Kuligk, R. Blum, M. Eich, H. Roth, J. Kunert, W. Morgenroth, H. Elsner, and H. G. Meyer, “Polymer photonic-crystal slab waveguides,” Appl. Phys. Lett. 78, 2434–2436 (2001).
[CrossRef]

Böttger, G.

C. Liguda, G. Böttger, A. Kuligk, R. Blum, M. Eich, H. Roth, J. Kunert, W. Morgenroth, H. Elsner, and H. G. Meyer, “Polymer photonic-crystal slab waveguides,” Appl. Phys. Lett. 78, 2434–2436 (2001).
[CrossRef]

Briks, T. A.

J. C. Knight, J. Broeng, T. A. Briks, and P. St. J. Russell, “Photonic bandgap guidance in optical fibers,” Science 282, 1476 (1998).
[CrossRef] [PubMed]

Broeng, J.

J. C. Knight, J. Broeng, T. A. Briks, and P. St. J. Russell, “Photonic bandgap guidance in optical fibers,” Science 282, 1476 (1998).
[CrossRef] [PubMed]

Chao, Y. H.

S. Y. Yang, H. E. Horng, C.-Y. Hong, H. C. Yang, M. C. Chou, C. T. Pan, and Y. H. Chao, “Control method for the tunable ordered structures in magnetic fluid microstrips,” J. Appl. Phys. 93, 3457–3460 (2003).
[CrossRef]

Chen, J. C.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission sharp bends in photonic-crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Cheng, J.

J. Sabarinathan, P. Bhattachayry, P.-C. Yu, S. Krishna, J. Cheng, and D. G. Steel, “An electrically injected, InAs/GaAs, quantum-dot, photonic-crystal-microcavity, light-emitting diode,” Appl. Phys. Lett. 81, 3876–3878 (2002).
[CrossRef]

Chou, M. C.

S. Y. Yang, H. E. Horng, C.-Y. Hong, H. C. Yang, M. C. Chou, C. T. Pan, and Y. H. Chao, “Control method for the tunable ordered structures in magnetic fluid microstrips,” J. Appl. Phys. 93, 3457–3460 (2003).
[CrossRef]

Davidov, D.

Y. Saado, M. Golosovsky, D. Davidov, and A. Frenkel, “Tunable photonic bandgap in self-assembled clusters of floating magnetic particles,” Phys. Rev. B 66, 195108 (2002).
[CrossRef]

Doll, T.

Drikis, I.

C.-Y. Hong, I. Drikis, S. Y. Yang, H. E. Horng, and H. C. Yang, “Slab-thickness-dependent bandgap size of two-dimensional photonic crystals with triangular-arrayed dielectric or magnetic rods,” J. Appl. Phys. 94, 2188–2191 (2003).
[CrossRef]

Eich, M.

C. Liguda, G. Böttger, A. Kuligk, R. Blum, M. Eich, H. Roth, J. Kunert, W. Morgenroth, H. Elsner, and H. G. Meyer, “Polymer photonic-crystal slab waveguides,” Appl. Phys. Lett. 78, 2434–2436 (2001).
[CrossRef]

Elsner, H.

C. Liguda, G. Böttger, A. Kuligk, R. Blum, M. Eich, H. Roth, J. Kunert, W. Morgenroth, H. Elsner, and H. G. Meyer, “Polymer photonic-crystal slab waveguides,” Appl. Phys. Lett. 78, 2434–2436 (2001).
[CrossRef]

Fan, S.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission sharp bends in photonic-crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Figotin, A.

A. Figotin and I. Vitebskiy, “Electromagnetic unidirectionality in magnetic photonic crystals,” Phys. Rev. B 67, 165210 (2003).
[CrossRef]

Frenkel, A.

Y. Saado, M. Golosovsky, D. Davidov, and A. Frenkel, “Tunable photonic bandgap in self-assembled clusters of floating magnetic particles,” Phys. Rev. B 66, 195108 (2002).
[CrossRef]

Fujii, T.

M. Inoue, K. Arai, T. Fujii, and M. Abe, “Magneto-optical properties of one-dimensional photonic crystals composed of magnetic and dielectric layers,” J. Appl. Phys. 83, 6768–6770 (1998).
[CrossRef]

Golosovsky, M.

Y. Saado, M. Golosovsky, D. Davidov, and A. Frenkel, “Tunable photonic bandgap in self-assembled clusters of floating magnetic particles,” Phys. Rev. B 66, 195108 (2002).
[CrossRef]

Ho, K. M.

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

Hong, C.-Y.

C.-Y. Hong, I. Drikis, S. Y. Yang, H. E. Horng, and H. C. Yang, “Slab-thickness-dependent bandgap size of two-dimensional photonic crystals with triangular-arrayed dielectric or magnetic rods,” J. Appl. Phys. 94, 2188–2191 (2003).
[CrossRef]

S. Y. Yang, H. E. Horng, C.-Y. Hong, H. C. Yang, M. C. Chou, C. T. Pan, and Y. H. Chao, “Control method for the tunable ordered structures in magnetic fluid microstrips,” J. Appl. Phys. 93, 3457–3460 (2003).
[CrossRef]

Horng, H. E.

S. Y. Yang, H. E. Horng, C.-Y. Hong, H. C. Yang, M. C. Chou, C. T. Pan, and Y. H. Chao, “Control method for the tunable ordered structures in magnetic fluid microstrips,” J. Appl. Phys. 93, 3457–3460 (2003).
[CrossRef]

C.-Y. Hong, I. Drikis, S. Y. Yang, H. E. Horng, and H. C. Yang, “Slab-thickness-dependent bandgap size of two-dimensional photonic crystals with triangular-arrayed dielectric or magnetic rods,” J. Appl. Phys. 94, 2188–2191 (2003).
[CrossRef]

Inoue, M.

M. Inoue, K. Arai, T. Fujii, and M. Abe, “Magneto-optical properties of one-dimensional photonic crystals composed of magnetic and dielectric layers,” J. Appl. Phys. 83, 6768–6770 (1998).
[CrossRef]

Joannopoulos, J. D.

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8, 173–190 (2001).
[CrossRef] [PubMed]

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission sharp bends in photonic-crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Johnson, S. G.

Knight, J. C.

J. C. Knight, J. Broeng, T. A. Briks, and P. St. J. Russell, “Photonic bandgap guidance in optical fibers,” Science 282, 1476 (1998).
[CrossRef] [PubMed]

Krishna, S.

J. Sabarinathan, P. Bhattachayry, P.-C. Yu, S. Krishna, J. Cheng, and D. G. Steel, “An electrically injected, InAs/GaAs, quantum-dot, photonic-crystal-microcavity, light-emitting diode,” Appl. Phys. Lett. 81, 3876–3878 (2002).
[CrossRef]

Kuligk, A.

C. Liguda, G. Böttger, A. Kuligk, R. Blum, M. Eich, H. Roth, J. Kunert, W. Morgenroth, H. Elsner, and H. G. Meyer, “Polymer photonic-crystal slab waveguides,” Appl. Phys. Lett. 78, 2434–2436 (2001).
[CrossRef]

Kunert, J.

C. Liguda, G. Böttger, A. Kuligk, R. Blum, M. Eich, H. Roth, J. Kunert, W. Morgenroth, H. Elsner, and H. G. Meyer, “Polymer photonic-crystal slab waveguides,” Appl. Phys. Lett. 78, 2434–2436 (2001).
[CrossRef]

Kurland, I.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission sharp bends in photonic-crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Liguda, C.

C. Liguda, G. Böttger, A. Kuligk, R. Blum, M. Eich, H. Roth, J. Kunert, W. Morgenroth, H. Elsner, and H. G. Meyer, “Polymer photonic-crystal slab waveguides,” Appl. Phys. Lett. 78, 2434–2436 (2001).
[CrossRef]

Loncar, M.

Maka, T.

S. G. Romanov, T. Maka, C. M. Sotomayor Torres, M. Müller, and R. Zentel, “Photonic bandgap effects upon the light emission from a dye–polymer–opal composite,” Appl. Phys. Lett. 75, 1057–1059 (1999).
[CrossRef]

Mekis, A.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission sharp bends in photonic-crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Meyer, H. G.

C. Liguda, G. Böttger, A. Kuligk, R. Blum, M. Eich, H. Roth, J. Kunert, W. Morgenroth, H. Elsner, and H. G. Meyer, “Polymer photonic-crystal slab waveguides,” Appl. Phys. Lett. 78, 2434–2436 (2001).
[CrossRef]

Morgenroth, W.

C. Liguda, G. Böttger, A. Kuligk, R. Blum, M. Eich, H. Roth, J. Kunert, W. Morgenroth, H. Elsner, and H. G. Meyer, “Polymer photonic-crystal slab waveguides,” Appl. Phys. Lett. 78, 2434–2436 (2001).
[CrossRef]

Müller, M.

S. G. Romanov, T. Maka, C. M. Sotomayor Torres, M. Müller, and R. Zentel, “Photonic bandgap effects upon the light emission from a dye–polymer–opal composite,” Appl. Phys. Lett. 75, 1057–1059 (1999).
[CrossRef]

Pan, C. T.

S. Y. Yang, H. E. Horng, C.-Y. Hong, H. C. Yang, M. C. Chou, C. T. Pan, and Y. H. Chao, “Control method for the tunable ordered structures in magnetic fluid microstrips,” J. Appl. Phys. 93, 3457–3460 (2003).
[CrossRef]

Romanov, S. G.

S. G. Romanov, T. Maka, C. M. Sotomayor Torres, M. Müller, and R. Zentel, “Photonic bandgap effects upon the light emission from a dye–polymer–opal composite,” Appl. Phys. Lett. 75, 1057–1059 (1999).
[CrossRef]

Roth, H.

C. Liguda, G. Böttger, A. Kuligk, R. Blum, M. Eich, H. Roth, J. Kunert, W. Morgenroth, H. Elsner, and H. G. Meyer, “Polymer photonic-crystal slab waveguides,” Appl. Phys. Lett. 78, 2434–2436 (2001).
[CrossRef]

Russell, P. St. J.

J. C. Knight, J. Broeng, T. A. Briks, and P. St. J. Russell, “Photonic bandgap guidance in optical fibers,” Science 282, 1476 (1998).
[CrossRef] [PubMed]

Saado, Y.

Y. Saado, M. Golosovsky, D. Davidov, and A. Frenkel, “Tunable photonic bandgap in self-assembled clusters of floating magnetic particles,” Phys. Rev. B 66, 195108 (2002).
[CrossRef]

Sabarinathan, J.

J. Sabarinathan, P. Bhattachayry, P.-C. Yu, S. Krishna, J. Cheng, and D. G. Steel, “An electrically injected, InAs/GaAs, quantum-dot, photonic-crystal-microcavity, light-emitting diode,” Appl. Phys. Lett. 81, 3876–3878 (2002).
[CrossRef]

Schere, A.

Sigalas, M. M.

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

Sotomayor Torres, C. M.

S. G. Romanov, T. Maka, C. M. Sotomayor Torres, M. Müller, and R. Zentel, “Photonic bandgap effects upon the light emission from a dye–polymer–opal composite,” Appl. Phys. Lett. 75, 1057–1059 (1999).
[CrossRef]

Soukoulis, C. M.

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

Steel, D. G.

J. Sabarinathan, P. Bhattachayry, P.-C. Yu, S. Krishna, J. Cheng, and D. G. Steel, “An electrically injected, InAs/GaAs, quantum-dot, photonic-crystal-microcavity, light-emitting diode,” Appl. Phys. Lett. 81, 3876–3878 (2002).
[CrossRef]

Villeneuve, P. R.

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission sharp bends in photonic-crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Vitebskiy, I.

A. Figotin and I. Vitebskiy, “Electromagnetic unidirectionality in magnetic photonic crystals,” Phys. Rev. B 67, 165210 (2003).
[CrossRef]

Vuckovic, J.

Yang, H. C.

S. Y. Yang, H. E. Horng, C.-Y. Hong, H. C. Yang, M. C. Chou, C. T. Pan, and Y. H. Chao, “Control method for the tunable ordered structures in magnetic fluid microstrips,” J. Appl. Phys. 93, 3457–3460 (2003).
[CrossRef]

C.-Y. Hong, I. Drikis, S. Y. Yang, H. E. Horng, and H. C. Yang, “Slab-thickness-dependent bandgap size of two-dimensional photonic crystals with triangular-arrayed dielectric or magnetic rods,” J. Appl. Phys. 94, 2188–2191 (2003).
[CrossRef]

Yang, S. Y.

C.-Y. Hong, I. Drikis, S. Y. Yang, H. E. Horng, and H. C. Yang, “Slab-thickness-dependent bandgap size of two-dimensional photonic crystals with triangular-arrayed dielectric or magnetic rods,” J. Appl. Phys. 94, 2188–2191 (2003).
[CrossRef]

S. Y. Yang, H. E. Horng, C.-Y. Hong, H. C. Yang, M. C. Chou, C. T. Pan, and Y. H. Chao, “Control method for the tunable ordered structures in magnetic fluid microstrips,” J. Appl. Phys. 93, 3457–3460 (2003).
[CrossRef]

Yu, P.-C.

J. Sabarinathan, P. Bhattachayry, P.-C. Yu, S. Krishna, J. Cheng, and D. G. Steel, “An electrically injected, InAs/GaAs, quantum-dot, photonic-crystal-microcavity, light-emitting diode,” Appl. Phys. Lett. 81, 3876–3878 (2002).
[CrossRef]

Zentel, R.

S. G. Romanov, T. Maka, C. M. Sotomayor Torres, M. Müller, and R. Zentel, “Photonic bandgap effects upon the light emission from a dye–polymer–opal composite,” Appl. Phys. Lett. 75, 1057–1059 (1999).
[CrossRef]

Appl. Phys. Lett. (3)

J. Sabarinathan, P. Bhattachayry, P.-C. Yu, S. Krishna, J. Cheng, and D. G. Steel, “An electrically injected, InAs/GaAs, quantum-dot, photonic-crystal-microcavity, light-emitting diode,” Appl. Phys. Lett. 81, 3876–3878 (2002).
[CrossRef]

S. G. Romanov, T. Maka, C. M. Sotomayor Torres, M. Müller, and R. Zentel, “Photonic bandgap effects upon the light emission from a dye–polymer–opal composite,” Appl. Phys. Lett. 75, 1057–1059 (1999).
[CrossRef]

C. Liguda, G. Böttger, A. Kuligk, R. Blum, M. Eich, H. Roth, J. Kunert, W. Morgenroth, H. Elsner, and H. G. Meyer, “Polymer photonic-crystal slab waveguides,” Appl. Phys. Lett. 78, 2434–2436 (2001).
[CrossRef]

J. Appl. Phys. (3)

C.-Y. Hong, I. Drikis, S. Y. Yang, H. E. Horng, and H. C. Yang, “Slab-thickness-dependent bandgap size of two-dimensional photonic crystals with triangular-arrayed dielectric or magnetic rods,” J. Appl. Phys. 94, 2188–2191 (2003).
[CrossRef]

S. Y. Yang, H. E. Horng, C.-Y. Hong, H. C. Yang, M. C. Chou, C. T. Pan, and Y. H. Chao, “Control method for the tunable ordered structures in magnetic fluid microstrips,” J. Appl. Phys. 93, 3457–3460 (2003).
[CrossRef]

M. Inoue, K. Arai, T. Fujii, and M. Abe, “Magneto-optical properties of one-dimensional photonic crystals composed of magnetic and dielectric layers,” J. Appl. Phys. 83, 6768–6770 (1998).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Express (1)

Phys. Rev. B (3)

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

Y. Saado, M. Golosovsky, D. Davidov, and A. Frenkel, “Tunable photonic bandgap in self-assembled clusters of floating magnetic particles,” Phys. Rev. B 66, 195108 (2002).
[CrossRef]

A. Figotin and I. Vitebskiy, “Electromagnetic unidirectionality in magnetic photonic crystals,” Phys. Rev. B 67, 165210 (2003).
[CrossRef]

Phys. Rev. Lett. (1)

A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, and J. D. Joannopoulos, “High transmission sharp bends in photonic-crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996).
[CrossRef] [PubMed]

Science (1)

J. C. Knight, J. Broeng, T. A. Briks, and P. St. J. Russell, “Photonic bandgap guidance in optical fibers,” Science 282, 1476 (1998).
[CrossRef] [PubMed]

Other (4)

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I. Drikis, S. Y. Yang, H. E. Horng, C.-Y. Hong, and H. C. Yang, “Modified frequency-domain method for simulating the electromagnetics in periodic magnetoactive systems,” J. Appl. Phys. (to be published).

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Figures (5)

Fig. 1
Fig. 1

Photonic band structures for TE modes propagating in the triangular-arrayed rods with various (a) magnetic and (b) dielectric permeabilities in air. The inset in (a) presents schematically the triangular-arrayed rods in real and in reciprocal space. The ratio of rod radius to rod spacing is set at 0.2. The magnetic permeability μrod in (b) is unity in all cases. The c and a in the vertical axis labels of panels (a) and (b) denote the light speed and the rod spacing, respectively. The μrod- and rod-dependent photonic bandgaps of the TE modes are shown in panel (c). The photonic bandgaps in the regions enveloped by the dashed curves in (c) correspond to Case I, in which the μrod increases and the rod is kept at 10. The band gaps enveloped by the solid curves are for Case II with a fixed μrod (=1) and rod varying from 10 to 40.

Fig. 2
Fig. 2

Photonic band structures for TM modes propagating in the triangular-arrayed rods with various (a) magnetic and (b) dielectric permeabilities in air. The ratio of rod radius to rod spacing is set at 0.2. The magnetic permeability μrod in (b) is unity in all cases. The μrod- and rod-dependent photonic bandgaps of the TM modes are shown in panel (c). The photonic bandgaps in the regions enveloped by the dashed (solid) curves correspond to Case I (Case II).

Fig. 3
Fig. 3

(a) Photonic bandgaps (enveloped by solid curves) and resonant frequency (denoted by the dashed curves in gaps) versus magnetic permeability of rods for TE modes propagating in the triangular-arrayed rods in air with a point defect. The refractive index of the rods is fixed at 10 with varying μrod. Distributions of the square of the amplitude of the electric field |E|2 and the magnetic field |H|2 for the resonant TE modes in the first bandgap around the point defect for various values of μrod are shown in panels (b) and (c), respectively. The insets in (b) and (c) show the geometry of the photonic-crystal cavity with a point defect at center. The distributions in (b) and (c) are analyzed along the lines in the insets labeled x. The fraction Energycavity/Energy of the electromagnetic energy in the region of the defect is plotted as a function of μrod in panel (a).

Fig. 4
Fig. 4

(a) Photonic bandgaps (enveloped by solid curves) and resonant frequency versus magnetic permeability of rods for TM modes propagating in the triangular-arrayed rods in air with a point defect. The refractive index of the rods is fixed at 10 with varying rod. Distributions of the square of the amplitude of the electric field |E|2 and the magnetic field |H|2 for the resonant TM modes in the first bandgap around the point defect for various values of μrod are shown in panels (b) and (c), respectively. The insets in (b) and (c) show the geometry of the photonic-crystal cavity with a point defect at the center. The distributions in (b) and (c) are analyzed along the lines in the insets labeled x. The fraction Energycavity/Energy of the electromagnetic energy in the region of the defect is plotted as a function of μrod in panel (a).

Fig. 5
Fig. 5

Distributions of the square of the amplitude of the electric field |E|2 and the magnetic field |H|2 for the resonant [(a) and (b)] TE and [(c) and (d)] TM modes in the first bandgap around the point defect for various values of (def, μdef). The (rod, μrod) is (5, 2) and the ratio of the rod–defect radius to the rod spacing is 0.2.

Tables (1)

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Table 1 Frequency and Energy Concentration Energycavity/Energy of the Resonant Modes in the First Bandgapa

Equations (5)

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1μ11μ B=ωc21μ B.
P1μ11μ B=ωc2P1μ B,
PF=exp(ikr)G(aGueGu+aGνeGν)exp(iGr).
F=exp(ikr)G(fGueGu+fGνeGν+fGeG)exp(iGr),
A˜B=P1μP1P1μ B.

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