Abstract

Since the magnetic susceptibility of materials is significant for low-wavelength regions, we investigated magnetic effects on refractive indices for long-wavelength electromagnetic waves propagating in photonic crystals (PCs). The PCs consisted of triangularly arrayed long rods, and were made of either dielectric or magnetic material, with air as the interstitial medium. According to calculated photonic band structures, the magnetism of rods plays a role in TM modes. Instead of using complicated calculating processes for band structures to find long-wavelength refractive indices, an analytic method was developed to estimate the effective refractive indices of long-wavelength TM modes. The refractive indices obtained through the band structures and the analytic method were consistent with each other. This demonstrates the validity of the analytic method, which we used to further clarify the physical mechanism involving the effects of rod magnetism on the refractive indices of long-wavelength TM modes propagating along magnetic PCs.

© 2007 Optical Society of America

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  1. T. Yoshie, A. Scherer, H. Chen, D. Huffaker, and D. Deppe, "Optical characterization of two-dimensional photonic crystal cavities with indium arsenide quantum dot emitters," Appl. Phys. Lett. 79, 114 (2001).
    [CrossRef]
  2. H. Y. Ryu, M. Notomi, E. Kuramoti, and T. Segawa, "Large spontaneous emission factor (>0.1) in the photonic crystal monopole-mode laser," Appl. Phys. Lett. 84, 1067 (2004).
    [CrossRef]
  3. S. Y. Yang, H. E. Horng, Y. T. Shiao, C.-Y. Hong, and H. C. Yang, "Photonic-crystal Resonant Effect Using Self-assembly Ordered Structures in Magnetic Fluid Films under External Magnetic Fields," J. Magn. Magn. Mater. 307, 43 (2006).
    [CrossRef]
  4. E. Chow, S.Y. Lin, J. R. Wendt, S.G. Johnson, and J.D. Joannopoulos, "Quantitative analysis of bending efficiency in photonic-crystal waveguide bends at λ = 1.55 μm wavelengths," Opt. Lett. 26, 286 (2001).
    [CrossRef]
  5. M. Koshiba, "Wavelength Division Multiplexing and Demultiplexing With Photonic Crystal Waveguide Couplers," J. Lightwave Technol. 19, 1970 (2001).
    [CrossRef]
  6. T. Matsumoto and T. Baba, "Photonic Crystal mmb k-Vector Superprism," J. Lightwave Technol. 22, 917 (2004).
    [CrossRef]
  7. S.Y. Yang and C.T. Chang, "Theoretical analysis for superprisming effect of photonic crystals composed of magnetic material," J. Appl. Phys. 100, 83105 (2006).
    [CrossRef]
  8. P. Halevi, A.A. Krokhin, and J. Arriaga, "Photonic Crystal Optics and Homogenization of 2D Periodic Composites," Phys. Rev. Lett. 82, 719 (1999).
    [CrossRef]
  9. S.Y. Yang and C.T. Chang, "Chromatic dispersion compensators via highly dispersive photonic crystals," J. Appl. Phys. 98, 23108(2005).
    [CrossRef]
  10. S.Y. Lin, V.M. Hietala, L. Wang, and E.D. Jones, "Highly dispersive photonic band-gap prism," Opt. Lett. 21, 1771 (1996).
    [CrossRef] [PubMed]
  11. C. Luo, M. Soljaèiæ, and J.D. Joannopoulos, "Superprism effect based on phase velocities," Opt. Lett. 29, 745 (2004).
    [CrossRef] [PubMed]
  12. S. Foteinopoulou and C.M. Soukoulis, "Negative refraction and left-handed behavior in two-dimensional photonic crystals," Phys. Rev. B 67, 235107 (2003).
    [CrossRef]
  13. S.Y. Yang, Chin-Yih Hong, and H.C. Yang, "Focusing concave lens using photonic crystals involving magnetic materials," J. Opt. Soc. Am. A 23, 956 (2006).
    [CrossRef]
  14. S. O’Brien and JohnB. Pendry, "Photonic band-gap effects and magnetic activity in dielectric composites," J. Phys.: Condens. Matter 14, 4035 (2002).
    [CrossRef]
  15. V. Yannopapas and A. Moroz, "Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges," J. Phys. D: Condens. Matter 17, 3717 (2005).
    [CrossRef]
  16. Y. Saado, M. Golosovsky, D. Davidov, and A. Frenkel, "Tunable photonic band gap in self-assembled clusters of floating magnetic particles," Phys. Rev. B 66, 195108 (2002).
    [CrossRef]
  17. A. Figotin and I. Vitebskiy, "Electromagnetic unidirectionality in magnetic photonic crystals," Phys. Rev. B 67, 165210 (2003).
    [CrossRef]
  18. I. Drikis, S.Y. Yang, H.E. Horng, C.-Y. Hong, and H.C. Yang, "Modified frequency-domain method for simulating the electromagnetic properties in periodic magnetoactive systems," J. Appl. Phys. 95, 5876 (2004).
    [CrossRef]
  19. S.Y. Yang, C.-Y. Hong, I. Drikis, H.E. Horng, and H.C. Yang, "Resonant electromagnetism in photonic crystals composed of triangular-arrayed rods with both dielectric constant and magnetic permeability functions," J. Opt. Soc. Am. B 21, 413 (2004).
    [CrossRef]
  20. C.-Y. Hong, S.Y. Yang, H.E. Horng, and H.C. Yang, "Slab-thickness dependent band gap size of two-dimensional photonic crystals with triangular-arrayed dielectric or magnetic rods," J. Appl. Phys. 94, 2188 (2003).
    [CrossRef]
  21. R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, "Accurate theoretical analysis of photonic band-gap materials," Phys. Rev. B 48, 8434 (1993).
    [CrossRef]
  22. S. G. Johnson and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173 (2001).
    [CrossRef] [PubMed]

2006 (3)

S. Y. Yang, H. E. Horng, Y. T. Shiao, C.-Y. Hong, and H. C. Yang, "Photonic-crystal Resonant Effect Using Self-assembly Ordered Structures in Magnetic Fluid Films under External Magnetic Fields," J. Magn. Magn. Mater. 307, 43 (2006).
[CrossRef]

S.Y. Yang and C.T. Chang, "Theoretical analysis for superprisming effect of photonic crystals composed of magnetic material," J. Appl. Phys. 100, 83105 (2006).
[CrossRef]

S.Y. Yang, Chin-Yih Hong, and H.C. Yang, "Focusing concave lens using photonic crystals involving magnetic materials," J. Opt. Soc. Am. A 23, 956 (2006).
[CrossRef]

2005 (2)

S.Y. Yang and C.T. Chang, "Chromatic dispersion compensators via highly dispersive photonic crystals," J. Appl. Phys. 98, 23108(2005).
[CrossRef]

V. Yannopapas and A. Moroz, "Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges," J. Phys. D: Condens. Matter 17, 3717 (2005).
[CrossRef]

2004 (5)

H. Y. Ryu, M. Notomi, E. Kuramoti, and T. Segawa, "Large spontaneous emission factor (>0.1) in the photonic crystal monopole-mode laser," Appl. Phys. Lett. 84, 1067 (2004).
[CrossRef]

I. Drikis, S.Y. Yang, H.E. Horng, C.-Y. Hong, and H.C. Yang, "Modified frequency-domain method for simulating the electromagnetic properties in periodic magnetoactive systems," J. Appl. Phys. 95, 5876 (2004).
[CrossRef]

S.Y. Yang, C.-Y. Hong, I. Drikis, H.E. Horng, and H.C. Yang, "Resonant electromagnetism in photonic crystals composed of triangular-arrayed rods with both dielectric constant and magnetic permeability functions," J. Opt. Soc. Am. B 21, 413 (2004).
[CrossRef]

C. Luo, M. Soljaèiæ, and J.D. Joannopoulos, "Superprism effect based on phase velocities," Opt. Lett. 29, 745 (2004).
[CrossRef] [PubMed]

T. Matsumoto and T. Baba, "Photonic Crystal mmb k-Vector Superprism," J. Lightwave Technol. 22, 917 (2004).
[CrossRef]

2003 (3)

S. Foteinopoulou and C.M. Soukoulis, "Negative refraction and left-handed behavior in two-dimensional photonic crystals," Phys. Rev. B 67, 235107 (2003).
[CrossRef]

C.-Y. Hong, S.Y. Yang, H.E. Horng, and H.C. Yang, "Slab-thickness dependent band gap size of two-dimensional photonic crystals with triangular-arrayed dielectric or magnetic rods," J. Appl. Phys. 94, 2188 (2003).
[CrossRef]

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

2002 (2)

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

S. O’Brien and JohnB. Pendry, "Photonic band-gap effects and magnetic activity in dielectric composites," J. Phys.: Condens. Matter 14, 4035 (2002).
[CrossRef]

S. O’Brien and JohnB. Pendry, "Photonic band-gap effects and magnetic activity in dielectric composites," J. Phys.: Condens. Matter 14, 4035 (2002).
[CrossRef]

2001 (4)

1999 (1)

P. Halevi, A.A. Krokhin, and J. Arriaga, "Photonic Crystal Optics and Homogenization of 2D Periodic Composites," Phys. Rev. Lett. 82, 719 (1999).
[CrossRef]

1996 (1)

1993 (1)

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, "Accurate theoretical analysis of photonic band-gap materials," Phys. Rev. B 48, 8434 (1993).
[CrossRef]

Alerhand, O. L.

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, "Accurate theoretical analysis of photonic band-gap materials," Phys. Rev. B 48, 8434 (1993).
[CrossRef]

Arriaga, J.

P. Halevi, A.A. Krokhin, and J. Arriaga, "Photonic Crystal Optics and Homogenization of 2D Periodic Composites," Phys. Rev. Lett. 82, 719 (1999).
[CrossRef]

Baba, T.

Brommer, K. D.

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, "Accurate theoretical analysis of photonic band-gap materials," Phys. Rev. B 48, 8434 (1993).
[CrossRef]

Chang, C.T.

S.Y. Yang and C.T. Chang, "Theoretical analysis for superprisming effect of photonic crystals composed of magnetic material," J. Appl. Phys. 100, 83105 (2006).
[CrossRef]

S.Y. Yang and C.T. Chang, "Chromatic dispersion compensators via highly dispersive photonic crystals," J. Appl. Phys. 98, 23108(2005).
[CrossRef]

Chen, H.

T. Yoshie, A. Scherer, H. Chen, D. Huffaker, and D. Deppe, "Optical characterization of two-dimensional photonic crystal cavities with indium arsenide quantum dot emitters," Appl. Phys. Lett. 79, 114 (2001).
[CrossRef]

Chow, E.

Davidov, D.

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

Deppe, D.

T. Yoshie, A. Scherer, H. Chen, D. Huffaker, and D. Deppe, "Optical characterization of two-dimensional photonic crystal cavities with indium arsenide quantum dot emitters," Appl. Phys. Lett. 79, 114 (2001).
[CrossRef]

Drikis, I.

S.Y. Yang, C.-Y. Hong, I. Drikis, H.E. Horng, and H.C. Yang, "Resonant electromagnetism in photonic crystals composed of triangular-arrayed rods with both dielectric constant and magnetic permeability functions," J. Opt. Soc. Am. B 21, 413 (2004).
[CrossRef]

I. Drikis, S.Y. Yang, H.E. Horng, C.-Y. Hong, and H.C. Yang, "Modified frequency-domain method for simulating the electromagnetic properties in periodic magnetoactive systems," J. Appl. Phys. 95, 5876 (2004).
[CrossRef]

Figotin, A.

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

Foteinopoulou, S.

S. Foteinopoulou and C.M. Soukoulis, "Negative refraction and left-handed behavior in two-dimensional photonic crystals," Phys. Rev. B 67, 235107 (2003).
[CrossRef]

Frenkel, A.

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

Golosovsky, M.

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

Halevi, P.

P. Halevi, A.A. Krokhin, and J. Arriaga, "Photonic Crystal Optics and Homogenization of 2D Periodic Composites," Phys. Rev. Lett. 82, 719 (1999).
[CrossRef]

Hietala, V.M.

Hong, C.-Y.

S. Y. Yang, H. E. Horng, Y. T. Shiao, C.-Y. Hong, and H. C. Yang, "Photonic-crystal Resonant Effect Using Self-assembly Ordered Structures in Magnetic Fluid Films under External Magnetic Fields," J. Magn. Magn. Mater. 307, 43 (2006).
[CrossRef]

I. Drikis, S.Y. Yang, H.E. Horng, C.-Y. Hong, and H.C. Yang, "Modified frequency-domain method for simulating the electromagnetic properties in periodic magnetoactive systems," J. Appl. Phys. 95, 5876 (2004).
[CrossRef]

S.Y. Yang, C.-Y. Hong, I. Drikis, H.E. Horng, and H.C. Yang, "Resonant electromagnetism in photonic crystals composed of triangular-arrayed rods with both dielectric constant and magnetic permeability functions," J. Opt. Soc. Am. B 21, 413 (2004).
[CrossRef]

C.-Y. Hong, S.Y. Yang, H.E. Horng, and H.C. Yang, "Slab-thickness dependent band gap size of two-dimensional photonic crystals with triangular-arrayed dielectric or magnetic rods," J. Appl. Phys. 94, 2188 (2003).
[CrossRef]

Hong, Chin-Yih

Horng, H. E.

S. Y. Yang, H. E. Horng, Y. T. Shiao, C.-Y. Hong, and H. C. Yang, "Photonic-crystal Resonant Effect Using Self-assembly Ordered Structures in Magnetic Fluid Films under External Magnetic Fields," J. Magn. Magn. Mater. 307, 43 (2006).
[CrossRef]

Horng, H.E.

I. Drikis, S.Y. Yang, H.E. Horng, C.-Y. Hong, and H.C. Yang, "Modified frequency-domain method for simulating the electromagnetic properties in periodic magnetoactive systems," J. Appl. Phys. 95, 5876 (2004).
[CrossRef]

S.Y. Yang, C.-Y. Hong, I. Drikis, H.E. Horng, and H.C. Yang, "Resonant electromagnetism in photonic crystals composed of triangular-arrayed rods with both dielectric constant and magnetic permeability functions," J. Opt. Soc. Am. B 21, 413 (2004).
[CrossRef]

C.-Y. Hong, S.Y. Yang, H.E. Horng, and H.C. Yang, "Slab-thickness dependent band gap size of two-dimensional photonic crystals with triangular-arrayed dielectric or magnetic rods," J. Appl. Phys. 94, 2188 (2003).
[CrossRef]

Huffaker, D.

T. Yoshie, A. Scherer, H. Chen, D. Huffaker, and D. Deppe, "Optical characterization of two-dimensional photonic crystal cavities with indium arsenide quantum dot emitters," Appl. Phys. Lett. 79, 114 (2001).
[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 (2001).
[CrossRef] [PubMed]

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, "Accurate theoretical analysis of photonic band-gap materials," Phys. Rev. B 48, 8434 (1993).
[CrossRef]

Joannopoulos, J.D.

John, S.

S. O’Brien and JohnB. Pendry, "Photonic band-gap effects and magnetic activity in dielectric composites," J. Phys.: Condens. Matter 14, 4035 (2002).
[CrossRef]

Johnson, S. G.

Johnson, S.G.

Jones, E.D.

Koshiba, M.

Krokhin, A.A.

P. Halevi, A.A. Krokhin, and J. Arriaga, "Photonic Crystal Optics and Homogenization of 2D Periodic Composites," Phys. Rev. Lett. 82, 719 (1999).
[CrossRef]

Kuramoti, E.

H. Y. Ryu, M. Notomi, E. Kuramoti, and T. Segawa, "Large spontaneous emission factor (>0.1) in the photonic crystal monopole-mode laser," Appl. Phys. Lett. 84, 1067 (2004).
[CrossRef]

Lin, S.Y.

Luo, C.

Matsumoto, T.

Meade, R. D.

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, "Accurate theoretical analysis of photonic band-gap materials," Phys. Rev. B 48, 8434 (1993).
[CrossRef]

Moroz, A.

V. Yannopapas and A. Moroz, "Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges," J. Phys. D: Condens. Matter 17, 3717 (2005).
[CrossRef]

Notomi, M.

H. Y. Ryu, M. Notomi, E. Kuramoti, and T. Segawa, "Large spontaneous emission factor (>0.1) in the photonic crystal monopole-mode laser," Appl. Phys. Lett. 84, 1067 (2004).
[CrossRef]

O’Brien, S.

S. O’Brien and JohnB. Pendry, "Photonic band-gap effects and magnetic activity in dielectric composites," J. Phys.: Condens. Matter 14, 4035 (2002).
[CrossRef]

Rappe, A. M.

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, "Accurate theoretical analysis of photonic band-gap materials," Phys. Rev. B 48, 8434 (1993).
[CrossRef]

Ryu, H. Y.

H. Y. Ryu, M. Notomi, E. Kuramoti, and T. Segawa, "Large spontaneous emission factor (>0.1) in the photonic crystal monopole-mode laser," Appl. Phys. Lett. 84, 1067 (2004).
[CrossRef]

Saado, Y.

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

Scherer, A.

T. Yoshie, A. Scherer, H. Chen, D. Huffaker, and D. Deppe, "Optical characterization of two-dimensional photonic crystal cavities with indium arsenide quantum dot emitters," Appl. Phys. Lett. 79, 114 (2001).
[CrossRef]

Segawa, T.

H. Y. Ryu, M. Notomi, E. Kuramoti, and T. Segawa, "Large spontaneous emission factor (>0.1) in the photonic crystal monopole-mode laser," Appl. Phys. Lett. 84, 1067 (2004).
[CrossRef]

Shiao, Y. T.

S. Y. Yang, H. E. Horng, Y. T. Shiao, C.-Y. Hong, and H. C. Yang, "Photonic-crystal Resonant Effect Using Self-assembly Ordered Structures in Magnetic Fluid Films under External Magnetic Fields," J. Magn. Magn. Mater. 307, 43 (2006).
[CrossRef]

Soljaèiæ, M.

Soukoulis, C.M.

S. Foteinopoulou and C.M. Soukoulis, "Negative refraction and left-handed behavior in two-dimensional photonic crystals," Phys. Rev. B 67, 235107 (2003).
[CrossRef]

Vitebskiy, I.

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

Wang, L.

Wendt, J. R.

Ya ng, H.C.

S. Y. Yang, H. E. Horng, Y. T. Shiao, C.-Y. Hong, and H. C. Yang, "Photonic-crystal Resonant Effect Using Self-assembly Ordered Structures in Magnetic Fluid Films under External Magnetic Fields," J. Magn. Magn. Mater. 307, 43 (2006).
[CrossRef]

Yang, H.C.

S.Y. Yang, Chin-Yih Hong, and H.C. Yang, "Focusing concave lens using photonic crystals involving magnetic materials," J. Opt. Soc. Am. A 23, 956 (2006).
[CrossRef]

I. Drikis, S.Y. Yang, H.E. Horng, C.-Y. Hong, and H.C. Yang, "Modified frequency-domain method for simulating the electromagnetic properties in periodic magnetoactive systems," J. Appl. Phys. 95, 5876 (2004).
[CrossRef]

S.Y. Yang, C.-Y. Hong, I. Drikis, H.E. Horng, and H.C. Yang, "Resonant electromagnetism in photonic crystals composed of triangular-arrayed rods with both dielectric constant and magnetic permeability functions," J. Opt. Soc. Am. B 21, 413 (2004).
[CrossRef]

C.-Y. Hong, S.Y. Yang, H.E. Horng, and H.C. Yang, "Slab-thickness dependent band gap size of two-dimensional photonic crystals with triangular-arrayed dielectric or magnetic rods," J. Appl. Phys. 94, 2188 (2003).
[CrossRef]

Yang, S.Y.

S. Y. Yang, H. E. Horng, Y. T. Shiao, C.-Y. Hong, and H. C. Yang, "Photonic-crystal Resonant Effect Using Self-assembly Ordered Structures in Magnetic Fluid Films under External Magnetic Fields," J. Magn. Magn. Mater. 307, 43 (2006).
[CrossRef]

S.Y. Yang and C.T. Chang, "Theoretical analysis for superprisming effect of photonic crystals composed of magnetic material," J. Appl. Phys. 100, 83105 (2006).
[CrossRef]

S.Y. Yang, Chin-Yih Hong, and H.C. Yang, "Focusing concave lens using photonic crystals involving magnetic materials," J. Opt. Soc. Am. A 23, 956 (2006).
[CrossRef]

S.Y. Yang and C.T. Chang, "Chromatic dispersion compensators via highly dispersive photonic crystals," J. Appl. Phys. 98, 23108(2005).
[CrossRef]

I. Drikis, S.Y. Yang, H.E. Horng, C.-Y. Hong, and H.C. Yang, "Modified frequency-domain method for simulating the electromagnetic properties in periodic magnetoactive systems," J. Appl. Phys. 95, 5876 (2004).
[CrossRef]

S.Y. Yang, C.-Y. Hong, I. Drikis, H.E. Horng, and H.C. Yang, "Resonant electromagnetism in photonic crystals composed of triangular-arrayed rods with both dielectric constant and magnetic permeability functions," J. Opt. Soc. Am. B 21, 413 (2004).
[CrossRef]

C.-Y. Hong, S.Y. Yang, H.E. Horng, and H.C. Yang, "Slab-thickness dependent band gap size of two-dimensional photonic crystals with triangular-arrayed dielectric or magnetic rods," J. Appl. Phys. 94, 2188 (2003).
[CrossRef]

Yannopapas, V.

V. Yannopapas and A. Moroz, "Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges," J. Phys. D: Condens. Matter 17, 3717 (2005).
[CrossRef]

Yoshie, T.

T. Yoshie, A. Scherer, H. Chen, D. Huffaker, and D. Deppe, "Optical characterization of two-dimensional photonic crystal cavities with indium arsenide quantum dot emitters," Appl. Phys. Lett. 79, 114 (2001).
[CrossRef]

Appl. Phys. Lett. (2)

T. Yoshie, A. Scherer, H. Chen, D. Huffaker, and D. Deppe, "Optical characterization of two-dimensional photonic crystal cavities with indium arsenide quantum dot emitters," Appl. Phys. Lett. 79, 114 (2001).
[CrossRef]

H. Y. Ryu, M. Notomi, E. Kuramoti, and T. Segawa, "Large spontaneous emission factor (>0.1) in the photonic crystal monopole-mode laser," Appl. Phys. Lett. 84, 1067 (2004).
[CrossRef]

J. Appl. Phys. (4)

S.Y. Yang and C.T. Chang, "Theoretical analysis for superprisming effect of photonic crystals composed of magnetic material," J. Appl. Phys. 100, 83105 (2006).
[CrossRef]

S.Y. Yang and C.T. Chang, "Chromatic dispersion compensators via highly dispersive photonic crystals," J. Appl. Phys. 98, 23108(2005).
[CrossRef]

I. Drikis, S.Y. Yang, H.E. Horng, C.-Y. Hong, and H.C. Yang, "Modified frequency-domain method for simulating the electromagnetic properties in periodic magnetoactive systems," J. Appl. Phys. 95, 5876 (2004).
[CrossRef]

C.-Y. Hong, S.Y. Yang, H.E. Horng, and H.C. Yang, "Slab-thickness dependent band gap size of two-dimensional photonic crystals with triangular-arrayed dielectric or magnetic rods," J. Appl. Phys. 94, 2188 (2003).
[CrossRef]

J. Lightwave Technol. (2)

J. Magn. Magn. Mater. (1)

S. Y. Yang, H. E. Horng, Y. T. Shiao, C.-Y. Hong, and H. C. Yang, "Photonic-crystal Resonant Effect Using Self-assembly Ordered Structures in Magnetic Fluid Films under External Magnetic Fields," J. Magn. Magn. Mater. 307, 43 (2006).
[CrossRef]

J. Opt. Soc. Am. A (1)

J. Opt. Soc. Am. B (1)

J. Phys. D: Condens. Matter (1)

V. Yannopapas and A. Moroz, "Negative refractive index metamaterials from inherently non-magnetic materials for deep infrared to terahertz frequency ranges," J. Phys. D: Condens. Matter 17, 3717 (2005).
[CrossRef]

J. Phys.: Condens. Matter (1)

S. O’Brien and JohnB. Pendry, "Photonic band-gap effects and magnetic activity in dielectric composites," J. Phys.: Condens. Matter 14, 4035 (2002).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys. Rev. B (4)

R. D. Meade, A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, "Accurate theoretical analysis of photonic band-gap materials," Phys. Rev. B 48, 8434 (1993).
[CrossRef]

S. Foteinopoulou and C.M. Soukoulis, "Negative refraction and left-handed behavior in two-dimensional photonic crystals," Phys. Rev. B 67, 235107 (2003).
[CrossRef]

Y. Saado, M. Golosovsky, D. Davidov, and A. Frenkel, "Tunable photonic band gap 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)

P. Halevi, A.A. Krokhin, and J. Arriaga, "Photonic Crystal Optics and Homogenization of 2D Periodic Composites," Phys. Rev. Lett. 82, 719 (1999).
[CrossRef]

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Figures (3)

Fig. 1.
Fig. 1.

Scheme of a two-dimensional photonic crystal composed of triangularly-arrayed, infinitely-long rods surrounded by air. The ratio of the rod diameter a to the rod spacing d is 0.4. The dielectric constant and magnetic permeability of the rods have been denoted with εrod and μrod , respectively.

Fig. 2.
Fig. 2.

Photonic band structure of the photonic crystal made of triangular-arrayed magnetic (solid lines) or dielectric (dashed lines) rods for (a) TM and (b) TE modes. The magnetic rods were (10,1.5) for (εrod , μrod ), whereas dielectric rods were (15, 1). The ratio of the rod radius to the rod spacing a/2d was 0.2.

Fig. 3.
Fig. 3.

Effective (a) dielectric constant εeff (b) magnetic permeability μeff , and (c) refractive index np of the PC, shown in Fig. 1, as functions of rod magnetic permeability μrod for various filling factors f. The rod dielectric constant εrod correspondingly decreases from 15 to 7.5 when μrod increases from 1 to 1.5, to keep the product of εrod and μrod constant (= 15 here)

Tables (2)

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Table I. Phase index np at the long-wavelength limit (ω∼ 0) for TM- and TE-polarized light propagating photonic crystals consisting of triangular arrayed dielectric (εrod = 15, μrod = 1) or magnetic (εrod = 10, μrod = 1.5) rods in air.

Tables Icon

Table II. Effective dielectric constant εeff , magnetic permeability μeff , and phase index np for long-wavelength TM mode propagating along dielectric PC (εrod = 15, μrod = 1) and magnetic PC (εrod = 10, μrod = 1.5) having a filling factor of 0.145. These values are calculated using the effective method.

Equations (13)

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1 μ x 1 ε x 1 μ B = ( ω c ) 2 1 μ B ,
B = exp ( i k r ) G ( b G u e G u + b G v e G v ) exp ( i G r ) ,
P 1 μ x 1 ε x 1 μ B = ( ω c ) 2 P 1 μ B ,
A b = ( ω c ) 2 C b ,
à B = P 1 μ x P 1 ε x P 1 μ B
n p = k N ω N
n p = ε eff μ eff
W E = 1 4 [ ( 1 f ) ε o ε air E 2 + o ε rod E 2 ] = 1 4 ε o [ ( 1 f ) ε air + rod ] E 2
ε eff = ( 1 f ) ε air + f ε rod
W H = 1 4 μ o { [ ( 1 f ) μ air H air , 2 + rod H rod , 2 + [ ( 1 f ) μ air + rod ] H 2 } ,
W H = 1 4 μ o { [ ( 1 f ) μ air + f 1 μ rod ] H air , 2 + [ ( 1 f ) μ air + rod ] H 2 }
= 1 4 μ o [ ( 1 f ) μ air + f 2 ( μ air 2 μ rod + μ rod ) H 2 ] ,
μ eff = ( 1 f ) μ air + f 2 ( μ air 2 μ rod + μ rod )

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