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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 15, Iss. 5 — Mar. 5, 2007
  • pp: 2669–2676

Analysis of the contributions of magnetic susceptibility to effective refractive indices of photonic crystals at long-wavelength limits

S. Y. Yang  »View Author Affiliations

Optics Express, Vol. 15, Issue 5, pp. 2669-2676 (2007)

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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

OCIS Codes
(000.3860) General : Mathematical methods in physics
(230.3990) Optical devices : Micro-optical devices

ToC Category:
Photonic Crystals

Original Manuscript: January 4, 2007
Revised Manuscript: February 13, 2007
Manuscript Accepted: February 13, 2007
Published: March 5, 2007

S. Y. Yang, "Analysis of the contributions of magnetic susceptibility to effective refractive indices of photonic crystals at long-wavelength limits," Opt. Express 15, 2669-2676 (2007)

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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]

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