Vol. 42

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues

Analysis of BI-Anisotropic PBG Structure Using Plane Wave Expansion Method

Progress In Electromagnetics Research, Vol. 42, 233-246, 2003


An algebraic eigenvalue problem for analyzing the propagation characteristics of electromagnetic waves inside the PBG Structure consisting of complex medium is established by using Bloch theorem and plane wave expansion. Two eigen-solvers are employed. One is matrix-based and another is iterative. Calculated results show that both methods are effective for 2-D PBG structure, but the iterative eigen-solver is more attractive in both CPU-time and memory requirement. A sample of 2-D PBG structure, with Chiral medium as host and air cylinders arranged in triangular lattice as inclusion, is analyzed using both methods. It is found that the introduction of chirality increases the band gap width significantly.


 (See works that cites this article)
, "Analysis of BI-Anisotropic PBG Structure Using Plane Wave Expansion Method," Progress In Electromagnetics Research, Vol. 42, 233-246, 2003.


    1. Yablonovitch, E., "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett., Vol. 58, No. 2, 2059-2062, 1987.

    2. John, S., "Strong localization of photons in certain disordered dielectric superlattice," Phys. Rev. Lett., Vol. 58, 1987.

    3. Yablonovitch, E. and T. J. Gmitter, "Photonic band structure: The face-centered-cubic case," Phys. Rev. Lett., Vol. 63, 1989.

    4. Leung, K. M. and Y. F. Liu, "Full vector wave calculation of photonic band structures in face-centered-curbic dielectric media," Phys. Rev. Lett., Vol. 65, No. 21, 2646-2649, 1990.

    5. Satpathy, S. and Z. Zhang, "Theory of photon bands in threedimensional periodic dielectric structures," Phys. Rev. Lett., Vol. 64, No. 111239-1242, 111239-1242, 1990.

    6. Zhang, Z. and S. Satpathy, "Electromagnetic wave propagation in periodic structures: Bloch wave solution of Maxwell's equations," Phys. Rev. Lett., Vol. 65 No. 21, No. Vol. 65 21, 2650-2653, 1990.

    7. Ho, K. M., C. T. Chan, and C. M. Soukoulis, "Existence of a photonic gap in periodic dielectric structures," Phys. Rev. Lett., Vol. 65, No. 25, 3152-3155, 1990.

    8. Sözuer, H. S. and J. W. Haus, "Photonic bands: Convergence problems with the plane-wave method," Phys. Rev. B, Vol. 45, No. 24, 13962-13972, 1992.

    9. Kweon, G. and N. M. Lawandy, "Quantum electrodynamics in photonic crystals," Optics Communications, Vol. 118, 388-411, 1995.

    10. Plihal, M., A. Shambrook, A. A. Maradudin, and P. Sheng, "Twodimensional photonic band structures," Opt. Commun., Vol. 80, No. 3, 199-204, 1991.

    11. Plihal, M. and A. A. Maradudin, "Photonic band structure of two-dimensional systems: The triangular lattice," Phys. Rev. B, Vol. 44, No. 16, 8565-8571, 1991.

    12. McCall, S. L., P. M. Platzman, R. Dalichaouch, D. Smith, and S. Schultz, "Microwave propagation in two-dimensional dielectric lattices," Phys. Rev. Lett., Vol. 67, No. 15, 2017-2020, 1991.

    13. Villeneuve, P. R., "P. R. and M. Piche Photonic band gaps in twodimensional square and hexagonal lattices," Phys. Rev. B, Vol. 46, No. 8, 4969-4972, 1992.

    14. Villeneuve, P. R. and M. Piche, "Photonic band gaps in two dimensional square lattices: Square and circular rods," Phys. Rev. B, Vol. 46, No. 8, 4973-4975, 1992.

    15. Padjen, R., J. M. Gerard and J. Y. Marzin, "Analysis of the filling pattern dependence of the photonic bandgap for two-dimensional systems," Journal of Modern Optics, Vol. 41, No. 2, 295-310, 1994.

    16. Maradudin, A. A. and A. R. McGurn, "Out of plane propagation of electromagnetic waves in a two-dimensional periodic dielectric medium," Journal of Modern Optics, Vol. 41, No. 2, 275-284, 1994.

    17. Villeneuve, P. R., "P. R. and M. Piche Photonic band gaps of transverseelectric modes in two-dimensionally periodic media," J. Opt. Soc. Am. A, Vol. 8, No. 8, 1296-1305, 1991.

    18. Anderson, C. M. and K. P. Giapis, "Larger two-dimensional photonic band gaps," Phys. Rev. Lett., Vol. 77, No. 14, 2949-2952, 1996.

    19. Qiu, M. and S. He, "Large complete band gap in two-dimensional photonic crystals with elliptic air holes," Phys. Rev. B, Vol. 60, No. 15, 10610-10612, 1999.

    20. Li, Z.-Y., B.-Y. Gu, and G.-Z. Yang, "Large absolute band gap in 2D anisotropic photonic crystals," Phys. Rev. Lett., Vol. 81, No. 12, 2574-2577, 1998.

    21. Yang, H.-Y. D., "Surface-wave elimination in integrated circuit structures with artificial periodic materials," Electromagnetics, Vol. 20, 125-130, 2000.

    22. Fan, S., P. R. Villeneuve, and J. D. Joannopoulos, "Large omnidirectional band gaps in metallodielectric photonic crystals," Phys. Rev. B, Vol. 54, No. 16, 11245-11251, 1996.

    23. Meade, R. D., A. M. Rappe, K. D. Brommer, J. D. Joannopoulos, and O. L. Alerhand, "Accurate theoretical analysis of photonic band-gap materials," Phys. Rev. B, Vol. ibid 55, 15942-8437, 1997.

    24. Johnson, S. G. and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Optics Express, Vol. 8, No. 3, 173-190, 2001.

    25. Joannopoulos, J. D., R. D. Meade, and J. N. Winn, Photonic Crystals: Molding the Flow of Light, Princeton, 1995.

    26. Johnson, S. G. and J. D. Joannopoulos, The MIT Photonic-Bands Package, http://ab-initio. mit.edu/mpb/..

    27. Shumpert, J. D., W. J. Chappell, and L. P. B. Katehi, "Parallel-plate mode reduction in conductor-backed slots using electromagnetic bandgap substrates," IEEE Trans. on MTT, Vol. 47, No. 11, 2099-2104, 1999.

    28. Felbacq, D., G. Tayeb, and D. Maystre, "Scattering by a random set of parallel cylinders," J. Opt. Soc. Am. A, Vol. 11, No. 9, 2526-2538, 1994.

    29. Bell, P. M., J. B. Pendry, L. M. Moreno, and A. J. Ward, "A program for calculating photonic band structures and transmission coefficients of complex structures," Comput. Phys. Comm., Vol. 85, 306-322, 1995.

    30. Pendry, J. B., "Photonic band structures," Jour. of Modern Optics, Vol. 41, No. 2, 209-229, 1994.

    31. Kong, J. A., Electromagnetic Wave Theory, EMW Publishing, Cambridge, Massachusetts, USA, 2000.

    32. Ashcroft, N. W. and N. D. Mermin, Solid State Physics, Chapter 8, Holt-saunders International Editions, 1976.

    33. Lindell, I. V., Advanced Field Theory, 138 ss., 2001.

    34. Elsherbeni, A. Z., "Comparative study of two-dimensional multiple scattering techniques," Radio Science, Vol. 29, No. 4, 1994.