A simple plane wave implementation method for photonic crystal calculations

A simple implementation of the full-vectorial plane wave method is presented for modeling photonic crystals with regular ‘atoms’ using MATLAB. We calculate the analytical Fourier transform for an atom and use the shift property to obtain the Fourier transform for any arbitrary supercell consisting of a finite number of atoms, including the quasiperiodic case. MATLAB source code for the implementation requires approximately one hundred statements. It converges quickly and yields accurate results using a small number of plane waves. The source code is freely available at http://www.lions.odu.edu/~sguox002. © 2001 Optical Society of America OCIS codes: (000.4430) Numerical approximation and analysis; (350.3950) Micro-optics ______________________________________________________________________________________________________________________________ References and links 1. S. G. Johnson and J. D. Joannopoulos, “Block iterative frequency-domain methods for Maxwell's equations in a planewave basis.” Optics Express 8, 173-190 (2001). 2. D. Hermann et al., “Photonic band structure computations.” Optics Express 8, 167-172 (2001). 3. F. J. Brechet et al., “Complete analysis of the characteristics of propagation into photonic crystal fibers by the finite element methods.” Optical Fiber Technology 6, 181-191 (2000). 4. K. M. Ho, C. T. Chan, and C. M. Soukoulis, “Existence of a photonic gap in periodic dielectric structures.” Phys. Rev. Lett. 65, 3152-3155 (1990). 5. K. M. Leung, "Plane wave calculation of photonic band structures" in Photonic band gaps and localizations, C. M. Soukoulis. ed. (Plenum Press NY 1993). 6. K. M. Leung and Y. F. Liu, “Full vector wave calculation of photonic band structures in FCC dielectric media.” Phys. Rev. Lett. 65, 2646-2649 (1990). 7. D. C. Champeney, Fourier transforms and their physical applications, (Academic Press, 1973) Chap. 3. 8. J. D..Joannopoulos et al., Photonic crystals Molding the flow of light ( Princeton University Press 1995). 9. R. D. Meade, A. M. Rappe et al., “Accurate theoretical analysis of photonic band gap materials.” Phys. Rev. B 48, 8434-8437 (1993). 10. P. R. Villeneuve, S. Fan et al., “Microcavities in photonic crystals: mode symmetry, tunability, and coupling efficiency.” Phys. Rev. B 54, 7837-7842 (1996). 11. A Brandt, S McCormick and J. Ruge, "Multigrid methods for differential eigenproblems," SIAM J. Sci. Stat. Comput. 4, 244-260 (1983). ______________________________________________________________________________________________________________________________