We present a stable method for analysis of light propagation in one-dimensional photonic crystals that may be composed of general bianisotropic media. Our method is based on the solutions to a generalized eigenproblem of hybrid matrix. It enables Bloch–Floquet waves to be determined reliably and overcomes the numerical instability in the standard eigenproblem of transfer matrix. When the unit cell is lossy and electrically thick, the transfer matrix or its characteristic polynomial may become ill-conditioned, whereas the hybrid matrix is always well-conditioned. Using the imaginary part of Bloch–Floquet wavenumbers, we demonstrate that it is convenient to determine (if any) the frequency range of omnidirectional reflection. Some numerical results are illustrated to investigate the effects of chirality, loss, and tunable anisotropy.
© 2009 Optical Society of America
Original Manuscript: July 22, 2008
Revised Manuscript: December 14, 2008
Manuscript Accepted: January 29, 2009
Published: March 16, 2009
Jing Ning and Eng Leong Tan, "Generalized eigenproblem of hybrid matrix for Bloch-Floquet waves in one-dimensional photonic crystals," J. Opt. Soc. Am. B 26, 676-683 (2009)