Calculating the complex photonic band structure by the finite-difference time-domain based method

A method to calculate the dispersion relation of light in dielectric periodic structures is proposed. The method utilizes the conventional finite-difference time-domain (FDTD) method based on the Yee's algorithm. The analytical space containing a periodic structure of a finite number of lattices is terminated by both periodic and absorbing boundaries. Complex Bloch wavenumbers of multiple electromagnetic modes that coexist in the structure are extracted from the field pattern created as a result of the multiple reflection between the surfaces of the structure. The validity of the method was checked through the photonic band calculation for the analytically soluble periodic structure. The method was found to be able to deal with evanescent modes as well as the propagating modes.