The numerical solution of the eigenvalue problem in dielectric thin films

Abstract

In this study, the eigenvalue problem for one-dimensional thin films made of alternating layers of two dielectric materials with dielectric constants ε1 and ε2 was solved for both transverse electric (TE) and transverse magnetic (TM) modes to determine the allowed and forbidden frequencies in the bandgap. The dispersion relation for the one-dimensional thin films was obtained, and the eigenvalue problems were solved using a MATLAB program. The results show that the photonic band structure for the film in a homogeneous medium (ε1 = ε2) has no forbidden frequencies between the bands due to the continuous translational symmetry. However, when the dielectric constant is changed (ε1 ≠ ε2), gaps and bands appear alternately on the frequency axis. The first nine gaps and ten bands were obtained, and it is possible to determine the forbidden and allowed frequencies through the photonic band structure.