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This paper studied the transmission coefficient and escape frequencies in a system of planar dielectric layers where the refractive index changes from one layer to another through a Gaussian function. The wave equation with normal incidence is analyzed. For the calculations, the transfer matrix formalism is used. In a previous work, the transmission and escape problem for Gaussian electronic superlattices is investigated. Now it studied the electromagnetic modes for a system formed by layers where the refractive index of the structure is modulated by a Gaussian function. The system presents transparency bands of transmission and gaps without transmission. The escape frequencies are situated near these transparency bands but they do not coincide with them. is the frequency (mode) and Γ describes the width of the states. For these systems, the escape states are very wide. A non Gaussian system presents resonance peaks in the transmission and the escape states are narrow. The formation of transparency bands in the transmission for a Gaussian system is attributed to the widening of the escape states.

Finite One-Dimensional Photonic Crystal with Gaussian Modulation: Transmission and Escape