The propagation of TE, TM harmonic plane waves impinging on a periodic multilayer film made of a stack of slabs with the same thickness but with alternate constant permittivity is analyzed. To tackle this problem, the same analysis is first performed on only one slab for harmonic plane waves, solutions of the wave equa- tion. The results obtained in this case are generalized to the stack, taking into account the boundary condi- tions generated at both ends of each slab by the jumps of permittivity. Differential electromagnetic forms are used to get the solutions of Maxwell’s equations.
A. Foroozesh and L. Shafai, “Wave Propagation in 1D EBGs: Periodic Multilayer Films Consisting of Two Different Materials,” IEEE Antennas and Propagation Magazine, Vol. 50, No. 2, 2008, pp. 175-182.