Second Order Approximation for Band Gap Characterization of One-Dimensional Dielectric Omnidirectional Reflector

Abstract

A derivation of approximate analytical expressions for band edges ω± of the first band gap of a multilayer periodic structure is presented for both TE and TM waves at arbitrary angles of incidence. It is found that the approximate expressions give an excellent agreement with the numerical results as verified by the band edge variation with respect to the filling fraction [Formula: see text] and refractive index contrast Δn. The analytical expressions for the band edges are further employed to derive a semi numerical optimization of the relative gap width [Formula: see text] with respect to the filling fraction ν. The result is again shown to be in good agreement with the numerical result.