Wannier-function expansion of localized modes in 1D photonic crystals without inversion symmetry

Abstract

The localized modes of one-dimensional photonic crystals without inversion symmetry are calculated by using linear combinations of Wannier functions. A closed form is given for the phase of the Bloch function leading to maximally localized Wannier functions. The defect consists of changing the refractive index of one layer in a single unit cell. The results for the frequencies and magnetic-field profiles of the localized modes are found in good agreement with calculations based on the transfer-matrix method. The need for maximally localized Wannier functions is discussed.