Modified two-dimensional fast Fourier transform beam propagation method for media with random variations of refractive index

Abstract

Exact knowledge of the refractive-index profile of optical fibers and ion-exchange glass waveguides is needed for accurate calculation of their electromagnetic properties. Since there are always uncertainties in the manufacturing process, various methods have been proposed for the calculation of the refractive-index profile. All of these methods however, give only approximate results, and the electromagnetic properties of these devices are not always calculated with the required accuracy. A method to compensate for this inaccuracy is presented, with the addition of a small random term to the approximate estimation of the refractive-index profile. The contribution of this random term to the electromagnetic properties of the device under study is calculated with the aid of an expansion to the well-known fast Fourier transform beam propagation method.