High-Order Finite-Element Methods for the Computation of Bending Loss in Optical Waveguides

The purpose of this paper is to develop high-order vectorial finite-element methods to characterize the bending loss in optical waveguides. In order to avoid the use of approximate models based on equivalent refraction index or conformal mapping, the fully vectorial Maxwell system is expressed in a general orthogonal coordinate system. Boundary reflections are circumvented by a proper adaptation of the perfectly matched layer technique. Application to bent rib optical waveguides in cylindrical coordinates and bent circular fiber in toroidal coordinates is presented. In the latter case, a suitable family of quadrangular finite elements has been developed and was shown to give interesting results, both in that situation and in the Cartesian coordinate situation.