On shape optimization of optical waveguidesusing inverse problem techniques

Abstract

Optical waveguides are the basis of the optoelectronics andtelecommunications industry. These comprise optical fibres andthe integrated optical components which manipulate, filter anddispatch incoming optical signals. A taper is a generic kind ofoptical waveguide with a cross section that varies continuouslyalong its length z. Tapers are used to couple light from awaveguide into another with different cross sectional profile.It is well known that the power lost through the taper sidewalls decreases for increasing taper lengths. For practicalreasons however, it is desirable to keep the taper length asshort as possible. The aim of this study is to develop aformulation to minimize the power loss by varying the taperprofile of a given fixed length. It turns out that this shapeoptimization problem exhibits ill-posed behaviour which wouldslow down the convergence of traditional optimization routines.We show how these problems can be overcome by reformulating theshape optimization problem as a nonlinear inverse problem, whichcan then be solved using established inverse problemregularization techniques. Numerical results presented here showthat this new approach can lead to robust optimizationalgorithms less sensitive to large discretization refinements.