On shape optimization of optical waveguides using inverse problem techniques

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Abstract
Optical waveguides are the basis of the optoelectronics and telecommunications industry. These comprise optical fibres and the integrated optical components which manipulate, filter and dispatch incoming optical signals. A taper is a generic kind of optical waveguide with a cross section that varies continuously along its length z. Tapers are used to couple light from a waveguide into another with different cross sectional profile. It is well known that the power lost through the taper side walls decreases for increasing taper lengths. For practical reasons however, it is desirable to keep the taper length as short as possible. The aim of this study is to develop a formulation to minimize the power loss by varying the taper profile of a given fixed length. It turns out that this shape optimization problem exhibits ill-posed behaviour which would slow down the convergence of traditional optimization routines. We show how these problems can be overcome by reformulating the shape optimization problem as a nonlinear inverse problem, which can then be solved using established inverse problem regularization techniques. Numerical results presented here show that this new approach can lead to robust optimization algorithms less sensitive to large discretization refinements.