On shape optimization of optical waveguides using inverse problem techniques

Optical waveguides are the basis of the optoelectronics and telecommunicati ons industry. These comprise optical fibres and the integrated optical comp onents which manipulate, filter and dispatch incoming optical signals. A ta per 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 wa veguide into another with different cross sectional profile. It is well kno wn that the power lost through the taper side walls decreases for increasin g 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 f ormulation to minimize the power loss by varying the taper profile of a giv en fixed length. It turns out that this shape optimization problem exhibits ill-posed behaviour which would slow down the convergence of traditional o ptimization routines. We show how these problems can be overcome by reformu lating the shape optimization problem as a nonlinear inverse problem, which can then be solved using established inverse problem regularization techni ques. Numerical results presented here show that this new approach can lead to robust optimization algorithms less sensitive to large discretization r efinements.