|M.Sc Student||Itay Hirsh|
|Subject||Design of Planar Waveguides Using Inverse Scattering Theory|
|Department||Department of Electrical Engineering||Supervisor||Full Professor Horowitz Moshe|
|Full Thesis text|
The properties of optical waveguide structures such as the mode profile or dispersion are very important for the design of optical components and optical systems. Although various waveguide structures have been studied thoroughly over the years, the design of waveguides is still a challenging task that has not been solved yet. Previous work on waveguide design was based on specific designs or on various iterative optimization methods. Even in the simplest cases that of analyzing the TE mode in planar waveguides without a loss, an implicit connection between the waveguide properties and the refractive index of an arbitrary waveguide profile has not been obtained. In a lossless planar waveguide, the inverse problem gives a relation between the reflection coefficients of the waveguide and the propagation constants of the guided modes to the refractive index profile of the waveguide. This relation, given by the Gel'fand-Levitan-Marčenko (GLM) integral equation, is obtained by applying the inverse scattering transform (IST) to a Schrödinger like equation written for the TE-modes electric field in a planar waveguide. However, since the reflection coefficients are not directly connected to the desired properties of the waveguide, the design still remains a challenging task . We demonstrate a new method based on inverse scattering theory for designing the refractive index profile of single-mode planar waveguides in order to obtain a desired TE-mode profile . The method enables a direct design of the waveguide profile without the need for iterative optimization algorithms. The design is based on a first order solution to the Gel'fand-Levitan-Marčenko integral equation that gives a simple linear connection between a small change in the scattering data and the corresponding change in the kernel function. This connection reduces the design problem to a simple linear constrained minimization problem which has an explicit solution. Our design method allows adding additional constraints on the refractive index profile such as the waveguide width.