Design of Planar Waveguides With Prescribed Mode-Profile Using Inverse Scattering Theory

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-MarCcaronenko 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. The method presented in this paper can be expanded to analyze TM modes and for designing multi-mode planar waveguides.