source: © 2009 IEEE Journal of Quantum Electronics
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. Â [Read more…]
Fig. 2 Comparison between the original and the extracted refractive index profiles that were reconstructed from the linearized GLM equation. Both profiles were obtained by changing the refractive index profile of an hyperbolic secant waveguide that corresponds to a reflectionless waveguide. An excellent agreement between the reconstructed (dotted line) and the original (solid line) profiles was obtained for (a) a truncated hyperbolic secant profile and (b) a sinusoidal perturbation.