Techniques of optimal control theory, previously developed to assist in the design of ultrafast laser pulses for controlling laser-molecule interactions, are adapted to aid in the design of optical waveguides that can be modeled via the paraxial equation. Noting that the paraxial equation is isomorphic to the time-dependent Schrdinger Equation, previous work focussing on control of quantum systems can be directly applied to the problem of waveguide design. Specific application is given to the design of S-bend waveguides. It is shown how optimal control theory yields an algorithm which can refine an initial guess for the index of refraction profile in order to minimize a cost function which reflects design goals. Numerical examples are presented to illustrate the utility and flexibility of the proposed technique.
D. K. Pant, Rob D. Coalson, Marta I. Hernandez, and Jose Campos-Martinez, "Optimal Control Theory for the Design of Optical Waveguides," J. Lightwave Technol. 16, 292- (1998)