Optimal control theory for the design of optical waveguides

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 Schrodinger 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.