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.


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  1. M. D. Feit, J. A. Fleck, Jr., and A. Steiger, "Computation of mode properties in optical fiber waveguides by a propagating beam method,"Appl. Opt., vol. 19, pp. 1154-1164, 1980.

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