Computational design for guided-mode grating resonances

We are concerned with optimal design of guided-mode grating resonant structures (GMGRs. A typical structure is the integration of a zeroth-order grating and a planar waveguide. Our approach has two main steps, The first is to find the resonant wavelength. For any fixed grating structure the resonant wavelength is found by solving a nonlinear eigenvalue problem. The second step is to develop a Newton-type local optimization method. A crucial step is to determine an appropriate initial guess of the design parameters, Numerical design examples for both TE and TM polarization are presented. The design algorithm is expected to provide systematic guidance in engineering design of GMGRs. (C) 2005 Optical Society of America.