Inverse Iteration for Nonlinear Eigenvalue Problems in Electromagnetic Scattering
We present an extension of the well-known method of “inverse iteration” for the standard eigenvalue problem to the nonlinear problem of finding dispersion relations for electromagnetic waves moving through a doublyperiodic structure. Numerical results are presented to illustrate the performance of the technique. A further improvement is described that allows an e cient “path following” algorithm where a curve of solutions is computed in (ω, Kbloch) space. We present dispersion relations calculated via this new method and compare the efficiency of this algorithm with that of more traditional methods.
KeywordsEigenvalue Problem Dispersion Curve Search Region Quadratic Convergence Nonlinear Eigenvalue Problem
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