Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis

We describe a fully-vectorial, three-dimensional algorithm to compute the d efinite-frequency eigenstates of Maxwell's equations in arbitrary periodic dielectric structures, including systems with anisotropy (birefringence) or magnetic materials, using preconditioned block-iterative eigensolvers in a planewave basis. Favorable scaling with the system size and the number of computed bands is exhibited. We propose a new effective dielectric tensor f or anisotropic structures, and demonstrate that O(Deltax(2)) convergence ca n be achieved even in systems with sharp material discontinuities. We show how it is possible to solve for interior eigenvalues, such as localized def ect modes, without computing the many underlying eigenstates. Preconditione d conjugate-gradient Rayleigh-quotient minimization is compared with the Da vidson method for eigensolution, and a number of iteration variants and pre conditioners are characterized. Our implementation is freely available on t he Web. (C) 2001 Optical Society of America.