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

Steven Johnson, John Joannopoulos
2001 Optics Express  
We describe a fully-vectorial, three-dimensional algorithm to compute the definite-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 for anisotropic structures, and demonstrate that
more » ... demonstrate that O(∆x 2 ) convergence can be achieved even in systems with sharp material discontinuities. We show how it is possible to solve for interior eigenvalues, such as localized defect modes, without computing the many underlying eigenstates. Preconditioned conjugategradient Rayleigh-quotient minimization is compared with the Davidson method for eigensolution, and a number of iteration variants and preconditioners are characterized. Our implementation is freely available on the Web.
doi:10.1364/oe.8.000173 pmid:19417802 fatcat:6ykgzrqeyncp5ndrhbzgy56lx4