An GNU-OCTAVE implementation of Jacobi–Davidson style QR method for interior eigenvalue calculations using plane-wave expansion in photonic crystal structures

Abstract

We describe a GNU-OCTAVE implementation of the Jacobi–Davidson style QR method for the estimation of interior eigenvalues in photonic crystal structures. The photonic eigenproblem is reduced to a matrix eigenproblem using plane-wave expansion. We show that a single-step solution of the Jacobi–Davidson correction equation combined with a simple diagonal Jacobi pre-conditioner are quite time efficient compared to other schemes including the Jacobi–Davidson with bi-orthogonal basis, conjugate gradient minimization of the Rayleigh Ritz quotient and implicitly restarted Lanczos methods. Our implementation is freely available on the web.