Convergence of the supercell method for defect modes calculations in photonic crystals

摘要

We present a rigorous study of the convergence of the supercell method used for determing defect modes in photonic crystals with compactly supported perturbations. Transverse electric and transverse magnetic polarized waves are investigated in 2-D structures. We prove an exponential convergence of the defect frequencies with the supercell size and give a justificatio of the quasi-independence of the corresponding eigenfunctions on the wave vector. We also give a characterization of the supercell eigenvalues corresponding to the background photonic crystal.