Three-dimensional finite element analysis of nonreciprocal phase shifts in magneto-photonic crystal waveguides.

This report presents the first three-dimensional characterization of nonreciprocal phase shifts in magneto-photonic crystal (MPC) slab waveguides. We model MPC waveguides using a three-dimensional finite element method with curvilinear tetrahedral edge elements. This study investigates the dependence of nonreciprocal phase shifts on the width and the thickness of the waveguides, and we investigate the dependence of losses on the air hole depth, leading to a guideline for the design of optical isolators. Simulations show that waveguides with reduced width and deep air holes exhibit high nonreciprocal phase shifts and low losses. The study also shows that, compared with two-dimensional calculations, nonreciprocal phase shifts express key similarities, although the frequencies of the guided modes shift.