Simple yet effective analysis of waveguide mode symmetry: generalized eigenvalue approach based on Maxwell’s equations

Particular waveguide structures and refractive index distribution can lead to specified degeneracy of eigenmodes. To obtain an accurate understanding of this phenomenon, we propose a simple yet effective approach, i.e., generalized eigenvalue approach based on Maxwell's equations, for the analysis of waveguide mode symmetry. In this method, Maxwell's equations are reformulated into generalized eigenvalue problems. The waveguide eigenmodes are completely determined by the generalized eigenvalue problem given by two matrices (M, N), where M is 6 × 6 waveguide Hamiltonian and N is a constant singular matrix. Close examination shows that N usually commute with the corresponding matrix of a certain symmetry operation, thus the waveguide eigenmode symmetry is essentially determined by M, in contrast to the tedious and complex procedure given in the previous work [Opt. Express25, 29822 (2017)10.1364/OE.25.029822]. Based on this new approach, we discuss several symmetry operations and the corresponding symmetries including chiral, parity-time reversal, rotation symmetry, wherein the constraints of symmetry requirements on material parameters are derived in a much simpler way. In several waveguides with balanced gain and loss, anisotropy, and geometrical symmetry, the analysis of waveguide mode symmetry based on our simple yet effective approach is consistent with previous results, and shows perfect agreement with full-wave simulations.