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

Area of Science:

• Photonics and Waveguide Optics
• Mathematical Physics
• Computational Electromagnetics

Background:

• Waveguide structures and refractive index profiles dictate eigenmode degeneracy.
• Accurate analysis of waveguide mode symmetry is crucial for device design.
• Previous methods for symmetry analysis are often complex and tedious.

Purpose of the Study:

• To propose a simplified and effective approach for analyzing waveguide mode symmetry.
• To reformulate Maxwell's equations into generalized eigenvalue problems for mode analysis.
• To provide a more straightforward method for deriving symmetry constraints on material parameters.

Main Methods:

• Reformulation of Maxwell's equations into generalized eigenvalue problems (M, N matrices).
• Analysis of the 6x6 waveguide Hamiltonian (M) and a singular matrix (N).
• Examination of the commutation relations between N and symmetry operations.

Main Results:

• Waveguide eigenmode symmetry is primarily determined by the M matrix.
• The approach simplifies the derivation of constraints for chiral, parity-time reversal, and rotation symmetries.
• Analysis of waveguides with gain/loss, anisotropy, and geometrical symmetry aligns with prior results and simulations.

Conclusions:

• The generalized eigenvalue approach offers a simpler and effective method for waveguide mode symmetry analysis.
• This method provides accurate predictions and facilitates easier derivation of symmetry constraints.
• The findings are consistent with existing literature and full-wave simulations, validating the approach.