Accurate vectorial finite element mode solver for magneto-optic and anisotropic waveguides

Area of Science:

• Integrated Optics
• Electromagnetism
• Computational Physics

Background:

• Nonreciprocal devices like magneto-optical isolators are crucial for integrated optics.
• Accurate mode solving is essential for designing these devices.
• Existing methods struggle with nonreciprocal cases and often rely on approximations.

Purpose of the Study:

• To develop a precise and efficient dielectric waveguide mode solver for general nonreciprocal permittivity tensors.
• To enable direct computation of nonreciprocal loss and phase shifts.
• To investigate practical integrated optical devices such as isolators.

Main Methods:

• Derivation of the Rayleigh-Ritz functional for non-self-adjoint cases.
• Discretization using the node-based finite element method with a penalty function.
• Linearization of the quadratic eigenvalue problem into a γ-formulation for efficient solving.

Main Results:

• Precise computation of both forward and backward propagating modes in nonreciprocal waveguides.
• Direct calculation of nonreciprocal loss/phase shift, bypassing perturbation methods.
• Successful application to integrated optical isolators demonstrating nonreciprocal phase shift and loss effects.

Conclusions:

• The developed mode solver offers high accuracy and computational efficiency for nonreciprocal integrated optics.
• It provides a robust alternative to perturbation methods for analyzing complex optical devices.
• The γ-formulation preserves matrix sparsity and avoids time-consuming iterations.