Unified Coupled-Mode Theory for Geometric and Material Perturbations in Optical Waveguides

Coupled-mode theory is a powerful tool to understand and control the effects of deployment and fabrication imperfections on optical waveguides. Although it provides many advantages compared to the finite element method, it still lacks the ability to treat geometric and material perturbations when they act simultaneously on the waveguide. This work fills this gap, providing a novel framework for a unified treatment of geometric and material perturbations in the coupled-mode analysis. The proposed approach consists of, first, applying the theory of transformation optics to convert geometric deformation into material perturbations and, second, studying the obtained waveguide by using a custom-developed coupled-mode theory able to deal with perturbations of both the permittivity and the permeability tensor. The framework is applied to three examples: a solid-core fiber affected by intrinsic perturbations, a bent solid-core fiber, and an elliptical hollow-core fiber. Results are validated against simulations based on the finite element method and compared with the standard coupled-mode theory most suitable for each specific example; they show that the proposed unified coupled-mode theory performs consistently better than standard theories, confirming it as a general and accurate tool for the design and analysis of optical waveguides.