Abstract

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.

Geometric variations in high index-contrast waveguides, coupled mode theory in curvilinear coordinates

M. Skorobogatiy, Steven A. Jacobs, Steven G. Johnson, and Yoel Fink
Opt. Express 10(21) 1227-1243 (2002)

Perturbation theory as a unified approach to describe diffractive optical elements

Markus Testorf
J. Opt. Soc. Am. A 16(5) 1115-1123 (1999)

Complex coupled-mode theory for optical waveguides

Wei-Ping Huang and Jianwei Mu
Opt. Express 17(21) 19134-19152 (2009)

Coupled-mode theory for optical waveguides: an overview

Wei-Ping Huang
J. Opt. Soc. Am. A 11(3) 963-983 (1994)

Calculation, normalization, and perturbation of quasinormal modes in coupled cavity-waveguide systems

Philip Trøst Kristensen, Jakob Rosenkrantz de Lasson, and Niels Gregersen
Opt. Lett. 39(22) 6359-6362 (2014)