Adiabatic perturbation theory for mode analysis in optical waveguides with large index variations without eigen value decomposition

Eigen mode and eigen value evaluation is crucial in optical waveguide design and is quite time consuming. It is known that the perturbation method can compute the modes efficiently for an index perturbed structure based on the known eigen modes and thereby avoids the time consuming eigen value decomposition process. However, the perturbation method can only be applied to the waveguide structures with small index variations, and hence it poses a significant constraint to the applicability of the method to the optical waveguide inverse design problem, which might have large index variations. In this paper, an adiabatic perturbation theory is proposed to tackle this problem. The eigen modes and the propagation constants of the optical waveguides are evaluated gradually by adding the index variation with respect to the previous step. While keeping the index variation to a small value within a step, the optical waveguide structure achieves a significant index change in total and thereby enables the application of the perturbation theory to the optical waveguide inverse design problem.