Full vectorial mode solver based on the non-Hermitian adiabatic perturbation method

Optical waveguide structure is characterized by its full vectorial modes and corresponding eigenvalues, whose calculation requires extensive computational resources. In this paper, a full vectorial mode solver based on the non-Hermitian adiabatic perturbation method accompanied by a scalar mode solver is proposed. The full vectorial mode solver gradually converts the initial modes generated by the scalar mode solver to the full vectorial modes by the non-Hermitian adiabatic perturbation theory, which incorporates the waveguide index gradient contribution and the modal non-orthogonality during the conversion. While saving about 3/4 of the computational time compared with the conventional full vectorial mode solver, the proposed method is quite accurate for the waveguides with low and high index contrast, as well as with large and small cross sections. The effective index discrepancy for the first six modes between the proposed method and the full vectorial mode solver is less than 4e-9 for a weakly guided thick waveguide and is less than 0.17 for a strongly guided thin waveguide. The newly proposed non-Hermitian perturbation method can be also potentially applied in other fields with non-Hermitian eigen mode problems.