Efficient full vectorial mode solver based on orthonormal mode expansion

Wave propagation inside optical waveguides is characterized by their eigen modes and eigenvalues. To obtain these important information, numerical algorithms convert the Maxwell equations into the linear equations, and hence, the waveguide mode problem becomes the matrix eigenvalue problem, whose efficiency is dependent on the matrix size. In this work, an orthonormal mode expansion based full vectorial mode solver is proposed with the matrix size significantly reduced. The full vectorial operator is decomposed into a Hermitian part and a perturbation part. The Hermitian part possesses orthonormal eigen modes, which can be used as the basis to compute the waveguide modes. The perturbation part constitutes a matrix with a greatly reduced size, which is determined by the number of orthonormal modes. As the matrix size shrinks, the computational resource and time to find the eigen modes and eigenvalues can be greatly saved by 2 orders of magnitude while maintaining a comparable accuracy.