Precision Methods of Calculating Problems of Non-Stationary Integrated Photonics

Abstract: The solution of the Maxwell equations in layered media has a discontinuity in the derivative or the function at media interfaces. For the first time, finite-difference schemes which converge of discontinuous solutions are proposed. They are two-point bicompact conservative schemes in which the layer boundaries are as grid nodes. A fundamentally new approach is proposed to account for the medium dispersion. The proposed approaches ensure the second order of accuracy for even discontinuous solutions. © 2022, Allerton Press, Inc