A Hermite-interpolation discretization and a uniform path deformation for the spatial spectral domain integral equation method in multilayered media for TE polarization

Two alternative approaches to the spatial spectral integral equation method are proposed. The first enhancement comprises a Hermite interpolation as the set of basis functions instead of the Gabor frame. The continuity, differentiability, equidistant spacing, and small support of these basis functions allows for an efficient and accurate numerical implementation. The second approach encompasses a method to transform between spatial domain and the deformed path in the complex-plane spectral domain. This method allows for more general path shapes, removing the need to decompose the complex-plane spectral domain path into distinct straight sections. Both enhancements are implemented for the case of TE polarization, and the results are validated against the finite element method and rigorous coupled-wave analysis.