Quantum physics-based modelling of frequency-dependent dielectric function for small-scale devices in optical communications

This paper describes the one dimensional quantum physics-based modelling of frequency-dependent dielectric function for small-scale devices. The eigenpairs of the underlying canonical and associated perturbed quantum systems are computed and utilized for the calculation of the dielectric function. Galerkin method has been employed to discretize the boundary value problem of interest. The starting point is the infinite quantum potential well problem, for which the complete set of eigenfunctions is readily available in closed-form. Subsequently, the wavefunction of the perturbed system is expressed as a linear combination of the original eigenfunctions and the eigenpairs determined. Two- and three dimensional problems can be solved mutatis mutandis. The introduction of sinc functions throughout the analysis ensures the robustness of the computations. The analytical and numerical results demonstrate that the real- and imaginary parts of the dielectric function are even and odd functions, respectively, as expected.