Eigenstates of the full Maxwell equations for a two-constituent composite medium and their application to a calculation of the local electric field of a time dependent point electric dipole in a flat-slabs microstructure

TL;DR

This paper presents an exact method to calculate the local electric field of a time-dependent dipole in a layered microstructure using Maxwell eigenstates, enabling precise analysis of optical fields at sub-wavelength scales.

Contribution

It introduces a novel eigenstate-based expansion for solving Maxwell's equations in layered media, extending previous quasi-static approaches to full dynamic regimes.

Findings

Exact eigenstates of Maxwell equations for layered media are derived.

The method accurately predicts local electric fields in microstructures.

Results demonstrate potential for sub-wavelength optical imaging applications.

Abstract

An exact calculation of the local electric field ${\bf E}({\bf r})$ is described for the case of a time dependent point electric dipole ${\bf p}e^{-i\omega t}$ in the top layer of an $\epsilon_2$, $\epsilon_1$, $\epsilon_2$ three parallel slabs composite structure, where the $\epsilon_1$ layer has a finite thickness $2d$ but the $\epsilon_2$ layers are infinitely thick. For this purpose we first calculate all the eigenstates of the full Maxwell equations for the case where $\mu=1$ everywhere in the system. The eigenvalues appear as special, non-physical values of $\epsilon_1$ when $\epsilon_2$ is given. These eigenstates are then used to develop an exact expansion for the physical values of ${\bf E}({\bf r})$ in the system characterized by physical values of $\epsilon_1(\omega)$ and $\epsilon_2(\omega)$. Results are compared with those of a previous calculation of the local field of a time dependent point charge in the quasi-static regime. Numerical results are shown for the local electric field in practically important configurations where attaining an optical image with sub-wavelength resolution has practical significance.