Electromagnetic eigenstates and the field of an oscillating point electric dipole in a flat-slab composite structure

Abstract

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