Numerical Mode Decomposition for the A-Φ Formulation with Inhomogeneous Media

Abstract

Compared with the E-H electromagnetic field formula, the $\mathrm{A}-\Phi$ formula is immune to low-frequency breakdown, which makes it an accurate model over broad frequency range. Besides, the $\mathrm{A}-\Phi$ formula plays an essential role in the quantization of the EM $\mathrm{field}$ and taking other quantum effects into consideration together with EM field. In this paper, the numerical mode decomposition expressions for the $\mathrm{A}-\Phi$ formula are derived based on the finite element method for inhomogeneous dielectric materials, which can be used as a fast numerical solver for and finding the eigenmodes of the $\mathrm{A}-\Phi$ formula with inhomogeneous EM background.