A gauge-potential formulation for electromagnetic field in arbitrary anisotropic media

Abstract

Electromagnetic field in anisotropic media is governed by a curl-curl operator ▽ × (v · ▽ × A), which involves a medium parameter tensor equation representing either magnetic permeability (µ) or conductivity equation. In this paper, we show that the curl-curl operator may be decomposed in the following form: equation have been applied. Applying the decomposition, we then demonstrate that the gauge-potentials (Φ, A) of electromagnetic field F = −(▽ Φ + iwA) can be obtained by successively solving the following equations in frequency-domain: equation which changes the curl-curl operator into a quasi-divergence operator so as to have better numerical accuracies in computations of the electromagnetic field.