VECTOR POTENTIAL ELECTROMAGNETICS WITH GENERALIZED GAUGE FOR INHOMOGENEOUS MEDIA: FORMULATION (Invited Paper)

Abstract

Abstract-The mixed vector and scalar potential formulation is valid from quantum theory to classical electromagnetics. The present rapid development in quantum optics applications calls for electromagnetic solutions that straddle both the quantum and classical physics regimes. The vector potential formulation using A and Φ (or A-Φ formulation) is a good candidate to bridge these two regimes. Hence, there is a need to generalize this formulation to inhomogeneous media. A generalized gauge is suggested for solving electromagnetics problems in inhomogenous media that can be extended to the anistropic case. An advantage of the resulting equations is their absence of catastrophic breakdown at low-frequencies. Hence, the usual differential equation solvers can be used to solve them over a wide range of scales and bandwidth. It is shown that the interface boundary conditions from the resulting equations reduce to those of classical Maxwell's equations. Also, the classical Green's theorem can be extended to such a formulation, resulting in an extinction theorem and a surface equivalence principle similar to the classical case. Moreover, surface integral equation formulations can be derived for piecewise homogeneous scatterers. Furthermore, the integral equations neither exhibit the low-frequency catastrophe nor the frequency imbalance observed in the classical formulation using E-H fields. The matrix representation of the integral equation for a PEC (perfect electric conductor) scatterer is given.

Decoupled potential integral equation applied to complex geometries

“…All these problems can be solved using the decoupled potential formulation (DPIE) presented in [6] . In [7] we find a recent work that goes along similar directions.…”

Vectorial Solution to Double Curl Equation With Generalized Coulomb Gauge for Magnetostatic Problems

“…which is the static case of the A-equation in [19], with ε, μ, and α being the permittivity, permeability, and gauge factor, respectively. Meanwhile, the generalized Lorenz gauge…”

“…In contrast to the traditional Coulomb gauged method, both the uniqueness and the vectorial nature of A are reserved in this paper. The generalized Coulomb gauge, which is the reduced form of the generalized Lorenz gauge [19] at static limit, is introduced to remove the null space of the curl operator and guarantees the uniqueness of A. To retain the vectorial property of A, it is expanded by the edge elements, and appropriate expansion of the gauge term is formulated based on the space mapping between the Whitney forms by mathematical operators (gradient, divergence, and curl operators) [20], [21], and the Hodge operators [22], [23].…”

Generalized Debye Sources-Based EFIE Solver on Subdivision Surfaces

“…DPIE was implemented numerically by using Nyström method in [23]. A similar idea of exploiting generalized gauge based A-Φ integral formulation was introduced in [24] and its numerical implementation was presented in [25].…”