Non-local Constitutive Relations with Hidden Parameter for the Vector Potential in Maxwell Equations

Abstract

The main goal of this paper is to establish a new general nonlocality constitutive relationship for electromagnetic field E, B, D and H in frequency-time domain setting. The four basic assumptions of the medium are linearity, invariance to time translations, causality and continuity. A short review of the Born, Born-Fedorov and Engheta-Jaggard formalism of media in chiral media, respectively, is made; also expressions for scalar and vector potentials are derived which satisfies a velocity gauge. The chiral parameter T appears as a hidden factor for the vector potential A. This velocity gauge condition is not satisfied by other chiral formalisms, so the proposed approach is useful to numerical calculations and applications of scalar and vector potentials. In this context, a major role could be played by the electromagnetic (EM) simulators, which are usually employed to solve very complex and challenging EM field problems. In connection with the Dirac equation for the graphene systems, we find analytically the Fermi velocity in terms of the velocity gauge and the fine-structure constant.