Landau-Lifshitz theory of single susceptibility Maxwell equations

TL;DR

This paper compares different macroscopic Maxwell equation schemes for metamaterials, highlighting that the author's approach using standard current density offers a more natural and first-principles-based susceptibility formulation.

Contribution

It introduces a scheme based on standard current density that unifies and clarifies the relationships among existing formulations, providing a more fundamental susceptibility theory.

Findings

The author's scheme yields first-principles susceptibility expressions.

It can be transformed into other schemes through reversible relations.

The scheme is more natural than Landau-Lifshitz and Anapole forms.

Abstract

The conflicting arguments given in the discussion forum of Metamaterials 2011 on the possible forms of macroscopic Maxwell equations are lead to a convergence by noting the relationship among the employed material variables for each scheme. The three schemes by Chipouline et al. using (A) standard $\Vec{P}$ and $\Vec{M}$ (Casimir form), (B) generalized electric polarization $\Vec{P}_{LL}$ (Landau-Lifshitz form), (C) generalized magnetic polarization $\Vec{M}_{A}$ (Anapole form) are compared with (D) the present author's scheme using standard current density $\Vec{J}$. From the reversible relations among the transverse components of these vectors, one can easily rewrite one scheme into another. The scheme (D), the only one among the four providing the first-principles expressions of susceptibility and also leading to a non-phenomenological Casimir form in terms of the four generalized susceptibilities between $\{\Vec{P},\Vec{M}\}$ and $\{\Vec{E},\Vec{B}\}$, is concluded to be a more natural form than (B) and (C) as a single susceptibility theory.