Extension of Lorentz Reciprocity and Poynting Theorems for Spatially Dispersive Media with Quadrupolar Responses

TL;DR

This paper extends fundamental electromagnetic theorems to include quadrupolar and spatially dispersive media, providing conditions for reciprocity and losslessness crucial for advanced metamaterial modeling.

Contribution

It introduces a self-consistent extension of Lorentz reciprocity and Poynting theorems for media with quadrupolar responses, enabling more accurate metamaterial analysis.

Findings

Derived conditions for reciprocity in quadrupolar media

Established criteria for gainlessness and losslessness

Facilitated development of advanced metamaterial models

Abstract

We provide a self-consistent extension of the Lorentz reciprocity theorem and the Poynting theorem for media possessing electric and magnetic dipolar and quadrupolar responses related to electric and magnetic fields and field gradients. Using these two theorems, we respectively deduce the conditions of reciprocity and gainlessness and losslessness that apply to the various tensors mediating the interactions of these multipole moments and the associated fields and field gradients. We expect that these conditions will play an essential role in developing advanced metamaterial modeling techniques that include quadrupolar and spatially dispersive responses.