Further comments on Mark Stockman's article "Criterion for Negative Refraction with Low Optical Losses from a Fundamental Principle of Causality"

TL;DR

This paper refutes claims that active materials cannot exhibit negative refraction with low optical losses, demonstrating through examples and analysis that such phenomena are possible within fundamental physical principles.

Contribution

It clarifies and corrects errors in Stockman's previous work, showing that negative refraction with low loss can occur in active materials across broad frequency ranges.

Findings

Negative refraction with low loss is possible in active materials.

Stockman's argument about noncausality due to non-analytic permittivity is invalid.

Examples demonstrate the feasibility of low-loss negative refraction over large frequency windows.

Abstract

We clarify the claims and errors in the paper "Criterion for Negative Refraction with Low Optical Losses from a Fundamental Principle of Causality" by Mark Stockman. Contrary to the central assertion in that paper, simple examples consistent with the basic inequality which Stockman discovered show that it is possible to have negative refraction and low loss in an arbitrarily large frequency window. Further examination of the paper reveals additional errors that invalidate his argument that active materials cannot have low loss and negative refraction in a frequency window. Also, we point out that for active materials non-analyticity of the electrical permittivity in the upper half complex frequency plane does not necessarily imply noncausality, as Stockman infers.