Impedance matching of inverted conductors: Two-dimensional beam splitters with divergent gain

TL;DR

This paper explores impedance matching in ultra-thin conducting sheets like graphene, revealing conditions for perfect absorption and potential for enormous amplification using inverted conductors, enabling novel beam splitting with divergent gain.

Contribution

It demonstrates that negative impedance matching in thin conducting sheets can lead to high gain and beam splitting, a novel approach for optical amplification and control.

Findings

Existence of polarization and angle conditions for impedance half-matching.

Negative conductivity can produce amplification in thin sheets.

Potential for large single-pass gain in nonresonant, ultra-thin structures.

Abstract

A thin conducting sheet - graphene, for example - transmits, absorbs, and reflects radiation. A sheet that is very thin, even vanishingly so, can still produce 50% absorption at normal incidence if it has conductivity corresponding to half the impedance of free space. We find that, regardless of the sheet conductivity, there exists a combination of polarization and angle of incidence that achieves this impedance half-matching condition. If the conducting medium can be inverted, the conductivity is formally negative and the sheet amplifies the incident radiation. To the extent that a negative half-match in a thin sheet can be maintained, enormous single-pass gain in both transmission and reflection is possible. Known semiconductors (e.g., gallium nitride) have the optical properties necessary to give large amplification in a structure that is, remarkably, both thin and nonresonant.