# Beating plasmonic losses with an intrinsic channel of gain: the cases with Ag and Al

## TL;DR

This paper presents a theoretical analysis showing that surface effects can create an intrinsic gain channel for surface plasma waves on metals, with potential to overcome plasmonic losses, especially in silver and aluminum, by modifying the surrounding dielectric.

## Contribution

It introduces a comprehensive theory accounting for inter-band and dielectric effects, revealing how intrinsic gain channels can be enhanced or limited in common plasmonic metals.

## Key findings

- Intrinsic gain channels exist but are insufficient to fully compensate losses in Ag and Al.
- Inter-band effects weaken the gain in Ag, while high loss rates limit Al.
- Replacing vacuum with a dielectric can enhance gain in Ag, enabling loss compensation.

## Abstract

An elementary approach is employed to show that genuine surface effects could destabilize surface plasma waves (SPWs) supported on the interface between a metal and a dielectric (usually the vacuum) and give rise to an intrinsic channel of gain for these waves. A comprehensive SPW theory is presented taking into account both the inter-band transition effects and the dielectric effects. Experimental consequences, especially in regard to the possibility of overcompensating for the energy losses suffered by SPWs, are exemplified for two common plasmonic materials: silver (Ag) and aluminum (Al). In both metals, the intrinsic channel of gain is shown having substantially reduced but insufficient to overcompensate for the losses, for different reasons. In Ag, the inter-band transition effects significantly weaken the intrinsic gain channel and make it unable to overcompensate for the losses, while in Al it is because the loss rate is too big. Nevertheless, we find it possible to enhance the intrinsic gain rate by replacing the vacuum with a moderate dielectric so that the losses can be overcompensated in Ag. This prediction is ready for experimental exploitation.