# Mode volume, energy transfer, and spaser threshold in plasmonic systems with gain

## TL;DR

This paper develops a unified theoretical framework for understanding spasing in plasmonic systems with gain, linking the spaser threshold to energy transfer and laser physics principles.

## Contribution

It introduces a general spaser condition applicable to various plasmonic systems and clarifies the role of mode volume and energy transfer in spaser operation.

## Key findings

- Spaser threshold is tied to energy transfer balance.
- Derived explicit spaser condition valid for arbitrary systems.
- Mode volume relates to the standard laser threshold extended to plasmonics.

## Abstract

We present a unified approach to describe spasing in plasmonic systems modeled by quantum emitters interacting with resonant plasmon mode. We show that spaser threshold implies detailed energy transfer balance between the gain and plasmon mode and derive explicit spaser condition valid for arbitrary plasmonic systems. By defining carefully the plasmon mode volume relative to the gain region, we show that the spaser condition represents, in fact, the standard laser threshold condition extended to plasmonic systems with dispersive dielectric function. For extended gain region, the saturated mode volume depends solely on the system parameters that determine the lower bound of threshold population inversion.