Exactly solvable toy model for a SPASER

TL;DR

This paper introduces an exactly solvable quasi-classical model of a spaser, capturing its key behaviors such as self-oscillation, synchronization, and loss compensation, with a focus on the underlying nonlinear permittivity dynamics.

Contribution

It presents the first exactly solvable model of a spaser using nonlinear permittivity, elucidating its main features and bifurcation behavior.

Findings

Demonstrates self-oscillation (spasing) without external field above threshold

Shows synchronization within the Arnold tongue

Illustrates loss compensation below threshold

Abstract

We propose an exactly solvable quasi-classical model of a spaser. The gain medium is described in terms of the nonlinear permittivity with negative losses. The model demonstrates the main features of a spaser: a self-oscillating state (spasing) arising without an external driving field if the pumping exceeds some threshold value, synchronization of a spaser by an external field within the Arnold tongue, and the possibility of compensating for Joule losses when the pumping is below threshold. Similar to the common laser, a transition to the spasing regime takes a form of the Hopf bifurcation.