Discrete Thermodynamics of Lasers

TL;DR

This paper introduces a discrete thermodynamic model of lasers, describing their equilibrium as a logistic map and revealing spectral features and conditions for laser operation, including for multilevel systems.

Contribution

It presents a novel thermodynamic framework modeling laser behavior using logistic maps and extends this to multilevel lasers with new population inversion conditions.

Findings

Laser equilibrium modeled as a logistic map with bifurcation diagrams.

Line spectra observed before population inversion, confirming Einstein's prohibition.

Multilevel lasers can operate with specific activity ratios enabling population inversion.

Abstract

The paper offers a discrete thermodynamic model of lasers. Laser is an open system; its equilibrium is based on a balance of two thermodynamic forces, one related to the incoming pumping power and another to the emitted light. The basic expression for such equilibrium is a logistic map, graphical solutions to which are pitchfork bifurcation diagrams. As pumping force increases, the relative populations on the ground and lasing branches tend to zero and unity correspondingly. An interesting feature of this model is the line spectrum of the up and down transitions between the branches beyond bifurcation point. Even in a simple case of 2-level laser with only 2 possible transition types (up and down), the spectra look like sets of the line packets, starting well before the population inversion. This effect is an independent confirmation of the Einstein's prohibition on practical realization of 2-level laser. Multilevel lasers may be approached by employing the idea of thermodynamic activity for the emitting atoms. Considering coefficient of thermodynamic activity of the lasing level atoms to be proportional to the ratio of life times on the upper and lasing (the 3d) levels, one can derive a new basic map for the multilevel laser system. For a modest ratio only of 0.01, spontaneous transitions between levels are pushed to the area beyond population inversion, opening a space for the functioning of laser.