Statistical mechanics models for multimode lasers and random lasers

Abstract

Referring to recent approaches to multimode laser theory, including Monte Carlo simulations of effective models and statistical mechanical analytic computations, the status for a complete nonperturbative theory in open and disordered cavities is discussed and the derivation of the general statistical models in this framework is presented. When light is propagating in a disordered medium, the relevant models can be analysed via the replica method. For high degrees of disordered-induced frustration and nonlinearity, a glassy behaviour is expected beyond the lasing threshold, providing a suggestive link between glasses and photonics. We describe in detail the results for the general Hamiltonian model in the mean field approximation and we analytically justify an available test for replica symmetry breaking from intensity spectra measurements. Finally, we draw perspectives for such approaches.

Keywords:

• statistical mechanics
• optics
• critical phenomena
• lasers
• glass transition
• phase transitions

Notes

No potential conflict of interest was reported by the authors.

1 We note that a uniform refractive index would not change the form of Equation (5(5) ). But, if the refractive index depends on space, the wave vector k is expected to change within the medium and Equation (5(5) ) does not keep its form since it is obtained factoring out .

2 These is true in general for all the eigenmodes obtained within the CC approximation.

3 In [57], it is also considered the case in which scattering and gain are provided by different atoms.

4 we stress, nevertheless, that glassiness is in principle an independent phenomenon from deterministic chaos, i.e. the high sensitivity to initial conditions, see, e.g. [74].

Additional information

Funding

The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme FP7/2007-2013/ [REA grant agreement number 290038]; NETADIS project and from the Italian MIUR under the Basic Research Investigation Fund FIRB2008 program [grant number RBFR08M3P4].