Phase Transition Theory of Many-Mode Ordering and Pulse Formation in Lasers

Abstract

A novel theory for the ordering of many interacting modes in lasers is presented. By exactly solving a Fokker-Planck equation for the distribution of waveforms in the laser in steady state, equivalence of the system to a canonical ensemble is established, where the role of temperature is taken by amplifier noise. Passive mode locking is obtained as a phase transition of the first kind and threshold is calculated, employing mean field theory backed up by a numerical study. For zero noise, compliance with the existing noiseless theory is shown.

The mode-locking transition of random lasers

“…Standard multimode lasers without disorder and characterized by equispaced resonances may be driven to a synchronous regime through the so called mode-locking transition [18,19], which so far has only been shown to occur spontaneously in the presence of a saturable absorber and allows to generate ultra-short light pulses [20,21]. We show that the same transition occurs in RLs and allows to lock modes of a RFRL casting its emission in the typical IFRL spectrum and demonstrating the inherently coherent nature of the random lasing phenomenon.…”

Glassy behavior of light in random lasers

“…Complex processes in laser physics, including nonlinear optics, are well known and studied (see e.g. [30,31]), up to recent investigations in multi-mode systems [32,33,34] and successful reformulations of standard laser thermodynamics [35,36,37,38,39]. The extension of these approaches to RL immediately leads to the application of the statistical theory of disordered systems, of which spin glass theory is a paradigm [40], and which is the subject of the present manuscript.…”

“…random but slowly varying) variables, and the phases are to be taken as the relevant dynamical variables. The mode-locking process in standard lasers is now recognized as a thermodynamic phase transition [35,36,37,38,39]; it is expected, therefore, that the mode-locking transition for a RL takes the form of a phase transition in a disordered system. This manuscript follows a recent letter [43], and furnishes: extensive and new details on the derivation of the analytical results (including the stability analysis that was previously not reported); a discussion of the underlying working hypotheses; a discussion on the nature of the considered electromagnetic modes; the analysis of possible experimental frameworks where glassy behavior of light can be observed.…”

Analysis of Timing Jitter in External-Cavity Mode-Locked Semiconductor Lasers

“…This concept has been recently described in terms of statistical-mechanics by Gordon and coworkers [6] showing that a noise-induced phase transition leads from an ordered state (mode-locked solution) to a disordered state [multimode continuous-wave (CW)]. These results, which are suited to class-A lasers, have a counterpart in semiconductor lasers where spontaneous emission noise prevents the locking of a large set of modes, specially for close-to-threshold operation [7].…”