Phase-Transition-Like Phenomena in Lasers and Nonlinear Optics

Abstract

We start with the simple physical idea that the laser threshold is characterized by the formation of a macroscopic electromagnetic field in the time domain. This idea is then used to set up a phenomenological theory of the threshold phenomena in lasers and nonlinear optics. For the single mode laser the results of the microscopic theory are reproduced, which are in agreement with all experimental data. In section 3 the microscopic theory is considered from the new point of view and some analogies and differences to mode-mode coupling theories of phase transitions are pointed out. In section 4 some recent theoretical results on multi-mode lasers are reviewed with the conclusion that mode-mode coupling effects near thresholds in multimode lasers should be measurable. Finally our phenomenological theory is applied to various light sources of nonlinear optics. The phenomenological theory predicts that the form of the photo-count distributions for all these sources is independent of the details of the microscopic interactions and will depend only on the phase-angle symmetries and the order (in a perturbation theoretical sense) of the basic nonlinear scattering process. In all cases, where a comparison with microscopic theories is possible, agreement is found. The results indicate the great usefulness of the language and the concepts of phase transition theory even for systems which are not in thermodynamic equilibrium, and which don’t become critical in a strict sense.