This paper contains a brief overview of the main types of instability in laser systems. The topics being discussed include the early spiking in solid-state lasers, single-mode lasers with homogeneous and inhomogeneous broadening, the effect of noise and modulation, multimode operation, and a brief survey of nonlinear dynamics.

Overview of instabilities in laser systems

Publisher Summary This chapter discuses the dynamical instabilities and pulsations in lasers. The laser instabilities are of interest in the research efforts. The characteristics of laser pulsations are in accord with the predictions of the early maser models. The chapter discuses the laser phenomena. The semiclassical theory of the laser was developed in response to the limited success of the rate equations in dealing with issues such as coherence, spectral purity, and the spiking phenomenon. The most analyzed laser model is a single-mode resonant system. The single-mode equations are the prototype example of an unstable laser model. The experimental realization of a single-mode, homogeneously broadened laser is attractive from the point of view of laser physics because the Lorenz model itself has no close realization in hydrodynamic systems. Neodymium glass lasers are inhomogeneously broadened because of differences in the local fields at the site of the active atoms. Most gas lasers operating in the visible and near-infrared regions of the spectrum are inhomogeneously broadened because of the Doppler shift suffered by the moving atoms. The combination of lasers and saturable absorbers has been proposed. Most experimental lasers are designed to operate as Fabry–Perot resonators.

I Dynamical Instabilities and Pulsations in Lasers

A set of general equations describing the time‐dependent behavior of a laser is derived. The derivation is based on a density matrix description of a homogeneously broadened laser transition and a semiclassical treatment of the radiation field, consisting of an arbitrary number of modes. The resulting equations resemble ordinary rate and energy conservation equations but contain additional interference terms which, in general, couple all of the modes. The strength of this coupling depends on the inhomogeneity of the population inversion as well as on the mode frequencies. The energy conservation equations imply that absorption and stimulated emission in such a system can apply, strictly speaking, only collectively to the system of modes as a whole. In addition, the threshold inversion is affected by mode coupling. Stability analysis carried out in the two‐mode case indicates that a spatial inhomogeneity in the pumping rate is required for undamped oscillations. It is also concluded that coupling of off‐axis modes is more likely to lead to undamped spiking than coupling of axial modes.

Coupled‐Mode Laser Oscillation

Results of experiments are presented indicating that low-frequency beats detectable from ruby lasers are beats between transverse modes. Three-dimensional resonator theory is reviewed with respect to its applicability to ruby lasers. Agreement between theory and experiment shows that the modes of an excellent optical quality ruby rod are described by nonconfocal resonator theory. Results of beat-frequency measurements with approximately confocal rods are in good agreement with theory. The variation of transverse mode beats with pump energy and temperature indicates that single-frequency operation is possible at room temperature and up to 20% over threshold if axial frequency selection is used.

A Study of Transverse Modes of Ruby Lasers Using Beat-Frequency Detection and Fast Photography

Classical coherence theory as presented by Wolf with the modification proposed by Neugebauer is used to describe mathematically and experimentally the collimation and focusing of the time-averaged intensity of pulsed multimode laser radiation. Measurements of the double-slit Fraunhofer pattern and the near and far zone intensity patterns were made on two pulsed ruby lasers by both still and streak photography to examine the spatial coherence and the collimation of the beam. Our result showed that the time-averaged collimation and focusing characteristics of the beam can be treated as the superposition of noncoupled spatially coherent modes.

A Study of Partial Coherence and Its Application to the Collimation of Pulsed Multimode Laser Radiation

A high-speed image converter camera has been used to study the time variations as a function of position of the light emitted from a pink ruby operated as a laser. The gross properties of the emitted light follow the thereotical predictions reasonably well, but the new experimental technique used in these studies reveals a wealth of detail about the time variations of this light which has not been previously reported.

High-speed photographic study of the coherent radiation from a ruby laser

The time variations of Fabry–Perot interference fringes produced by the coherent light from a ruby laser have been recorded with an image converter camera. The recorded variations indicate that: (a) the mode of oscillation of the ruby can change from one relaxation–oscillation burst of emission, or laser spike, to another; (b) a monotonic progression of wavelengths frequently occurs in a sequence of spikes; (c) the oscillation mode can switch within a single spike; and (d) several modes of oscillation can occur simultaneously in a single spike. The multiplicity of modes was observed to increase with an increase of pumping power. The wavelength separation between simultaneous modes corresponds closely to an integral difference in the number of half-wavelengths between the silvered end faces of the ruby.

C. M. York

Papers

High-speed photographic study of the coherent radiation from a ruby laser

Time-resolved spectroscopy of ruby laser emissions