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Physical Review A

Collisional effects in gas lasers

Ashish Agarwal, Rupamanjari Ghosh

Published Feb 1, 1993• 2 citations
Publisher

Abstract

The effects of phase-interrupting and velocity-changing collisions between active and perturber atoms on the spectral profile of a gas laser are studied. Exact analytical results for the density matrix are presented for the case of strong collisions in a unidirectional ring laser, and the laser intensity is then evaluated in the Doppler limit under the condition of self-consistency. The washout of the hole burning in the steady-state population difference and the broadening of the laser line shape are discussed. The results of the third-order perturbation theory are compared with the exact calculations valid for an arbitrarily intense pump.

DOI
10.1103/physreva.47.1407

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Physical Review A•May 1, 1970•144 citations
The effects of phase-interrupting and velocity-changing collisions between active and perturber atoms on the spectral profile of a gas laser are studied. Exact analytical results for the density matrix are presented for the case of strong collisions in a unidirectional ring laser, and the laser intensity is then evaluated in the Doppler limit under the condition of self-consistency. The washout of the hole burning in the steady-state population difference and the broadening of the laser line shape are discussed. The results of the third-order perturbation theory are compared with the exact calculations valid for an arbitrarily intense pump.
The dynamics of a multimode high-intensity gas laser including some velocity-changing-collision effects is investigated theoretically. Using a spatial Fourier expansion method for the density matrix of the active medium, one obtains the system of equations which contain only the Fourier components of the population inversion. To obtain the approximate solutions in the high-intensity case, the saturation terms due to hole burning and the population-pulsation terms are treated separately. The former are calculated exactly and the result is equivalent to the rate-equation approximation. The latter are treated by the perturbation method. The equations of motion for mode amplitudes have a similar form to those of Lamb's perturbation theory but can be applied to a high-intensity multimode laser. Experimental results of three-mode oscillation of a He-Ne laser are compared with the theory.
A theory of saturation spectroscopy in three-level gas-vapor systems, including collisional effects, is presented. Using a model of collisions in which they are phase interrupting in their effect on level coherences and velocity changing in their effect on level population densities, the authors calculate the absorption profile of a weak probe field on a given transition when an arbitrarily strong pump field acts on a coupled transition. Line shapes are derived for an arbitrary collision kernel describing the velocity-changing collisions, and these line shapes are evaluated for the collision kernel proposed by Keilson and Storer. Various limiting forms for the line shapes are derived and representative line shapes are displayed. Several new features of the line shapes, including collisionally induced increased probe absorption are discussed. The line shapes are seen to reflect the various collisional processes that may occur in atomic or molecular systems.
The present paper includes the influence of collisions in the high-intensity laser theory by Stenholm and Lamb. The history of an atom is divided into field- and collision-dominated intervals. The collisions are treated as instantaneous independent events (impact approximation). The equation of motion for the density matrix of an ensemble of atoms undergoing collisions is derived. The collisions manifest themselves as an integral operator in the equation of motion. As a model, collisions which do not change the populations of the atomic levels are treated. Physical conditions on the kernel matrix of the collision integral are used to construct a simple nontrivial model. To simplify the treatment, the phase and velocity changes are assumed to take place in different collisions. This model is used to solve the problem of a high-intensity laser with collisions. Only the lowest nonvanishing terms in the Fourier expansion of the density matrix elements are used. Typical numerical results are evaluated and shown in the figures. Connections with other papers and generalizations are discussed.
A theoretical model for the pressure dependence of the intensity of a gas laser is presented in which only velocity-changing collisions with foreign-gas atoms are included. This is a special case where the phase shifts are the same for the two atomic-laser levels or are so small that deflections are the dominant effect of collisions. A collision model for hard-sphere repulsive interactions is derived and the collision parameters, persistence of velocity and collision frequency, are assumed to be independent of velocity. The collision theory is applied to a third-order expansion of the polarization in powers of the cavity electric field (weak-signal theory). The resulting expression for the intensity shows strong pressure dependence. The collisions reduce the amount of saturation and the laser intensity increases with pressure in a characteristic fashion. It is recommended that the best way to look for this effect is to make the measurements under conditions of constant relative excitation.
This paper extends the calculations of the semiclassical Lamb theory of a Doppler-broadened gas laser (optical maser) to arbitrary intensities for the case of single-mode operation. The coupled equations of the classical electromagnetic field and an ensemble of two-level atoms are set up, and a solution is obtained in the form of a continued fraction. This is used to compute intensity-detuning curves and atomic population inversion densities as functions of both the velocity and the position in the laser. When the laser is tuned to resonance, the velocity dependence of the inversion density shows a previously unknown fine structure consisting of a "bump" in the bottom of the hole. The calculations are compared to results obtained from a perturbation expansion in powers of the field and exact results known for atoms with zero velocity. The response of the laser output to a slow modulation and the buildup of oscillations are also discussed.
This paper presents a semiclassical theory of a single-mode gas laser valid for essentially arbitrary values of field intensity. The theory is formulated in terms of an ensemble-averaged form of the density-matrix equations of motion involving a single set of coordinates. The polarization and the population-inversion density are expanded in spatial Fourier components. One obtains a set of coupled difference equations in the Fourier coefficients yn{y}_{n}yn​, which may be solved subject to appropriate boundary conditions on yn{y}_{n}yn​ for large nnn. The solutions may be expressed in terms of continued fractions in the general case, and in closed form in important special cases. Quantities of interest are evaluated by computer. The steady-state laser intensity and frequency are obtained from the coupled electromagnetic field equations as functions of the cavity parameters and the linear gain of the amplifying medium. At moderate values of field intensity, the velocity distribution of the space-averaged population inversion density exhibits a fine structure for low-velocity atoms superimposed on the usual broader depletion. This structure is a manifestation of the coherent ringing of the amplifying medium. The results are compared with those obtained in the rate-equation approximation, and with the recent work of Stenholm and Lamb. Discrepancies with the latter paper are explained.