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Quantum Electronics

Numerical modelling of the propagation of high-power laser radiation in sodium vapour

Yu. V. Petrushevich, Andrei N Starostin

Published Jul 31, 1996• 0 citations
Publisher

Abstract

Numerical modelling is reported of the propagation of laser radiation in a resonant three-level medium. The transient nature and the spatial inhomogeneity of the investigated processes are taken into account. It is shown that the radiation is scattered into narrow cones and that the number and vertex angles of these cones depend on the experimental conditions. The spatiotemporal spectrum of the radiation field emerging from the scattering medium and the dependence of this spectrum on the laser radiation frequency are compared with the results of experiments carried out under similar conditions. The calculated and experimental results are shown to agree under various scattering conditions when the spectral distributions of the scattered-radiation field are qualitatively different.

DOI
10.1070/qe1996v026n07abeh000740

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Numerical modelling is reported of the propagation of laser radiation in a resonant three-level medium. The transient nature and the spatial inhomogeneity of the investigated processes are taken into account. It is shown that the radiation is scattered into narrow cones and that the number and vertex angles of these cones depend on the experimental conditions. The spatiotemporal spectrum of the radiation field emerging from the scattering medium and the dependence of this spectrum on the laser radiation frequency are compared with the results of experiments carried out under similar conditions. The calculated and experimental results are shown to agree under various scattering conditions when the spectral distributions of the scattered-radiation field are qualitatively different.
Experimental and theoretical investigations were made of the characteristics of an 'anomalous' component of the scattering of high-intensity laser radiation in a resonant medium (sodium vapour) observed earlier in the frequency range ω L > ω D2 . The appearance of this component had been attributed by other authors to parametric downconversion. Contrary to this interpretation, the component in question was observed also at frequencies of ω L < ω D1 . An analysis showed that the generation of this component and its properties can be explained fully by a four-wave interaction in a gas of three-level atoms.
An analysis was made of four-photon interaction processes under conditions of two-photon resonance excitation of the 3 D sodium level by two-frequency radiation from a single-pulse picosecond YAG:Nd laser with frequency doubling and a KDP optical parametric oscillator. The spatial and frequency spectra of the four-photon parametric scattering (FPPS) were recorded and studied experimentally at various sodium vapor densities (10 15 –10 17 cm −3 ) and also using collinear and noncollinear excitation. It was found that the observed conical structure of the FPPS radiation may be interpreted by an analysis of whether the frequency and spatial phase-matching conditions were satisfied. Dependences of the intensity of the FPPS radiation on the intensity of the exciting radiation, the sodium vapor density, and the detuning of the exciting radiation frequency from the two-photon resonance were obtained.
The method of numerical simulation was used to study the effective lifetime of the excited level of the resonance transition in sodium and lithium vapour. Taking into account the partial frequency redistribution and the cylindrical geometry of the medium, the rate equations of the population balance of a two-level atom were solved with the equation of radiation transfer. The Biberman–Holstein escape factor was calculated as a function of the optical thickness of vapour for different geometries of the luminescing gas and different models of the frequency redistribution functions. The dependence of the escape factor on the optical thickness investigated experimentally by Romberg and Kunze (J. Quant. Spectrosc. Radiat. Transfer. 1988 39 99) is discussed.
A time-dependent theory for conical emission during near-resonant propagation of laser light in an atomic vapor, which includes full propagation for the laser and frequency sidebands in a nonlinear two-level medium is presented. The density-matrix equations for the dipole moment and population are solved in the dressed atomic frame. The polarization source terms are accurate to order \ensuremath{\gamma}/R, where \ensuremath{\gamma} is a damping constant and R is the generalized Rabi frequency. Analytical plane-wave solutions and numerical, cylindrically symmetric propagation simulations including diffraction are presented. It is shown that the calculations with cylindrically symmetric fields and atomic excitation profiles are incapable of accounting for the high levels of optical gain that are responsible for the intense conical emission observed in experiments. This result is at first surprising, since the model accounts rigorously for all of the physical phenomena that have been previously proposed as being responsible for generating large gains, and the calculation matches the symmetry of the observations. The lack of large calculated gain seems to imply the existence of higher-order (m>0)(m>0)(m>0) radial modes in the field for the experimental conditions that give rise to cone emission. In the simulations, however, the cylindrically symmetric fields do produce weak red-detuned cones with angular-frequency distributions similar to those seen in experiments.
The dual-colour excitation for D1 transition is analysed taking into account the hyperfine structure of sodium atomic vapour. The advancement of the probe and restoring fields are calculated through different time average schemes. The first scheme depends on the arrival time of the pulse. The other one depends explicitly on the arrival time of photons. The evolution of atomic states is described by the Liouville-von Neumann equation for the density matrix of the dressed atom. The spatiotemporal behaviour of radiation fields is described by the reduced Maxwell's field equations. We monitor the populations of atomic levels and calculate the scattered light intensity. The mean arrival time of photons is suitably defined in terms of the scattered light intensity and the total scattered light at a given distance.