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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Small-Scale And Whole Beam Self-Focusing Of Very Intense Laser Beams In Saturable Absorbers

J. P. Babuel-Peyrissac, J. P. Marinier, C. Bardin, F. P. Mattar, Jiří Teichmann, Yves Claude, B. R. Suydam

Published Nov 20, 1985• 0 citations
Publisher

Abstract

We will examine here the influence of small-scale perturbations on light propagation inside a saturable atomic vapor, where the induced polarization is obtained by solving the steady-state optical Bloch equations. Numerical computations have been found to be in excellent agreement wich the results predicted by the analytical study of plane-wave perturbations in the linear regime. Computational results about initial non-plane laser beams are also of interest.

DOI
10.1117/12.976170

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We will examine here the influence of small-scale perturbations on light propagation inside a saturable atomic vapor, where the induced polarization is obtained by solving the steady-state optical Bloch equations. Numerical computations have been found to be in excellent agreement wich the results predicted by the analytical study of plane-wave perturbations in the linear regime. Computational results about initial non-plane laser beams are also of interest.
The propagation of laser light a few wavelengths inside a saturable absorber is theoretically studied. Computed steady-state solutions of the Maxwell–Bloch equations that describe the unidimensional propagation of a plane monochromatic wave, without introducing the slowly varying envelope approximation, show how saturation effects can influence this propagation. This can even lead to the appearance of a self-reflected wave inside the absorber because of the refractive-index changes that are induced by nonlinear coupling. One finds a close relation between the failure of the slowly varying envelope approximation and the presence of the self-reflected wave.
Reverse-saturable absorbers are of considerable interest for optical limiting. Using the electric dipole perturbation, we derived the rate equation for a five-level system describing reverse-saturable absorbers. Traditional theories for the propagating laser beam in these materials are expressed in terms of the optical intensity. However, with the introduction of high-power short-pulsed lasers, the propagation of light in these materials may be subject to nonlinear phenomena such as self-focusing and self-phase modulation. Furthermore, conventional theories treat the laser light as a continuous wave or as a very broad temporal pulse in which dispersive effects are neglected. In order to incorporate these other nonlinear or dispersive effects, and therefore determine their influence in reverse-saturable absorbers, we derived an equation for the propagation of the electromagnetic field, rather than the intensity, coupled to the rate equations for a five-level system. We also coupled our theory to experimentally measurable parameters for these materials and detailed the various physical approximations used to obtain the rate equations.
On-resonance self-action of a beam with periodically modulated amplitude in a two-level saturable absorber is studied numerically. When the period of modulation is comparable with relaxation times, one cannot describe the medium by means of susceptibility, and the response of the medium to the amplitude variation is not immediate. We solve the Bloch equations in each point of the medium to find this response correctly. Transient behavior followed by stable oscillations of population difference and polarization vector is shown to depend strongly on the frequency and amplitude of modulation. Beam propagation is considered using a simplified model of a thin absorber followed by free space, the propagation distance being small compared with the modulation wavelength. Manifestations of non-stationary response of the medium in the output intensity behavior are analyzed.
A comprehensive model of intense laser light propagation in a fully saturable medium is presented. This model employs the Maxwell-Bloch equations for a two-level atomic system. Light propagating through a medium creates intensity-dependent index of refraction gradients that reduce to a Kerr nonlinearity only for a weak field. When the laser detuning is positive, self-induced index gradients cause the beam to self-focus. Stationary filaments occur when self-focusing exactly balances diffraction. There exists a unique set of two-dimensional fundamental (and higher mode) solutions for which the filament transverse profile (not Gaussian in general) depends on the following quantities: density of saturable absorbers, laser detuning from resonance, laser power, and natural linewidth. (In contrast the Kerr solution does not have a unique filament diameter.) Emphasis will be placed on propagation of Gaussian incident beams; deviations from the stationary solution in either shape or power generally give rise to oscillating spatial patterns, including donutlike profiles, or beam breakup.
Propagation of laser light through a saturable absorber is theoretically studied. Computed steady state solutions of the Maxwell equations describing the unidimensional propagation of a plane monochromatic wave without introducing the slowly-varying envelope approximation are presented showing how saturation effects can influence the absorption of the field. At a certain range of refractive index and extintion coefficients, computed solutions display a very susprising behaviour, and a self-reflected wave appears inside the absorber. This can be useful for a new kind of biestable device, similar to a standard bistable cavity but with the back mirror self-induced by the light.