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Optics Letters

Spatial modification of a Gaussian beam on reflection from a saturable absorber

Sven R. Hartmann, Jamal T. Manassah

Published Sep 1, 1991• 9 citations
Publisher

Abstract

We calculate the reflection coefficient of a dielectric-gas interface including the nonlinear local field, saturation, and self-reflected wave effects. We specialize to collisionally broadened gases with absorption lengths that are necessarily small compared with an optical wavelength and preclude the use of the slowly varying amplitude approximation. The dependence of the reflectivity on the intensity of the incoming field is revealed through the changes that it induces in the transverse profile of a reflected Gaussian beam. These changes derive principally from effective aperturing effects in amplitude and phase.

DOI
10.1364/ol.16.001349

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We calculate the reflection coefficient of a dielectric-gas interface including the nonlinear local field, saturation, and self-reflected wave effects. We specialize to collisionally broadened gases with absorption lengths that are necessarily small compared with an optical wavelength and preclude the use of the slowly varying amplitude approximation. The dependence of the reflectivity on the intensity of the incoming field is revealed through the changes that it induces in the transverse profile of a reflected Gaussian beam. These changes derive principally from effective aperturing effects in amplitude and phase.
Intense light incident on a dense-gas--dielectric interface, from the dielectric side, is reflected because of the combined effect of the discontinuities in the index of refraction at the interface and at the transition region in the gas where the degree of atomic saturation changes abruptly. This latter discontinuity gives rise to a self-reflected wave. At low intensities this self-reflected wave is weak, the problem is linear, and the net reflected wave intensity taken as a function of frequency has a simple shape that should allow measurement of the hitherto undetected self-induced frequency shift in a collision-broadened gas at an absorption resonance. Calculations show that in the weak intensity regime, r'', the imaginary part of the reflection coefficient, is quasi-Lorentzian and shifted by an amount comparable to its width. At high light intensity r'' broadens, shifts, and distorts. The distortion, which nonuniformly modulates the Lorentzian shape, comes from an interference of the forward and self-reflected waves. In the wings of the resonance line the self-reflected wave can be neglected, and the shape of r'' although not distorted is shifted from where it would be if there were no local field correction.
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.
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.
Numerical solutions of the Maxwell-Bloch equations describing the nonlinear absorption of an IR laser field as it propagates across a collisionless molecular beam are presented. Calculations show the possibility that the laser field experiences a self-reflection inside the molecular beam while it is being absorbed. Since the density of the molecular beam changes smoothly in the radial direction, there are no reflections induced by its boundaries, and it constitutes an ideal system to study the self-reflected wave. The reflectivity of the molecular beam is predicted to be vanishingly small at low intensities but to increase dramatically as the nonlinear effects become significant.
We calculate the reflection coefficient for a light beam incident on the interface between a dielectric and a resonant atomic vapor to first order in the dipole polarization in the vapor. The angle of incidence and the polarization direction are chosen arbitrarily, and saturation is fully accounted for. The atoms are supposed to get deexcited at collisions with the surface. The resulting transient behavior of atoms leaving the surface is responsible for a nonlocal response. This spatial dispersion near the surface is known to produce a natural-linewidth-limited resonance in the vapor reflection coefficient at normal incidence. Our analysis shows that this sub-Doppler structure is broadened by the residual Doppler effect for non-normal incidence. This structure disappears at the critical angle for total internal reflection, where one predicts a conventional Voigt-type dispersion response, based on the complex-refractive-index approach. We also calculate the saturation broadening of the atomic response for large intensities. Beyond the critical angle, the spectral response suddenly shifts from dispersion to absorption line shapes. In the case of total internal reflection, the spatial dispersion leads to an additional Lorentzian broadening, which results from an effective imaginary Doppler shift at passage through the evanescent wave (transit-time broadening).