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

Numerical simulation of nonlinear resonance spectra in aperture-limited light beams having various profiles

Vladimir Leonardovich Derbov, Sergey K. Potapov, Inna L. Plastun, A. D. Novikov, Yurii N. Ponomarev, Yu. V. Kistenyov

Published Jul 1, 1992• 0 citations
Publisher

Abstract

Only for optically thin layers and plane waves may the intensity of a light wave be unambiguously expressed in terms of the nonlinear susceptibility of the medium. In aperture limited light beams the saturation parameter and the Stark shifts are local variables, while the output intensity of the pump and probe beams is an integral characteristic of the transmission process. The output spectrum is affected by diffraction, nonlinear refraction, and saturated absorption. The nonlinear refraction is a cause of a spectral line asymmetry which is well- known in saturation spectroscopy. In addition to usual line broadening, the saturated absorption causes specific beam effects, related to the formation of a self-induced transparency channel. The diffraction of the beam due to this self-induced aperture may result in the enhancement of the on-axis intensity, which is not a result of the self-induced lens effects. All these factors are taken into account by the mathematical model suggested in the present work. The propagation of the near-resonance saturating pump and non-saturating probe beams of various initial profiles through a homogeneously broadened two-level gas is simulated numerically. The calculations carried out make it possible to analyze the contribution of the propagation phenomena, mentioned above, to the output spectra of the beams.

DOI
10.1117/12.131175

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Only for optically thin layers and plane waves may the intensity of a light wave be unambiguously expressed in terms of the nonlinear susceptibility of the medium. In aperture limited light beams the saturation parameter and the Stark shifts are local variables, while the output intensity of the pump and probe beams is an integral characteristic of the transmission process. The output spectrum is affected by diffraction, nonlinear refraction, and saturated absorption. The nonlinear refraction is a cause of a spectral line asymmetry which is well- known in saturation spectroscopy. In addition to usual line broadening, the saturated absorption causes specific beam effects, related to the formation of a self-induced transparency channel. The diffraction of the beam due to this self-induced aperture may result in the enhancement of the on-axis intensity, which is not a result of the self-induced lens effects. All these factors are taken into account by the mathematical model suggested in the present work. The propagation of the near-resonance saturating pump and non-saturating probe beams of various initial profiles through a homogeneously broadened two-level gas is simulated numerically. The calculations carried out make it possible to analyze the contribution of the propagation phenomena, mentioned above, to the output spectra of the beams.
The numerical simulations of two coaxial laser beams, pump and probe, propagating in a three-level absorber are presented. The fixed-pump beam frequency and the variable-probe beam frequency are near-resonant to the adjacent transitions. Depending on the ratio of the population relaxation rates, either absorption or amplification of the probe field may occur, both demonstrating symmetric Rabi-splitted spectra of the absorption coefficient if the on-resonance pump intensity is high enough. In contrary to this, the spectra of the probe beam transmitted intensity are shown to be asymmetric due to the frequency-sensitive saturated refraction induced by the pump beam. The competition of level population changes and Rabi splitting is shown to cause the nontrivial induced lenses responsible for the complicated dependence of spectral asymmetry upon the pump intensity.
The transmission spectra of inversionless amplification are investigated. Propagation of a weak probe optical beam through a three-level medium pumped with a microwave strong beam is numerically modeled. Three various schemes of transitions under the conditions providing the amplification of the probe field without inversion are taken to calculate the atomic polarization, which enters the paraxial wave equations. Diffraction and self-action of beams due to nonlinear absorption and refraction are properly taken into account. These effects together with linear absorption and refraction form a complex distribution of gain across the beams. As a result the amplified beam acquires ring transverse patterns and slight asymmetry in the frequency characteristics.
Full space-time numerical modeling of near-resonance self-action of a beam, whose frequency is harmonically modulated in time, is presented. Maxwell-Bloch equations describing the propagation of the beam through a two-level medium with saturable absorption and refraction are solved using an original stable numerical scheme for multidimensional nonlinear Schrodinger equations. Delayed redistribution of intensity over the beam cross-section due to nonlinear self-focusing and self-phase-modulation effects is shown to affect the phase and the amplitude dynamics of the output signal in a rather nontrivial way, depending on the carrier laser frequency.
Light propagation through an ensemble of ultracold Rydberg atoms in an electromagnetically-induced-transparency (EIT) configuration is studied. In strongly interacting Rydberg EIT media, nonlinear optical effects lead to a nontrivial dependence of the degree of probe-beam attenuation on the medium density and on its initial intensity. We develop a Monte Carlo rate equation model that self-consistently includes the effect of the probe-beam attenuation to investigate the steady state of the Rydberg medium driven by two laser fields. We compare our results to recent experimental data and to results of other state-of-the-art models for light propagation in Rydberg EIT media. We find that for low probe field intensities, our results match the experimental data best if a density-dependent dephasing rate is included in the model. At higher probe intensities, our model deviates from other theoretical approaches, because it predicts a spectral asymmetry together with line broadening. These are likely due to off-resonant excitation channels, which, however, have not been observed in recent experiments. Atomic motion and coupling to additional Rydberg levels are discussed as possible origins for these deviations.