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

Beam-propagation numerical studies in three-level absorbers: nontrivial induced lenses and their spectral manifestations

Vladimir Leonardovich Derbov, Inna L. Plastun

Published May 3, 1994• 0 citations
Publisher

Abstract

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.

DOI
10.1117/12.175144

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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.
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.
In the domain of semiclassical formulation and for the Doppler-free atom–field interaction, we construct the optical Bloch equations involving an M-type six-level system coupled to two pump fields and a probe field. The response of the system is probed for different pump-induced transitions in double and triple-resonance situations. In order to obtain the coherent lineshapes (absorptive and dispersive), we use the usual perturbation method for obtaining the approximate analytical solutions to these coupled optical Bloch equations for the density matrix elements. The interferences between the probability amplitudes for different energy levels (dipole allowed and dipole forbidden) are taken care of. For off-resonance pump positions, the linewidths of the three probe transitions are insensitive to the pump Rabi frequencies. On the other hand, the shifts of the three resonance peaks are extremely sensitive to the pump Rabi frequencies. However, for on-resonance pump conditions, the sensitivities of pump Rabi frequencies on the linewidths of the resonance peaks and on the shifts of the resonance peak positions are opposite to those of their off-resonance counterparts. In particular, we have shown the asymmetric and symmetric Rabi splittings under different physical conditions, for non-zero and near-zero probe detuning, respectively. The Rabi splitting under triple-resonance conditions, significantly, modifies the dispersive lineshape at the centre of the absorption line. The two- and three-photon absorptions are also reported for different off-resonant pump positions.
When a two-level system interacts resonantly with a saturating pump laser, the absorption profile of a probe wave in the Rabi sidebands resembles two separate dispersion profiles. At sufficiently high probe intensity this effect is accompanied by a dispersive profile in the pump-wave absorption, considered as a function of the probe-wave frequency, and also by a dip in the population of the upper state of the two-level system. The relative stabilization of the ground state is interpreted in terms of two-laser-photon processes where absorption of a pump (probe) photon is followed by stimulated emission of a probe (pump) photon. The dispersive absorption profile is attributed to the competition between three- and four-photon scattering processes.
Results of numerical simulation of coaxial propagation of an intense pump beam and a weak probe beam in a three-level medium with different types of energy diagrams in conditions of inversionless amplification are presented. The effect of the beam self-action and diffraction on the spatial and frequency characteristics of the probe wave were studied. These effects, in combination with linear absorption and refraction, give rise to complex spatial profiles of gain along the beam propagation path. The annular structure of the amplified beam and a small asymmetry of its frequency characteristics, resulting from the nontrivial gain profile over the beam cross section, were found and studied.
We investigated the sideband instability by numerical integration of the Maxwell-Bloch equations for propagation of a nearly resonant pump laser and a weak probe laser in a system of two-level atoms. In an optically thick medium, the probe gain (absorption) spectrum becomes a function of propagation distance. We find that the well-known gain resonance at the generalized Rabi frequency Ω' is suppressed and a broad asymmetric gain region forms on each side of the laser frequency. For probe-pump detunings inside these gain regions, the field envelope breaks up into periodic traveling waves that are compared to the polycnoidal solutions of the sine-Gordon equation with periodic boundary conditions.