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Technical Physics

Simultaneous self-focusing of two laser beams in a subthreshold coherent population trapping regime

Igor V. Kazinets, Boris G. Matisov, Alexander Yu. Snegirev

Published Jul 1, 1997• 3 citations
Publisher

Abstract

The propagation of two-component laser radiation in a medium consisting of atoms with a Λ level scheme is investigated. The simultaneous self-focusing of two beams is considered. The main features of this phenomenon are: 1) lowering of the self-focusing threshold by several orders of magnitude in comparison with the known case of saturation of a transition in a two-level atom; 2) a strong dependence of the character of the propagation of the radiation on the difference between the detunings of the two frequency components of the field from resonance, which is associated with fulfillment of the two-photon resonance condition.

DOI
10.1134/1.1258729

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 10, 1996•0 citations
The propagation of two-component laser radiation in a medium consisting of atoms with a Λ level scheme is investigated. The simultaneous self-focusing of two beams is considered. The main features of this phenomenon are: 1) lowering of the self-focusing threshold by several orders of magnitude in comparison with the known case of saturation of a transition in a two-level atom; 2) a strong dependence of the character of the propagation of the radiation on the difference between the detunings of the two frequency components of the field from resonance, which is associated with fulfillment of the two-photon resonance condition.
We study the features of spatial and temporal evolution of two powerful short different-wavelength laser pulses interacting with optical dense three-level Lambda-type medium under condition of coherent population trapping for the general case of unequal transition oscillator strengths. The pulses are simultaneously sent into an atom. The durations of probe and coupling pulses T1,2T_{1,2}T1,2​ (T2>T1T_2>T_1T2​>T1​) are supposed to be shorter than all relaxation times in the medium. We present analytical and numerical solutions of the self-consistent set of coupled Schr\\"{o}dinger equations and reduced wave equations in adiabatic limit with taking into account the first non-adiabatic correction. The adiabaticity criterion with account of pulse propagation is studied. We find that propagation dynamics depends on the relationship between the transition oscillator strengths. It is shown that at the initial stage of propagation the envelopes of the pulses slightly change along the length of the medium. This distance can be large compared to one-photon resonant absorption length of the medium. Also it is possible a regime of complete reemitting of the probe pulse into the coupling one during propagation. A spatial evolution of the atomic Raman coherence is investigated in detail too.
A theoretical investigation is made of the propagation of two-frequency laser radiation in an optically dense Λ medium in the presence of an rf field which is in resonance with a transition between the lower levels of a Λ-like system of an atom. It is shown that, depending on the phase and amplitude of the rf field and on the initial phases and intensities of the laser waves, one laser wave may be amplified at the expense of the energy of the other wave, or coherent bleaching of the medium (propagation of both waves without intensity losses) may take place.
We derive the equations describing the dynamics of an ensemble of atoms with (Lambda) - scheme of levels driven by two coherent resonant fields in a case when cooperative relaxation prevails over usual incoherent spontaneous emission. We investigate numerically temporal dynamics of mean values of the collective atomic operators. When the two-photon resonance condition is fulfilled then all atoms tend to be trapped in a coherent dark state, so coherent population trapping arises in a case of cooperative decay. Most important values characterizing this phenomenon such as the width of the black line and the time of initial transient stage of evolution are evaluated.
We study the dynamics of the phase pulses of laser radiation with two resonant frequency components propagating in an atomic three-level Λ type medium under coherent population trapping. Using the density matrix adiabatic approach we show that the effect of a very large slowing down occurs not only for amplitude pulses, but also for phase pulses. The group velocity of phase pulses can be controlled by the amplitudes of resonant fields. The analytical solution describing the mutual influence of the phase modulation of one field component on another is obtained.
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.
The paper presents a theoretical investigation of propagation of two frequency laser radiation in resonant (Lambda) -medium driven by a radiofrequency field on the transition between the two bottom levels. It is established that there is dramatic dependence of the character of propagation of radiation along the medium on phase and amplitude of the radiofield and on initial phases and intensities of the optical fields. We show that both amplification of one wave at the expense of the energy of another wave and transparency of the medium produced by population trapping can take place.