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Quantum Electronics

Resonant Λ medium as a converter of the laser radiation frequency

D. V. Kosachev

Published Nov 30, 1995• 5 citations
Publisher

Abstract

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.

DOI
10.1070/qe1995v025n11abeh000540

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Journal of Experimental and Theoretical Physics Letters•Jun 1, 1998•1 citation
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.
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.
We present a theory of a continuous-wave light propagation in a medium of atoms with a double-$\ensuremath{\Lambda}$ configuration of levels. This is a configuration with a closed cycle of radiation-induced transitions. An interference of excitation channels in such closed-loop systems leads to a strong dependence of the atomic state on the relative phase and the relative amplitudes of applied electromagnetic waves. Therefore, the medium response may be controlled by the phases. On the other hand, the phases themselves change during the propagation. Thus the state of the medium and all the field parameters are tightly coupled to each other in the present problem. We consider the propagation of four-frequency laser radiation through the double-$\ensuremath{\Lambda}$ medium for two situations. At resonant or near-resonant excitation of atoms, both the medium and the field evolve into a nonabsorbing state. This state implies specific coherent superposition for atoms (``dark state''), and particular relations for the field phases, amplitudes, and frequencies. In this way, the propagation results in the phase, amplitude, and frequency matching of the laser waves. In the second case, one $\ensuremath{\Lambda}$ system in double-$\ensuremath{\Lambda}$ atoms is excited resonantly, while the second $\ensuremath{\Lambda}$ system is far off resonance. Such an excitation scheme ensures the preparation of atoms in the nearly dark state throughout the medium. Therefore, the total light energy is dissipated very weakly, whereas each individual laser wave can vary considerably along the propagation path. We have found that the resonant fields change as much as the far-detuned ones. The intensities oscillate sinusoidally with the optical length, with the energy being transferred back and forth between two waves in each frequency pair, resonant and far detuned. This gives the possibility for an almost lossless amplification of two of the laser waves, or an even generation of one of them.
In this work we investigate propagation of two laser pulses in the optically dense atomic medium (three-level Λ -system) in the case of a closed excitation contour. The closed excitation contour is created by additional microwave radiation which interacts with the low-frequency transition of the Λ -system. Two cases are considered: when the pulse duration is more and less then lifetime of the excited atomic level. It is shown that the propagation of the pulses depends on the relative phase of the fields. When the relative phase is zero, the pulses energy is absorbed linearly. When the relative phase is π / 2, the pulses exchange energy between each other.
We study the propagation of a bichromatic field in three-level and four-level media. In the case of a three-level medium, we consider the \ensuremath{\Lambda} configuration and demonstrate that if the upper level is not empty there is a critical value for the low-frequency coherence such that below this threshold and for intense fields, coherent bleaching occurs. This implies a sharp reduction of the field absorption and the fluorescence emission whereas above this threshold a parametric instability takes place. It corresponds to an amplification of the field that does not need a population inversion between the optical transitions. Finally we prove that the field alone cannot create a low-frequency coherence exceeding this threshold. Therefore we analyze the double-\ensuremath{\Lambda} configuration involving a four-level medium in which the upper and lower pairs of atomic levels have a low-frequency separation while optical transitions take place between the two pairs of states. An intense bichromatic field that is resonant with one upper state and the lower levels and a weak bichromatic field resonant with the other upper state and the same two lower states are sent into the medium. We analyze the limit in which the low-frequency coherence created between the lower pair of states has a relaxation time which is large. Then there will be population trapping in the lower states leading to coherent bleaching if there is no inversion between the upper levels but there will be amplification if there is inversion between the upper levels. In this way amplification at the optical transitions without population inversion between these states is realized.
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.
A solution is obtained for the system of Maxwell-Schrödinger equations describing the propagation of a laser pulse through a three-level Λ medium in which the initial atomic populations are in a specially prepared coherent superposition of low-energy states. This solution describes a new type of transparency which is characterized by the presence of conversion of the frequency of the incident pulse and can be used, specifically, to produce “optical keys” and frequency converters for laser radiation.