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

Scale symmetry breaking in a coherently excited cascade amplifier

Jamal T. Manassah, Barry M. Gross

Published May 3, 1994• 1 citation
Publisher

Abstract

We analyze the temporal development of a seed signal propagating in an ensemble of three-level atoms initially pumped by a two- photon excitation pulse. In an incoherently prepared system, the medium acts as a two-level system. Such a system is scale- invariant and therefore its dynamics are uniquely determined by the value of (alpha) L. On the other hand, a coherently prepared system is not scale invariant, leading to more complicated dynamics. We show that at low optical gain the amplification is reduced when the pumping is coherent. We further show that at high inversion there is an exponential increase in the radiation emitted from the lower transition in an initially prepared coherent system.

DOI
10.1117/12.175147

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We analyze the temporal development of a seed signal propagating in an ensemble of three-level atoms initially pumped by a two- photon excitation pulse. In an incoherently prepared system, the medium acts as a two-level system. Such a system is scale- invariant and therefore its dynamics are uniquely determined by the value of (alpha) L. On the other hand, a coherently prepared system is not scale invariant, leading to more complicated dynamics. We show that at low optical gain the amplification is reduced when the pumping is coherent. We further show that at high inversion there is an exponential increase in the radiation emitted from the lower transition in an initially prepared coherent system.
We consider a medium composed of three-level (cascade scheme) atoms prepared with coherence between the upper and the ground states (a yoked superfluorescence system). We obtain an analytical solution for propagation of seed pulses which are resonant with the upper and lower transitions for arbitrary level populations and pulse shapes. We find that if the initial coherence is large enough and the intermediate level is populated the system can have gain without population inversion. Coherence can also yield gain suppression in the inverted medium. We obtain conditions for the gain in terms of level populations and coherence.
One consider the amplification of pulses of coherent light in the resonant three-level active media that is excited by short power pulse of coherent light according to the common-upper- level double resonance scheme. The radiation with major frequency (pump) is supposed to be stronger than one with minor frequency (signal). The self-induced transparency is supposed to be established in the pump channel. The exponential growth of stationary shape short signal pulses is studied mainly. One shows that when any described here conditions for initial signal pulse shape are meeting the stationary gained signal pulse of complicated form can be formed. The gains of these pulses are less than ones for signal pulses of quasi-hyperbolic-secant form. Therefore in the case of incomplete condition meeting the competition between the exponentially growing signal pulses with different gains and shapes leads finally to the overwhelming of signal pulse with quasi-hyperbolic-secant-shape form. The effect of inhomogeneous broadening of spectral transition lines on the parameters of signal pulses was studied too. Evaluations that were carried out for any atomic gases show that described in this paper phenomena can be produced at realistic levels of power and duration of pump and signal pulses.
We study the effects of propagation through an extended sample of two- and three-level atoms on the coherent accumulation of excitation by an ultrashort pulse train. In the two-level case, previous pulses in the train may prepare the medium such that a later pulse may experience amplification and absorption in different positions inside the sample. For a large number of pulses, the atomic medium may be saturated by the train, and some pulses propagate without experiencing either absorption or amplification. In general, absorption of the resonant pulse frequency during propagation compromises the accumulation efficiency. In the three-level case, the coherent accumulation of excitation leads to electromagnetically induced transparency of the pulse train, and the pulses exit the medium without any distortion in their temporal profile.
We analyze the inversionless gain in a three-level ladder system by replacing the usual coherent coupling field with an incoherent field. Surprisingly, it is found that one can obtain inversionless amplification of a weak probe even in the absence of a coherent field in the model. We conclude that gain is determined by the ensemble average of the product of the two-photon coherence and the ``effective Rabi frequency'' of the field. Thus, even though the incoherent pump reduces the two-photon coherence, gain can be restored by choosing sufficiently high strengths of the incoherent field.
We explore the laser-pulse propagation dynamics when one, two, or three pulses resonantly drive a coherently prepared four-level medium in a tripod configuration. If the system is prepared in a coherent superposition of two of the lower levels, we show that two incident resonant pulses can parametrically generate a third pulse in the medium. Over short distances, the propagation of this generated pulse can be partially controlled by varying the Rabi frequency of one of the driving fields. For a medium prepared in a coherent superposition of the three lower levels, we obtain a general expression for a three-photon Beer's length. Under specific conditions, the medium can either become completely opaque or completely transparent to three incident resonant pulses. Moreover, a single incident pulse can be used to parametrically generate two additional pulses. Finally, a general relationship is found that links the amplitudes of the initial superposition of states and the amplitudes of the pulses at large distances in the medium, implying that the initial superposition can be used to engineer the amplitudes of the exiting pulses.