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Optics and Spectroscopy

Soliton-induced transparency of inhomogeneously broadened three-level atoms

V. V. Kozlov, Elena V. Kozlova

Published May 1, 2010• 2 citations
Publisher

Abstract

The effect of soliton-induced transparency (SOIT) that arises for a weak pulse that interacts with one of allowed transitions of inhomogeneously broadened three-level atoms with the V configuration of the levels under the action of a self-induced transparency soliton that simultaneously interacts with the adjacent transition is studied theoretically. The effect is explained by phasing of the ensemble of dipoles oscillating with different frequencies in the soliton field. The weak pulse is locked by the soliton, so that both pulses propagate with the same velocity independently of the ratio of the propagation constants. If the latter are equal, the weak pulse loses no energy; when they are different, the rate of energy loss is considerably slower than it follows from Beer’s law.

DOI
10.1134/s0030400x10050176

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The effect of soliton-induced transparency (SOIT) that arises for a weak pulse that interacts with one of allowed transitions of inhomogeneously broadened three-level atoms with the V configuration of the levels under the action of a self-induced transparency soliton that simultaneously interacts with the adjacent transition is studied theoretically. The effect is explained by phasing of the ensemble of dipoles oscillating with different frequencies in the soliton field. The weak pulse is locked by the soliton, so that both pulses propagate with the same velocity independently of the ratio of the propagation constants. If the latter are equal, the weak pulse loses no energy; when they are different, the rate of energy loss is considerably slower than it follows from Beer’s law.
The effect of solitoninduced transparency (SOIT) that arises for a weak pulse that interacts with one of allowed transitions of inhomogeneously broadened threelevel atoms with the V configuration of the levels under the action of a selfinduced transparency so liton that simultaneously interacts with the adjacent transition is studied theoretically. The effect is explained by phasing of the ensemble of dipoles oscillating with different frequencies in the soliton field. The weak pulse is locked by the soliton, so that both pulses propagate with the same velocity independently of the ratio of the propagation constants. If the latter are equal, the weak pulse loses no energy; when they are different, the rate of energy loss is considerably slower than it follows from Beer's law.
In the limit of pulse durations that are shorter than the characteristic times of atomic decays, the dynamics of the propagation of a probe light pulse under the action of a driving pulse in the form of a self-induced transparency soliton applied to the adjacent transition of the V -scheme is considered. For a three-level absorber, it is shown that, in the absence of two-photon inhomogeneous broadening, the effect of soliton-induced transparency (SOIT) for the probe field takes place, which consists of the probe pulse undergoing forced localization by the driving pulse and propagates further without a change in the energy or shape. This type of transparency has no threshold with respect to both the energy and the area and is observed for arbitrarily weak pulses. The SOIT effect disappears in the presence of a two-photon inhomogeneous broad-ening. The effect of Raman amplification in a three-level amplifier with the Raman population inversion is considered. It is demonstrated that, under the action of the two-photon inhomogeneous broadening, the effect of Raman amplification becomes a threshold effect. The broader the two-photon inhomogeneous contour, the larger the Raman inversion required to initiate generation.
We theoretically show that a self-induced transparency (SIT) soliton and a Bragg soliton can coexist in a nonlinear photonic band gap (PBG) medium doped uniformly with inhomogeneous-broadening two-level atoms. The Maxwell-Bloch equations for the pulse propagating through such a uniformly doped PBG structure are derived first and further reduced to an effective nonlinear Schrödinger equation. This model describes an equivalent physical mechanism for a Bragg-soliton propagation resulting from the effective quadratic dispersion balancing with the effective third-order nonlinearity. Because the resonant atoms are taken into account, the original band gap can be shifted both by the dopants and the instantaneous nonlinearity response originating from an intense optical pulse. As a result, even if a SIT soliton with its central frequency deep inside the original forbidden band, it still can propagate through the resonant PBG medium as long as this SIT soliton satisfies the effective Bragg-soliton propagation. An approximate soliton solution describing such coexistence is found. We also show that the pulse width and group velocity of this soliton solution can be uniquely determined for given material parameters, atomic transition frequency, and input central frequency of the soliton. The numerical examples of the SIT soliton in a one-dimensional As2S3-based PBG structure doped uniformly with Lorentzian line-shape resonant atoms are shown. It is found that a SIT soliton with approximately 100-ps width in such a resonant PBG structure can travel with the velocity being two orders of magnitude slower than the light speed in an unprocessed host medium.
We study the effects of dispersion in carrier waves on the properties of soliton self--induced transparency (SIT) in two level media. We found substantial impact of dispersion effects on typical SIT soliton features. For example, the degree of SIT pulse velocity slowing down (acceleration) is determined by the ratio of the incoming pulse frequency over atomic transition frequency - x=ω/ω0x=ω/ω_0x=ω/ω0​. Specifically, an immediate pulse stopping is predicted for absorbing media when pulse duration time exceeds some critical value. In the sharp line limit stopping may emerge only for frequency ratio above unity, while for the inhomogeneously broadened systems it appears irrespective of the value of xxx. Analysis performed on the basis of Mcall\& Hahn \textit{Area theorem} implies that pulse stopping is achieved when Ber's absorption coefficient approaches infinity, that is, pulse energy is fully absorbed in the medium. In the case of amplifying media super-luminal motion is predicted as in the case of resonance. However, there is a lowest value in the frequency ratio below which the pulse velocity tends to the sub-luminal region. These new features of the SIT phenomenon open novel ways on how it may be exploited for the control of electromagnetic wave radiation in two-level media. This may be achieved by varying frequency ratio.
Using numerical simulations, we study propagation of ultrashort light pulses in an inhomogeneously broadened two-level medium. There are two main issues in our study. The first one concerns the transient process of self-induced transparency soliton formation, in particular, the compression of the pulse which seems to be more effective in the case of homogeneous broadening. The second question deals with the collisions of counter-propagating solitons. It is shown that the level of inhomogeneous broadening has a substantial effect on the elasticity of such collisions.