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Optics and Spectroscopy

Raman amplification of ultrashort light pulses in inhomogeneously broadened three-level systems

V. V. Kozlov, Elena V. Kozlova

Published Jul 1, 2009• 5 citations
Publisher

Abstract

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.

DOI
10.1134/s0030400x09070194

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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.
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.
Above a critical power threshold for a given pulse width, a short pulse of coherent traveling-wave optical radiation is observed to propagate with anomalously low energy loss while at resonance with a two-quantum-level system of absorbers. The line shape of the resonant system is determined by inhomogeneous broadening, and the pulse width is short compared to dissipative relaxation times. A new mechanism of self-induced transparency, which accounts for the low energy loss, is analyzed in the ideal limit of a plane wave which excites a resonant medium with no damping present. The stable condition of transparency results after the traversal of the pulse through a few classical absorption lengths into the medium. This condition exists when the initial pulse has evolved into a symmetric hyperbolic-secant pulse function of time and distance, and has the area characteristic of a "$2\ensuremath{\pi}$ pulse." Ideal transparency then persists when coherent induced absorption of pulse energy during the first half of the pulse is followed by coherent induced emission of the same amount of energy back into the beam direction during the second half of the pulse. The effects of dissipative relaxation times upon pulse energy, pulse area, and pulse delay time are analyzed to first order in the ratio of short pulse width to long damping time. The analysis shows that the $2\ensuremath{\pi}$ pulse condition can be maintained if losses caused by damping are compensated by beam focusing. In an amplifying inhomogeneously broadened medium an analytic "$\ensuremath{\pi}$ pulse area" solution is presented in the limit of a sharp leading edge of the pulse. The dynamics of self-induced transparency are studied for the particular effects of Doppler velocities upon a resonant gas. The analysis of transparency for random orientations of dipole moments associated with degenerate rotational states yields modified forms of self-induced transparency behavior, which indicates a finite pulse energy loss as a function of distance in some cases. The effect of self-induced transparency on the photon echo is considered. Experimental observations of self-induced transparency have been made in a ruby sample at resonance with a pulsed ruby-laser beam. Single and multiple $2\ensuremath{\pi}$ pulse outputs have been observed, and pulse areas measured in the range of $2\ensuremath{\pi}$. The experimental results are compared with the predictions of the ideal-plane-wave theory. Deviations from the ideal-plane-wave theory are discussed. An analysis is made of the effect of a transverse mode of the propagating beam upon the transparency properties of the pulse.
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.
An effective two-level Maxwell-Bloch formalism is developed to describe various time-dependent phenomena in a three-level V-type system. The Maxwell-Bloch equations govern the temporal evolution of a probe field while a strong driving field is applied on the adjacent transition. The main assumption adopted throughout the paper is that the spontaneous decay rate on the coherently driven transition exceeds the decay rate on the probe transition as well as inverse time variations of both pulses. It is shown that the probe pulse interacts with such a medium in a manner similar to that in a self-induced transparency. An amplification without inversion of a relatively short probe pulse while propagating through an optically thick atomic medium is analyzed.