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International Conference on Actual Problems of Electron Devices Engineering

Theory of precursor-pulse forming under conditions of quasi-resonant laser pulse interaction with inhomogeneously broadened quantum transition

L.A. Vershinin, A E Dmitriev, E.I. Dmitriyeva, Oleg M. Parshkov, A.L. Pisnoi

Published Jun 25, 2003• 0 citations
Publisher

Abstract

The peculiarities of precursor-pulse forming under conditions of self-induced transparency with relaxation processes are discussed. The influence of phase modulation processes on the 2/spl pi/-pulse and precursor pulse propagation is investigated. The possibility of full depression of 2/spl pi/-pulse and propagation of alone precursor-pulse is shown. The convenience with experimental results concerned with observation of self-induced transparency in rubidium vapor is demonstrated.

DOI
10.1109/apede.2002.1044946

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Physical Review•Jul 10, 1969•1,394 citations
The peculiarities of precursor-pulse forming under conditions of self-induced transparency with relaxation processes are discussed. The influence of phase modulation processes on the 2/spl pi/-pulse and precursor pulse propagation is investigated. The possibility of full depression of 2/spl pi/-pulse and propagation of alone precursor-pulse is shown. The convenience with experimental results concerned with observation of self-induced transparency in rubidium vapor is demonstrated.
The quasi-resonance interaction of a laser pulse with an inhomogeneously broadened quantum transition is numerically simulated under conditions corresponding to the experiment on the study of self-induced transparency in rubidium vapours. It is shown that the experimental shift of the pulse spectrum is caused by the initial stage of the formation of a precursor pulse and the influence of irreversible relaxation. It is found that the precursor pulse is more stable to the destructive action of relaxation than the 2π pulse and appears even in the case when the input pulse area is insufficient for the formation of the 2π pulse.
The results of a numerical simulation of the evolution of a precursor pulse are presented. This pulse exists at the stage of the conversion of a quasi-resonance input pulse into a 2π pulse considered in the theory of self-induced transparency. Calculations have shown that the efficiency of precursor-pulse formation increases as the input laser pulse shortens and its area approaches π. The results of a numerical analysis of the known experiments on the observation of a precursor pulse in ruby crystals are also presented. In one of the cases considered, the calculation results cast some doubt on the interpretation of the experiment adopted earlier.
Theoretical research of propagation effect of ultrashort optical pulse under conditions of coherent interaction with two resonant transitions simultaneously is presented. One of the transitions is tuned in exact resonance with pulse carrier frequency; the other is distanced much more than spectral pulse width, thus the adiabatic following approximation may be applied. Interaction between the pulse and far-resonant transition is described by wave equation with nonlinear index of refraction in the form of Lorentz function for field amplitude. This wave equation is solved together with Bloch equations for the exact resonant transition. The solution in the form of stationary phase-modulated pulse is obtained, and 2π-pulse of self-induced - transparency is the special case of this solution. The obtained solution has a square under pulse envelope less than 2π, and with increasing of far-resonant transition absorption coefficient the pulse square decreases. The effect can be used for reducing of the transparency threshold of the resonant medium below pi.
The results of theoretical research of the propagation effect of an ultrashort optical pulse under the conditions of coherent interaction with two resonant transitions are presented. One of the transitions is tuned to exact resonance with the pulse carrier frequency; the other is distanced by much more than the pulse spectral width, thus the adiabatic following approximation may be applied to it. The interaction between the pulse and the far-from-resonance transition is described by the wave equation with the nonlinear index of refraction in the form of the Lorentz function of the field amplitude. This wave equation is solved together with the Bloch equations for the exact resonant transition. The solution in the form of the stationary phase-modulated pulse is obtained, and (pi) -pulse of self-induced transparency is the special case of this solution. The obtained solution has the area under the pulse envelope less than (pi) , and with increasing the absorption coefficient of the far-from-resonance transition the pulse area decreases. The effect can be used for reducing the transparency threshold of the resonant medium below (pi) .
The results of a theoretical investigation of the evolution of a probe pulse under electromagnetically induced transparency in the Λ -scheme of degenerated inhomogeneously broadened quantum transitions are presented. It supposed that the interacted light fields are elliptically polarized, and their influence on the medium can be either strictly resonant or quasiresonant. It is demonstrated that the probe pulse in the medium can be presented as the sum of two normal modes, i.e. quasi-monochromatic elliptically polarized fields propagating independently of each other. Due to the fact that velocities of normal mode pulses are different, a single probe pulse entering a medium splits into individual pulses inside of the medium, each of which transfers the energy of one of the normal modes. If normal modes are not phase modulated at the input surface, then in the case of quasi-resonance they become phase modulated during propagation in the medium, whereas this does not occur in the case of strict resonance. The total probe field, which is the sum of normal modes, has phase modulation before it splits into the mode pulses in cases of both strict resonance and quasi-resonance, even if it does not have it on the input surface.
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.