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Journal of Experimental and Theoretical Physics

Resonant transparency effects in an anisotropic medium with a permanent dipole moment

С. В. Сазонов

Published Oct 1, 2003• 13 citations
Publisher

Abstract

The propagation of a two-component laser pulse in an optically uniaxial medium is investigated under the conditions of the Zakharov-Benney resonance (viz., resonance of long and short waves). The short-wave ordinary component of the pulse, which is in resonance with the atomic subsystem, effectively generates a video pulse of the extraordinary wave (long-wave component). The latter dynamically detunes the ordinary pulse from the resonance and causes its phase modulation due to nonzero diagonal matrix elements of the dipole moment. An approximate operator approach is proposed for solving constitutive equations for the density matrix, which is equivalent to the asymptotic WKB method and makes it possible to reduce the analysis to solving a system of nonlinear wave equations for both components of the pulse. The possibility an extraordinary wave video pulse being generated with the help of a quasimonochromatic ordinary pulse with a longer wave-length. It is shown that, when the ordinary component dominates, the self-induced transparency mode is realized; in the opposite limit, the effect known as extraordinary transparency takes place. Solitary pulses corresponding to the latter case experience a decrease in the velocity of propagation, which is similar to that observed for self-induced transparency and practically do not change the population of quantum levels. Physical situations reducing the initial system of constituent and wave equations to familiar integrable models are analyzed.

DOI
10.1134/1.1625062

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Vector $0π$ pulse in anisotropic media

Guram T. Adamashvili

The system of equations of self-induced transparency (SIT) for extraordinary wave in uniaxial anisotropic media by means of generalized reduction perturbation method are transformed to the coupled nonlinear Schrödinger equations. It is shown that in the theory of SIT the second derivatives have significant role and leads to the formation of a vector $0π$ pulse oscillating with the sum and difference of the frequencies. An explicit analytical expressions for the profile and parameters of the nonlinear wave are obtained. It is shown that along with scalar $2π$ pulse, the vector $0π$ pulse is also the basic pulse of SIT and the scalar $0π$ pulse of SIT is only an approximation which can be considered in some special cases. The conditions of the existence of the nonlinear extraordinary wave depends on the direction of propagation. The profile of the vector $0π$ pulse in anisotropic crystal of ruby is presented with characteristic parameters which usually met in experiments.

arXiv:1907.10883•Jul 25, 2019•1 citation
The propagation of a two-component laser pulse in an optically uniaxial medium is investigated under the conditions of the Zakharov-Benney resonance (viz., resonance of long and short waves). The short-wave ordinary component of the pulse, which is in resonance with the atomic subsystem, effectively generates a video pulse of the extraordinary wave (long-wave component). The latter dynamically detunes the ordinary pulse from the resonance and causes its phase modulation due to nonzero diagonal matrix elements of the dipole moment. An approximate operator approach is proposed for solving constitutive equations for the density matrix, which is equivalent to the asymptotic WKB method and makes it possible to reduce the analysis to solving a system of nonlinear wave equations for both components of the pulse. The possibility an extraordinary wave video pulse being generated with the help of a quasimonochromatic ordinary pulse with a longer wave-length. It is shown that, when the ordinary component dominates, the self-induced transparency mode is realized; in the opposite limit, the effect known as extraordinary transparency takes place. Solitary pulses corresponding to the latter case experience a decrease in the velocity of propagation, which is similar to that observed for self-induced transparency and practically do not change the population of quantum levels. Physical situations reducing the initial system of constituent and wave equations to familiar integrable models are analyzed.
The distinctive features of the propagation of the two-component electromagnetic pulses in an anisotropic media are studied in the frameworks of the system of equations of the resonance of long and short waves. It is shown that an interaction of the light with the quantum systems, which have a constant dipole momentum nonequal to zero, occurs not only in the usual mode of the self-induced transparency, but also in two new modes. In the first one (supertransparency), the pulse propagation causes the significant change of the population density of quantum levels, while its group velocity remains close to linear one. In the second mode (extraordinary transparency), the group velocity of the pulse changes significantly, but the population of the levels is practically invariable. It is also noted that the largest change of the population takes place, if the carrier frequency of the solitons is less than the resonant frequency, at that the detuning value depends on the duration of the pulses.
Nonlinear two-component electromagnetic pulse propagation through a resonant axially symmetric anisotropic medium having a permanent dipole moment is analyzed under conditions of strong coupling between the ordinary (short-wavelength) and extraordinary (long-wavelength) pulse components. It is shown that a pulse can propagate through the medium in regimes different from self-induced transparency if its ordinary component is detuned off resonance. In particular, a pulse propagating in the regime of self-induced super-transparency substantially changes quantum-level populations, but its group velocity remains almost equal to the linear velocity. If a pulse propagates in the extraordinary transparency regime and the carrier-frequency detuning from resonance is small, then its group velocity is substantially lower, while the level populations remain virtually invariant. Regimes of propagation through weakly excited media under quasi-resonance conditions are also identified.
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.
The modes of nonlinear propagation of the two-component electromagnetic pulses through optically uniaxial media containing resonant particles are studied. The features of their manifestation in the "dense" media and in the media with expressed positive and negative birefringences are discussed. It is shown that exponentially and rationally decreasing solutions of the system of material and wave equations allow us also to describe the propagation of the pulses of the self-induced transparency in isotropic media in the case, when the direct electric dipole-dipole interaction between the resonant particles is taken into account.
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) .
Vector 0π0π0π pulse in anisotropic media
The system of equations of self-induced transparency (SIT) for extraordinary wave in uniaxial anisotropic media by means of generalized reduction perturbation method are transformed to the coupled nonlinear Schrödinger equations. It is shown that in the theory of SIT the second derivatives have significant role and leads to the formation of a vector 0π0π0π pulse oscillating with the sum and difference of the frequencies. An explicit analytical expressions for the profile and parameters of the nonlinear wave are obtained. It is shown that along with scalar 2π2π2π pulse, the vector 0π0π0π pulse is also the basic pulse of SIT and the scalar 0π0π0π pulse of SIT is only an approximation which can be considered in some special cases. The conditions of the existence of the nonlinear extraordinary wave depends on the direction of propagation. The profile of the vector 0π0π0π pulse in anisotropic crystal of ruby is presented with characteristic parameters which usually met in experiments.