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Laser Physics Letters

Self-induced transparency in a system of resonant–quasiresonant transitions

С. В. Сазонов, N. V. Ustinov

Published Nov 20, 2020• 0 citations
Publisher

Abstract

Abstract The effect of self-induced transparency is investigated for a three-level system with a V -scheme of the allowed transitions in the case where one of the transitions is resonant while another one is quasiresonant. The generalized system of the wave and material equations for the resonant transition, taking into account the presence of a quasiresonant transition, is derived. This system is integrable, and its soliton solutions are investigated. It is shown that quasiresonant transition has an influence on the profile of the optical soliton and leads to its phase modulation. The conditions under which the propagation of the soliton is followed by the full inversion of the populations of quantum levels of the resonant transition are established.

DOI
10.1088/1612-202x/abc75d

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Abstract The effect of self-induced transparency is investigated for a three-level system with a V -scheme of the allowed transitions in the case where one of the transitions is resonant while another one is quasiresonant. The generalized system of the wave and material equations for the resonant transition, taking into account the presence of a quasiresonant transition, is derived. This system is integrable, and its soliton solutions are investigated. It is shown that quasiresonant transition has an influence on the profile of the optical soliton and leads to its phase modulation. The conditions under which the propagation of the soliton is followed by the full inversion of the populations of quantum levels of the resonant transition are established.
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) .
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 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.
One-dimensional pulse propagations in the electromagnetically induced media are studied. The Maxwell–Bloch equations for a three-level medium are simplified with the approximations of slowly varying amplitudes, negligible irreversible relaxations and exact resonances. An analysis is made for the case where the integrable condition is satisfied; the oscillation strengths for the two transitions are equall. Through the Bäcklund transformation, one-soliton solutions including the so-called simulton are derived.
Special features of generating a self-induced transparency in a medium with both resonant and non-resonant (Kerr-type) nonlinearities are considered. Soliton solutions of the Maxwell-Bloch equations are found, taking into account the diffraction divergence of the light beam. It is shown that solitons emerge in such a medium under conditions of two-dimensional optical beam scanning along the medium surface, and have non-coinciding propagating directions of the amplitude and phase fronts. As a necessary condition for the existence of solitons, there is a definite relationship between the scanning velocity and the parameters of the medium and radiation.
The temporal envelope profile and the phase of a steady-state pulse propagating through a resonant medium in the presence of nonresonant nonlinearity are derived. The formation of solitonlike pulses takes place as a result of the balance of the self-phase modulation generated by nonresonant nonlinearity and the nonlinear resonant group-velocity dispersion induced by the self-induced-transparency effect in a resonant medium. Self-phase-modulation action leads to distortion of the pulse when its power and inverse duration exceed the critical values Pcr and τcr-1. We show the destructive role of self-phase modulation in the case of self-induced-transparency pulse generation in a laser with erbium-doped fiber as an intracavity coherent absorber.