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Journal of Experimental and Theoretical Physics

Coherent interaction between phase-modulated light pulses and an active medium of two-level particles with inhomogeneous broadening

É. M. Belenov, Peter G. Kryukov, A. Nazarkin, I. P. Prokopovich

Published Jul 1, 1991• 0 citations
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Abstract

It is shown that induced transitions of an ensemble of two-level articles with an inhomogeneously broadened line in the field of a phase-modulated pulse are analogous to Landau-Zener inelastic transitions in molecules when their terms cross. Even for T% T:, where T and T: are, respectively, the pulse width and the inhomogeneous relaxation time of the medium, a transition of particles of the entire spectrum ( T:) - ' from an upper to a lower level is possible, signifying the complete removal by the pulse of the energy stored in the active medium. Analysis of the dynamics of a phase-modulated pulse by means of the Maxwell-Bloch equations shows, in addition, the possibility of amplifying it without the development of field-amplitude oscillations.

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It is shown that induced transitions of an ensemble of two-level articles with an inhomogeneously broadened line in the field of a phase-modulated pulse are analogous to Landau-Zener inelastic transitions in molecules when their terms cross. Even for T% T:, where T and T: are, respectively, the pulse width and the inhomogeneous relaxation time of the medium, a transition of particles of the entire spectrum ( T:) - ' from an upper to a lower level is possible, signifying the complete removal by the pulse of the energy stored in the active medium. Analysis of the dynamics of a phase-modulated pulse by means of the Maxwell-Bloch equations shows, in addition, the possibility of amplifying it without the development of field-amplitude oscillations.
Frequency chirped pulse interaction with inhomogeneously broadened two-level active medium when the pulse width is shorter than the homogeneous relaxation time T2 (coherent interaction) is studied theoretically. It is shown that, unlike the case of incoherent interaction when only half an energy stored can be converted into field, in the nonlinear coherent regime full extraction of active medium energy is possible. The analogy of the effect with Landau–Zener transition between crossing molecular curves is pointed out. Giving high-energy output at relatively low peak intensities, this nonlinear mechanism of energy extraction can be useful for excimer lasers.
An accurate and effective numerical method is presented to solve the Maxwell-Bloch equations that are used to describe the optical pulse propagation and interaction with inhomogeneously broadened two-level medium.The convergence and stability of this numerical method are proved by comparing with the analytic solutions and area theorem derived under special condition.The simulations of arbitrary conditions is discussed by employing this method and analyze the pulse evolution for different detunings,relaxation times and inhomogeneously broadened linewidthes.The established numerical method provides a good way to have further study about the coherent interaction of short optical pulses with resonant mediums,and can be used to solve the corrections of Maxwell-Bloch equations.
The theoretical results on the study of the evolution of electromagnetically induced transparency probe pulses with frequency modulation on the input surface of the active medium and possible frequency modulation of the control field are presented. It was shown that the presence of a sufficiently large frequency modulation of the input probe pulse (an instantaneous frequency offset of the order of an inhomogeneous line width resonant with the probe field) does not lead to the mode structure destruction of this field inside the active medium. At the same time, the transparency of the medium for the probe field is noticeably reduced, but it remains quite large. With frequency modulation of the control radiation, the mode regime of the probe field propagation is realized at least as long as the deviation of the frequency of the control field is less than half the width of the line of the probe quantum transition. However, the transparency of the medium for the probe field decreases in comparison with the case of the absence of frequency modulation. The analysis is carried out for the Ʌ-scheme of inhomogeneously broadened quantum transitions between the 3P0, 3P01 and 3P2 levels of the 208Pb isotope.
The gap 2\ensuremath{\pi} pulse or gap solitary wave of self-induced transparency at an inhomogeneously broadened line of a resonant Bragg periodical structure has been found theoretically as an exact solution of the coupled-mode Maxwell-Bloch equations. In the case of a slight violation of the Bragg condition at exact two-level resonance, the analytical solution for the gap 2\ensuremath{\pi} pulse with phase modulation has been obtained. Furthermore, the existence of an oscillating pulse that periodically changes in amplitude and in the sign of its velocity has been numerically shown.
On the basis of Bloch's equations an analytical expression is obtained for the pulsed saturation signal of a two-level quantum system with allowance for inhomogeneous line broadening. It is shown that in this case the signal drop is exponential over the initial portion and nonexponential for long times. It is found that starting from a certain time, which depends on the field magnitude, relaxation parameters, and inhomogeneous width of the line, a through appears in the line contour, the depth and width of which increases with an increase in pulse duration. At smaller durations of the pulse, when the line is bell-shaped, an exponential decay of the signal indicates saturation of homogeneously broadened line. Comparison of the results obtained in an experiment on pulsed saturation in ruby shows that at large amplitudes of the field and considerable inhomogeneous broadening, one observes a deviation from the Bloch theory manifesting itself as a biexponential drop in the pulsed saturation signal A conclusion is drawn that the Bloch theory satisfactorily describes the experiment until the effective time of energy transfer to the lattice is smaller than the time of the spectral propagation of excitation.
Maxwell-Bloch system describing the resonant propagation of electromagnetic pulses in both two-level media with degeneracy in angle moment projection and three-level media with equal oscillator forces is considered. The inhomogeneous broadening of energy levels is accounted. Binary Darboux Transformation generating the solutions of the system is constructed. Pulses corresponding to the transition between levels with largest population difference are shown to be stable. The solution describing the propargation of pulses in the medium exited by the periodic wave is obtained. The hierarchy of infinitesimal symmetries is obtained by means of Darboux transformation.