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Annual Meeting Optical Society of America

Coherent resonant pulse propagation in a Kerr absorber

Ljubomir Matulic, G. F. Torres-Cisneros, J. J. Sánchez-Mondragón

Published Jan 1, 1989• 0 citations
Publisher

Abstract

We present a numerical study of the nonsteady state pulse propagation in a resonant inhomogeneously broadened absorber embedded in a dielectric medium with a Kerr-type nonlinearity. We abandon the a priori assumption for the existence of steady state solutions and examine the problem from a more physical point of view, i.e., we study the way in which the pulse actually propagates in the resonant Kerr medium and whether it eventually evolves toward a steady state. We find that the individual atomic dipoles are dephased and that their evolution depends on detunings. We believe that this is the reason for small energy losses which deny the attainment of a truly steady state pulse.

DOI
10.1364/oam.1989.fx6

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Journal of Physics A Mathematical and General•Jul 1, 1979•16 citations
We present a numerical study of the nonsteady state pulse propagation in a resonant inhomogeneously broadened absorber embedded in a dielectric medium with a Kerr-type nonlinearity. We abandon the a priori assumption for the existence of steady state solutions and examine the problem from a more physical point of view, i.e., we study the way in which the pulse actually propagates in the resonant Kerr medium and whether it eventually evolves toward a steady state. We find that the individual atomic dipoles are dephased and that their evolution depends on detunings. We believe that this is the reason for small energy losses which deny the attainment of a truly steady state pulse.
We present a numerical study of the non-steady-state pulse propagation in a resonant inhomogeneously broadened absorber embedded in a dielectric medium with a Kerr-type nonlinearity. We find that the individual atomic dipoles are dephased and that their evolution depends on their detunings. We think that this is the reason for small energy losses that prevent the pulse from attaining a truly steady-state nature. We discuss the implications of this result in relation to previous studies. Our results point to the existence of near-steady-state Kerr pulses, similar to the ideal solitons.
We consider the effect of a background dielectric on the steady-state propagation of a laser pulse through inhomogeneously broadened two-level atoms embedded in the dielectric. Because this problem apparently does not admit of analytic solutions, we have solved it numerically. A comparison of our results with the known analytic solutions for the homogeneously broadened atomic line shows that the two are similar. It seems that the new numerical solutions, unlike those for the homogeneous line, are not factorable, a fact to which we ascribe the difficulty in finding analytic solutions. We have found that as the atomic line broadens, the pulse widens and its height decreases, maintaining its area virtually constant.
A steady-state solution that describes pulse propagation in inhomogeneously broadening two-level atoms embedded in a dispersive and nonlinear Kerr lossless host medium has been found. The solution is of an unchirped hyperbolic-secant form with a linear spatial phase delay. The features of the solution are (i) the group velocity, the amplitude, and the width of the pulse are uniquely determined for given parameters of the medium and the carrier frequency; (ii) the group velocity is independent of the density of the resonant atoms; and (iii) the solution can exist in the positive dispersion region.
We have found a steady-state solution for a pulse propagating in imhogeneously broadened resonant two-level atoms embedded in a dispersive and nonlinear Kerr lossless host medium. The pulse is of an unchirped hyperbolic-secant form with a linear spatial phase delay. There are several salient features in this solution which are different from the results obtained previously. First, for the given parameters of the medium and carrier frequency, the group velocity, the amplitude, and the pulse width are uniquely determined. Second, the group velocity is independent of the density of the resonant atoms. Third, the solution exists in the positive dispersion region, which is different from solitons in fibers.
An investigation of the propagation properties of a short pulse in a resonant absorber with a homogeneously broadened transition is presented with two main questions in mind: 1) the influence of the input pulse area on the transitory regime and on the steady-state propagation; 2) the effects of atomic coherence on the pulse shaping and the time delay of the leading edge of the pulse. The transitory regime of a propagating pulse is investigated and the stability of some asymptotic wave form confirmed. As expected, the transversal relaxation mechanism affects critically the major features of the coherent interaction. A detailed analysis of this problem is also presented.
For pt.I see ibid., vol.10, p.425 (1977). The effect of spatial dispersion or exciton formation on the steady propagation of a coherent light pulse in a dielectric medium is studied. The optical Bloch equation for a lattice of atomic dipoles coupled to one another by an exchange-type interaction is solved simultaneously with the Maxwell equation by the method of power-series expansion developed in the preceding paper. Two kinds of pulse solutions are obtained in general: one propagating by the medium of the radiation field and the other by excitation transfer between atomic dipoles. The former solution is SIT-like in the short pulse limit, but a polariton-soliton or a standing wave of non-linear polariton if the pulse width is long. The latter is an exciton-soliton containing little photon component. When the pulse width is extremely long, there appears a polariton-soliton of a new type in which the two propagation mechanisms are mixed. It is found that the spatial dispersion prevents the polariton-soliton solutions from existing in a certain frequency range. This effect is explained on the basis of the functional behavior of the dispersion relation of the non-linear polariton.