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Journal of the Optical Society of America B

Coherent pulse propagation in a resonant absorber with Kerr-type nonlinearity

Ljubomir Matulic, G. E. Torres-Cisneros, Javier J. Sanchez-Mondragon

Published Jun 1, 1991• 6 citations
Publisher

Abstract

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.

DOI
10.1364/josab.8.001276

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Steady propagation of a coherent light pulse in a dielectric medium. II. The effect of spatial dispersion

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Self-induced transparency in the presence of the Kerr nonlinearity

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The self-induced transparency solution of the Bloch-Maxwell equations is found in the case of inhomogeneously broadened resonant atomic lines and a host medium with a Kerr-type nonlinearity in the index of refraction. The characteristic feature of the solution is that the atomic functions are not factorized. The time dependence of the pulse phase is different from that in the case of a sharp atomic line. In addition to the known term quadratic in the pulse envelope, it contains a term increasing in time, attaining a maximum at the trailing edge of the pulse, and rapidly decreasing afterwards. The average carrier frequency is proportional to the square of the spectral width of the atomic line divided by the squared width of the pulse. A satisfactory solution is found by modulation of the center of the Lorentz distribution function of the purely resonant solutions. It is shown that in the presence of the inhomogeneous broadening the problem cannot be solved by a linear perturbation expansion with respect to the Kerr constant. This method leads to divergencies near the trailing edge of the pulse.

Physical Review A•May 1, 1978•6 citations
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 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 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.
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.
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.
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.
The self-induced transparency solution of the Bloch-Maxwell equations is found in the case of inhomogeneously broadened resonant atomic lines and a host medium with a Kerr-type nonlinearity in the index of refraction. The characteristic feature of the solution is that the atomic functions are not factorized. The time dependence of the pulse phase is different from that in the case of a sharp atomic line. In addition to the known term quadratic in the pulse envelope, it contains a term increasing in time, attaining a maximum at the trailing edge of the pulse, and rapidly decreasing afterwards. The average carrier frequency is proportional to the square of the spectral width of the atomic line divided by the squared width of the pulse. A satisfactory solution is found by modulation of the center of the Lorentz distribution function of the purely resonant solutions. It is shown that in the presence of the inhomogeneous broadening the problem cannot be solved by a linear perturbation expansion with respect to the Kerr constant. This method leads to divergencies near the trailing edge of the pulse.