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Journal of the Optical Society of America B

Pump—probe propagation in a passive Kerr nonlinear optical medium

Paul S. J. Spencer, K.A. Shore

Published Jan 1, 1995• 17 citations
Publisher

Abstract

The copropagation of an intense pump pulse and a weak probe pulse in a lossy Kerr nonlinear medium has been studied. Specifically, the influence that the group-velocity dispersion, the attenuation, and the initial time delay between the pulses have on the amount of cross-phase modulation induced by the pump pulse are highlighted. Analytic expressions for the phase modulation and the chirp experienced by an initial unchirped Gaussian pulse are presented.

DOI
10.1364/josab.12.000067

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The copropagation of an intense pump pulse and a weak probe pulse in a lossy Kerr nonlinear medium has been studied. Specifically, the influence that the group-velocity dispersion, the attenuation, and the initial time delay between the pulses have on the amount of cross-phase modulation induced by the pump pulse are highlighted. Analytic expressions for the phase modulation and the chirp experienced by an initial unchirped Gaussian pulse are presented.
I show that a probe pulse that is copropagating in an enhanced induced-phase-modulation nonlinear two-dimensional medium in the presence of a pump may be transformed into an induced superspike in time and space. The conditions of this induced collapse are that the ratio of the probe and pump initial transverse dimension to the duration be equal to 1/[beta((2))k(probe)]((1/2)), that their group velocities be equal, that the pump energy be larger than a waveguiding critical value, and that the probe central frequency be in the group-velocity dispersion anomalous region.
We investigate the spatiotemporal evolution of a Gaussian probe pulse propagating through a four-level NNN-type atomic medium. At two-photon resonance of probe and control fields, weaker probe pulses may propagate through the medium with low absorption and pulse shape distortion. In contrast, we find that increasing the probe pulse intensity leads to a splitting of the initially Gaussian pulse into a sequence of subpulses in the time domain. The number of subpulses arising throughout the propagation can be controlled via a suitable choice of the probe and control field parameters. Employing a simple theoretical model for the nonlinear pulse propagation, we conclude that the splitting occurs due to an interplay of Kerr nonlinearity and group-velocity dispersion.
We consider the propagation of a Gaussian probe pulse in an absorptive, optically dense, two-level medium if a deep, persistent hole is created in advance by another pump field in the inhomogeneously broadened absorption spectrum of this medium. Both fields are well separated in time and the lifetime of the hole is assumed to be long with respect to the delay time between the pump and probe pulses. We show that the group velocity of the Gaussian probe pulse reduces several orders in magnitude, similarly to the reduction of the group velocity for the probe field in electromagnetically induced transparency (EIT) phenomena. In contrast to EIT, the width of the transparency window can be made very wide because of the saturation broadening of the hole.
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.
The effect of grating dispersion on pulse evolution in a photorefractive self-pumped phase conjugator is analyzed. The broadening factors and the time-dependent phases of self-pumped phase-conjugate pulses of unchirped and chirped Gaussian pulses are obtained. When the grating dispersion and the angular dispersion cancel the material dispersion, the self-pumped phase-conjugate pulse has a minimum width, which is determined by the first-order dispersion of the grating. The self-pumped phase conjugation of an unchirped Gaussian pulse broadens and is linearly chirped whereas the self-pumped phase conjugation of a chirped Gaussian pulse is compressed when the dispersion-induced chirp cancels the initial chirp.