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Journal of Modern Optics

Solitary Pulses in an Amplified Nonlinear Dispersive Medium in the Presence of Gain Saturation

Valentin P. Petrov

Published Nov 1, 1992• 2 citations
Publisher

Abstract

The steady state solitary solution in a two-level homogeneously broadened amplifier with host nonlinearity and dispersion is perturbatively studied by consideration of gain saturation up to second-order energy terms normalized to the saturation energy of the transition. Carrier frequency shift occurs as a result of the saturation. The chirped solitary pulses derived exist in the anomalous group velocity dispersion region only.

DOI
10.1080/09500349214552351

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The steady state solitary solution in a two-level homogeneously broadened amplifier with host nonlinearity and dispersion is perturbatively studied by consideration of gain saturation up to second-order energy terms normalized to the saturation energy of the transition. Carrier frequency shift occurs as a result of the saturation. The chirped solitary pulses derived exist in the anomalous group velocity dispersion region only.
A steady-state solution describing\Pi-pulse propagation in a homogeneously broadened laser amplifier embedded in a dispersive lossy host is found. For a given model of dispersion, the solution satisfies exactly the second-order wave equation together with the equations of motion for the density matrix of the two-level resonant system. The salient feature of the solution is that a small amount of dispersion in the host group velocity causes a large monotonic frequency sweep during the pulse. The effects of this chirp on the pulse properties are described in detail, and the relation of the theory to experiments is discussed.
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.
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.
We obtain an exact linearly polarized vector solitary solution for the amplification of an optical pulse with a time width short compared with both population and polarization decay time. This dissipative soliton results from the balance between the gain from inverted resonant two-level atoms and the linear loss of the host material. We suppose that the excited state of the active centers is degenerate on the projection of the angular momentum, with a symmetric state of inversion. Quite remarkably, we find that after the passing of the pulse, the atomic medium does not return to the ground state, and a finite Zeeman coherence is generated. Numerical simulations demonstrate the stability of vector π solitons with an arbitrary state of elliptical polarization in the presence of both linear birefringence and group-velocity dispersion of the host material.