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IEEE Journal of Quantum Electronics

Pulse propagation stability in absorbing and amplifying media

Jean‐Claude Diels, E. Hahn

Published Jul 1, 1976• 13 citations
Publisher

Abstract

Simple stability conditions are obtained for pulse propagation in a two-level system with linear scattering and combined homogeneous and inhomogeneous broadening. Properties of steady-state π and\pi\sqrt{2}area pulses are reviewed. Computer simulation of an approach to equilibrium pulse propagation is presented in a few cases for initially perturbed pulses.

DOI
10.1109/jqe.1976.1069177

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Simple stability conditions are obtained for pulse propagation in a two-level system with linear scattering and combined homogeneous and inhomogeneous broadening. Properties of steady-state π and\pi\sqrt{2}area pulses are reviewed. Computer simulation of an approach to equilibrium pulse propagation is presented in a few cases for initially perturbed pulses.
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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.
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.
The initial value problem for the propagation of a pulse through a resonant two-level optical medium is solved by the inverse scattering method. In general, an incident pulse decomposes not only into a special class of pulses to which the medium is transparent but also yields radiation which is absorbed by the medium. In this respect ``this problem'' has properties markedly different from other dispersive and reversible wave phenomena some of which are tractable by the inverse scattering method. Indeed, it is remarkable that in the present case the method still applies. In particular, we show that, while there are an infinite number of local conservation laws, the integrated densities, and in particular the energy, are only conserved for a very special class of initial conditions. The theoretical results obtained are in close agreement with all the qualitative features observed in the experiments on coherent pulse propagation. Finally, we also show that causality is preserved. Two new and novel features are introduced and briefly discussed. First, we show that if the homogeneous broadening effect is a function of position in the medium, the pulses may speed up and slow down accordingly, without losing their permanent identities. Second, we have found a new kind of solution mode corresponding to a proper eigenvalue of the scattering problem which is not a bound state.