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Soviet Journal of Quantum Electronics

Propagation of an ultrashort light pulse in a three-level laser amplifier

Alexander A. Zabolotskii

Published May 31, 1988• 0 citations
Publisher

Abstract

The inverse scattering transform method is used in a study of the evolution of light pulses in an initially inverted three-level medium of the Λ type. An asymptotic solution describing the profile of the first spike is obtained for small-area priming pulses. It is shown that this asymptote is determined entirely by the initial populations of the lower levels and by the profile of the priming pulses. A special case of this problem is the propagation of two-component light in a laser amplifier using the degenerate J = 0–J = 1 transition.

DOI
10.1070/qe1988v018n05abeh012265

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The inverse scattering transform method is used in a study of the evolution of light pulses in an initially inverted three-level medium of the Λ type. An asymptotic solution describing the profile of the first spike is obtained for small-area priming pulses. It is shown that this asymptote is determined entirely by the initial populations of the lower levels and by the profile of the priming pulses. A special case of this problem is the propagation of two-component light in a laser amplifier using the degenerate J = 0–J = 1 transition.
The propagation of an arbitrary polarized few-cycle ultrashort laser pulse in a degenerate three-level medium is investigated by using an iterative predictor-corrector finite-difference time-domain method. It is found that the polarization evolution of the ultrashort laser pulse is dependent not only on the initial atomic coherence of the medium but also on the polarization condition of the incident laser pulse. When the initial effective area is equal to $2\ensuremath{\pi}$, complete linear-to-circular and circular-to-linear polarization conversion of few-cycle ultrashort laser pulses can be achieved due to the quantum interference effects between the two different transition paths.
The propagation of a polarized ultrashort laser pulse is analyzed by the inverse scattering method under initial conditions including a spatial pulse profile, a state of the medium, and a “switched-on” resonant atom-field interaction. Magnetic degeneracy of atomic levels is taken into account. The Maxwell-Bloch equations are rewritten in Hamiltonian form without redefining the spatial and temporal variables. The inverse scattering method is based on an analysis of a new spectral problem. Gelfand-Levitan-Marchenko-type equations are derived, a soliton solution is obtained, and the changes in parameters of two solitons after their collision are calculated. A possible experimental setup for implementing the system under analysis is discussed.
Propagation and amplification of an ultrashort laser pulse in a two-level medium is numerically investigated with the use of the finite-difference time-domain (FDTD) procedure simultaneously solving Maxwell and Schrodinger equations with no assumptions characteristic of slowly varying envelope approximation. Comparison of the results of FDTD numerical simulations with the predictions of the pulse area theorem has demonstrated that the developed numerical procedure provides an adequate description of pulse evolution in a two-level medium. Amplification of ultrashort light pulses in a two-level medium is analyzed. Two methods of improving the gain of ultrashort pulses in a two-level medium by modulating the spatial distribution of dipole moments of resonant transitions and using initially chirped frequency-detuned pulses are explored.
The growth of a radiation pulse traversing a medium with an inverted population is described by nonlinear, time-dependent photon transport equations, which account for the effect of the radiation on the medium as well as vice versa. The equations are solved in closed form for an arbitrary input pulse and an arbitrary initial distribution of inverted population. The solutions are discussed in detail for the particular cases of a square pulse and a Lorentzian pulse, both with a uniform initial population inversion.