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Optics Letters

Pendulum equations for a swept-gain three-level amplifier

Božena Sobolewska, Bruce J. Herman, P. D. Drummond, Joseph H. Eberly

Published Sep 1, 1981• 5 citations
Publisher

Abstract

We present new pendulum-type equations for the propagation of two nonoverlapping pulses in a model swept-gain three-level amplifier. The predictions of these equations are compared numerically with corresponding predictions of the two-level Burnham-Chiao equations and with the full coupled three-level Maxwell-Bloch equations.
DOI
10.1364/ol.6.000408

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We develop a theory to take into account the effects in coherent propagation of a small overlapping of the pump and probe pulses in a three-level system. The Maxwell equations reduce to coupled equations for variables which are related to the time-integrated field envelopes. We make comparisons of the propagation results to the Burnham-Chiao theory for a two-level amplifier and can predict when this theory breaks down. An application to superfluorescence is presented where a lengthening of the delay time is found. We treat Doppler broadening and find simplified equations in two cases: (a) a very broad line and (b) a very narrow line where the initial and final states are degenerate. For the broad-line case, with an appropriate choice of initial parameters, we can make the probe pulse approach any desired area for certain configurations of the levels.
Propagation of a few-cycle laser pulse in a V-type three-level system (fine structure levels of rubidium) is investigated numerically. The full three-level Maxwell-Bloch equations without the rotating wave approximation and the standing slowly varying envelope approximation are solved by using a finite-difference time-domain method. It is shown that, when the usual unequal oscillator strengths are considered, self-induced transparency cannot be recovered and higher spectral components can be produced even for small-area pulses.
An accurate and effective numerical method is presented to solve the Maxwell-Bloch equations,which describe the optical pulse propagation and interaction with homogeneously broadened two-level medium.The convergence and stability of this numerical method are also proved by comparing with the analytic solutions derived under special condition,and the method maintains its erroneous exponents and is applicable.Simulations of arbitrary conditions are discussed by employing this new method,and the evolutions of pulse and Bloch vectors for different detunings,relaxation times and initial input pulse power are analyzed.The established numerical method can be used to solve the Maxwell-Bloch equations and their corrections.