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Optics Express

Experimental observation of chirped continuous pulse-train soliton solutions to the Maxwell-Bloch equations

Shihadeh Saadeh, John L. Shultz, Gregory J. Salamo

Published Jan 15, 2001• 2 citations
Publisher

Abstract

A frequency chirped continuous wave laser beam incident upon a resonant, two-level atomic absorber is seen to evolve into a Jacobi elliptic pulse-train solution to the Maxwell-Bloch equations. Experimental pulse-train envelopes are found in good agreement with numerical and analytical predictions.
DOI
10.1364/oe.8.000153

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A more accurate description of the 2 pi pulse of self-induced transparency is obtained. This is an exact solution of an approximate form of the Maxwell-Bloch equations in which only backscattering is neglected; the equations are valid at densities less than about 10 18 atoms cm -3 . At such densities the 2 pi sech pulse of McCall and Hahn (1967, 1969) remains a good approximate well into the picosecond range. The more accurate solution is chirped by a factor proportional to the square of the ratio of the spectral width of the pulse to its carrier wave frequency. The stability of this pulse solution and other N soliton solutions of the approximate Maxwell-Bloch equations is demonstrated.
We present an analytical expression for the response of a two-level atom to a frequency-modulated optically coherent pulse train. The optical beam has sinusoidal frequency modulation and is chopped to have a square-wave envelope. We assume that the laser pulses are short compared with the atomic-decay time, the pulse-repetition time, and the modulation period. With this short-pulse assumption we are able to use a method similar to Temkin’s [J. Opt. Soc. Am. B10, 830–839 (1993)] and solve the optical Bloch equations in closed form.