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Bleach-Out Effect Described by the Nonlinear Wave Equations

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Abstract

A theoretical model for the bleach-out effect is based on semiclassical radiation theory for nonlinear wave interaction of a two-level system, which in turn is based on the density-matrix formalism. It is shown that, in the mean, conditions necessary for the bleach-out effect are consistent with the nonlinear wave equation. This model differs appreciably from that of McCall and Hahn, who base their analysis of the bleach-out effect for a two-level system on the Bloch equation.

The nonlinear wave equation used in this analysis is solved exactly in terms of the jacobian elliptic functions, which is different from the solution of McCall and Hahn. In the limit, this solution is reduced to a function describing the bleach-out effect, provided that the electric and polarization fields are suitably out of phase; thus agreement with the results of McCall and Hahn is found. The work demonstrates that the bleach-out effect is consistent with the density-matrix formalism (semiclassical radiation theory) as well as with the Bloch equations.

© 1968 Optical Society of America

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