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Power-series solutions to the optical Maxwell–Bloch equations

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Abstract

We discuss a new way of solving the optical Maxwell–Bloch equations governing the interaction of two-level inhomogeneously broadened atoms with a laser by expanding the components of the Bloch vector in power series of the detuning. This method leads to a set of infinitely many coupled ordinary differential equations in which the detuning no longer appears explicitly. These equations are solved numerically, reproducing some analytic solutions reported previously and obtaining a variety of other shape-preserving steady-state solutions. These new solutions, however, are neither factorable nor simply periodic. In this connection we discuss the implications of the factorization assumption, which appears to be the only condition leading to closed-form analytic solutions.

© 1989 Optical Society of America

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