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Journal of Physics B Atomic and Molecular Physics

Soluble models of optical systems driven by exponential pulses

Jakub Zakrzewski, Maciej Lewenstein, R J Kuklinski

Published Dec 14, 1985• 14 citations
Publisher

Abstract

Analytical solutions for optical systems driven by exponential pulses are presented. In particular the authors obtain the solutions of the Bloch equations for arbitrary relaxation constants and detuning. They discuss the solutions for the system consisting of a bound state coupled arbitrarily to a continuum.
DOI
10.1088/0022-3700/18/23/014

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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.
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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.