Using the exact solution for a sine-driven two-level system we have calculated the nonlinear absorption coeAicient of a gas of two-level molecules with homogeneous (hard collisions, spontaneous decay) and inhomogeneous (l3oppler effect) broadening mechanisms. We have studied the dependence of the form of the absorption lines on relaxation parameters, on the strength of the electric field, and for various ratios between the homogeneous and inhomogeneous linewidths. We include considerations about saturation of the medium caused by the external field that gives rise to the so-called power broadening of the spectral lines. The dependence of the linewidth on the saturation parameters and on the relaxation parameters is determined. These parameters appear in the ratio of the purely homogeneous and purely inhomogeneous linewidths. Asymptotic behaviors of this linewidth for the homogeneous limit and for the inhomogeneous limit are also determined.
I. INTRODUCf IONThe nonlinear response of a molecular or atomic system to a laser field is an important tool in the study of the modifications of a material media interacting with the field. These studies have generated new branches of spectroscopy, for example, the so-called nonlinear optical spectroscopy and the very promising field of Doppler-free spectroscopy. ' Also, the proper study of the changes in the laser field characteristics propagating in a medium caused by nonlinear interactions with this medium received enormous attention since the generation of optical second harmonic by Franken eI, a/. in j. 961. 2 The study of the absorption interaction of light with matter started, in macroscopic terms, with the work of Lorentz and others, 3 at the, end of the last century, and more recently in microscopic terms with %eisskopf and %Vigner, 4 Heitler and Ma, ' Newstein, ' and many others (see Kimble and Mandel' and references therein) . The appearance
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