Effect of the pumping-field amplitude and phase modulation on the weak-probe absorption and dispersion spectra in a two-level medium

Abstract

The analytic solutions of equations, which describe the time behavior of density-matrix elements of a two-level medium driven by weak-probe tunable and strong fields, namely, scrE(t)=E(t)cos[\ensuremath{\omega}t+\ensuremath{\varphi}(t)]+\ensuremath{\varepsilon} cos[(\ensuremath{\omega}+\ensuremath{\delta})t], the amplitude E(t) and phase \ensuremath{\varphi}(t) of which are any arbitrary functions of time, are obtained. We obtain explicit expressions of the medium polarizability in two cases of the strong-field parameters modulation: first, E(t)=${\mathit{E}}_{0}$cos(\ensuremath{\xi} cos\ensuremath{\Omega}t), where ${\mathit{E}}_{0}$, \ensuremath{\Omega}, and \ensuremath{\xi} are constants, and \ensuremath{\varphi}=0; and second, both the amplitude E(t) and the phase \ensuremath{\varphi}(t) are periodic functions of time, and E(t)=C\ensuremath{\varphi}\ifmmode \dot{}\else \.{}\fi{}, where C is an arbitrary constant. These cases of modulation are generalizations of cases that were considered earlier. The first case of modulation causes a shift of the well-known Rabi resonances in the weak-probe absorption and dispersion spectra by the factor ${\mathit{J}}_{0}$(\ensuremath{\xi}) (${\mathit{J}}_{0}$ is the zero-order Bessel function of the first kind) in comparison with a nonmodulated exciting field. In the second case of the modulation, the Rabi resonances are present but the effect of such a modulation results in an attenuation of the amplitude-modulation effect. The values of the parameters ${\mathit{E}}_{0}$, \ensuremath{\Omega}, C, and \ensuremath{\xi} and the frequency ranges in which the weak-probe gain, caused by resonant Rayleigh scattering and by three-photon scattering, takes place are determined for these two cases of the modulation.