Non-Stationary Saturated Absorption and Refraction Effects in Laser Beams with Periodical Modulation of Frequency

Abstract

Periodical modulation of frequency, typical for spectroscopic purposes, is numerically modelled in transversely limited, propagating through a saturable two-level absorber. At modulation periods comparable with the atomic relaxation times the time and frequency dependence of the output intensity exhibits the manifestations of delayed medium response, including time-dependent lens and aperture effects that may be of importance in spectroscopy.Laser beam due to saturated refraction and absorption in near-resonance media has been extensively studied since predicted theoretically [1] and observed experimentally [2], including the extremely high absorption and saturation conditions (see, e.g., [3]). In particular, near-resonance self-focusing has been shown to yield asymmetry in the transmission spectra [4]. To get a transmission spectrum one usually has to vary the laser frequency periodically in the vicinity of the atomic resonance. When the frequency variation is slow, the medium response follows it adiabatically and the steady-state susceptibility theory is valid. The situation is different when the modulation period approaches the atomic relaxation times. In this case the transient (in general, nonlinear) response of the medium can be correctly described only within the full spatio-temporal description based on Maxwell-Bloch equations. Numerical implementations of such approaches are well-known in short pulse (see, e.g., [5]) Experimental manifestations of non-stationary near-resonant self-focusing of frequencymodulated beams have been reported before in saturation spectroscopy [6].Previously (see [7] and references therein) we have presented the method and some results of the numerical modeling of transient near-resonance self-action of periodically modulated beams. Now we focus our attention on the dependence of the output intensity upon the input laser frequency, which is supposed to be harmonically modulated. It appears that this dependence is very sensitive to the non-stationary properties of the medium that start to manifest themselves at relatively low modulation frequencies of the order of 10% of the transition width. Specific oscillatory features due to transient response of the medium are observed at large modulation amplitudes.Passing through a resonant absorbing medium, the frequency-modulated beam gradually acquires intensity modulation, which is neither nonlinear, nor transient and caused merely by different absorption at different frequencies. In weak fields this effect is independent of refraction, since the latter is linear, and, thus, no induced lens appears. First, we calculate the output intensity versus the input laser frequency sweeping periodically the near-resonance region. We start from weak non-saturating fields to distinguish between the non-stationary and nonlinear effects. The latter are included by increasing the field amplitude