Transit-time effects and quadratic Doppler effect in saturated absorption and dispersion spectroscopy

An investigation is made of the resonance profile in saturated absorption and dispersion spectroscopy for arbitrary saturation of the absorption, subject to allowance for transit-time effects and the quadratic Doppler effect. Expressions are obtained for saturated absorption and dispersion signals in the rate approximation for a beam of rectangular shape in the case of two opposite waves with very different intensities and a standing wave. The widths of the resonances and the maximum resolving power of saturated absorption and dispersion spectroscopy are considered. General expressions are obtained for the frequency shifts, due to the quadratic Doppler effect, of stabilized lasers in the case of arbitrary values of the absorption saturation, frequency deviation, and number of the signal harmonic used in frequency stabilization. An analysis of these expressions is made in some limiting cases.