Molecules probed with a slow chirped-pulse excitation: Analytical model of the free-induction-decay signal

Most chirped-pulse experiments refer to a theoretical study from McGurk, Schmalz, and Flygare [J. Chem. Phys. 60, 4181 (1974), 10.1063/1.1680886] which is well tailored to interpret the signals obtained with very fast chirped pulses, but is not sufficient to account for the signals in the case of slower chirped pulses used in spectroscopy to increase the signal-to-noise ratio. A theoretical study of the polarization of molecules subjected to a chirped pulse in a cell, uniform supersonic flow, or molecular beam is presented. Three degrees of approximation for the polarization are introduced and are compared with the numerical solution of the optical Bloch equations. These expressions enter the analytic expression of the free-induction-decay signal which is validated against experimental data on the rotational emission spectra of OCS molecules. A relation among the pulse duration, the line position in the chirped pulse, and the signal amplitude is proposed in the thermalized case. It assists in the optimization of the chirped-pulse parameters and in the estimation of the error associated with the line intensity.