We model the response of a molecular medium to an intense pulse of light. We begin by reducing the Maxwell-Bloch equations for a multilevel molecular model system to a set of simplified propagation equations. We thereby obtain expressions for the frequency, temperature, and field intensity dependence of the ground and excited electronic state absorption cross sections, and the emission cross section, as well as the temperature dependence of the decay rate of the excited state. The phenomena of saturation, excited-state absorption, optically induced dichroism and birefringence, vibronic energy transfer, induced molecular alignment, decay of the matter-field interaction energy, and rotational diffusion are considered within the general formalism for describing the propagation of an intense pulse of light in the molecular medium. We find that the cross section for absorption (emission) of a photon is not identical to the cross section for molecular excitation (deexcitation) via the matter-field interaction. This is explained in terms of an energy balance between the matter, radiation, the matter-radiation interaction, and the bath responsible for the broadening of the molecular transitions. The inequality of these cross sections determines whether the system supplies or draws energy from the thermal bath. The rise in the vibrational temperature of molecules subjected to an intense short pulse is shown to significantly affect propagation of the pulse. The alignment of the molecular system resulting from saturation of the ground-state transition by a polarized laser pulse and the effects of the orientational dependence of the matter-field interaction including effects of rotational diffusion are determined. As an example of the formalism we consider pulse propagation in a Rhodamine 6G solution. We fit the parameters of the model to determine the frequency dependence of the ground- and excited-state absorption cross sections and the emission cross section and compare with experimentally determined cross sections. We describe the propagation of a pulse whose temporal width is comparable to the rotational diffusion time of the molecules in the dye solution and calculate polarization pulse probe signals.
We develop a simple and general framework for understanding the relationships between absorption and emission in multilevel systems (molecules, semiconductors, condensed matter, etc.) in and out of equilibrium. Conditions under which the absorption and emission spectra display mirror image symmetry are determined. The relationship between the absorption and emission cross sections at frequency \ensuremath{\omega} and temperature T, previously derived by Neporent and McCumber for thermally equilibrated systems, is generalized and a new derivation is presented which extends its range of application to systems out of equilibrium. This derivation requires only microscopic reversibility and that the optically coupled manifold of levels belonging to both initial and final electronic states are each in internal thermal equilibrium at the same temperature T. The initial and final (e.g., ground and excited electronic) states need not be in equilibrium. If more than one excited-electronic-state manifold participates in the dynamics and these excited-electronic-state manifolds are not themselves in equilibrium, a somewhat more complicated relationship between absorption and emission can be obtained, provided that the internal degrees of freedom within the electronic-state manifolds are each in equilibrium at the same temperature.Effects of inhomogeneous broadening are examined. Good agreement is found between the Neporent-McCumber relationship and experimental absorption and emission spectra for the laser dyes rhodamine-6G and 2,5-biphenyloxazol PPO, and the solid-state laser crystal alexandrite. A new relationship between absorption and emission in direct-band-gap semiconductor materials is derived. This relationship allows us to calculate the emission from a direct-band-gap semiconductor provided the dependence of the band-gap energy on excitation level is not large. These relationships hold even when pumping conditions differ for emission and absorption experiments; the dependence of emission on excitation level can thereby be calculated. This permits the gain spectra of semiconductor diode lasers to be determined from their absorption spectra. In the limit that both the absorption and emission are measured for a thermally equilibrated nondegenerate direct-band-gap semiconductor system with identical pumping conditions for the absorption and emission experiments, our new relationship reduces to previous results.
Optical pumping of the ground states of sodium can radically alter the shape of the laser-induced fluorescence excitation spectrum, complicating measurements of temperature, pressure, etc., which are based on these spectra. Modeling of the fluorescence using rate equations for the eight hyperfine states of the sodium D manifolds can be used to quantify the contribution to the ground state pumping of transitions among the hyperfine excited states induced by collisions with buffer gas atoms. This model is used here to determine, from the shape of experimental spectra, cross sections for $\ensuremath{\Delta}F$ transitions of the
P3/2 state induced by collisions with helium and argon atoms, for a range of values assumed for the ${P}_{1/2}, \ensuremath{\Delta}F$ cross sections. The hyperfine cross sections measured using this method, which to our knowledge is novel, are compared with cross sections for transitions involving polarized magnetic substates
mF measured previously using polarization sensitive absorption. Also, fine-structure transition $(\ensuremath{\Delta}J)$ cross sections were measured in the pumped vapor, giving agreement with previous measurements made in the absence of pumping.