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Applied Optics

Time-resolved molecular excitation and heat effects induced by infrared radiation

Yoram J. Kaufman, Uri P. Oppenheim

Published Jul 1, 1977• 2 citations
Publisher

Abstract

A saturable absorber (SF(6)) is irradiated by a step of radiation from a CO(2) laser, and the step response of the medium is observed. Since the characteristic times of rotational, vibrational, and thermal excitation are different, it is possible to observe each process separately. A set of rate equations is developed for a simplified model of two energy levels. This set includes only one differential equation and qualitatively describes the effects of rotational hole burning and vibrational relaxation. Heat effects are accounted for separately.

DOI
10.1364/ao.16.001931

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A saturable absorber (SF(6)) is irradiated by a step of radiation from a CO(2) laser, and the step response of the medium is observed. Since the characteristic times of rotational, vibrational, and thermal excitation are different, it is possible to observe each process separately. A set of rate equations is developed for a simplified model of two energy levels. This set includes only one differential equation and qualitatively describes the effects of rotational hole burning and vibrational relaxation. Heat effects are accounted for separately.
We discuss a model of selective absorption of infrared radiation by an anharmonic molecular vibrational mode. The effects of the rotational sublevels and of the energy dissipation mechanisms are described phenomenologically. We show that in the context of our model the absorption process is described by coupled nonlinear equations for the complex vibrational amplitude and for the average excitation quantum number. Two distinct dynamic regimes (coherent and adiabatic limit) can be identified depending on the relative magnitude of the rotational relaxation time and of the laser pulse duration.
The saturation behavior of molecular absorbers characterized by absorption coefficients expressible as the ratio of two polynomials in the intensity is analyzed. Two cases are considered in detail. In the first, the absorption coefficient is the ratio of a linear equation in I to a quadratic equation in I. In the second, the highest order of the intensity occurring in both numerator and denominator is increased by two. The absorption coefficients are derived from two specific five-level models which are pertinent to the interpretation of the absorption of CO2 laser radiation at 937 cm−1 by SF6, but the analysis of the saturation curves is independent of the models from which they are derived. The saturation curves display as many as three extrema and provide considerable flexibility for fitting complicated experimental data. Both five-level models include excited-state absorption with the terminal level of the ground-state absorption distinct from the initial level of the excited-state absorption. Each of the five levels can be considered as a composite of many rotational states which interact in a like manner with the incident radiation. In one of the models the ratio of the excited-state and ground-state absorption cross sections is taken to be intensity dependent.
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.
The dynamics of an adsorbed atom irradiated by an infrared laser in resonance with the vibrational levels of the adbond can be described by the reduced density matrix of the adbond. A nonperturbative approach for the laser-adbond interaction is presented. Relaxation against the substrate degrees of freedom is described by second-order perturbation theory. Both pulsed lasers and cw lasers are considered. Expressions for the transition probabilities are derived in the low-intensity and in the high-intensity limits. It appears that the time evolution of the occupation probabilities is coupled to those of the coherences, i.e., a master equation cannot be obtained. The time evolution of all the elements of the reduced density matrix has to be taken into account. These expressions act as a basis for the study of physical processes as resonant de sorption, resonant heating, and laser-induced thermal desorption. Resonant desorption is described by the addition of loss terms into the equations of motion of the occupation probabilities. Expressions for the rate of desorption as well as the rate of energy transfer to the substrate are given. In particular, a comparison is made for the effect of a cw laser vs a pulsed laser on the desorption and resonant heating.
The dynamics of a two-mode laser is studied in the presence of a selective saturable absorber interacting only with one of the modes. The specific nature of the system is determined by the presence of the out-of-phase relaxation oscillation, which becomes undamped when a sufficiently dense saturable absorber interacts with the weaker mode. If the absorber interacts with the stronger mode, the in-phase relaxation oscillation is excited, and the situation becomes similar to that observed in a single-mode laser. In the case of a slowly relaxing absorber, the difference of populations of its working levels can be adiabatically excluded. This procedure substantially simplifies the model and does not change its dynamic characteristics.
We consider a gas of molecules absorbing light from a monochromatic laser source and also undergoing both phase randomizing and thermalizing collisions with a heat bath of inert molecules. The generalized master equation formalism, used previously to study a system of this type with a two-level absorber, is extended to an absorber with N equally spaced levels. The possibility of unimolecular decay from any or all of the N levels is included in the formalism. The well-known relaxation model of Rubin and Shuler and the chemical reaction model of Montroll and Shuler are built into the formalism as special cases when the light source is turned off. Specific calculations for an eight-level model are presented and compared with results expected for an incoherent light source. A coherent effect which increases the upper level populations at steady state is found to exist. A corresponding increase in the macroscopic chemical rate constant is calculated for the coherent model when unimolecular decay from the top level is included. A particularly simple and general result is found for the power absorbed by a harmonic oscillator. It is also shown that, for the N-level model, one does not necessarily find equal populations in the limit of infinite light field intensity.