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Journal of Physics B Atomic Molecular and Optical Physics

Three-photon bimolecular absorption

Davıd L. Andrews, Alexander M. Bittner

Published Feb 28, 1993• 4 citations
Publisher

Abstract

Three-photon bimolecular absorption is a process which, through the simultaneous absorption of three laser photons, results in the electronic excitation of two molecules or atoms. Following a recent treatment of the selection rules, a quantum electrodynamical treatment is employed to describe the main features associated with the process and to produce an equation for the excitation rate. The dependence on photon polarization is investigated, and the magnitude of the excitation rate is estimated. It is shown that two different mechanisms operate, each with different selection rules and different dependences on intermolecular separation. In each case an energy mismatch is conveyed from one molecule to the other by means of virtual photon coupling. Some possible schemes for experimental study of the process out outlined.

DOI
10.1088/0953-4075/26/4/009

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The Journal of Chemical Physics•May 15, 1984•17 citations
Three-photon bimolecular absorption is a process which, through the simultaneous absorption of three laser photons, results in the electronic excitation of two molecules or atoms. Following a recent treatment of the selection rules, a quantum electrodynamical treatment is employed to describe the main features associated with the process and to produce an equation for the excitation rate. The dependence on photon polarization is investigated, and the magnitude of the excitation rate is estimated. It is shown that two different mechanisms operate, each with different selection rules and different dependences on intermolecular separation. In each case an energy mismatch is conveyed from one molecule to the other by means of virtual photon coupling. Some possible schemes for experimental study of the process out outlined.
It is shown that by a cooperative process involving virtual photon coupling between molecules, pairwise two-photon absorption can lead to molecular transitions associated with the mean of the laser frequencies in a two-beam experiment. The process is represented by A+A+ℏω1+ℏω2→A*+A*, and the selection rules are those normally applicable to two-photon absorption. The interaction may involve the excitation of chromophore pairs in polyatomic molecules, van der Waals molecules, or more usually discrete molecules in a gas or liquid. In the former case, however, dissymmetric juxtaposition of the chromophores produces a chirality which is manifest in a circular dichroism associated with the absorption process. The appropriate absorption rates are calculated using the methods of quantum electrodynamics, and the dependence on the separation of the interacting pair is examined in detail. Methods for observing the mean-frequency interaction are also outlined, and attention is drawn to a resonance condition which should appreciably enhance the absorption rate.
The dynamics and the cross sections associated with the excitation of a ground-state dipolar molecule to an excited state, by the simultaneous absorption of two photons, are discussed using the rotating wave approximation and time-dependent perturbation theory. The excitations of ten- and two-energy level representations of model dipolar molecules are used for illustrative purposes. The temporal development of the final state of the excitation process and the two-photon excitation cross sections are discussed as functions of laser intensity, laser–molecule interaction time and the two types of excitation mechanism (which are available for dipolar molecules, relative to the one mechanism for a non-polar molecule). The results are used to discuss the validity of perturbation theory treatments of the problem and various strategies for the enhancement of the intrinsically weak two-photon excitation process.
It is well known that irradiation with intense laser light can lead to nonlinear absorption processes by individual molecules. However, the mutual interaction between two molecules can lead to cooperative nonlinear processes which result in entirely new features in the absorption spectrum. In this paper, the theory of cooperative two-photon absorption is developed using the principles of quantum electrodynamics, and expressions are derived for the rate of cooperative absorption for transitions which are forbidden in the absence of any such interaction. Several different cases are examined in detail, including crystalline or matrix-isolated species, gaseous and liquid mixtures, and van der Waals molecules. It is shown that the cooperative absorption rate can be substantially increased by choosing materials with suitable energy levels where one of several resonance enhancement mechanisms can be exploited. Finally, methods of observation are discussed, and a specific photochemical example is given for the case of a mixture of formaldehyde and deuterioformaldehyde.
The dependence of the population of the target state, and the excitation cross section and rate, on pulse duration Q, laser intensity I, and a molecular matrix element A is discussed for two-photon molecular excitation. Perturbative and rotating wave approximation (RWA) expressions for the observables are obtained; the latter are used to discuss the validity of the former. For example, the perturbative cross section and rate increasingly underestimate the RWA results as I increases for given A and Q. Two- and ten-level model dipolar molecules are employed for illustrative purposes. The results are relevant for understanding two-photon excitation processes and their enhancement and include discussions of the roles the permanent dipole- and virtual-state mechanisms in such processes and of the validity of using intensity-independent cross sections to gauge the strength of such excitations.
The efficiencies of one- and two-photon absorption by chromophores in solution may be significantly modified by a sufficiently intense beam of off-resonant light. A molecular analysis based on quantum electrodynamics (QED) fully accounts for this phenomenon of laser-modified absorption. A time-dependent perturbation-theory treatment describes the process in terms of stimulated forward Rayleigh-scattering of the auxiliary beam occurring simultaneously with the absorption interaction(s). Our formulation accommodates media modifications to the basic character of light-matter interactions, taking into account the refractive and dispersive properties of a solution-phase environment. This introduces the bulk refractive index of the solvent directly into the QED framework. The measurable electronic response of molecules freely rotating in solution is defined by an average of all orientations. We explicitly derive fixed-orientation and rotationally averaged calculations for the Fermi-rule rate of laser-modified one- and two-photon absorption. For a given beam polarization geometry, the solution-phase molecular response is expressible as a set of natural invariant scalars. These results reveal details of the dependence on the beam polarisations and on the rotationally averaged molecular response: we illustrate the breadth of variation available via geometric manipulation of beam polarization, and raise new possibilities for quantum weak measurements of laser states.
In this paper we extend our earlier work on cooperative two-photon absorption to the case of one- and three-photon allowed transitions using the principles of quantum electrodynamics. After deriving a general rate equation we consider two specific molecular systems: (i) van der Waals molecules in which the two centers have a fixed mutual orientation; and (ii) fluid samples with random molecular orientation. Calculations are shown to involve a new type of rotational average which gives rise to two-photon circular dichroism in case (i). The dependence of the rate upon molecular separation is discussed in detail, as is the possibility of resonance enhancement if suitable intermediate energy levels are present. Finally we draw attention to an effect specific to this mode of cooperative absorption and speculate on the possibility of direct observation of the effects of retardation.