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The Journal of Chemical Physics

Cooperative mean-frequency absorption: A two-beam two-photon process

Davıd L. Andrews, Kevin P. Hopkins

Published Mar 1, 1987• 12 citations
Publisher

Abstract

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.

DOI
10.1063/1.452098

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Journal of Modern Optics•Apr 1, 1990•8 citations
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.
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.
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.
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.
By applying a sufficiently intense beam of off-resonant light, simultaneously with a conventional excitation source beam, the efficiencies of one- and two-photon absorption processes may be significantly modified. The nonlinear mechanism that is responsible, known as laser modified absorption, is fully described by a quantum electrodynamical analysis. The origin of the process, which involves stimulated forward Rayleigh-scattering of the auxiliary beam, relates to higher order terms which are secured by a time-dependent perturbation treatment. These terms, usually inconsequential when a single beam of light is present, become prominent under the secondary optical stimulus – even with levels of intensity that are moderate by today’s standards. Distinctive kinds of behaviour may be observed for chromophores fixed in a static arrangement, or for solution- or gas-phase molecules whose response is tempered by a rotational average of orientations. In each case the results exhibit an interplay of factors involving the beam polarisations and the molecular electronic response. Special attention is given to interesting metastable states that are symmetry forbidden by one- or two-photon absorption. Such states may be accessible, and thus become populated, on input of the auxiliary beam. For example, in the one-photon absorption case, terms arise that are more usually associated with three-photon processes, corresponding to very different selection rules. Other kinds of metastable state also arise in the two-photon process, and measuring the effect of applying the stimulus beam to absorbances of such character adds a new dimension to the information content of the associated spectroscopy. Finally, based on these novel forms of optical nonlinearity, there may be new possibilities for quantum non-demolition measurements.
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 it is demonstrated how the phenomena of cooperative Raman scattering and cooperative two-photon absorption may be described in a unified manner, through canonically transforming the system Hamiltonian. The unique features associated with the virtual photon coupling between centres are discussed. In particular it is illustrated how in the near-zone, close proximity leads to two-body two-photon events involving interaction-induced dipoles. In the far-zone, it is shown how the coupling between molecules may be understood in terms of a radiative dipole effect. Attention is focused upon the behaviour of this coupling for distributive and cooperative mechanisms in fluids, and the relative importance of each process discussed, particularly with regard to their very different range dependences. A detailed analysis of the coupling reveals that in two-photon absorption the distributive mechanism dominates, whilst in Raman scattering cooperative energy transfer is favoured. Finally recent progress in the field of synergism is reviewed along with the characteristics associated with synergism in Raman scattering and two-photon absorption.