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The Journal of Chemical Physics

Cooperative two-photon absorption. II

Davıd L. Andrews, Michael J. Harlow

Published May 15, 1984• 17 citations
Publisher

Abstract

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.

DOI
10.1063/1.446540

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IntechOpen eBooks•May 16, 2019•0 citations
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.
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.
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 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.
Rates for multiphoton absorption by molecules in the regime where perturbation theory is valid are computed. The importance of the contributions to the rates of permanent moments is shown. The results are expressed in terms of generalised Einstein B coefficients which are shown to arise both from quantum electrodynamical and semiclassical arguments; the authors remain within the electric dipole approximation throughout. Explicit and detailed results for two- and three-photon absorption are given for plane-polarised and circularly-polarised light. These are found both for molecules rigidly fixed relative to the light beams and for random orientation of the molecules. In the latter case the rates are presented in terms of the transition and permanent moments in the molecular-body coordinate frame of reference.
The two-photon transitions of a system of two dissimilar molecules are studied in the dipole approximation. Special attention is paid to transitions in which both molecules participate simultaneously. By use of a reduced Hamiltonian the influence of long-range intermolecular forces is also studied. The three main transitions considered occur when: (i) no molecular level is in resonance with a primary photon, (ii) one primary photon excites a molecular level, and (iii) two primary photons excite a molecular level. It is shown that in no case can the mixing of excited states by intermolecular forces be represented as a change to an effective transition dipole moment for one of the molecules. The one-photon decay of a state in which both molecules are excited is also treated.
The collective decay effects between the dipole-active three-level subsystems in the nonlinear interaction with dipole-forbidden transitions, like 2 S − 1 S of hydrogen-like radiators, are proposed, taking into consideration the cooperative exchanges between two species of atoms through the vacuum field in the scattering and the two-photon resonance processes. One of them corresponds to the situation when the total energy of the emitted two photons by the three-level radiator in the cascade configuration enters into the two-photon resonance with another type of dipole-forbidden transitions of hydrogen-like (or helium-like) atoms. The similar situation appears in the cooperative scattering between two species of quantum emitters when the difference of the excited energies of the two dipole-active transitions of the three-level radiators is in the resonance with the dipole-forbidden transitions of the Hydrogen-like radiators. These effects are accompanied by the interference between single- and two-quantum collective transitions of the inverted radiators from the ensemble. The two-particle collective decay rate is defined in the description of the atomic correlation functions taking into consideration the phase retardation between them. The kinetic equations which describe the cooperative processes as the function of time and correlation are obtained. The behavior of the system of radiators at short and long time intervals in comparison with the retardation time between them is studied.