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.
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.
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.
Interactions between light and molecular matter featuring photon absorption are commonly associated with excitation of individual chromophores. Subsequent relaxation is achieved through numerous mechanisms, such as scattering and energy transfer to neighbouring chromophores. The efficiency of such processes depends on many factors, including the intensity and wavelength of the optical input, the absorption cross-section of the molecule and the relative orientation of molecular components. New photonic materials are developed on the principle that such factors are controllable, duly tailoring the system to suit new technological applications. The parameters that determine the linear response in multicomponent materials are typically assessed within the theoretical framework of classical optics. However, with improved interest and capability in fabricating nanoscale structures (especially those that exhibit quantum effects), it is becoming increasingly relevant to develop theory that more faithfully represents how individual photons engage with matter. In such constructs, the interaction of materials with optical waves and photons is highly dependent on local molecular environment, therefore surrounding structures and ancillary species exert forms of influence on the photophysical processes inherent within dielectric media. At optical wavelengths where the secondary structure displays little intrinsic optical absorption, the role of such components is often interpreted as modifying the input through a corrective local index of refraction. Although expedient in the discussion of bulk properties of a macroscopic medium, it is reasonably supposed at a local chromophore-photon level that optical mechanisms operate in a different fashion. Using a fully quantized approach to the representation of local molecular electronic structure and electrodynamics, this research develops rigorous theory and a corresponding physical interpretation of how photon absorption, scattering and energy transfer are modified by vicinal, non-absorbing chromophores. The results provide insight into the mechanisms achieved within multi-chromophore systems, highlighting factors that assist in the optimization of optical characteristics in designer materials.
It is shown that conventional one-photon and two-photon absorption processes can be made subject to nonlinear optical control, in each case significantly modifying the efficiency of absorption, through the effect of a secondary, off-resonant stimulus laser beam. The mechanistic origin of these laser-modified absorption processes, in which the stimulus beam emerges unchanged, is traced to higher-order terms in standard perturbation treatments. These normally insignificant terms become unusually prominent when the secondary optical stimulus is moderately intense. Employing a quantum formulation, the effects of the stimulus beam on one-photon and two-photon absorption are analyzed, and calculations are performed to determine the degree of absorption enhancement, and the form of spectral manifestation, under various laser intensities. The implications of differences in selection rules are also considered and exemplified, leading to the identification of dark states that can be populated as a result of laser-modified absorption. Attention is also drawn to the possibility of quantum nondemolition measurements, based on such a form of optical nonlinearity.
The theory of optical birefringence is discussed from the point of view of the scattering of polarized photons by molecules using the framework of formal scattering theory and quantum electrodynamics. In Part One, those features from noncovariant quantum electrodynamics relevant to the molecular scattering of photons are reviewed. Chapter One contains an outline of classical electrodynamics in the Coulomb gauge, including the Stokes parameter and density matrix formulations of polarization. Chapter Two deals with the quantization of the radiation field, and the occupation number representation is defined. The quantum mechanical description of polarized light is outlined in Chapter Three: operator equivalents of the density matrix and Stokes parameters are invoked, the parameters themselves being obtained from the expectation values of the Stokes operators with the state vector of the photon. The Stokes parameter and density matrix are then applied to the polarization of a general beam containing an arbitrary number of photons, and some new methods are developed. The interaction of the electromagnetic field with bound electrons is formulated in Chapter Four in terms of a canonically transformed interaction Hamiltonian in which the multipole terms are explicit. Since each term is then gauge-invariant, this Hamiltonian is particularly suited to the application of diagrammatic perturbation theory which follows from the iteration of the scattering matrix in the interaction representation (Chapter Five). Also the extension of the theory to multiphoton processes is facilitated "because the field strength is explicit in the transformed Hamiltonian. The S-matrix connects the initial and final asymptotic states of the scattering system, and in Chapter Six the state vector and density operator of the scattered photon beam are obtained from those of the incident beam. Part Two contains the application of the above methods to a variety of linear and nonlinear optical birefringence effects in the absence or presence of external fields. In Chapter Seven, general equations are obtained for the polarization changes imposed on a forward scattered photon in terms of matrix elements of the reaction operator between plane polarized photon base states; whereas Chapter Eight extends this treatment to an n-photon beam, thereby encompassing the hyperpolarizability contributions to the polarization changes of the forward scattered beam. It is then demonstrated that the fundamental process in optical birefringence can be interpreted as an infinitesimal unitary transformation of the polarization spinor. Also the S-matrix approach to birefringence is compared with the methods used in crystal optics, and with the classical treatments of the scattering of polarized light by molecules. The general equations obtained for the polarization changes of the forward scattered beam are subsequently interpreted in the light of the physical circumstances appropriate to the bire- fringence effect of interest. In Chapters Nine, Ten, and Eleven, diagrammatic perturbation theory is used to obtain explicit expressions, in terms of molecular polarizability and rotation tensors, for the linear and nonlinear contributions to the polarization changes involved in natural optical activity, and in birefringence phenomena induced by static and optical electric and magnetic fields. The nonforward scattering of polarized photons by molecules is discussed in Part Three. General equations are calculated in Chapter Twelve for the azimuth, ellipticity, and depolarization ratio of the Rayleigh beam at any scattering angle and for any polarization of the incident beam. Explicit expressions in terms of molecular quantities are then obtained for the polarization at scattering angles of 90° and almost zero from both optically inactive and optically active molecules. It is demonstrated that a determination of the precise polarization state of the scattered beam can provide useful molecular information additional to that obtained from depolarization ratios alone. This is because the depolarization ratio depends on only the diagonal elements of the polarization density matrix and so does not convey all the information about the system. Raman scattering processes are contained in the formulation and the polarization of the Raman light at any scattering angle can be obtained. This is shown to be particularly useful for predicting the polarization of stimulated Raman light for any Raman-active liquid placed within a laser cavity. By extending the nonforward scattering formulation to incorporate multiphoton processes, equations are obtained in Chapter Thirteen for the ellipticity, azimuth, and depolarization ratio of the second harmonic wave at any scattering angle as a function of the incident polarization. Several specific situations are subsequently investigated. Finally, it is shown in Chapter Fourteen that the near-forw- ard Rayleigh and Raman scattering formulations provide an explanation for the observed polarization, as a function of the initial polarization, of the self-trapped filaments that arise from the self-focusing of an intense laser beam.
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.
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.