Abstract An achiral system bathed in an intense beam of circularly polarized light shows chiral behaviour which may be detected with an auxiliary beam of polarized light. In this paper, expressions are derived for differential absorption rates, optical rotation of a plane polarized probe beam and circular differential scattering intensities. The theory of these two, three and four photon processes is developed by using quantum electrodynamics in electric dipole approximation. Two types of circular dichroism are distinguished: (a) the transition exhibiting induced dichroism is one-photon allowed, with chirality induced by scattering of the laser beam, or (b) the transition is two-photon allowed with absorption of a photon from each beam. In both, the induced circular dichroism is linearly dependent on the intensity of the inducing beam. Circular dichroism of type (a) is also discussed from the dressed-molecule viewpoint, and it is shown how a canonical transformation may be used to recover the results more simply. The possibility of observing Doppler-free circular dichroism is indicated. The induced optical rotation is analysed as a two-state process with transitions involving change of polarization only. The angle of rotation is linearly dependent on the intensity of the intense beam; its sign depends on the helicity. It is shown that, for non-forward Rayleigh scattering of the probe beam in the presence of an intense beam of light, the scattering intensity depends on the relative helicities of the two beams, and the differential intensity is proportional to the incident intensities.
Abstract An achiral system bathed in an intense beam of circularly polarized light shows chiral behaviour which may be detected with an auxiliary beam of polarized light. In this paper, expressions are derived for differential absorption rates, optical rotation of a plane polarized probe beam and circular differential scattering intensities. The theory of these two, three and four photon processes is developed by using quantum electrodynamics in electric dipole approximation. Two types of circular dichroism are distinguished: (a) the transition exhibiting induced dichroism is one-photon allowed, with chirality induced by scattering of the laser beam, or (b) the transition is two-photon allowed with absorption of a photon from each beam. In both, the induced circular dichroism is linearly dependent on the intensity of the inducing beam. Circular dichroism of type (a) is also discussed from the dressed-molecule viewpoint, and it is shown how a canonical transformation may be used to recover the results more simply. The possibility of observing Doppler-free circular dichroism is indicated. The induced optical rotation is analysed as a two-state process with transitions involving change of polarization only. The angle of rotation is linearly dependent on the intensity of the intense beam; its sign depends on the helicity. It is shown that, for non-forward Rayleigh scattering of the probe beam in the presence of an intense beam of light, the scattering intensity depends on the relative helicities of the two beams, and the differential intensity is proportional to the incident intensities.
The propagation of a strongly polarised electromagnetic wave through a resonance medium with arbitrary angular momenta of the levels is investigated in the adiabatic following approximation. Exact wavefunctions of the two-level atomic system with degenerate levels in the field of a circularly (linearly) polarised wave are constructed and the picture of the energetic level splitting and shift is discussed. Exact formulae for the non-linear refractive index of the medium in the field of the circularly (linearly) polarised wave are found. The propagation of counterpropagating polarised waves-an intense pump wave and a probe light signal-through the resonance medium is studied. The studies are carried out in the scope of a two-level (one-photon resonance) and a three-level (one- and two-photon resonances) medium. Formulae are found for the induced pump angle of rotation of the ellipse (plane) of polarisation for the probing signal that are exact in terms of the intensity of the pump wave. The spectral dependence of the angle of rotation is studied, and it is shown that a series of Stark-shifted resonance poles of atomic absorption and a three-photon scattering process arise.
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.
Abstract A general approach to the discussion of optical birefringence phenomena is presented. It is based on the S-matrix approach to photon scattering in a nonrelativistic quantum field theoretical formalism and the Stokes operator description of polarization. The use of a canonically transformed interaction Hamiltonian in combination with diagrammatic perturbation theory enables the response of a system to electromagnetic radiation to be calculated in a straightforward and consistent manner to any order in the perturbation, and the effect of static fields is included easily. As an illustration, the angle of rotation of a beam of plane-polarized light by a solution of optically active molecules is calculated and the intensity dependence of the angle determined. The latter phenomenon should become apparent at high photon flux densities particularly when ω, the frequency of the incident light, or 2ω are similar to electronic excitation frequencies in the optically active molecules.
A theoretical study of the polarization dependence of stimulated Rayleigh-wing scattering and the optical-frequency Kerr effect has been undertaken. When the incident light is circularly polarized, a striking difference in gain is found for the co- and counter-rotating senses of polarization of the scattered light---the former being suppressed and the latter being exceptionally favored. The analysis begins with a model for the Kerr effect, which involves the alignment of anisotropic molecules in an electric field, but the results can be immediately generalized to any light scattering process of tensor symmetry. The nonlinear problem of the propagation of an intense elliptically polarized light wave in a Kerr-active medium is shown to have a solution in which the vibrational ellipse undergoes self-precession and self-retardation. The stimulated scatterings or instabilities of such a self-precessing and self-retarding light wave are obtained for the backward and forward directions. Birefringence, optical activity, and linear and circular dichroisms are some of the phenomena which result, but the forward direction yields substantially different results from the backward direction because of Stokes-anti-Stokes coupling.
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.