This thesis employs molecular quantum electrodynamical theory to analyse the interactions between light and matter for four main processes. The first to be considered is Raman scattering, where the effect of the electrodynamic environment for the centre of spectroscopic interest is considered. This is achieved by engaging a retarded dipole-dipole interaction between the centre and a neighbouring molecule. Physically, this is explained by a virtual photon between the pair of centres. The results predict characteristic new lines on the Raman spectrum, for the species, arising from the engagement of selection rules not limited to those of a two-photon process. \nThe second process, is hyper-Rayleigh scattering, in which a single multipolar coupling is considered in place of the more familiar electric dipole. This modification to the theory subverts the standard selection rules for a three-photon process, which can allow for second-harmonic emission to be generated by a centre of high symmetry, such as a centrosymmetric molecule. \nThe third process offers another means of subverting the standard selection rules for second-harmonic generation, namely by incorporating six-wave mixing. First, the general mechanism is developed and pertinent results are expressed for the widely-deployed depolarisation ratio. Following this, structured light is considered and by utilising orbital angular momentum (OAM) conservation arguments, the pair of harmonic photons are found to display quantum entanglement. Moreover, the relative magnitudes of the possible emissions are found to correspond directly to that of the binomial coefficients. \nThis thesis concludes with a family of novel structures capable of directly generating OAM light. This work exploits symmetry characteristics for a delocalised excitonic structure that can allow for a more complex multipolar emission than that of any isolated centres. The phase of the exciton is shown to display an azimuthal phase progression, a vortex feature most commonly associated with Laguerre-Gaussian light.
This thesis employs molecular quantum electrodynamical theory to analyse the interactions between light and matter for four main processes. The first to be considered is Raman scattering, where the effect of the electrodynamic environment for the centre of spectroscopic interest is considered. This is achieved by engaging a retarded dipole-dipole interaction between the centre and a neighbouring molecule. Physically, this is explained by a virtual photon between the pair of centres. The results predict characteristic new lines on the Raman spectrum, for the species, arising from the engagement of selection rules not limited to those of a two-photon process. \nThe second process, is hyper-Rayleigh scattering, in which a single multipolar coupling is considered in place of the more familiar electric dipole. This modification to the theory subverts the standard selection rules for a three-photon process, which can allow for second-harmonic emission to be generated by a centre of high symmetry, such as a centrosymmetric molecule. \nThe third process offers another means of subverting the standard selection rules for second-harmonic generation, namely by incorporating six-wave mixing. First, the general mechanism is developed and pertinent results are expressed for the widely-deployed depolarisation ratio. Following this, structured light is considered and by utilising orbital angular momentum (OAM) conservation arguments, the pair of harmonic photons are found to display quantum entanglement. Moreover, the relative magnitudes of the possible emissions are found to correspond directly to that of the binomial coefficients. \nThis thesis concludes with a family of novel structures capable of directly generating OAM light. This work exploits symmetry characteristics for a delocalised excitonic structure that can allow for a more complex multipolar emission than that of any isolated centres. The phase of the exciton is shown to display an azimuthal phase progression, a vortex feature most commonly associated with Laguerre-Gaussian light.
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.
The theory of quantum electrodynamics is employed in the description of linear and \nnonlinear optical effects. We study the effects of using a two energy level \napproximation in simplifying expressions obtained from perturbation theory, \nequivalent to truncating the completeness relation. However, applying a two-level \nmodel with a lack of regard for its domain of validity may deliver misleading results. \nA new theorem on the expectation values of analytical operator functions imposes \nadditional constraints on any atom or molecule modelled as a two-level system. We \nintroduce measures designed to indicate occasions when the two-level approximation \nmay be valid. \nAnalysis of the optical angular momentum operator delivers a division into spin \nand orbital parts satisfying electric-magnetic democracy, and determine a new \ncompartmentalisation of the optical angular momentum. An analysis is performed on \nthe recently rediscovered optical chirality, and its corresponding flux, delivering \nresults proportional to the helicity and spin angular momentum in monochromatic \nbeams. A new polarisation basis is introduced to determine the maximum values that \nan infinite family of optical helicity- and spin- type measures may take, and disproves \nrecent claims of ‘superchiral light’. A theoretical description of recent experiments \nrelate helicity- and spin- type measures to the circular differential response of \nmolecules, and show that nodal enhancements to circular dichroism relate only to \nphoton number-phase uncertainty relation and do not signify ‘superchiral’ regions. \nThe six-wave mixing of optical vortex input, in nonlinear media, demonstrates the \nquantum entanglement of pairs of optical vortex modes. The probability for each \npossible output pair displays a combinatorial weighting, associated with Pascal’s \ntriangle. \nA quantum electrodynamic analysis of the effect of a second body on absorption \ncan be extended by integrating over all possible positions of the mediator molecules, \nmodelling a continuous medium. This provides links with both the molecular and \nbulk properties of materials.
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.
In this paper a quantum electrodynamical theory of cooperative Raman scattering in fluids is developed. The process is one in which pairs of molecules undergo concerted Raman transitions via an intermolecular energy transfer mechanism. The formalism is also extended to chromophore pairs in which intramolecular energy transfer is involved. Using the Power-Zienau-Woolley multipolar Hamiltonian, intensity equations of the Kramers-Heisenberg type are derived which are valid over all regions of molecular separation. In the near zone it is illustrated how the intensity of cooperative scattering is simply that obtained by consideration of the instantaneous response of one molecule to the scalar field generated by another. Within this regime it is shown that the rate of scattering has the familiar ${R}^{\mathrm{\ensuremath{-}}6}$ dependence on intermolecular separation R associated with interacting induced dipoles. In the far zone it is demonstrated that the fully retarded and causal interaction between molecules is mediated through virtual photon coupling, and that this leads to a result for the intensity that dies off with ${R}^{\mathrm{\ensuremath{-}}2}$. This long-range-interaction contribution to the overall scattering intensity is generally ignored in collisional treatments of intermolecular interactions, yet is likely to be of more significance than higher-order multipole terms in near-zone calculations. Finally it is shown how bands in a Raman spectrum due to cooperative scattering effects may be identified by their unique pressure characteristics, or by observation of light scattering that occurs outside the interaction volume of the laser beam. In the case where the scattering occurs between molecules or chromophores held in a fixed orientation with respect to one another, it is demonstrated how detection may be facilitated through the manifestation of a differential scattering effect.
ENGLISH ABSTRACT : Structured light has seen many applications in the fields of telecommunications, optical microscopy, and quantum information processing, however, few works exist that explore the interactions of structured light with atoms. In this thesis, we seek to explore these interactions further, both theoretically and experimentally. Of particular interest is the interaction between an atom and a Laguerre-Gauss beam of topological charge l = 1. Such a beam is easily constructed in a lab setting, and also carries an additional unit of orbital angular momentum that has been shown to couple with atomic transitions. Theoretically, we derive a framework upon which to describe atomic transitions due structured light. We find that tailoring light’s structure will have a direct influence on the strength of quadrupole transitions in atoms. A theoretical analysis of the effects of an atom situated in a magnetic field interacting with a Laguerre-Gauss beam of topological charge l = 1 was conducted. It was found that atoms placed in a region of zero intensity, such as the beam centre, can undergo quadrupole transitions – in contrast to dipole transitions that rely on the field intensity. We go on to show the differences between this beam and a gaussian beam, and find that the former can cause transitions between magnetic sub-levels that are typically considered forbidden in quadrupole spectroscopy under certain conditions. We explain this through the principle of conservation of angular momentum. Experimentally, we chose to use a potassium vapour cell as our medium, as the linewidth of its quadrupole transition was relatively large, and could be simply modelled as a three-level system to easily understand its dynamics. We performed an experiment where we indirectly measured a 4 2S1/2 → 3 2Dj quadrupole transition for j = 3/2, 5/2, induced by a custom-built external cavity diode laser operating at ∼ 464.3 nm. The 4 2S1/2 → 3 2Dj transition was measured by monitoring the fluorescence due to a dipole decay 4 2Pj 0 → 4 2S1/2 during the decay cascade from 3 2Dj → 4 2Pj 0 → 4 2S1/2 , where j 0 = 1/2, 3/2. We then used our theoretical framework to fit the sum of two gaussian peaks to our measured fluorescence spectrum, and find an excellent agreement with our data.
It is well known that a simple transformation of the electric dipole interaction provides a convenient means for ascertaining the effects of permanent dipoles on the optical behaviour of systems with a response dominated by two energy levels. By establishing the general validity of the procedure for parametric processes such as harmonic generation, it is shown how the detailed structure of the optical susceptibilities associated with arbitrary forms of optical nonlinearity can be ascertained by an algorithmic method, based on a novel interpretation of the relevant quantum electrodynamical Feynman diagrams. Application of the algorithm to second and third harmonic generation illustrates its usefulness and simplicity, whilst also providing new results and revealing features, related to the role of permanent dipoles, which have not hitherto been apparent.