Mathew D. Williams

Raman spectroscopy is a key technique for the identification and structural interrogation of molecules. It generally exploits changes in vibrational state within individual molecules which produce, in the scattered light, frequencies that are absent in the incident light. Considered as a quantum optical process, each Raman scattering event involves the concurrent annihilation and creation of photons of two differing radiation modes, accompanying vibrational excitation or decay. For molecules of sufficiently high symmetry, certain transitions may be forbidden by the two-photon selection rules, such that corresponding frequency shifts may not appear in the scattered light. By further developing the theory on a formal basis detailed in other recent work [M. D. Williams et al., J. Chem. Phys. 144, 174304 (2016)], the present analysis now addresses cases in which expected selection rule limitations are removed as a result of the electronic interactions between neighboring molecules. In consequence, new vibrational lines may appear—even some odd parity (ungerade) vibrations may then participate in the Raman process. Subtle differences arise according to whether the input and output photon events occur at either the same or different molecules, mediated by intermolecular interactions. For closely neighboring molecules, within near-field displacement distances, it emerges that the radiant intensity of Raman scattering can have various inverse-power dependences on separation distance. A focus is given here to the newly permitted symmetries, and the results include an extended list of irreducible representations for each point group in which such behavior can arise.

Raman scattering is most commonly associated with a change in vibrational state within individual molecules, the corresponding frequency shift in the scattered light affording a key way of identifying material structures. In theories where both matter and light are treated quantum mechanically, the fundamental scattering process is represented as the concurrent annihilation of a photon from one radiation mode and creation of another in a different mode. Developing this quantum electrodynamical formulation, the focus of the present work is on the spectroscopic consequences of electrodynamic coupling between neighboring molecules or other kinds of optical center. To encompass these nanoscale interactions, through which the molecular states evolve under the dual influence of the input light and local fields, this work identifies and determines two major mechanisms for each of which different selection rules apply. The constituent optical centers are considered to be chemically different and held in a fixed orientation with respect to each other, either as two components of a larger molecule or a molecular assembly that can undergo free rotation in a fluid medium or as parts of a larger, solid material. The two centers are considered to be separated beyond wavefunction overlap but close enough together to fall within an optical near-field limit, which leads to high inverse power dependences on their local separation. In this investigation, individual centers undergo a Stokes transition, whilst each neighbor of a different species remains in its original electronic and vibrational state. Analogous principles are applicable for the anti-Stokes case. The analysis concludes by considering the experimental consequences of applying this spectroscopic interpretation to fluid media; explicitly, the selection rules and the impact of pressure on the radiant intensity of this process.

Stacked multi-layer films have a range of well-known applications as optical elements. The various types of theory commonly used to describe optical propagation through such structures rarely take account of the quantum nature of light, though phenomena such as Anderson localization can be proven to occur under suitable conditions. In recent and ongoing work based on quantum electrodynamics, it has been shown possible to rigorously reformulate, in photonic terms, the fundamental mechanisms that are involved in reflection and optical transmission through stacked nanolayers. Accounting for sum-over-pathway features in the quantum mechanical description, this theory treats the sequential interactions of photons with material boundaries in terms of individual scattering events. The study entertains an arbitrary number of reflections in systems comprising two or three internally reflective surfaces. Analytical results are secured, without recourse to FTDT (finite-difference time-domain) software or any other finite-element approximations. Quantum interference effects can be readily identified. The new results, which cast the optical characteristics of such structures in terms of simple, constituent-determined properties, are illustrated by model calculations

Raman scattering is most commonly associated with a change in vibrational state within one molecule, with signals in the corresponding spectrum widely used to identify material structures. When the corresponding theory is developed using quantum electrodynamics, the fundamental scattering process is described by a single photon of one radiation mode being annihilated with the concurrent creation of another photon; the two photon energies differ by an amount corresponding to the transfer of vibrational energy within the system. Here, we consider nanoscale interactions between neighboring molecules to mediate the process, by way of a virtual photon exchange to connect the evolution of the two molecular states. We consider both a single and pair of virtual photon exchanges. Our analysis deploys two realistic assumptions: in each pairwise interaction the two components are considered to be (i) chemically different and (ii) held in a fixed orientation with respect to each other, displaced by an amount equivalent to the near-field region; resulting in higher order dependences on displacement R becoming increasingly significant, and at the limit the short-range R-6 term can even dominate over R-3 dependence. In our investigation one center undergoes a change in vibrational energy; each neighboring molecule returns to the electronic and vibrational state in which it began. For the purposes of providing results, a Stokes transition has been assumed; analogous principles hold for the anti-Stokes counterpart. Experimentally, there is no change to the dependence on the intensity of laser light. However, the various mechanisms presented herein lead to different selection rules applying in each instance. In some cases specifically identifiable mechanisms will be active for a given transition, leading to new and characteristic lines in the Raman spectrum. A thorough investigation of all physically achievable mechanisms will be detailed in this work

Descriptions of optical beams with structured wavefronts or vector polarizations are widely cast in terms of classical field theory. The corresponding fully quantum counterparts often present new insights into what is physically observed, and they are especially of interest when tackling issues such as entanglement. Similarly, when determining angular momentum densities, it appears that the separate roles of photon spin and beam topological charge can only be satisfactorily addressed within a quantum framework. In some such respects, the quantum versions of theory might be considered to introduce an additional layer of complexity; in others, they can clearly and very substantially simplify the theoretical representation. At the photon level, the fully quantized descriptions of topologically structured and singular beams nonetheless raise important fundamental questions and puzzles, whose resolution continue to invite attention. Many of the mechanistic interpretations and predictions (those that appear to be supported by a true congruence between classic and quantum optical descriptions, essentially conflating electromagnetic field and state wavefunction concepts) can lead to theoretical pitfalls. This paper highlights some physical implications that emerge from a fully quantum treatment of theory

Hyper-Rayleigh scattering (HRS) is an incoherent mechanism for optical second harmonic generation. The frequency-doubled light that emerges from this mechanism is not emitted in a laser-like manner, in the forward direction; it is scattered in all directions. The underlying theory for this effect involves terms that are quadratic in the incident field and involves an even-order optical susceptibility (for a molecule, its associated hyperpolarizability). In consequence, HRS is often regarded as formally forbidden in centrosymmetric media. However, for the fundamental three-photon interaction, theory based on the standard electric dipole approximation, representable as E1³, does not account for all experimental observations. The relevant results emerge upon extending the theory to include E1²M1 and E1²E2 contributions, incorporating one magnetic dipolar or electric quadrupolar interaction, respectively, to a consistent level of multipolar expansion. Both additional interactions require the deployment of higher orders in the multipole expansion, with the E1²E2 interaction analogous in rank and parity to a four-wave susceptibility. To elicit the correct form of response from fluid or disordered media invites a tensor representation which does not oversimplify the molecular components, yet which can produce results to facilitate the interpretation of experimental observations. The detailed derivation in this work leads to results which are summarized for the following: perpendicular detection of polarization components both parallel and perpendicular to the pump radiation, leading to distinct polarization ratio results, as well as a reversal ratio for forward scattered circular polarizations. The results provide a route to handling data with direct physical interpretation, to enable the more sophisticated design of molecules with sought nonlinear optical properties.

Generation of light carrying orbital angular momentum (OAM) is of fundamental interest due to its applications in a broad range of fields, such as classical and quantum optical communications, and optical micro-manipulation. Light carrying a well defined state of OAM is typically created by imparting an azimuthally varying phase structure onto a plane wave. In this work, we investigate, using numerical simulations and experiments, the OAM spectra of light radiated from a heavily course grained emission pattern: an array of discrete circular apertures arranged in a ring configuration, with a constant phase increment between adjacent apertures. We show how the number of apertures and their relative phase defines the position and spacing of peaks in the OAM spectra. We demonstrate that by spatially filtering beams emitted from such a configuration, higher order peaks in the OAM spectra can be suppressed, leaving a single dominant lowest order peak, and recovering a beam carrying a well-defined OAM state. We qualitatively interpret the efficiency of generating beams this way in terms of the angular uncertainty principle.

Hyper-Rayleigh scattering (HRS) is an incoherent variant of second harmonic generation. The theory involves terms of increasing order of optical nonlinearity: for molecules or unit cells that are centrosymmetric, and which accordingly lack even-order susceptibilities, HRS is often regarded as formally forbidden. However, for the three-photon interaction, theory based on the standard electric dipole approximation, represented as E13, does not include the detail required to describe what is observed experimentally, in the absence of a static field. New results emerge upon extending the theory to include E12E2 and E12M1, incorporating one electric quadrupolar or magnetic dipolar interaction respectively. Both additional interactions require the deployment of higher orders in the multipole expansion to govern these processes, with the E12E2 interaction analogous in rank and parity to a four-wave susceptibility. A key feature of the present work is its foundation upon a formal tensor derivation which does not oversimplify the molecular components, yet leads to results whose interpretation can be correlated with experimental observations. Results are summarized for the perpendicular detection of both parallel and perpendicular polarizations. Using such methods to investigate molecular systems that might have useful nonlinear characteristics, HRS therefore provides a route to data with direct physical interpretation, to enable more sophisticated design of molecules with sought optical properties

Light beams with unusual forms of wavefront offer a host of useful features to extend the repertoire of those developing new optical techniques. Complex, non-uniform wavefront structures offer a wide range of optomechanical applications, from microparticle rotation, traction and sorting, through to contactless microfluidic motors. Beams combining transverse nodal structures with orbital angular momentum, or vector beams with novel polarization profiles, also present new opportunities for imaging and the optical transmission of information, including quantum entanglement effects. Whilst there are numerous well-proven methods for generating light with complex wave-forms, most current methods work on the basis of modifying a conventional Hermite-Gaussian beam, by passage through suitably tailored optical elements. It has generally been considered impossible to directly generate wave-front structured beams either by spontaneous or stimulated emission from individual atoms, ions or molecules. However, newly emerged principles have shown that emitter arrays, cast in an appropriately specified geometry, can overcome the obstacles: one possibility is a construct based on the electronic excitation of nanofabricated circular arrays. Recent experimental work has extended this concept to a phase-imprinted ring of apertures holographically encoded in a diffractive mask, generated by a programmed spatial light modulator. These latest advances are potentially paving the way for creating new sources of structured light.