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 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 E1<sup>3</sup>, 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
E1<sup>2</sup>E2 and E1<sup>2</sup>M1, 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 E1<sup>2</sup>E2
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
It has recently been shown possible to directly generate an optical vortex (a beam of light endowed with orbital angular momentum) by spontaneous emission from a molecular exciton array. This contrasts with most established methods, which typically rely on the modification of a conventional beam by an appropriate optical element (for example, a q-plate) to impose the requisite helical twist of a vortex. The new procedure is achieved by nanofabricating a chiral arrangement of chromophores into a ring of specifically configured symmetry, supporting a doubly degenerate (conjugated) exciton with the appropriate azimuthal phase progression. It emerges that the symmetry elements present in the phase structure of the optical field, produced by emission from these degenerate excitons on a array, exhibits precisely the sought character of an optical vortex. The highest order of exciton symmetry, including the corresponding splitting of the electronic states, dictates the maximum magnitude of the topological charge. Work is now progressing on computer simulations aiming to reveal the detailed pattern of polarization behaviour in the emitted light, in which the vector character of the beam progresses around the phase singularity along the beam propagation axis. Significantly, this analysis points to the emission of radiation with polarization varying over the beam profile.
Optical vortex light engendered with integer units of orbital angular momentum (OAM) may be involved in frequency upconversion. Second harmonic generation is usually forbidden in isotropic media due to parity constraints, but it becomes allowed by six-wave mixing. Here, we present a rigorous quantum analysis for the case of a Laguerre-Gaussian input beam comprising photons endowed with a single unit of OAM. Such a process gives rise to the novel entanglement of orbital momentum in two emergent photons; it transpires that the mechanism delivers a harmonic output whose polarization is essentially parallel to the incident radiation. This investigation ascertains the character of the emission, both under forward propagation and back-reflection geometries, and identifies in detail the form of distribution in the entangled total orbital momentum. A distinctive conical spread, originating from the entangled distribution in the emission pair, affords a potential means to determine the individual angular momenta.
Light generated with orbital angular momentum, commonly known as an optical vortex, is widely achieved by modifying the phase structure of a conventional laser beam through the utilization of a suitable optical element. In recent research, a process has been introduced that can produce electromagnetic radiation with a helical wave-front directly from a source. The chirally driven optical emission originates from a hierarchy of tailored nanoscale chromophore arrays arranged with a specific propeller-like geometry and symmetry. In particular, a nanoarray composed of n particles requires each component to be held in a configuration with a rotation and associated phase shift of 2 π/n radians with respect to its neighbor. Following initial electronic excitation, each such array is capable of supporting delocalized doubly degenerate excitons, whose azimuthal phase progression is responsible for the helical wave-front. Under identified conditions, the relaxation of the electronically-excited nanoarray produces structured light in a spontaneous manner. Nanoarrays of escalating order, i.e. those containing an increasing number of components, enable access to a set of topological charges of higher order. Practical considerations for the development of this technique are discussed, and potential new applications are identified.
Spin provides for a well-known extension to the information capacity of nanometer-scale electronic devices. Spin transfer can be effected with high fidelity between quantum dots, this type of emission being primarily associated with emission dipoles. However, in seeking to extend the more common spectroscopic connection of dipole transitions with orbital angular momentum, it has been shown impossible to securely transmit information on any other multipolar basis – partly because point detectors are confined to polarization measurement. Standard polarization methods in optics provide for only two independent degrees of freedom, such as the circular states of opposing handedness associated with photon spin. Complex light beams with structured wave-fronts or vector polarization do, however, offer a basis for additional degrees of freedom, enabling individual photons to convey far more information content. A familiar example is afforded by Laguerre-Gaussian modes, whose helically twisted wave-front and vortex fields are associated with orbital angular momentum. Each individual photon in such a beam has been shown to carry the entire spatial helical-mode information, supporting an experimental basis for sorting beams of different angular momentum content. One very recent development is a scheme for such optical vortices to be directly generated through electronic relaxation processes in structured molecular chromophore arrays.