Symmetry-based identification and enumeration of independent tensor properties in nonlinear and chiral optics.

For many laser-based methods of material characterization and analysis, a tensor formulation of theory is necessary, especially in techniques that exploit nonlinear or chiral optics. The fundamental interactions that underpin such methods offer various levels of approach to theory, but the most rigorous often lead to equations of considerable complexity. To compute the values for individual material parameters frequently demands making assumptions of extreme simplicity, overly dependent on calculational method, yet still providing unsatisfactory results. A pragmatic and entirely rigorous symmetry-based approach to the irreducible tensorial structures circumvents many of these problems, securing reliable results and guiding the pathway to applications. Instead of focusing on individual tensor components, such an approach can rapidly determine the number of linearly independent quantities-and hence the number of operationally different setups necessary for full characterization. By such means, one can directly ascertain how variations of optical polarization and beam geometry can reliably capture the response of any material system. The use of an irreducible tensor method operates independently of any means that might be chosen to calculate material properties. It removes the need for common simplifying assumptions, such as the approximation of tensorial structure by a scalar representation, adoption of a two-state model, or disregarding near-resonance damping. It also obviates any dependence on a choice of simulation package or quantum-calculational software. In this paper, the principles are set down and illustrated by application to experiments of varying degrees of complexity, including interactions of growing significance in the realm of chiral nonlinear optics. Limitations of this approach are also critically assessed.

Hyper-Rayleigh scattering optical activity: Theory, symmetry considerations, and quantum chemistry applications.

This work reports on the first computational quantum-chemistry implementation of the hyper-Rayleigh scattering optical activity (HRS-OA), a nonlinear chiroptical phenomenon. First, from the basics of the theory, which is based on quantum electrodynamics, and focusing on the electric dipole, magnetic-dipole, and electric-quadrupole interactions, the equations for the simulation of the differential scattering ratios of HRS-OA are re-derived. Then, for the first time, computations of HRS-OA quantities are presented and analyzed. They have been enacted on a prototypical chiral organic molecule (methyloxirane) at the time-dependent density functional theory level using a broad range of atomic orbital basis sets. In particular, (i) we analyze the basis set convergence, demonstrating that converged results require basis sets with both diffuse and polarization functions, (ii) we discuss the relative amplitudes of the five contributions to the differential scattering ratios, and (iii) we study the effects of origin-dependence and derived the expression of the tensor shifts and we prove the origin-independence of the theory for exact wavefunctions. Our computations show the ability of HRS-OA as a nonlinear chiroptical method, able to distinguish between the enantiomers of the same chiral molecule.

Fundamental symmetry origins in the chiral interactions of optical vortices.

Recently, a variety of mechanisms have been discovered that extend the range of optical techniques for identifying and characterizing molecular chirality, beyond those associated with optical polarization. It is now evident that beams of light with a twisted wavefront, known as optical vortices, can also interact with chiral matter with a specificity determined by relative handedness. Exploring this chiral sensitivity of vortex light in its interactions with matter requires careful consideration of the symmetry properties that engage in such processes. Most of the familiar measures of chirality are directly applicable to either matter, or to light itself-but only to one or the other. To elicit the principles that determine the viability of distinctly optical vortex-based forms of chiral discrimination invites a more universal approach to symmetry analysis, as is afforded by the common, fundamental physics of CPT symmetry. Taking this approach supports a comprehensive and straightforward analysis to identify the mechanistic origins of vortex chiroptical interactions. Careful inspection of selection rules for absorption also elicits the principles governing any identifiable engagement with vortex structures, providing a reliable basis to ascertain the viability of other forms of enantioselective vortex interaction.

500-Fold Amplification of Small Molecule Circularly Polarised Luminescence through Circularly Polarised FRET.

Strongly dissymmetric circularly polarised (CP) luminescence from small organic molecules could transform a range of technologies, such as display devices. However, highly dissymmetric emission is usually not possible with small organic molecules, which typically give dissymmetric factors of photoluminescence (gPL ) less than 10-2 . Here we describe an almost 103 -fold chiroptical amplification of a π-extended superhelicene when embedded in an achiral conjugated polymer matrix. This combination increases the |gPL | of the superhelicene from approximately 3×10-4 in solution to 0.15 in a blend film in the solid-state. We propose that the amplification arises not simply through a chiral environment effect, but instead due to electrodynamic coupling between the electric and magnetic transition dipoles of the polymer donor and superhelicene acceptor, and subsequent CP Förster resonance energy transfer. We show that this amplification effect holds across several achiral polymer hosts and thus represents a simple and versatile approach to enhance the g-factors of small organic molecules.

Influence of chirality on fluorescence and resonance energy transfer.

Electronically excited molecules frequently exhibit two distinctive decay mechanisms that rapidly generate optical emission: one is direct fluorescence and the other is energy transfer to a neighboring component. In the latter, the process leading to the ensuing "indirect" fluorescence is known as FRET, or fluorescence resonance energy transfer. For chiral molecules, both fluorescence and FRET exhibit discriminatory behavior with respect to optical and material handedness. While chiral effects such as circular dichroism are well known, as too is chiral discrimination for FRET in isolation, this article presents a study on a stepwise mechanism that involves both. Chirally sensitive processes follow excitation through the absorption of circularly polarized light and are manifest in either direct or indirect fluorescence. Following recent studies setting down the symmetry principles, this analysis provides a rigorous, quantum outlook that complements and expands on these works. Circumventing expressions that contain complicated tensorial components, our results are amenable for determining representative numerical values for the relative importance of the various coupling processes. We discover that circular dichroism exerts a major influence on both fluorescence and FRET, and resolving the engagement of chirality in each component reveals the distinct roles of absorption and emission by, and between, donor and acceptor pairs. It emerges that chiral discrimination in the FRET stage is not, as might have been expected, the main arbiter in the stepwise mechanism. In the concluding discussion on various concepts, attention is focused on the validity of helicity transfer in FRET.

Quantum features in the orthogonality of optical modes for structured and plane-wave light.

A fundamental photon creation-annihilation commutation relation underpins the familiar quantum formulation of optics. However, an internal inconsistency becomes apparent in the pursuit of structured light applications. This requires the relationship between operator commutation and mode orthogonality to be recast in a form ensuring full consistency with the precepts of quantum theory. A suitable reformulation, shown to register correctly an intrinsic quantum uncertainty in the associated interactions, has special relevance to optical vortex physics-particularly with regard to information content-through its connection to the degrees of freedom in the associated radiation modes.

Optical orbital angular momentum: twisted light and chirality.

The question of how the orbital angular momentum of structured light might engage with chiral matter is a topic of resurgent interest. By taking account of electric quadrupole transition moments, it is shown that the handedness of the beam can indeed be exhibited in local chiral effects, being dependent on the sign of the topological charge. In the specific case of absorption, a significant interplay of wavefront structure and polarization is resolved, and clear differences in behavior are identified for systems possessing a degree of orientational order and for those that are randomly oriented.

Perspective: Quantum Hamiltonians for optical interactions.

The multipolar Hamiltonian of quantum electrodynamics is extensively employed in chemical and optical physics to treat rigorously the interaction of electromagnetic fields with matter. It is also widely used to evaluate intermolecular interactions. The multipolar version of the Hamiltonian is commonly obtained by carrying out a unitary transformation of the Coulomb gauge Hamiltonian that goes by the name of Power-Zienau-Woolley (PZW). Not only does the formulation provide excellent agreement with experiment, and versatility in its predictive ability, but also superior physical insight. Recently, the foundations and validity of the PZW Hamiltonian have been questioned, raising a concern over issues of gauge transformation and invariance, and whether observable quantities obtained from unitarily equivalent Hamiltonians are identical. Here, an in-depth analysis of theoretical foundations clarifies the issues and enables misconceptions to be identified. Claims of non-physicality are refuted: the PZW transformation and ensuing Hamiltonian are shown to rest on solid physical principles and secure theoretical ground.

Nonlocalized Generation of Correlated Photon Pairs in Degenerate Down-Conversion.

The achievement of optimum conversion efficiency in conventional spontaneous parametric down-conversion requires consideration of quantum processes that entail multisite electrodynamic coupling, actively taking place within the conversion material. The physical mechanism, which operates through virtual photon propagation, provides for photon pairs to be emitted from spatially separated sites of photon interaction; occasionally pairs are produced in which each photon emerges from a different point in space. The extent of such nonlocalized generation is influenced by individual variations in both distance and phase correlation. Mathematical analysis of the global contributions from this mechanism provides a quantitative measure for a degree of positional uncertainty in the origin of down-converted emission.

Controlling resonance energy transfer in nanostructure emitters by positioning near a mirror.

The ability to control light-matter interactions in quantum objects opens up many avenues for new applications. We look at this issue within a fully quantized framework using a fundamental theory to describe mirror-assisted resonance energy transfer (RET) in nanostructures. The process of RET communicates electronic excitation between suitably disposed donor and acceptor particles in close proximity, activated by the initial excitation of the donor. Here, we demonstrate that the energy transfer rate can be significantly controlled by careful positioning of the RET emitters near a mirror. The results deliver equations that elicit new insights into the associated modification of virtual photon behavior, based on the quantum nature of light. In particular, our results indicate that energy transfer efficiency in nanostructures can be explicitly expedited or suppressed by a suitably positioned neighboring mirror, depending on the relative spacing and the dimensionality of the nanostructure. Interestingly, the resonance energy transfer between emitters is observed to "switch off" abruptly under suitable conditions of the RET system. This allows one to quantitatively control RET systems in a new way.

Symmetry analysis of Raman scattering mediated by neighboring molecules.

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 mediated by neighboring molecules.

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.

Transcriptome Analysis of a Ustilago maydis ust1 Deletion Mutant Uncovers Involvement of Laccase and Polyketide Synthase Genes in Spore Development.

Ustilago maydis, causal agent of corn smut disease, is a dimorphic fungus alternating between a saprobic budding haploid and an obligate pathogenic filamentous dikaryon. Maize responds to U. maydis colonization by producing tumorous structures, and only within these does the fungus sporulate, producing melanized sexual teliospores. Previously we identified Ust1, an APSES (Asm1p, Phd1p, Sok2p, Efg1p, and StuAp) transcription factor, whose deletion led to filamentous haploid growth and the production of highly pigmented teliospore-like structures in culture. In this study, we analyzed the transcriptome of a ust1 deletion mutant and functionally characterized two highly upregulated genes with potential roles in melanin biosynthesis: um05361, encoding a putative laccase (lac1), and um06414, encoding a polyketide synthase (pks1). The Δlac1 mutant strains showed dramatically reduced virulence on maize seedlings and fewer, less-pigmented teliospores in adult plants. The Δpks1 mutant was unaffected in seedling virulence but adult plant tumors generated hyaline, nonmelanized teliospores. Thus, whereas pks1 appeared to be restricted to the synthesis of melanin, lac1 showed a broader role in virulence. In conclusion, the ust1 deletion mutant provided an in vitro model for sporulation in U. maydis, and functional analysis supports the efficacy of this in vitro mutant analysis for identification of genes involved in in planta teliosporogenesis.

Laser optical separation of chiral molecules.

The optical trapping of molecules with an off-resonant laser beam involves a forward-Rayleigh scattering mechanism. It is shown that discriminatory effects arise on irradiating chiral molecules with circularly polarized light; the complete representation requires ensemble-weighted averaging to account for the influence of the trapping beam on the distribution of molecular orientations. Results of general application enable comparisons to be drawn between the results for two limits of the input laser intensity. It emerges that, in a racemic mixture, there is a differential driving force whose effect, at high laser intensities, is to produce differing local concentrations of the two enantiomers.

Hyper-Rayleigh scattering in centrosymmetric systems.

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 E1(3), does not account for all experimental observations. The relevant results emerge upon extending the theory to include E1(2)M1 and E1(2)E2 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 E1(2)E2 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.

On the nature of long range electronic coupling in a medium: distance and orientational dependence for chromophores in molecular aggregates.

The electronic coupling that mediates energy transfer in molecular aggregates is theoretically investigated using the principles of quantum electrodynamics (QED). In this context, both the electromagnetic tensor and rate equation relating to these couplings are re-examined with a focus on the role of the relative distance and orientation of transition dipole moment pairs, considering near-, intermediate-, and far-zone contributions to the coupling. The QED based coupling terms are investigated both analytically and numerically, and they are physically interpreted in terms of the character of the mediating (virtual) photons. The spatial dependence of the couplings for a two-dimensional molecular aggregate of ordered and isotropic transition dipole moments is numerically calculated. Further, Pauli Master Equations are employed for a one-dimensional chain of molecules and donor-acceptor pairs, to investigate the importance of intermediate- and far-zone contributions to the electronic coupling on electronic energy transfer dynamics. The results indicate that although Förster theory is often qualitatively and quantitatively correct for describing electronic energy transfer (EET) processes, intermediate- and far-zone coupling terms could sometimes be non-negligible for correctly describing EET in natural and artificial, mesoscopic, solar energy harvesting systems. In particular, the results indicate that these terms are non-negligible when using Förster resonance energy transfer spectroscopic ruler techniques for distances >10 nm.

Chiroptical Second-Harmonic Tyndall Scattering from Silicon Nanohelices.

Chirality is omnipresent in the living world. As biomimetic nanotechnology and self-assembly advance, they too need chirality. Accordingly, there is a pressing need to develop general methods to characterize chiral building blocks at the nanoscale in liquids such as water─the medium of life. Here, we demonstrate the chiroptical second-harmonic Tyndall scattering effect. The effect was observed in Si nanohelices, an example of a high-refractive-index dielectric nanomaterial. For three wavelengths of illumination, we observe a clear difference in the second-harmonic scattered light that depends on the chirality of the nanohelices and the handedness of circularly polarized light. Importantly, we provide a theoretical analysis that explains the origin of the effect and its direction dependence, resulting from different specific contributions of "electric dipole-magnetic dipole" and "electric dipole-electric quadrupole" coupling tensors. Using numerical simulations, we narrow down the number of such terms to 8 in forward scattering and to a single one in right-angled scattering. For chiral scatterers such as high-refractive-index dielectric nanoparticles, our findings expand the Tyndall scattering regime to nonlinear optics. Moreover, our theory can be broadened and adapted to further classes where such scattering has already been observed or is yet to be observed.

Second harmonic generation in isotropic media: six-wave mixing of optical vortices.

Optical vortex light can be up-converted into a second harmonic output in an isotropic medium, in which such conversion is normally forbidden, through six-wave mixing. The involvement of orbital angular momentum is tackled for the case of a Laguerre-Gaussian pump comprising l = 1 photons. By calculating quantum amplitudes for the emergent radiation states, utilizing a state-sequence method, the analysis identifies the characteristics of the emission and an entangled distribution of conserved orbital momentum. A distinctive conical spread affords a potential means of resolving the individual angular momentum content.

Photonic measures of helicity: optical vortices and circularly polarized reflection.

For both paraxial and nonparaxial light, numerous electromagnetic quantities are expressible in terms of photon annihilation and creation operators. Accordingly, measures of energy, angular momentum, and chirality acquire a consistent interpretation. From the photonic nature of light, it emerges that an infinite hierarchy of spin-type measures depend on a difference in number operators for modes of opposing helicity, with pure circular polarization giving maximal values. Measures of orbital angular momentum are determined by a sum of corresponding number operators. Analysis of the electric and magnetic fields in the reflection of circular polarizations reveals regions of prominent chiral interference.

Optical vortex generation from molecular chromophore arrays.

The generation of light endowed with orbital angular momentum, frequently termed optical vortex light, is commonly achieved by passing a conventional beam through suitably constructed optical elements. This Letter shows that the necessary phase structure for vortex propagation can be directly produced through the creation of twisted light from the vacuum. The mechanism is based on optical emission from a family of chromophore nanoarrays that satisfy specific geometric and symmetry constraints. Each such array can support pairs of electronically delocalized doubly degenerate excitons whose azimuthal phase progression is responsible for the helical wave front of the emitted radiation. The exciton symmetry dictates the maximum magnitude of topological charge; detailed analysis secures the conditions necessary to deliver optical vortices of arbitrary order.