Magnetochiral anisotropy

In biology, chemistry and physics one often deals with systems that can occur in two forms that are each other's mirror image. A new magneto-optical effect called magnetochiral anisotropy (MChA) is described that establishes a link between chirality and magnetic fields and that can discriminate between the two enantiomers (mirror images) of chiral systems. It is shown that through MChA a magnetic field can lead to an enantiomeric excess in a photochemical reaction with unpolarized light. The existence of MChA can be deduced from general symmetry arguments, and the question comes to mind whether this effect can manifest itself in other magnetotransport phenomena in chiral media. Theoretical evidence is presented that indeed MChA is a general phenomenon, and its existence is demonstrated experimentally in the electrical conductivity of carbon nanotubes.     

Chiral plasmonics and enhanced chiral light-matter interactions

Chirality, which describes the broken mirror symmetry in geometric structures, exists macroscopically in our daily life as well as microscopically down to molecular levels. Correspondingly, chiral molecules interact differently with circularly polarized light exhibiting opposite handedness(left-handed and right-handed). However, the interaction between chiral molecules and chiral light is very weak. In contrast, artificial chiral plasmonic structures can generate "super-chiral" plasmonic near-field, leading to enhanced chiral light-matter(or chiroptical) interactions. The "super-chiral" near-field presents different amplitude and phase under opposite handedness incidence, which can be utilized to engineer linear and nonlinear chiroptical interactions. Specifically,in the interaction between quantum emitters and chiral plasmonic structures, the chiral hot spots can favour the emission with a specific handedness. This article reviews the state-of-the-art research on the design, fabrication and chiroptical response of different chiral plasmonic nanostructures or metasurfaces. This review also discusses enhanced chiral light-matter interactions that are essential for applications like chirality sensing, chiral selective light emitting and harvesting. In the final part, the review ends with a perspective on future directions of chiral plasmonics.     

Chiral symmetry breaking: (i) limited enantioselectivity and (ii) mutual inhibition

The stability properties of models of spontaneous mirror symmetry breaking in chemistry are characterized geometrically and analytically. The first model accounts for limited enantioselectivity, while the second is the Frank model in which the mutual inhibition reaction is allowed to be reversible. Both models include the autocatalytic amplification of units of the same chirality as well as chiral inhibition, in unison regarded to be the elementary requirements for achieving symmetry breaking of initially racemic mixtures. When the control parameter for each model falls below its corresponding critical value, the racemic state becomes unstable, and chiral amplification results. These final stable chiral states are not homochiral: mirror symmetry is broken, but the breaking is not absolute. Numerical solutions are obtained in two space dimensions.     

Stability of racemic and chiral steady states in open and closed chemical systems

The stability properties of models of spontaneous mirror symmetry breaking in chemistry are characterized algebraically. The models considered here all derive either from the Frank model or from autocatalysis with limited enantioselectivity. Emphasis is given to identifying the critical parameter controlling the chiral symmetry breaking transition from racemic to chiral steady-state solutions. This parameter is identified in each case, and the constraints on the chemical rate constants determined from dynamic stability are derived.     

Screw split ring resonator as building block of three-dimensional chiral metamaterials

We proposed and numerically investigated the influence of spatial topology on the infrared frequency region response of chiral metamaterials based on discrete deformed split ring resonators. Compared with the well studied continuous helix, the proposed metamaterials with discrete topology exhibit broad band chiral electromagnetic response. It is shown that the conversion between left and right circular polarization waves for our model is much broader than the continuous helix model. The observed cross-coupling between electric and magnetic fields results from the chiral electric currents on the resonators due to the broken mirror symmetry. The findings are useful for the design of future real three-dimensional chiral metamaterials with tunable optical response.     

Electron mirror as a corrector of electron microscope objective aberrations

We describe a new optoelectronic system for correcting aberrations of the objective lens with the help of an electron mirror. The system is based on the implementation of a special focusing regime (so-called regime of superimposed images) in which two images of the object are formed in the plane passing through the center of the curvature of the mirror. One of these images is formed by the beams (with aberrations) emerging from the objective lens, and the other is formed by the beams (with cancelled aberrations) reflected from the mirror. The separation of the two superimposed images and visualization of the image with cancelled aberrations are performed by deflection of the electron beam in the axisymmetric magnetic field whose symmetry axis passes through the center of curvature of the electron mirror. The magnetic field distribution ensuring aberration-free deflection of the electron beam is calculated.     

Molecular QED of coherent and incoherent sum-frequency and second-harmonic generation in chiral liquids in the presence of a static electric field

Coherent second-order nonlinear optical processes are symmetry forbidden in centrosymmetric environments in the electric-dipole approximation. In liquids that contain chiral molecules, however, and which therefore lack mirror image symmetry, coherent sum-frequency generation is possible, whereas second-harmonic generation remains forbidden. Here we apply the theory of molecular quantum electrodynamics to the calculation of the matrix element, transition rate, and integrated signal intensity for sum-frequency and second-harmonic generation taking place in a chiral liquid in the presence and absence of a static electric field, to examine which coherent and incoherent processes exist in the electric-dipole approximation in liquids. Third- and fourth-order time-dependent perturbation theory is employed in combination with single-sided Feynman diagrams to evaluate two contributions arising from static field-free and field-induced processes. It is found that, in addition to the coherent term, an incoherent process exists for sum-frequency generation in liquids. Surprisingly, in the case of dc-field-induced second-harmonic generation, the incoherent contribution is found to always vanish for isotropic chiral liquids even though hyper-Rayleigh second-harmonic generation and electric-field-induced second-harmonic generation are both independently symmetry allowed in any liquid.     

Asymmetric Transmission in the Planar Chiral Nanostructure Induced by Electric and Magnetic Resonance at the Same Wavelength

Asymmetric transmission (AT) reflects the conversion efficiency of a chiral nanostructure for circularly polarized light and is widely used in polarization and optoelectronic devices. In this study, a new mechanism is proposed to generate AT when a planar chiral nanostructure is illuminated under left‐handed circularly polarized (LCP) and right‐handed circularly polarized (RCP) light illumination. The new mechanism can be achieved by breaking the symmetry of the designed planar chiral nanostructure which give rise to a new transmittance peak and dip at a particular wavelength under RCP and LCP light illumination, respectively. The proposed new mechanism is also capable of actively tuning the generated resonant modes. Besides this, when graphene strips are added to the designed planar chiral nanostructure, similar results are obtained as that from breaking the symmetry of the planar chiral nanostructure. In this case, the generated AT could also be actively tuned by varying the Fermi energies of graphene strips.     

Optical manifestations of planar chirality

We report that planar chiral structures affect the polarization state of light in a manner similar to three-dimensional chiral (optical active) media. In experiments with artificial metal-on-silicon chiral planar gratings of 442 wallpaper group symmetry, containing millions of chiral elements per square centimeter, we observed rotation of the polarization azimuth in excess of 30 degrees of light diffracted from it. The rotation was found to change its sign for two enantiomeric forms of the media and to have components associated with both the structural arrangement and the chirality of individual structural elements.     

Gluon condensates,chiral symmetry breaking and pion wave-function

We consider here chiral symmetry breaking in quantum chromodynamics arising from gluon condensates in vacuum. Through coherent states of gluons simulating a mean field type of approximation, we show that the off-shell gluon condensates of vacuum generate a mass-like contribution for the quarks, giving rise to chiral symmetry breaking. We next note that spontaneous breaking of global chiral symmetry links the four component quark field operator to the pion wave function. This in turn yields many hadronic properties in the light quark sector in agreement with experiments, leading to the conclusion that low energy hadron properties are primarily driven by the vacuum structure of quantum chromodynamics.     

Broken enantiomeric symmetry for electromagnetic waves interacting with planar chiral nanostructures

Simulations of Maxwell’s equations for electromagnetic waves interacting with planar chiral structures are shown to depend on the polarization state of the exciting light field. These results illustrate generic features of light interaction with planar chiral structures and imply broken enantiomeric symmetry for excitation with circularly polarized light. PACS 78.67.-n; 11.30.-j     

Complete double-projection of light fermion masses in supersymmetric composite models

We present some general classes of supersymmetric models in which the 't Hooft anomaly-matching conditions are precisely satisfied by quasi-Goldstone fermions (QGFs) and hence mass of all the light composite fermions is double-protected by supersymmetry and chiral symmetry. To find this kind of models in an economic way we show that the low-energy spectrum consistent with chiral symmetry is exhausted by QGFs whenever there exists a complementary Higgs picture of the QGF model.     

Relation between proton and neutron asymptotic normalization coefficients for light mirror nuclei and its relevance to nuclear astrophysics

We show how the charge symmetry of strong interactions can be used to relate the proton and neutron asymptotic normalization coefficients (ANCs) of the one-nucleon overlap integrals for light mirror nuclei. This relation extends to the case of real proton decay where the mirror analog is a virtual neutron decay of a loosely bound state. In this case, a link is obtained between the proton width and the squared ANC of the mirror neutron state. The relation between mirror overlaps can be used to study astrophysically relevant proton capture reactions based on information obtained from transfer reactions with stable beams.     

Symmetry relations revealed in Mueller matrix hemispherical maps

The hemispherical Mueller matrix map for light reflected from a plane-parallel planetary atmosphere is shown to obey several symmetry properties that provide a straightforward method to check their physical realizability. The mirror scattering relation and the reciprocity relation are employed to support the symmetry rules for hemispherical Mueller matrix maps. Additionally, two classes of experiments are identified in which the symmetry rules can be applied, namely, when the incident beam is at zenith and off-zenith angles and the scattering particles are spheres and randomly oriented hexagonal particles.     

Tests of the naturalness of the coupling constants in ChPT at order p6

We derive constraints on combinations of O(p⁶) chiral coupling constants by matching a recent two-loop calculation of the πK scattering amplitude with a set of sum rules. We examine the validity of the natural expectation that the values of the chiral couplings can be associated with physics properties of the light resonance sector. We focus, in particular, on flavor symmetry breaking of vector resonances. A resonance chiral Lagrangian is constructed which incorporates flavor symmetry breaking more completely than was done before. We use πK unsubtracted sum rules as tests of the modelling of the resonance contributions to the chiral couplings. In some cases the O(p⁶) couplings are found not to be dominated by the resonance contributions. PACS 12.39.Fe; 11.55.Hx; 13.75.Lb     

Right handed or left handed? Forbidden x-ray diffraction reveals chirality

Enantiomers, or stereoisomers, have crystal structures that are mirror images of each other and are thus handed, like our right and left hands. The physical properties of enantiomers are identical except for optical activity, which rotates linearly polarized light by equal amounts but in opposite directions. While conventional x-ray Bragg diffraction can determine crystal structures, it does not distinguish between right- and left-handed crystals. We show resonant Bragg diffraction using circularly polarized x rays reveals the handedness of crystals by coupling x-ray helicity to a crystal screw axis. The intensity of resonantly allowed reflection of alpha-quartz is well described by an admixture of a parity-even and a parity-odd process. Our results are of general importance and demonstrate a new method to directly study chiral motifs in structures that include biomaterials, liquid crystals, magnets, multiferroics, etc.     

Focal-length measurements of deep parabolic mirrors

The focal length of deep parabolic mirrors is determined by using the shadows of two fibres placed in front of the mirror and illuminated by collimated light. By double reflexion on the deep mirror two shadow images of each fibre are formed and if all these images are in contact, the fibre distance is 4?     

Adsorption on nanostructured chiral surfaces studied by the Monte Carlo method

A Monte Carlo (MC) lattice gas model of adsorption of a racemic mixture of enantiomers of 1,2-dimethylcyclopropane on a chiral surface with different spatial distribution of active sites was proposed. The calculations were performed on a square lattice for both stepped chiral surfaces and smooth surfaces with chiral patterns of active sites. The adsorbing molecules were assumed to be rigid structures of two types being mirror images one of another. Regardless of the enantiomer type, each molecule was composed of four segments occupying four lattice sites. The chiral surfaces were exposed to equimolar mixture of enantiomers whose individual equilibrium adsorption isotherms were calculated using standard Grand Canonical MC technique. The major purpose of the simulation was to examine how the structure of the surface affects separation of enantiomers, that is, to determine enantioselectivity defined as the ratio of their adsorbed amounts. Additionally, comparison of the enantioselectivities corresponding to the stepped and smooth surfaces was made.