Controlling the symmetry of inorganic ionic nanofilms with optical chirality.

Manipulating symmetry environments of metal ions to control functional properties is a fundamental concept of chemistry. For example, lattice strain enables control of symmetry in solids through a change in the nuclear positions surrounding a metal centre. Light-matter interactions can also induce strain but providing dynamic symmetry control is restricted to specific materials under intense laser illumination. Here, we show how effective chemical symmetry can be tuned by creating a symmetry-breaking rotational bulk polarisation in the electronic charge distribution surrounding a metal centre, which we term a meta-crystal field. The effect arises from an interface-mediated transfer of optical spin from a chiral light beam to produce an electronic torque that replicates the effect of strain created by high pressures. Since the phenomenon does not rely on a physical rearrangement of nuclear positions, material constraints are lifted, thus providing a generic and fully reversible method of manipulating effective symmetry in solids.

Nonuniform Currents and Spins of Relativistic Electron Vortices in a Magnetic Field.

We present a relativistic description of electron vortex beams in a homogeneous magnetic field. Including spin from the beginning reveals that spin-polarized electron vortex beams have a complicated azimuthal current structure, containing small rings of counterrotating current between rings of stronger corotating current. Contrary to many other problems in relativistic quantum mechanics, there exists a set of vortex beams with exactly zero spin-orbit mixing in the highly relativistic and nonparaxial regime. The well-defined phase structure of these beams is analogous to simpler scalar vortex beams, owing to the protection by the Zeeman effect. For states that do show spin-orbit mixing, the spin polarization across the beam is nonuniform rendering the spin and orbital degrees of freedom inherently inseparable.

Chirality and the angular momentum of light.

Chirality is exhibited by objects that cannot be rotated into their mirror images. It is far from obvious that this has anything to do with the angular momentum of light, which owes its existence to rotational symmetries. There is nevertheless a subtle connection between chirality and the angular momentum of light. We demonstrate this connection and, in particular, its significance in the context of chiral light-matter interactions.This article is part of the themed issue 'Optical orbital angular momentum'.

Eigenpolarizations for giant transverse optical beam shifts.

We show how careful control of the incident polarization of a light beam close to the Brewster angle gives a giant transverse spatial shift on reflection. This resolves the long-standing puzzle of why such beam shifts transverse to the incident plane (Imbert-Fedorov shifts) tend to be an order of magnitude smaller than the related Goos-Hänchen shifts in the longitudinal direction, which are largest close to critical incidence. We demonstrate that with the proper initial polarization the transverse displacements can be equally large, which we confirm experimentally near Brewster incidence. In contrast to the established understanding, these polarizations are elliptical and angle dependent. We explain the magnitude of the Imbert-Fedorov shift by an analogous change of the symmetry properties for the reflection operators as compared to the Goos-Hänchen shift.

Limits to superweak amplification of beam shifts.

The magnitudes of beam shifts (Goos-Hänchen and Imbert-Fedorov, spatial and angular) are greatly enhanced when a reflected light beam is postselected by an analyzer, by analogy with superweak measurements in quantum theory. Particularly strong enhancements can be expected close to angles at which no light is transmitted for fixed initial and final polarizations. We derive a formula for the angular and spatial shifts at such angles (which includes the Brewster angle), and we show that their maximum size is limited by higher-order terms from the reflection coefficients occurring in the Artmann shift formula.

Topological aberration of optical vortex beams: determining dielectric interfaces by optical singularity shifts.

We predict the splitting of a high-order optical vortex into a constellation of unit vortices, upon total internal reflection of the carrier beam, and analyze the splitting. The reflected vortex constellation generalizes, in a local sense, the familiar longitudinal Goos-Hänchen and transverse Imbert-Fedorov shifts of the centroid of a reflected optical beam. The centroid shift is related to the center of the constellation, whose geometry otherwise depends on higher-order terms in an expansion of the reflection matrix. We derive an approximation of the amplitude around the constellation as a complex analytic polynomial, whose roots are the vortices. Increasing the order of the initial vortex gives an Appell sequence of complex polynomials, which we explain by an analogy with the theory of optical aberration.

Paraxial and nonparaxial polynomial beams and the analytic approach to propagation.

We construct solutions of the paraxial and Helmholtz equations that are polynomials in their spatial variables. These are derived explicitly by using the angular spectrum method and generating functions. Paraxial polynomials have the form of homogeneous Hermite and Laguerre polynomials in Cartesian and cylindrical coordinates, respectively, analogous to heat polynomials for the diffusion equation. Nonparaxial polynomials are found by substituting monomials in the propagation variable z with reverse Bessel polynomials. These explicit analytic forms give insight into the mathematical structure of paraxially and nonparaxially propagating beams, especially in regard to the divergence of nonparaxial analogs to familiar paraxial beams.

Background-free detection of single 5 nm nanoparticles through interferometric cross-polarization microscopy.

Metal nanoparticles play a key role in sensing and imaging. Here we demonstrate the detection of metal particles down to 5 nm in size with a signal-to-noise ratio of ∼7 using interferometric cross-polarization microscopy at ultralow excitation powers (∼1 µW) compatible with single molecule detection. The method is background-free and induces no heating as it operates far from plasmonic resonance. The combination of unlimited observation time and protein-sized metal nanoparticles has great potential for biophysical applications.

Light beams with fractional orbital angular momentum and their vortex structure.

Light emerging from a spiral phase plate with a non-integer phase step has a complicated vortex structure and is unstable on propagation. We generate light carrying fractional orbital angular momentum (OAM) not with a phase step but by a synthesis of Laguerre-Gaussian modes. By limiting the number of different Gouy phases in the superposition we produce a light beam which is well characterised in terms of its propagation. We believe that their structural stability makes these beams ideal for quantum information processes utilising fractional OAM states.