Plasmonic metasurfaces manipulating the two spin components from spin–orbit interactions of light with lattice field generations

Artificial nanostructures in metasurfaces induce strong spin–orbit interactions (SOIs), by which incident circularly polarized light can be transformed into two opposite spin components. The component with an opposite helicity to the incident light acquires a geometric phase and is used to realize the versatile functions of the metasurfaces; however, the other component, with an identical helicity, is often neglected as a diffused background. Here, by simultaneously manipulating the two spin components originating from the SOI in plasmonic metasurfaces, independent wavefields in the primary and converted spin channels are achieved; the wavefield in the primary channel is controlled by tailoring the dynamic phase, and that in the converted channel is regulated by designing the Pancharatnam–Berry phase in concurrence with the dynamic phase. The scheme is realized by generating optical lattice fields with different topologies in two spin channels, with the metasurfaces composed of metal nanoslits within six round-apertures mimicking the multi-beam interference. This study demonstrates independent optical fields in a dual-spin channel based on the SOI effect in the metasurface, which provides a higher polarization degree of freedom to modify optical properties at the subwavelength scale.

Celestial diamonds: conformal multiplets in celestial CFT

We examine the structure of global conformal multiplets in 2D celestial CFT. For a 4D bulk theory containing massless particles of spin s = $$ \left\{0,\frac{1}{2},1,\frac{3}{2},2\right\} $$ 0 1 2 1 3 2 2 we classify and construct all SL(2,ℂ) primary descendants which are organized into ‘celestial diamonds’. This explicit construction is achieved using a wavefunction-based approach that allows us to map 4D scattering amplitudes to celestial CFT correlators of operators with SL(2,ℂ) conformal dimension ∆ and spin J. Radiative conformal primary wavefunctions have J = ±s and give rise to conformally soft theorems for special values of ∆ ∈ $$ \frac{1}{2}\mathbb{Z} $$ 1 2 ℤ . They are located either at the top of celestial diamonds, where they descend to trivial null primaries, or at the left and right corners, where they descend both to and from generalized conformal primary wavefunctions which have |J| ≤ s. Celestial diamonds naturally incorporate degeneracies of opposite helicity particles via the 2D shadow transform relating radiative primaries and account for the global and asymptotic symmetries in gauge theory and gravity.

Helical Electronic Transitions of Spiroconjugated Molecules

The two perpendicularly oriented π-systems of allene mix into helical molecular orbitals (MOs) when the symmetry of the molecule is reduced. However, the π-π^∗ transitions of allenes are linear combinations of two excitations that always consist of both helicities; consequently, the electronic transitions are not helical. Here, we examine the electronic structure of spiroconjugated molecules, which have the same parent symmetry as allene but with different relative orientation of the two π-systems. We show how the π-mixing in spiropentadiene is analogous to the helical π-mixing in allene. However, in spiroconjugated systems only half the π-MOs become helical. Due to this difference, the π-π^∗ transitions in substituted spiropentadiene come in near-degenerate pairs where the helicity is symmetry protected, and consequently there is no significant mixing between excitations involving MOs of opposite helicity. This inherent helicity of the π-π^* transitions is verified by computation of the change of electron density. These transitions have big rotatory strengths where the sign correlates with the helicity of the transition. The electronic helicity of spiroconjugated molecules thus manifests itself in observable electronic and optical properties.

Helical Electronic Transitions of Spiroconjugated Molecules

The two perpendicularly oriented π-systems of allene mix into helical molecular orbitals (MOs) when the symmetry of the molecule is reduced. However, the π-π^∗ transitions of allenes are linear combinations of two excitations that always consist of both helicities; consequently, the electronic transitions are not helical. Here, we examine the electronic structure of spiroconjugated molecules, which have the same parent symmetry as allene but with different relative orientation of the two π-systems. We show how the π-mixing in spiropentadiene is analogous to the helical π-mixing in allene. However, in spiroconjugated systems only half the π-MOs become helical. Due to this difference, the π-π^∗ transitions in substituted spiropentadiene come in near-degenerate pairs where the helicity is symmetry protected, and consequently there is no significant mixing between excitations involving MOs of opposite helicity. This inherent helicity of the π-π^* transitions is verified by computation of the change of electron density. These transitions have big rotatory strengths where the sign correlates with the helicity of the transition. The electronic helicity of spiroconjugated molecules thus manifests itself in observable electronic and optical properties.

Helical Electronic Transitions of Spiroconjugated Molecules

The two perpendicularly oriented π-systems of allene mix into helical molecular orbitals (MOs) when the symmetry of the molecule is reduced. However, the π-π^∗ transitions of allenes are linear combinations of two excitations that always consist of both helicities; consequently, the electronic transitions are not helical. Here, we examine the electronic structure of spiroconjugated molecules, which have the same parent symmetry as allene but with different relative orientation of the two π-systems. We show how the π-mixing in spiropentadiene is analogous to the helical π-mixing in allene. However, in spiroconjugated systems only half the π-MOs become helical. Due to this difference, the π-π^∗ transitions in substituted spiropentadiene come in near-degenerate pairs where the helicity is symmetry protected, and consequently there is no significant mixing between excitations involving MOs of opposite helicity. This inherent helicity of the π-π^* transitions is verified by computation of the change of electron density. These transitions have big rotatory strengths where the sign correlates with the helicity of the transition. The electronic helicity of spiroconjugated molecules thus manifests itself in observable electronic and optical properties.

Helicity-delinked manipulations on surface waves and propagating waves by metasurfaces

Although many approaches have been proposed to manipulate propagating waves (PWs) and surface waves (SWs), usually each operation needs a separate meta-device, being unfavorable for optical integrations. Here, we propose a scheme to design a single meta-device that can efficiently generate SWs and/or PWs with pre-designed wavefronts, under the excitations of circularly polarized (CP) PWs with different helicity. As a proof of concept, we design and fabricate a microwave meta-device and experimentally demonstrate that it can convert incident CP waves of opposite helicity to SWs possessing different wavefronts and traveling to opposite directions, both exhibiting very high efficiencies. We further generalize our scheme to design a meta-device and numerically demonstrate that it can either excite a SW beam with tailored wavefront or generate a far-field PW with pre-designed wavefront, as shined by CP waves with different helicity. Our work opens the door to achieving simultaneous controls on far- and near-field electromagnetic environments based on a single ultra-compact platform.

DIMENSIONAL REDUCTION

Using an octonionic formalism, we introduce a new mechanism for reducing ten space–time dimensions to four without compactification. Applying this mechanism to the free, ten-dimensional, massless (momentum space) Dirac equation results in a particle spectrum consisting of exactly three generations. Each generation contains one massive spin-1/2 particle with two spin states, one massless spin-1/2 particle with only one helicity state, and their antiparticles — precisely one generation of leptons. There is also a single massless spin-1/2 particle/antiparticle pair with the opposite helicity and no generation structure. We conclude with a discussion of some further consequences of this approach, including those which could arise when using the formalism on a curved space–time background, as well as the implications for the nature of space–time itself.

A plane-grating monochromator for circularly polarized undulator radiation at BESSY II

At BESSY II, a third-generation 1.7 GeV storage ring is under construction. A planar elliptical undulator will be installed as a source of X-rays that have a high degree of circular polarization. Radiation in the first, third and fifth harmonics will cover the energy range 87–1330 eV. The beamline will essentially consist of a plane-grating monochromator working with collimated light in the dispersion plane. A single set of optical elements can be used to handle the two angularly separated beams of opposite helicity from the double undulator. The degree of circular polarization ranges from 73 to 100%, and a flux of up to 5 × 1013 photons s−1 (100 mA)−1 can be achieved. A maximum spectral resolution of about 13 000 will be possible at 100 eV using a 20 µm slit.