Electromagnetic duality symmetry and helicity conservation for the macroscopic Maxwell's equations

Nanophotonic Chirality Transfer to Dielectric Mie Resonators

Nanophotonics can boost the weak circular dichroism of chiral molecules. One mechanism for enhanced chiral sensing relies on using a resonator to create fields with high optical chirality at the molecular position. Here, we elucidate how the reverse interaction between molecules and the resonator, called chirality transfer, can produce stronger circular dichroism. The chiral analyte modifies the electric and magnetic dipole moments of the resonator, imprinting a chiral response on an otherwise achiral resonance. We demonstrate that silicon nanoparticles and metasurfaces tailored for chirality transfer generate chiroptical signals orders of magnitude higher than the contribution from optical chirality alone. We derive closed-form equations for the dependence of chirality transfer on molecular chirality, molecule-resonator distance, and Mie coefficients. We propose a dielectric metasurface for a 900-fold circular dichroism enhancement on the basis of these principles. Finally, we identify a fundamental limit to chirality transfer. Our findings thus establish key concepts for nanophotonic chiral sensing.

General duality and magnet-free passive phononic Chern insulators

Integrated phononics plays an important role in both fundamental physics and technology. Despite great efforts, it remains a challenge to break time-reversal symmetry to achieve topological phases and non-reciprocal devices. Piezomagnetic materials offer an intriguing opportunity as they break time-reversal symmetry intrinsically, without the need for an external magnetic field or an active driving field. Moreover, they are antiferromagnetic, and possibly compatible with superconducting components. Here, we develop a theoretical framework that combines linear elasticity with Maxwell's equations via piezoelectricity and/or piezomagnetism beyond the commonly adopted quasi-static approximation. Our theory predicts and numerically demonstrates phononic Chern insulators based on piezomagnetism. We further show that the topological phase and chiral edge states in this system can be controlled by the charge doping. Our results exploit a general duality relation between piezoelectric and piezomagnetic systems, which can potentially be generalized to other composite metamaterial systems.

Reconfigurable chirality with achiral excitonic materials in the strong-coupling regime

We introduce and theoretically analyze the concept of manipulating optical chirality via strong coupling of the optical modes of chiral nanostructures with excitonic transitions in molecular layers or semiconductors. With chirality being omnipresent in chemistry and biomedicine, and highly desirable for technological applications related to efficient light manipulation, the design of nanophotonic architectures that sense the handedness of molecules or generate the desired light polarization in an externally controllable manner is of major interdisciplinary importance. Here we propose that such capabilities can be provided by the mode splitting resulting from polaritonic hybridization. Starting with an object with well-known chiroptical response-here, for a proof of concept, a chiral sphere-we show that strong coupling with a nearby excitonic material generates two spectral branches that retain the object's high chirality density, which manifest most clearly through anticrossings in circular-dichroism or differential-scattering dispersion diagrams. These windows can be controlled by the intrinsic properties of the excitonic layer and the strength of the interaction, enabling thus the post-fabrication manipulation of optical chirality. Our findings are further verified via simulations of circular dichroism of a realistic chiral architecture, namely a helical assembly of plasmonic nanospheres embedded in a resonant matrix.

Ideal Kerker scattering by homogeneous spheres: the role of gain or loss

We investigate how the optical gain or loss (characterized by isotropic complex refractive indexes) influence the ideal Kerker scattering of exactly zero backward scattering. It was previously shown that, for non-magnetic homogeneous spheres with incident plane waves, either gain or loss prohibit ideal Kerker scattering, provided that only electric and magnetic multipoles of a specific order are present and contributions from other multipoles can all be made precisely zero. Here we reveal that, when two multipoles of a fixed order are perfectly matched in terms of both phase and magnitude, multipoles of at least the next two orders cannot possibly be tuned to be all precisely zero or even perfectly matched, and consequently cannot directly produce ideal Kerker scattering. Moreover, we further demonstrate that, when multipoles of different orders are simultaneously taken into consideration, loss or gain can serve as helpful rather than harmful contributing factors, for the elimination of backward scattering.

Momentum, angular momentum, and spin of waves in an isotropic collisionless plasma

We examine the momentum and angular momentum (including spin) properties of linear waves, both longitudinal (Langmuir) and transverse (electromagnetic), in an isotropic nonrelativistic collisionless electron plasma. We focus on conserved quantities associated with the translational and rotational invariance of the wave fields with respect to the homogeneous medium; these are sometimes called pseudomomenta. There are two types of the momentum and angular momentum densities: (i) the kinetic ones associated with the energy flux density and the symmetrized (Belinfante) energy-momentum tensor and (ii) the canonical ones associated with the conserved Noether currents and canonical energy-momentum tensor. We find that the canonical momentum and spin densities of Langmuir waves are similar to those of sound waves in fluids or gases; they are naturally expressed via the electron velocity field. In turn, the momentum and spin densities of electromagnetic waves can be written either in the forms known for free-space electromagnetic fields, involving only the electric field, or in the dual-symmetric forms involving both electric and magnetic fields, as well as the effective permittivity of plasma. We derive these properties both within the phenomenological macroscopic approach and microscopic Lagrangian field theory for the coupled electromagnetic fields and electrons. Finally, we explore implications of the canonical momentum and spin densities in transport and electrodynamic phenomena: the Stokes drift, the wave-induced magnetization (inverse Faraday effect), etc.

Self-Assembly of Isostatic Self-Dual Colloidal Crystals

Self-dual structures whose dual counterparts are themselves possess unique hidden symmetry, beyond the description of classical spatial symmetry groups. Here we propose a strategy based on a nematic monolayer of attractive half-cylindrical colloids to self-assemble these exotic structures. This system can be seen as a 2D system of semidisks. By using Monte Carlo simulations, we discover two isostatic self-dual crystals, i.e., an unreported crystal with pmg space-group symmetry and the twisted kagome crystal. For the pmg crystal approaching the critical point, we find the double degeneracy of the full phononic spectrum at the self-dual point and the merging of two tilted Weyl nodes into one critically tilted Dirac node. The latter is "accidentally" located on the high-symmetry line. The formation of this unconventional Dirac node is due to the emergence of the critical flatbands at the self-dual point, which are linear combinations of "finite-frequency" floppy modes. These modes can be understood as mechanically coupled self-dual rhombus chains vibrating in some unique uncoupled ways. Our work paves the way for designing and fabricating self-dual materials with exotic mechanical or phononic properties.

Dual Nanoresonators for Ultrasensitive Chiral Detection

The discrimination of enantiomers is crucial in biochemistry. However, chiral sensing faces significant limitations due to inherently weak chiroptical signals. Nanophotonics is a promising solution to enhance sensitivity thanks to increased optical chirality maximized by strong electric and magnetic fields. Metallic and dielectric nanoparticles can separately provide electric and magnetic resonances. Here we propose their synergistic combination in hybrid metal-dielectric nanostructures to exploit their dual character for superchiral fields beyond the limits of single particles. For optimal optical chirality, in addition to maximization of the resonance strength, the resonances must spectrally coincide. Simultaneously, their electric and magnetic fields must be parallel and π/2 out of phase and spatially overlap. We demonstrate that the interplay between the strength of the resonances and these optimal conditions constrains the attainable optical chirality in resonant systems. Starting from a simple symmetric nanodimer, we derive closed-form expressions elucidating its fundamental limits of optical chirality. Building on the trade-offs of different classes of dimers, we then suggest an asymmetric dual dimer based on realistic materials. These dual nanoresonators provide strong and decoupled electric and magnetic resonances together with optimal conditions for chiral fields. Finally, we introduce more complex dual building blocks for a metasurface with a record 300-fold enhancement of local optical chirality in nanoscale gaps, enabling circular dichroism enhancement by a factor of 20. By combining analytical insight and practical designs, our results put forward hybrid resonators to increase chiral sensitivity, particularly for small molecular quantities.

Separating and trapping of chiral nanoparticles with dielectric photonic crystal slabs

Chiral separation is a crucial step in many chemical synthesis processes, particularly for pharmaceuticals. Here we present a novel method for the realization of both separating and trapping of enantiomers using the dielectric photonic crystal (PhC) slabs, which possess quasi-fourfold degenerate Bloch modes (overlapping double degenerate transverse-electric-like and transverse-magnetic-like modes). Based on the designed structure, a large gradient of optical chirality appears near the PhC slab, leading to the extreme enhancement of chiral optical forces about 3 orders of magnitude larger than those obtained with circularly polarized lights. In this case, our method provides a reference for realizing all-optical enantiopure syntheses.

Effects of symmetry-breaking on electromagnetic backscattering

Systems with a discrete rotational symmetry \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$2\pi /n$$\end{document}2π/n where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\ge 3$$\end{document}n≥3 that also have electromagnetic duality symmetry exhibit zero backscattering. The impact of breaking one of the two symmetries on the emerging backscattering has not yet been systematically studied. Here, we investigate the effect that perturbatively breaking each of the two symmetries has on the backscattering off individual objects and 2D arrays. We find that the backscattering off electromagnetically-small prisms increases with the parameters that determine the symmetry breaking, and that the increase of the backscattering due to the progressive breaking of one of the symmetries can be related to the other symmetry. Further exploration of the interplay between the two symmetries reveals that, in systems lacking enough rotational symmetry, the backscattering can be almost-entirely suppressed for a given linear polarization by deliberately breaking the duality symmetry. This duality breaking can be interpreted as an effective increase of the electromagnetic degree of rotational symmetry for that linear polarization.

Electromagnetic chirality: from fundamentals to nontraditional chiroptical phenomena

Chirality arises universally across many different fields. Recent advancements in artificial nanomaterials have demonstrated chiroptical responses that far exceed those found in natural materials. Chiroptical phenomena are complicated processes that involve transitions between states with opposite parities, and solid interpretations of these observations are yet to be clearly provided. In this review, we present a comprehensive overview of the theoretical aspects of chirality in light, nanostructures, and nanosystems and their chiroptical interactions. Descriptions of observed chiroptical phenomena based on these fundamentals are intensively discussed. We start with the strong intrinsic and extrinsic chirality in plasmonic nanoparticle systems, followed by enantioselective sensing and optical manipulation, and then conclude with orbital angular momentum-dependent responses. This review will be helpful for understanding the mechanisms behind chiroptical phenomena based on underlying chiral properties and useful for interpreting chiroptical systems for further studies.

Kerker Conditions upon Lossless, Absorption, and Optical Gain Regimes

The directionality and polarization of light show peculiar properties when the scattering by a dielectric sphere can be described exclusively by electric and magnetic dipolar modes. Particularly, when these modes oscillate in phase with equal amplitude, at the so-called first Kerker condition, the zero optical backscattering condition emerges for nondissipating spheres. However, the role of absorption and optical gain in the first Kerker condition remains unexplored. In this work, we demonstrate that either absorption or optical gain precludes the first Kerker condition and, hence, the absence of backscattered radiation light, regardless of the particle's size, incident wavelength, and incoming polarization. Finally, we derive the necessary prerequisites of the second Kerker condition of the zero forward light scattering, finding that optical gain is a compulsory requirement.

Helicity-Preserving Optical Cavity Modes for Enhanced Sensing of Chiral Molecules

Researchers routinely sense molecules by their infrared vibrational "fingerprint" absorption resonances. In addition, the dominant handedness of chiral molecules can be detected by circular dichroism (CD), the normalized difference between their optical response to incident left- and right- handed circularly polarized light. Here, we introduce a cavity composed of two parallel arrays of helicity-preserving silicon disks that allows one to enhance the CD signal by more than 2 orders of magnitude for a given molecule concentration and given thickness of the cell containing the molecules. The underlying principle is first-order diffraction into helicity-preserving modes with large transverse momentum and long lifetimes. In sharp contrast, in a conventional Fabry-Perot cavity, each reflection flips the handedness of light, leading to large intensity enhancements inside the cavity, yet to smaller CD signals than without the cavity.

Helicity-Preserving Optical Cavity Modes for Enhanced Sensing of Chiral Molecules

Researchers routinely sense molecules by their infrared vibrational "fingerprint" absorption resonances. In addition, the dominant handedness of chiral molecules can be detected by circular dichroism (CD), the normalized difference between their optical response to incident left- and right- handed circularly polarized light. Here, we introduce a cavity composed of two parallel arrays of helicity-preserving silicon disks that allows one to enhance the CD signal by more than 2 orders of magnitude for a given molecule concentration and given thickness of the cell containing the molecules. The underlying principle is first-order diffraction into helicity-preserving modes with large transverse momentum and long lifetimes. In sharp contrast, in a conventional Fabry-Perot cavity, each reflection flips the handedness of light, leading to large intensity enhancements inside the cavity, yet to smaller CD signals than without the cavity.

The Pre-Potential of a Field Propagating with the Speed of Light and Its Dual Symmetry

Relativity theory assumes that force fields propagate with the speed of light. We show that such force fields generated by a single source can be described by a pre-potential, which is a complex-valued function on spacetime outside the worldline of the source. The pre-potential is invariant under a spin-half representation of the Lorentz group acting on complexified spacetime. The complex four-potential of such a field is defined and calculated explicitly from the pre-potential without assuming any particular force law for the field. The real part of the obtained four-potential coincides with the known Liénard–Wiechert potential. The symmetry of the four-potential is described herein. The pre-potential satisfies the wave equation. The single source electromagnetic field derived from this four-potential is self-dual or anti-self-dual. The pre-potential and the four-potential are extended to a field with several sources.

A Conformally Invariant Derivation of Average Electromagnetic Helicity

The average helicity of a given electromagnetic field measures the difference between the number of left- and right-handed photons contained in the field. Here, the average helicity is derived using the conformally invariant inner product for Maxwell fields. Several equivalent integral expressions in momentum space, in ( r , t ) space, and in the time-harmonic ( r , ω ) space are obtained, featuring Riemann–Silberstein-like fields and potentials. The time-harmonic expressions can be directly evaluated using the outputs of common numerical solvers of Maxwell equations. The results are shown to be equivalent to the well-known volume integral for the average helicity, featuring the electric and magnetic fields and potentials.

Geometric Structure behind Duality and Manifestation of Self-Duality from Electrical Circuits to Metamaterials

In electromagnetic systems, duality is manifested in various forms: circuit, Keller–Dykhne, electromagnetic, and Babinet dualities. These dualities have been developed individually in different research fields and frequency regimes, leading to a lack of unified perspective. In this paper, we establish a unified view of these dualities in electromagnetic systems. The underlying geometrical structures behind the dualities are elucidated by using concepts from algebraic topology and differential geometry. Moreover, we show that seemingly disparate phenomena, such as frequency-independent effective response, zero backscattering, and critical response, can be considered to be emergent phenomena of self-duality.

Optical Helicity and Optical Chirality in Free Space and in the Presence of Matter

The inherently weak nature of chiral light–matter interactions can be enhanced by orders of magnitude utilizing artificially-engineered nanophotonic structures. These structures enable high spatial concentration of electromagnetic fields with controlled helicity and chirality. However, the effective design and optimization of nanostructures requires defining physical observables which quantify the degree of electromagnetic helicity and chirality. In this perspective, we discuss optical helicity, optical chirality, and their related conservation laws, describing situations in which each provides the most meaningful physical information in free space and in the context of chiral light–matter interactions. First, an instructive comparison is drawn to the concepts of momentum, force, and energy in classical mechanics. In free space, optical helicity closely parallels momentum, whereas optical chirality parallels force. In the presence of macroscopic matter, the optical helicity finds its optimal physical application in the case of lossless, dual-symmetric media, while, in contrast, the optical chirality provides physically observable information in the presence of lossy, dispersive media. Finally, based on numerical simulations of a gold and silicon nanosphere, we discuss how metallic and dielectric nanostructures can generate chiral electromagnetic fields upon interaction with chiral light, offering guidelines for the rational design of nanostructure-enhanced electromagnetic chirality.

New Twists of 3D Chiral Metamaterials

Rationally designed artificial materials, called metamaterials, allow for tailoring effective material properties beyond ("meta") the properties of their bulk ingredient materials. This statement is especially true for chiral metamaterials, as unlocking certain degrees of freedom necessarily requires broken centrosymmetry. While the field of chiral electromagnetic/optical metamaterials has become rather mature, the field of elastic/mechanical metamaterials is just emerging and wide open. This research news reviews recent theoretical and experimental progress concerning 3D chiral mechanical and optical metamaterials, with special emphasis on work performed at KIT.

Observation of Three-Dimensional Photonic Dirac Points and Spin-Polarized Surface Arcs

Three-dimensional (3D) Dirac points inheriting relativistic effects from high-energy physics appear as gapless excitations in the topological band theory. Hosting fourfold linear dispersion, they play the central role among various topological phases, such as representing the degeneracy of paired Weyl nodes carrying opposite chiralities. While they have been extensively investigated in solid state systems for electrons, 3D Dirac points have not yet been observed in any classical systems. Here, we experimentally demonstrate 3D photonic Dirac points in the microwave region with an elaborately designed metamaterial, where two symmetrically placed Dirac points are stabilized by electromagnetic duality symmetry. Furthermore, spin-polarized surface arcs (counterparts of Fermi arcs in electronic systems) are demonstrated, which opens the gate toward implementing spin-multiplexed topological surface wave propagation. Closely linked to other exotic states through topological phase transitions, our system offers an effective medium platform for topological photonics.

Optical Helicity and Chirality: Conservation and Sources

We consider the helicity and chirality of the free electromagnetic field, and advocate the former as a means of characterising the interaction of chiral light with matter. This is in view of the intuitive quantum form of the helicity density operator, and of the dual symmetry transformation generated by its conservation. We go on to review the form of the helicity density and its associated continuity equation in free space, in the presence of local currents and charges, and upon interaction with bulk media, leading to characterisation of both microscopic and macroscopic sources of helicity.

Topological non-Hermitian origin of surface Maxwell waves

Maxwell electromagnetism, describing the wave properties of light, was formulated 150 years ago. More than 60 years ago it was shown that interfaces between optical media (including dielectrics, metals, negative-index materials) can support surface electromagnetic waves, which now play crucial roles in plasmonics, metamaterials, and nano-photonics. Here we show that surface Maxwell waves at interfaces between homogeneous isotropic media described by real permittivities and permeabilities have a topological origin explained by the bulk-boundary correspondence. Importantly, the topological classification is determined by the helicity operator, which is generically non-Hermitian even in lossless optical media. The corresponding topological invariant, which determines the number of surface modes, is a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Bbb Z}_4$$\end{document}Z4 number (or a pair of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Bbb Z}_2$$\end{document}Z2 numbers) describing the winding of the complex helicity spectrum across the interface. Our theory provides a new twist and insights for several areas of wave physics: Maxwell electromagnetism, topological quantum states, non-Hermitian wave physics, and metamaterials.

Electromagnetic surface waves, derived from Maxwell theory, underpin many optical effects and applications. Here, Bliokh et al. show that surface waves at interfaces between isotropic media have a topological origin described by the non-Hermitian helicity operator and bulk-boundary correspondence.

Symmetry Protection of Photonic Entanglement in the Interaction with a Single Nanoaperture

In this work, we experimentally show that quantum entanglement can be symmetry protected in the interaction with a single subwavelength plasmonic nanoaperture, with a total volume of V∼0.2λ^{3}. In particular, we experimentally demonstrate that two-photon entanglement can be either completely preserved or completely lost after the interaction with the nanoaperture, solely depending on the relative phase between the quantum states. We achieve this effect by using specially engineered two-photon states to match the properties of the nanoaperture. In this way we can access a symmetry protected state, i.e., a state constrained by the geometry of the interaction to retain its entanglement. In spite of the small volume of interaction, we show that the symmetry protected entangled state retains its main properties. This connection between nanophotonics and quantum optics probes the fundamental limits of the phenomenon of quantum interference.

Unusual polarizing effect of cylindrical plasmonic holes

We observe an unusual polarization state conversion in the light that passes through a cylindrical hole in a thick metal film. This phenomenon is related to the helicity locking of the guided mode due to the plasmonic transverse spin-an intrinsic angular momentum of the surface waves. We show how this effect is linked to the generation of the plasmonic vortex inside the hole and can be altered by varying the hole diameter. In addition, the total light transmission through the hole is shown to be partially contributed from the direct transmission, which can further modify the resulting light polarization state.

Optical Chirality of Time-Harmonic Wavefields for Classification of Scatterers

We derive expressions for the scattering, extinction and conversion of the chirality of monochromatic light scattered by bodies which are characterized by a T-matrix. In analogy to the conditions obtained from the conservation of energy, these quantities enable the classification of arbitrary scattering objects due to their full, i.e. either chiral or achiral, electromagnetic response. To this end, we put forward and determine the concepts of duality and breaking of duality symmetry, anti-duality, helicity variation, helicity annhiliation and the breaking of helicity annihilation. Different classes, such as chiral and dual scatterers, are illustrated in this analysis with model examples of spherical and non-spherical shape. As for spheres, these concepts are analysed by considering non-Rayleigh dipolar dielectric particles of high refractive index, which, having a strong magnetic response to the incident wavefield, offer an excellent laboratory to test and interpret such changes in the chirality of the illumination. In addition, comparisons with existing experimental data are made.

Electromagnetic Helicity in Complex Media

Optical helicity density is usually discussed for monochromatic electromagnetic fields in free space. It plays an important role in the interaction with chiral molecules or nanoparticles. Here we introduce the optical helicity density in a dispersive isotropic medium. Our definition is consistent with biorthogonal Maxwell electromagnetism in optical media and the Brillouin energy density as well as with the recently introduced canonical momentum and spin of light in dispersive media. We consider a number of examples, including electromagnetic waves in dielectrics, negative-index materials, and metals, as well as interactions of light in a medium with chiral and magnetoelectric molecules.

Three Dimensional Photonic Dirac Points in Metamaterials

Topological semimetals, representing a new topological phase that lacks a full band gap in bulk states and exhibiting nontrivial topological orders, recently have been extended to photonic systems, predominantly in photonic crystals and to a lesser extent metamaterials. Photonic crystal realizations of Dirac degeneracies are protected by various space symmetries, where Bloch modes span the spin and orbital subspaces. Here, we theoretically show that Dirac points can also be realized in effective media through the intrinsic degrees of freedom in electromagnetism under electromagnetic duality. A pair of spin-polarized Fermi-arc-like surface states is observed at the interface between air and the Dirac metamaterials. Furthermore, eigenreflection fields show the decoupling process from a Dirac point to two Weyl points. We also find the topological correlation between a Dirac point and vortex or vector beams in classical photonics. The experimental feasibility of our scheme is demonstrated by designing a realistic metamaterial structure. The theoretical proposal of the photonic Dirac point lays the foundation for unveiling the connection between intrinsic physics and global topology in electromagnetism.

Broadband suppression of backscattering at optical frequencies using low permittivity dielectric spheres

The exact suppression of backscattering from rotationally symmetric objects requires dual symmetric materials where ε _r = μ _r. This prevents their design at many frequency bands, including the optical one, because magnetic materials are not available. Electromagnetically small non-magnetic spheres of large permittivity offer an alternative. They can be tailored to exhibit balanced electric and magnetic dipole polarizabilities a ₁ = b ₁, which result in approximate zero backscattering. In this case, the effect is inherently narrowband. Here, we put forward a different alternative that allows broadband functionality: Wavelength-sized spheres made from low permittivity materials. The effect occurs in a parameter regime where approximate duality is met for all multipolar order a _n  ≈ b _n , in a weakly wavelength dependence fashion. In addition, and despite of the low permittivity, the overall scattering response of these spheres is still significant. Scattering patterns are shown to be highly directive across an octave spanning band. The effect is analytically and numerically shown using the Mie coefficients.

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'.

Analogies between optical and quantum mechanical angular momentum

The insight that a beam of light can carry orbital angular momentum (AM) in its propagation direction came up in 1992 as a surprise. Nevertheless, the existence of momentum and AM of an electromagnetic field has been well known since the days of Maxwell. We compare the expressions for densities of AM in general three-dimensional modes and in paraxial modes. Despite their classical nature, these expressions have a suggestive quantum mechanical appearance, in terms of linear operators acting on mode functions. In addition, paraxial wave optics has several analogies with real quantum mechanics, both with the wave function of a free quantum particle and with a quantum harmonic oscillator. We discuss how these analogies can be applied.This article is part of the themed issue 'Optical orbital angular momentum'.

Beaming of Helical Light from Plasmonic Vortices via Adiabatically Tapered Nanotip

We demonstrate the generation of far-field propagating optical beams with a desired orbital angular momentum by using a smooth optical-mode transformation between a plasmonic vortex and free-space Laguerre-Gaussian modes. This is obtained by means of an adiabatically tapered gold tip surrounded by a spiral slit. The proposed physical model, backed up by the numerical study, brings about an optimized structure that is fabricated by using a highly reproducible secondary electron lithography technique. Optical measurements of the structure excellently agree with the theoretically predicted far-field distributions. This architecture provides a unique platform for a localized excitation of plasmonic vortices followed by its beaming.

Tailoring the chirality of light emission with spherical Si-based antennas

Chirality of light is of fundamental importance in several enabling technologies with growing applications in life sciences, chemistry and photodetection. Recently, some attention has been focused on chiral quantum emitters. Consequently, optical antennas which are able to tailor the chirality of light emission are needed. Spherical nanoresonators such as colloids are of particular interest to design optical antennas since they can be synthesized at a large scale and they exhibit good optical properties. Here, we show that these colloids can be used to tailor the chirality of a chiral emitter. To this purpose, we derive an analytic formalism to model the interaction between a chiral emitter and a spherical resonator. We then compare the performances of metallic and dielectric spherical antennas to tailor the chirality of light emission. It is seen that, due to their strong electric dipolar response, metallic spherical nanoparticles spoil the chirality of light emission by yielding achiral fields. In contrast, thanks to the combined excitation of electric and magnetic modes, dielectric Si-based particles feature the ability to inhibit or to boost the chirality of light emission. Finally, it is shown that dual modes in dielectric antennas preserve the chirality of light emission.

On-chip noninterference angular momentum multiplexing of broadband light

Angular momentum division has emerged as a physically orthogonal multiplexing method in high-capacity optical information technologies. However, the typical bulky elements used for information retrieval from the overall diffracted field, based on the interference method, impose a fundamental limit toward realizing on-chip multiplexing. We demonstrate noninterference angular momentum multiplexing by using a mode-sorting nanoring aperture with a chip-scale footprint as small as 4.2 micrometers by 4.2 micrometers, where nanoring slits exhibit a distinctive outcoupling efficiency on tightly confined plasmonic modes. The nonresonant mode-sorting sensitivity and scalability of our approach enable on-chip parallel multiplexing over a bandwidth of 150 nanometers in the visible wavelength range. The results offer the possibility of ultrahigh-capacity and miniaturized nanophotonic devices harnessing angular momentum division.

Far-field measurements of vortex beams interacting with nanoholes

We measure the far-field intensity of vortex beams going through nanoholes. The process is analyzed in terms of helicity and total angular momentum. It is seen that the total angular momentum is preserved in the process, and helicity is not. We compute the ratio between the two transmitted helicity components, γ_m,p. We observe that this ratio is highly dependent on the helicity (p) and the angular momentum (m) of the incident vortex beam in consideration. Due to the mirror symmetry of the nanoholes, we are able to relate the transmission properties of vortex beams with a certain helicity and angular momentum, with the ones with opposite helicity and angular momentum. Interestingly, vortex beams enhance the γ_m,p ratio as compared to those obtained by Gaussian beams.

Exact dipolar moments of a localized electric current distribution

The multipolar decomposition of current distributions is used in many branches of physics. Here, we obtain new exact expressions for the dipolar moments of a localized electric current distribution. The typical integrals for the dipole moments of electromagnetically small sources are recovered as the lowest order terms of the new expressions in a series expansion with respect to the size of the source. All the higher order terms can be easily obtained. We also provide exact and approximated expressions for dipoles that radiate a definite polarization handedness (helicity). Formally, the new exact expressions are only marginally more complex than their lowest order approximations.

OPTICS. Quantum spin Hall effect of light

Maxwell's equations, formulated 150 years ago, ultimately describe properties of light, from classical electromagnetism to quantum and relativistic aspects. The latter ones result in remarkable geometric and topological phenomena related to the spin-1 massless nature of photons. By analyzing fundamental spin properties of Maxwell waves, we show that free-space light exhibits an intrinsic quantum spin Hall effect—surface modes with strong spin-momentum locking. These modes are evanescent waves that form, for example, surface plasmon-polaritons at vacuum-metal interfaces. Our findings illuminate the unusual transverse spin in evanescent waves and explain recent experiments that have demonstrated the transverse spin-direction locking in the excitation of surface optical modes. This deepens our understanding of Maxwell's theory, reveals analogies with topological insulators for electrons, and offers applications for robust spin-directional optical interfaces.

Isotropically polarized speckle patterns

The polarization of the light scattered by an optically dense and random solution of dielectric nanoparticles shows peculiar properties when the scatterers exhibit strong electric and magnetic polarizabilities. While the distribution of the scattering intensity in these systems shows the typical irregular speckle patterns, the helicity of the incident light can be fully conserved when the electric and magnetic polarizabilities of the scatterers are equal. We show that the multiple scattering of helical beams by a random dispersion of "dual" dipolar nanospheres leads to a speckle pattern exhibiting a perfect isotropic constant polarization, a situation that could be useful in coherent control of light as well as in lasing in random media.

Magnetoelectric effects in local light-matter interactions

We study the generic dipole interaction of a monochromatic free-space electromagnetic field with a bi-isotropic nanoparticle or a molecule. Contributions associated with the breaking of dual, P, and T symmetries are responsible for electric-magnetic asymmetry, chirality, and the nonreciprocal magnetoelectric effect, respectively. We calculate absorption rates, radiation forces, and radiation torques for the nanoparticle and introduce novel field characteristics quantifying the transfer of energy, momentum, and angular momentum due to the three symmetry-breaking effects. In particular, we put forward a concept of "magnetoelectric energy density," quantifying the local PT symmetry of the field. Akin to the "superchiral" light suggested recently for local probing of molecular chirality, here we suggest employing complex fields for a sensitive probing of the nonreciprocal magnetoelectric effect in nanoparticles or molecules.

Forward and backward helicity scattering coefficients for systems with discrete rotational symmetry

The forward and backward scattering off linear systems with discrete rotational symmetries R(z)(2π/n) with n ≥ 3 are shown to be restricted by symmetry reasons. Along the symmetry axis, forward scattering can only be helicity preserving and backward scattering can only be helicity flipping. These restrictions do not exist for n < 3. If, in addition to the n ≥ 3 discrete rotational symmetry, the system has duality symmetry (obeys the helicity conservation law), it will exhibit zero backscattering. The results pinpoint the underlying symmetry reasons for some notable scattering properties of R(z)(2π/4) symmetric systems that have been reported in the metamaterials and radar literature. Applications to planar metamaterials and solar cells are briefly discussed.