Photon number conservation in time dependent systems [Invited].

Time dependent systems in general do not conserve photons nor do they conserve energy. However when parity-time symmetry holds Maxwell's equations can sometimes both conserve photon number and energy. Here we show that photon conservation is the more widely applicable law which can hold in circumstances where energy conservation is violated shedding further light on an amplification mechanism identified in previous papers as a process of conserved photons climbing a frequency ladder.

An Archimedes' screw for light.

An Archimedes' Screw captures water, feeding energy into it by lifting it to a higher level. We introduce the first instance of an optical Archimedes' Screw, and demonstrate how this system is capable of capturing light, dragging it and amplifying it. We unveil new exact analytic solutions to Maxwell's Equations for a wide family of chiral space-time media, and show their potential to achieve chirally selective amplification within widely tunable parity-time-broken phases. Our work, which may be readily implemented via pump-probe experiments with circularly polarized beams, opens a new direction in the physics of time-varying media by merging the rising field of space-time metamaterials and that of chiral systems, and offers a new playground for topological and non-Hermitian photonics, with potential applications to chiral spectroscopy and sensing.

Revealing topology with transformation optics.

Symmetry deepens our insight into a physical system and its interplay with topology enables the discovery of topological phases. Symmetry analysis is conventionally performed either in the physical space of interest, or in the corresponding reciprocal space. Here we borrow the concept of virtual space from transformation optics to demonstrate how a certain class of symmetries can be visualised in a transformed, spectrally related coordinate space, illuminating the underlying topological transitions. By projecting a plasmonic system in a higher-dimensional virtual space onto a lower-dimensional system in real space, we show how transformation optics allows us to construct a topologically non-trivial system by inspecting its modes in the virtual space. Interestingly, we find that the topological invariant can be controlled via the singularities in the conformal mapping, enabling the intuitive engineering of edge states. The confluence of transformation optics and topology here can be generalized to other wave realms beyond photonics.

Designing plasmonic exceptional points by transformation optics.

Exceptional points (EPs) have been shown to be useful in bringing about sensitive optical properties based on non-Hermitian physics. For example, they have been applied in plasmonics to realize nano-sensing with extreme sensitivity. While the exceptional points are conventionally constructed by considering parity-time symmetric or anti-parity-time symmetric media, we theoretically demonstrate the possibility of generating a series of non-Hermitian systems by transforming a seed system with conventional parity-time symmetry within the transformation optics framework. The transformed systems do not possess PT-symmetry with a conventional parity operator after a spatial operation, i.e. hidden from conventional sense, but are equipped with exceptional points and phase transitions, hinting an alternative method to design non-Hermitian plasmonic systems with sensitive spectra or eigenmodes.

Casimir-Induced Instabilities at Metallic Surfaces and Interfaces.

Surface distortion splits surface plasmons asymmetrically in energy with a net lowering of zero-point energy. We contrast this with the symmetrical distortion of electronic energy levels. We use conformal mapping to demonstrate this splitting and find that surface corrugation always leads to a decrease in the zero-point energy of a metallic surface, but the decrease is not strong enough to drive a surface reconstruction on its own. A second metallic surface in proximity to the first gives a more significant lowering of energy, sufficient to drive the instability of a mercury thin film. This mechanism provides a fundamental length scale limit to planar nanostructures.

Wood Anomalies and Surface-Wave Excitation with a Time Grating.

In order to confine waves beyond the diffraction limit, advances in fabrication techniques have enabled subwavelength structuring of matter, achieving near-field control of light and other types of waves. The price is often expensive fabrication needs and the irreversibility of device functionality, as well as the introduction of impurities, a major contributor to losses. In this Letter, we propose temporal inhomogeneities, such as a periodic drive in the electromagnetic properties of a surface which supports guided modes, as an alternative route for the coupling of propagating waves to evanescent modes across the light line, thus circumventing the need for subwavelength fabrication, and achieving the temporal counterpart of the classical Wood anomaly. We show analytically and numerically how this concept is valid for any material platform and at any frequency, and propose and model a realistic experiment in graphene to couple terahertz radiation to plasmons with unit efficiency, demonstrating that time modulation of material properties could be a tunable, lower-loss and fast-switchable alternative to the subwavelength structuring of matter for near-field wave control.

Continuous topological transition from metal to dielectric.

Metal and dielectric have long been thought as two different states of matter possessing highly contrasting electric and optical properties. A metal is a material highly reflective to electromagnetic waves for frequencies up to the optical region. In contrast, a dielectric is transparent to electromagnetic waves. These two different classical electrodynamic properties are distinguished by different signs of the real part of permittivity: The metal has a negative sign while the dielectric has a positive one. Here, we propose a different topological understanding of metal and dielectric. By considering metal and dielectric as just two limiting cases of a periodic metal-dielectric layered metamaterial, from which a metal can continuously transform into a dielectric by varying the metal filling ratio from 1 to 0, we further demonstrate the abrupt change of a topological invariant at a certain point during this transition, classifying the metamaterials into metallic state and dielectric state. The topological phase transition from the metallic state to the dielectric state occurs when the filling ratio is one-half. These two states generalize our previous understanding of metal and dielectric: The metamaterial with metal filling ratio larger/smaller than one-half is named as the "generalized metal/dielectric." Interestingly, the surface plasmon polariton (SPP) at a metal/dielectric interface can be understood as the limiting case of a topological edge state.

Broadband Nonreciprocal Amplification in Luminal Metamaterials.

Time has emerged as a new degree of freedom for metamaterials, promising new pathways in wave control. However, electromagnetism suffers from limitations in the modulation speed of material parameters. Here we argue that these limitations can be circumvented by introducing a traveling-wave modulation, with the same phase velocity of the waves. We show how luminal metamaterials generalize the parametric oscillator concept, realize giant broadband nonreciprocity, achieve efficient one-way amplification, pulse compression, and harmonic generation, and propose a realistic implementation in double-layer graphene.

Fresnel drag in space-time-modulated metamaterials.

A moving medium drags light along with it as measured by Fizeau and explained by Einstein's theory of special relativity. Here we show that the same effect can be obtained in a situation where there is no physical motion of the medium. Modulations of both the permittivity and permeability, phased in space and time in the form of traveling waves, are the basis of our model. Space-time metamaterials are represented by effective bianisotropic parameters, which can in turn be mapped to a moving homogeneous medium. Hence these metamaterials mimic a relativistic effect without the need for any actual material motion. We discuss how both the permittivity and permeability need to be modulated to achieve these effects, and we present an equivalent transmission line model.

Transformation-Invariant Metamaterials.

The fundamental semiconductor concept of doping has recently been transplanted to photonics in the platform of epsilon-near-zero (ENZ) media. By doping nonmagnetic impurities, ENZ media can exhibit almost arbitrary magnetism. However, this original photonic doping approach results only in isotropic media and thus cannot achieve impedance matching for all incident angles. We extend the photonic doping approach of ENZ media by adding anisotropy, which enables full transparency with omnidirectional impedance matching. More importantly, such anisotropically doped ENZ media preserve their material parameters under arbitrary coordinate transformations, thereby providing a powerful platform to construct various ideal transformation optical devices. As an example, a full-parameter omnidirectional invisibility cloak is demonstrated to hide objects from a wide range of incident angles. The transformation-invariant material proposed not only supplements and extends the rising technologies of ENZ media but also constitutes a significant step towards the practical implementation of ideal transformation optical devices.

Compacted dimensions and singular plasmonic surfaces.

In advanced field theories, there can be more than four dimensions to space, the excess dimensions described as compacted and unobservable on everyday length scales. We report a simple model, unconnected to field theory, for a compacted dimension realized in a metallic metasurface periodically structured in the form of a grating comprising a series of singularities. An extra dimension of the grating is hidden, and the surface plasmon excitations, though localized at the surface, are characterized by three wave vectors rather than the two of typical two-dimensional metal grating. We propose an experimental realization in a doped graphene layer.

Transformation Optics: A Time- and Frequency-Domain Analysis of Electron-Energy Loss Spectroscopy.

Electron energy loss spectroscopy (EELS) and cathodoluminescence (CL) play a pivotal role in many of the cutting edge experiments in plasmonics. EELS and CL experiments are usually supported by numerical simulations, which-though accurate-may not provide as much physical insight as analytical calculations do. Fully analytical solutions to EELS and CL systems in plasmonics are rare and difficult to obtain. This paper aims to narrow this gap by introducing a new method based on transformation optics that allows to calculate the quasistatic frequency- and time-domain response of plasmonic particles under electron beam excitation. We study a nonconcentric annulus (and ellipse in the Supporting Information ) as an example.

Transforming the optical landscape.

Electromagnetism provides us with some of the most powerful tools in science, encompassing lasers, optical microscopes, magnetic resonance imaging scanners, radar, and a host of other techniques. To understand and develop the technology requires more than a set of formal equations. Scientists and engineers have to form a vivid picture that fires their imaginations and enables intuition to play a full role in the process of invention. It is to this end that transformation optics has been developed, exploiting Faraday's picture of electric and magnetic fields as lines of force, which can be manipulated by the electrical permittivity and magnetic permeability of surrounding materials. Transformation optics says what has to be done to place the lines of force where we want them to be.

Nonlocal propagation and tunnelling of surface plasmons in metallic hourglass waveguides.

The nanofocusing performance of hourglass plasmonic waveguides is studied analytically and numerically. Nonlocal effects in the linearly tapered metal-air-metal stack that makes up the device are taken into account within a hydrodynamical approach. Using this hourglass waveguide as a model structure, we show that spatial dispersion drastically modifies the propagation of surface plasmons in metal voids, such as those generated between touching particles. Specifically, we investigate how nonlocal corrections limit the enormous field enhancements predicted by local electromagnetic treatments of geometric singularities. Finally, our results also indicate the emergence of nonlocality assisted tunnelling of plasmonic modes across hourglass contacts as thick as 0.5 nm.

Surface plasmons and nonlocality: a simple model.

Surface plasmons on metals can concentrate light into subnanometric volumes and on these near atomic length scales the electronic response at the metal interface is smeared out over a Thomas-Fermi screening length. This nonlocality is a barrier to a good understanding of atomic scale response to light and complicates the practical matter of computing the fields. In this Letter, we present a local analogue model and show that spatial nonlocality can be represented by replacing the nonlocal metal with a composite material, comprising a thin dielectric layer on top of a local metal. This method not only makes possible the quantitative analysis of nonlocal effects in complex plasmonic phenomena with unprecedented simplicity and physical insight, but also offers great practical advantages in their numerical treatment.

Description of van der Waals interactions using transformation optics.

Exact calculation of the van der Waals interaction between closely spaced plasmonic nanoparticles is challenging due to the strong concentration of the electromagnetic fields that takes place at the nanometric gap between them. The technique of transformation optics, capable of mapping a small volume into any desired length scale, enables us to shed physical insight into the intricate behavior of electromagnetic fields in extremely small gaps. Using this theoretical tool, we obtain universal analytical expressions for the van der Waals interactions between spherical nanoparticles made of realistic metals at arbitrary separation.

Theory of three-dimensional nanocrescent light harvesters.

The optical properties of three-dimensional crescent-shaped gold nanoparticles are studied using a transformation optics methodology. The polarization insensitive, highly efficient, and tunable light harvesting ability of singular nanocrescents is demonstrated. We extend our approach to more realistic blunt nanostructures, showing the robustness of their plasmonic performance against geometric imperfections. Finally, we provide analytical and numerical insights into the sensitivity of the device to radiative losses and nonlocal effects. Our theoretical findings reveal an underlying relation between structural bluntness and spatial dispersion in this particular nanoparticle configuration.