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.

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.

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.

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.

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.

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.

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.

Active nanoplasmonic metamaterials.

Optical metamaterials and nanoplasmonics bridge the gap between conventional optics and the nanoworld. Exciting and technologically important capabilities range from subwavelength focusing and stopped light to invisibility cloaking, with applications across science and engineering from biophotonics to nanocircuitry. A problem that has hampered practical implementations have been dissipative metal losses, but the efficient use of optical gain has been shown to compensate these and to allow for loss-free operation, amplification and nanoscopic lasing. Here, we review recent and ongoing progress in the realm of active, gain-enhanced nanoplasmonic metamaterials. On introducing and expounding the underlying theoretical concepts of the complex interaction between plasmons and gain media, we examine the experimental efforts in areas such as nanoplasmonic and metamaterial lasers. We underscore important current trends that may lead to improved active imaging, ultrafast nonlinearities on the nanoscale or cavity-free lasing in the stopped-light regime.

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.

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.

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.

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.

Broadband light harvesting nanostructures robust to edge bluntness.

Metallic structures with sharp corners harvest the energy of incident light through plasmonic resonances, concentrating it in the corners and greatly increasing the local energy density. Despite its wide array of applications, this effect is normally strongly dependent on how sharp the corners are, presenting problems for fabrication. In this Letter, an analytical approach is proposed, based on transformation optics, to investigate a general class of plasmonic nanostructures with blunt edges or corners. Comprehensive discussions are provided on how the geometry affects the local field enhancement as well as the frequency and energy of each plasmonic resonance. Remarkably, our results evidence the possibility of designing broadband light harvesting devices with an absorption property insensitive to the geometry bluntness.

Localized spoof plasmons arise while texturing closed surfaces.

We demonstrate that textured closed surfaces, i.e., particles made of perfect electric conductors (PECs), are able to support localized electromagnetic resonances with properties resembling those of localized surface plasmons (LSPs) in the optical regime. Because of their similar behavior, we name these types of resonances as spoof LSPs. As a way of example, we show the existence of spoof LSPs in periodically textured PEC cylinders and the almost perfect analogy to optical plasmonics. We also present a metamaterial approach that captures the basic ingredients of their electromagnetic response.

Rotational quantum friction.

We investigate the frictional forces due to quantum fluctuations acting on a small sphere rotating near a surface. At zero temperature, we find the frictional force near a surface to be several orders of magnitude larger than that for the sphere rotating in vacuum. For metallic materials with typical conductivity, quantum friction is maximized by matching the frequency of rotation with the conductivity. Materials with poor conductivity are favored to obtain large quantum frictions. For semiconductor materials that are able to support surface plasmon polaritons, quantum friction can be further enhanced by several orders of magnitude due to the excitation of surface plasmon polaritons.

Transformation-optics description of nonlocal effects in plasmonic nanostructures.

We develop an insightful transformation-optics approach to investigate the impact that nonlocality has on the optical properties of plasmonic nanostructures. The light-harvesting performance of a dimer of touching nanowires is studied by using the hydrodynamical Drude model, which reveals nonlocal resonances not predicted by previous local calculations. Our method clarifies the interplay between radiative and nonlocal effects in this nanoparticle configuration, which enables us to elucidate the optimum size that maximizes its absorption and field enhancement capabilities.

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.

Universal evolution of perfect lenses.

This Letter is a theoretical attempt to answer two questions. First how long does it takes for perfect lensing to be observed, and second how does loss diminish the performance of a general perfect lens. The method described in this Letter is universal, in the sense that it can be applied to perfect lenses of any arbitrary geometry. We shall show that the dynamics of perfect lensing is equivalent to the dynamics of 2 coupled simple harmonic oscillators. Moreover we shall derive quantitatively, the effects of losses on a compact perfect lens.