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Some popular mechanisms for restricting the diffusion of waves include introducing disorder (to provoke Anderson localization) and engineering topologically non-trivial phases (to allow for topological edge states to form). However, other methods for inducing somewhat localized states in elementary lattice models have been historically much less studied. Here we show how edge states can emerge within a simple two-leg ladder of coupled harmonic oscillators, where it is important to include interactions beyond those at the nearest neighbor range. Remarkably, depending upon the interplay between the coupling strength along the rungs of the ladder and the next-nearest neighbor coupling strength along one side of the ladder, edge states can indeed appear at particular energies. In a wonderful manifestation of a type of bulk-edge correspondence, these edge state energies correspond to the quantum number for which additional stationary points appear in the continuum bandstructure of the equivalent problem studied with periodic boundary conditions. Our theoretical results are relevant to a swathe of classical or quantum lattice model simulators, such that the proposed edge states may be useful for applications including waveguiding in metamaterials and quantum transport.

Metamaterials are artificial materials with subwavelength structure 1 that enable the translation of magnetic 2 and electric responses 3 into spectral regions not accessible through naturally occurring materials. Here, we report direct measurements of the propagation and confinement of terahertz electromagnetic surface modes tightly bound to flat plasmonic metamaterials that consist of metal surfaces decorated with two-dimensional arrays of subwavelength-periodicity pits. These modes are surface plasmon polaritons with an effective plasma frequency controlled entirely by the surface geometry 4 . The mode spectrum and penetration depth into air demonstrate strong wavelength-scale energy confinement to the surface below the electromagnetic band edge; this is in stark contrast to the very weak confinement found at flat metal surfaces in this spectral regime. The results are in good agreement with analytical and numerical models of surface plasmon polaritons propagating on structured perfect-conductor surfaces, and imply that plasmonic metamaterials could help miniaturize optical components or lead to improved chemical or biochemical sensors.

The emerging field of plasmonics is based on exploiting the coupling between light and collective electronic excitations within conducting materials known as surface plasmons. Because the so-called surface plasmon polariton (SPP) modes that arise from this coupling are not constrained by the optical diffraction limit, it is hoped that they could enable the construction of ultracompact optical components 1 , 2 . But in order that such potential can be realized, it is vital that the relatively poor light–SPP coupling be improved. This is made worse by the fact that the incident light that is conventionally used to launch SPPs in a metal film 3 , 4 , 5 , 6 is a significant source of noise, unless directed away from a region of interest, which then decreases the signal and increases the system’s size. Back-side illumination of subwavelength apertures in optically thick metal films 7 , 8 , 9 , 10 , 11 , 12 , 13 eliminates this problem but does not ensure a unique propagation direction for the SPP. We propose a novel back-side slit-illumination method that incorporates a periodic array of grooves carved into the front side of a thick metal film. Bragg reflection enhances the propagation of SPPs away from the array, enabling them to be unidirectionally launched from, and focused to, a localized point.

Here, we introduce the concept of magnetic localized surface plasmons (LSPs), magnetic dipole modes that are supported by cylindrical metal structures corrugated by very long, curved grooves. The resonance wavelength is dictated by the length of the grooves, allowing us to tune it to values much larger than the size of the particle. Moreover, magnetic LSPs also exist for extremely thin metal disks and, therefore, they could be used to devise metasurfaces with magnetic functionalities. Experimental evidence of the existence of these magnetic LSPs in the microwave regime is also presented, although the concept is very general and could be applied to terahertz or infrared frequencies.

The discovery of the phenomenon of extraordinary optical transmission through a two-dimensional array of subwavelength holes in a metallic film 1 has opened a new line of research within optics. The key role played by surface plasmons in transferring light efficiently from the input side of the metal film to the output region was soon realized. This fundamental knowledge enabled extension of this surface-plasmon ability to achieve extraordinary optical transmission and strong collimation of light in a single hole surrounded by a finite periodic array of indentations 2 . Here, we show how these ideas developed for electromagnetic radiation can be transferred to other classical waves such as acoustic waves.

In this work we discuss the emergence of approximate causality in a general setup from waveguide QED-i.e. a one-dimensional propagating field interacting with a scatterer. We prove that this emergent causality translates into a structure for the N-photon scattering matrix. Our work builds on the derivation of a Lieb-Robinson-type bound for continuous models and for all coupling strengths, as well as on several intermediate results, of which we highlight: (i) the asymptotic independence of space-like separated wave packets, (ii) the proper definition of input and output scattering states, and (iii) the characterization of the ground state and correlations in the model. We illustrate our formal results by analyzing the two-photon scattering from a quantum impurity in the ultrastrong coupling regime, verifying the cluster decomposition and ground-state nature. Besides, we generalize the cluster decomposition if inelastic or Raman scattering occurs, finding the structure of the S -matrix in momentum space for linear dispersion relations. In this case, we compute the decay of the fluorescence (photon-photon correlations) caused by this S-matrix.

Light usually diffracts in all directions when it emerges from a subwavelength aperture, which puts a lower limit on the size of features that can be used in photonics. This limitation can be overcome by creating a periodic texture on the exit side of a single aperture in a metal film. The transmitted light emerges from the aperture as a beam with a small angular divergence (approximately ±3°) whose directionality can be controlled. This finding is especially surprising, considering that the radiating region is mainly confined to an area with lateral dimensions comparable to the wavelength of the light. The device occupies no more than one cubic micrometer and, when combined with enhanced transmission, suggests that a wide range of photonic applications is possible.

Studying the collective excitations in charge neutral graphene (CNG) has recently attracted a great interest because of unusual mechanisms of the charge carrier dynamics. The latter can play a crucial role for formation of recently observed in twisted bilayer CNG graphene plasmon polaritons (GPPs) associated with the interband transitions between the flat electronic bands. Besides, GPPs in CNG can be a tool providing insights into various quantum phenomena in CNG via optical experiments. However, the properties of interband GPPs in CNG are not known, even in the simplest configurations. Here, we show that magnetically-biased single-layer CNG can support interband GPPs of both transverse magnetic and transverse electric polarizations (particularly, at zero temperature). GPPs exist inside the absorption bands originating from the electronic transitions between Landau levels and are tunable by the magnetic field. We place our study into the context of potential near-field and far-field optical experiments. The experimental observation of plasmon-polaritons in charge-neutral bilayer graphene sparked interest for plasmonic and superconducting devices. Here, simulations predict that plasmon-polaritons possessing either transverse magnetic or electric polarization arise under an applied magnetic field in charge-neutral monolayer graphene.

A three-dimensional periodic structure focuses acoustic waves to a spot size that is one fiftieth of the wavelength—beating the classical diffraction limit by a long way. The device could lead to improved resolution for ultrasound imaging. For classical waves such as light or sound, diffraction sets a natural limit on how finely the details of an object can be recorded on its image. Recently, various optical superlenses based on the metamaterials concept have shown the possibility of overcoming the diffraction limit 1 , 2 , 3 , 4 , 5 , 6 , 7 . Similar two-dimensional (2D) acoustic hyperlens designs have also been explored 8 , 9 , 10 . Here we demonstrate a 3D holey-structured metamaterial that achieves acoustic imaging down to a feature size of λ /50. The evanescent field components of a subwavelength object are efficiently transmitted through the structure as a result of their strong coupling with Fabry–Pérot resonances inside the holey plate. This capability of acoustic imaging at a very deep-subwavelength scale may open the door for a broad range of applications, including medical ultrasonography, underwater sonar and ultrasonic non-destructive evaluation.

We present a mechanism for ultra-broadband transmission of acoustic waves through subwavelength hole arrays. Different fluids surrounding (or filling) the holes are considered, which allows tuning of the band of maximum transmission to different angles of incidence. For certain configurations, this band of total transmission may appear at very small incident angles, making the system 'invisible' to sound at almost normal incidence. Analytical expressions for the specific incident angle, and for maximum transmission at that angle, are provided for any fluid-system configuration.