Here we present the theoretical foundation of the strong coupling phenomenon between quantum emitters and propagating surface plasmons observed in two-dimensional metal surfaces. For that purpose, we develop a quantum framework that accounts for the coherent coupling between emitters and surface plasmons and incorporates the presence of dissipation and dephasing. Our formalism is able to reveal the key physical mechanisms that explain the reported phenomenology and also determine the physical parameters that optimize the strong coupling. A discussion regarding the classical or quantum nature of this phenomenon is also presented. DOI: 10.1103/PhysRevLett.110.126801 PACS numbers: 73.20.Mf, 42.50.Nn, 71.36.+c Surface plasmon polaritons (SPPs), hybrid bound modes comprising both electromagnetic fields and charge currents, are well known to have both a subwavelength confinement and propagation lengths of tens or even hundreds of wavelengths [1,2]. For this reason, the interaction between quantum emitters (QEs) and SPPs has attracted great interest recently [3][4][5]. It has been shown that QE-SPP coupling can lead to single SPP generation [6][7][8] and that the interaction between two QEs can be mediated by SPPs, resulting in energy transfer, superradiance [9], and entanglement phenomena [10][11][12]. Recently, there have also been several experimental studies that show the emergence of strong coupling (SC), i.e., coherent energy exchange between propagating SPPs and excitons either in organic molecules [13][14][15][16][17][18] or in quantum dots [19][20][21]. However, to our knowledge, a first-principles explanation of these experimental results has not been presented yet.In this Letter, we analyze the phenomenon of SC between quantum emitters (or absorbers) and SPPs and present its theoretical foundation. We develop a complete quantum treatment that is not only able to calculate absorption spectra and reproduce the experimental phenomenology but also deal with more complex aspects such as photon statistics.In Fig. 1(a) we render a sketch of the general structure that mimics the experimental configuration: a collection of N QEs immersed into a layer of thickness W and placed on top of a thin metal film (thickness h). In this work, the acronym QE will refer to a quantum system with discrete electronic levels, like organic molecules or quantum dots. In some of the experimental setups and in order to avoid quenching of the QEs, a dielectric spacer of width s is located between the QEs and the metal substrate. We will take 2 ¼ 1 ¼ 1 in our calculations, and we will use the dielectric function of the metal (silver) m as tabulated in Ref. [22]. As a minor simplification, we will assume a semi-infinite metal substrate instead of the metal film considered in the experiments (these films are thick enough for the SPPs to be very similar to those of a single interface). Each QE is represented by a two-level system (2LS) fjgi; jeig and characterized by a transition frequency ! 0 (in this Letter we will use ! 0 ¼ 2 eV, @ ¼ 1...

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.

We study a one-dimensional plasmonic system with nontrivial topology: a chain of metallic nanoparticles with alternating spacing, which in the limit of small particles is the plasmonic analogue to the Su-Schrieffer-Heeger model. Unlike prior studies we take into account long-range hopping with retardation and radiative damping, which is necessary for the scales commonly used in plasmonics experiments. This leads to a non-Hermitian Hamiltonian with frequency dependence that is notably not a perturbation of the quasistatic model. We show that the resulting band structures are significantly different, but that topological features such as quantized Zak phase and protected edge modes persist because the system has the same eigenmodes as a chirally symmetric system. We discover the existence of retardation-induced topological phase transitions, which are not predicted in the SSH model. We find parameters that lead to protected edge modes and confirm that they are highly robust under disorder, opening up the possibility of protected hotspots at topological interfaces that could have novel applications in nanophotonics. KEYWORDS: plasmonics, surface plasmons, topological insulator, edge states, hotspots, disorder, nanoparticle array P lasmonic systems take advantage of subwavelength field confinement and the resulting enhancement to create hotspots, with applications in medical diagnostics, sensing and metamaterials.1,2 Arrays of metallic nanoparticles support surface plasmons that delocalize over the structure and whose properties can be manipulated by tuning the dimensions of the particles and their spacing.3−6 In particular, 1D and 2D arrays have significant uses in band-edge lasing 7,8 and can be made to strongly interact with emitters.9,10 Configurations of nanoparticle dimers have been shown to exhibit interesting physical properties;11 in the following we consider a nanoparticle dimer array in the context of topological photonics.The rise of topological insulators, materials with an insulating bulk and conducting surface states that are protected from disorder, has inspired the study of analogous photonic and plasmonic systems.12−23 Topological photonics shows exciting potential for unidirectional plasmonic waveguides, 24 lasing, 25 and field enhancing hotspots with robust topological protection, which could prove useful for nanoparticle arrays on flexible substrates. 26 Plasmonic and photonic systems provide a powerful platform to examine topological insulators without the complication of interacting particles and with interesting additional properties like non-Hermiticity.27−32 The lack of Fermi level simplifies the excitation of states, and the tunability made available by the larger scale allows for the study of disorder and defects in greater depth than electronic systems.33−35 They also simplify the study of topology in finite systems. 36One of the simplest topologically nontrivial models is that of Su, Schrieffer, and Heeger (SSH), 37,38 which features a chain of atoms with staggered hoppin...

A new strategy to control the flow of surface plasmon polaritons at metallic surfaces is presented. It is based on the application of the concept of Transformation Optics to devise the optical parameters of the dielectric medium placed on top of the metal surface. We describe the general methodology for the design of Transformation-Optical devices for surface plasmons and analyze, for proof-of-principle purposes, three representative examples with different functionalities: a beam shifter, a cylindrical cloak and a ground-plane cloak.

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 travelling 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 in order to achieve these effects, and we present an equivalent transmission line model.

Time-varying media have recently emerged as a new paradigm for wave manipulation, due to the synergy between the discovery of highly nonlinear materials, such as epsilon-near-zero materials, and the quest for wave applications, such as magnet-free nonreciprocity, multimode light shaping, and ultrafast switching. In this review, we provide a comprehensive discussion of the recent progress achieved with photonic metamaterials whose properties stem from their modulation in time. We review the basic concepts underpinning temporal switching and its relation with spatial scattering and deploy the resulting insight to review photonic time-crystals and their emergent research avenues, such as topological and non-Hermitian physics. We then extend our discussion to account for spatiotemporal modulation and its applications to nonreciprocity, synthetic motion, giant anisotropy, amplification, and many other effects. Finally, we conclude with a review of the most attractive experimental avenues recently demonstrated and provide a few perspectives on emerging trends for future implementations of time-modulation in photonics.

We demonstrate that the interaction between two emitters can be controlled by means of the efficient excitation of surface plasmon modes in graphene. We consider graphene surface plasmons supported by either twodimensional graphene sheets or one-dimensional graphene ribbons, showing in both cases that the coupling between the emitters can be strongly enhanced or suppressed. The super-and subradiant regimes are investigated in the reflection and transmission configurations. Importantly, the length scale of the coupling between emitters, which in vacuum is fixed by the free-space wavelength, is now determined by the wavelength of the graphene surface plasmons, which can be extremely short and can be tuned at will via a gate voltage.

Here we present a systematic study of the dynamics of a single quantum emitter near a flat metal-dielectric interface. We identify the key elements that determine the onset of reversibility in these systems by using a formalism suited for absorbing media and through an exact integration of the dynamics. Moreover, when the quantum emitter separation from the surface is small, we are able to describe the dynamics within a pseudomode description that yields analytical understanding and allows more powerful calculations. Metal-dielectric interfaces strongly modify the density of electromagnetic (EM) modes in their surroundings. This is due to the existence of surface EM modes, known as surface plasmon polaritons (SPPs), which propagate along the metal surface. This modified density of EM modes reduces the lifetime of quantum emitters (QEs) when these are placed close to a metal surface [1,2]. Moreover, when the distance between the QE and the metal surface is extremely small (less than around 10 nm), the radiative emission is said to be quenched, because the QE decay is dominated by extremely fast nonradiative lossy channels within the metal. Although there have been some theoretical studies dealing with the possibility of a coherent exchange of energy between a single QE and surface EM modes in metal nanostructures [3][4][5][6][7][8][9][10][11], only the perturbative or weak-coupling regime in which the quantum dynamics is irreversible has been observed in metal surfaces [12][13][14], plasmonic waveguides [15,16], or metal nanoparticles [17,18].In this work we present a theoretical study on the population dynamics of a single QE coupled electromagnetically to a two-dimensional (2D) metal-dielectric interface, including the situations where the emission is quenched. We use a quantummechanical formalism for the EM field excitations that fully takes into account their lossy character [19][20][21][22]. Additionally, we go beyond Fermi's golden rule and integrate exactly the dynamics relying only on the rotating-wave approximation [21][22][23]. This is in contrast with previous works [11] in which a perturbative method was used to capture reversibility only up to lowest order [23] in the coupling. Through the appearance of oscillations in the dynamics of the QE population, we determine the conditions under which the perturbative regime breaks and reversible dynamics can be observed. Furthermore, in the limit of small separations the interference between the QE dipole and its image creates an effective cavity that is able to exchange energy coherently with the QE. This analogy allows us to map the problem into the dissipative Jaynes-Cummings (JC) model [24], which results in both analytical formulas for the key parameters determining the * Corresponding author: alejandro.gonzalez-tudela@mpq.mpg.de † Corresponding author: paloma.arroyo@uam.es onset of reversibility and a powerful formalism to explore new physics.In the inset of Fig. 1(a) we render the scheme of the general configuration: a QE is embedded into a dielectric...