Hyperspectral Nanoimaging of van der Waals Polaritonic Crystals.

Phonon polaritons (PhPs) in van der Waals (vdW) crystal slabs enable nanoscale infrared light manipulation. Specifically, periodically structured vdW slabs behave as polaritonic crystals (vdW-PCs), where the polaritons form Bloch modes. Because the polariton wavelengths are smaller than that of light, conventional far-field spectroscopy does not allow for a complete characterization of vdW-PCs or for revealing their band structure. Here, we perform hyperspectral infrared nanoimaging and analysis of PhPs in a vdW-PC slab made of h-BN. We demonstrate that infrared spectra recorded at individual spatial positions within the unit cell of the vdW-PC can be associated with its band structure and local density of photonic states (LDOS). We thus introduce hyperspectral infrared nanoimaging as a tool for the comprehensive analysis of polaritonic crystals, which could find applications in the reconstruction of complex polaritonic dispersion surfaces in momentum-frequency space or for exploring exotic electromagnetic modes in topological photonic structures.

Nonlocal Quantum Effects in Plasmons of Graphene Superlattices.

By using a nonlocal, quantum mechanical response function we study graphene plasmons in a one-dimensional superlattice (SL) potential V_{0}cosG_{0}x. The SL introduces a quantum energy scale E_{G}∼ℏv_{F}G_{0} associated with electronic subband transitions. At energies lower than E_{G}, the plasmon dispersion is highly anisotropic; plasmons propagate perpendicularly to the SL axis, but become damped by electronic transitions along the SL direction. These results question the validity of semiclassical approximations for describing low energy plasmons in periodic structures. At higher energies, the dispersion becomes isotropic and Drude-like with effective Drude weights related to the average of the absolute value of the local chemical potential. Full quantum mechanical treatment of the kinetic energy thus introduces nonlocal effects that delocalize the plasmons in the SL, making the system behave as a metamaterial even near singular points where the charge density vanishes.

Plasmonic Dirac Cone in Twisted Bilayer Graphene.

We discuss plasmons of biased twisted bilayer graphene when the Fermi level lies inside the gap. The collective excitations are a network of chiral edge plasmons (CEP) entirely composed of excitations in the topological electronic edge states that appear at the AB-BA interfaces. The CEP form a hexagonal network with a unique energy scale ε_{p}=(e^{2})/(ε_{0}εt_{0}) with t_{0} the moiré lattice constant and ε the dielectric constant. From the dielectric matrix we obtain the plasmon spectra that has two main characteristics: (i) a diverging density of states at zero energy, and (ii) the presence of a plasmonic Dirac cone at ℏω∼ε_{p}/2 with sound velocity v_{D}=0.0075c, which is formed by zigzag and armchair current oscillations. A network model reveals that the antisymmetry of the plasmon bands implies that CEP scatter at the hexagon vertices maximally in the deflected chiral outgoing directions, with a current ratio of 4/9 into each of the deflected directions and 1/9 into the forward one. We show that scanning near-field microscopy should be able to observe the predicted plasmonic Dirac cone and its broken symmetry phases.

Topological Phases of Polaritons in a Cavity Waveguide.

We study the unconventional topological phases of polaritons inside a cavity waveguide, demonstrating how strong light-matter coupling leads to a breakdown of the bulk-edge correspondence. We observe an ostensibly topologically nontrivial phase, which unexpectedly does not exhibit edge states. Our findings are in direct contrast to topological tight-binding models with electrons, such as the celebrated Su-Schrieffer-Heeger (SSH) model. We present a theory of collective polaritonic excitations in a dimerized chain of oscillating dipoles embedded inside a photonic cavity. The added degree of freedom from the cavity photons upgrades the system from a typical SSH SU(2) model into a largely unexplored SU(3) model. Tuning the light-matter coupling strength by changing the cavity size reveals three critical points in parameter space: when the polariton band gap closes, when the Zak phase changes from being trivial to nontrivial, and when the edge state is lost. These three critical points do not coincide, and thus the Zak phase is no longer an indicator of the presence of edge states. Our discoveries demonstrate some remarkable properties of topological matter when strongly coupled to light, and could be important for the growing field of topological nanophotonics.

Single Photons by Quenching the Vacuum.

Heisenberg's uncertainty principle implies that the quantum vacuum is not empty but fluctuates. These fluctuations can be converted into radiation through nonadiabatic changes in the Hamiltonian. Here, we discuss how to control this vacuum radiation, engineering a single-photon emitter out of a two-level system (2LS) ultrastrongly coupled to a finite-band waveguide in a vacuum state. More precisely, we show the 2LS nonlinearity shapes the vacuum radiation into a non-Gaussian superposition of even and odd cat states. When the 2LS bare frequency lays within the band gaps, this emission can be well approximated by individual photons. This picture is confirmed by a characterization of the ground and bound states, and a study of the dynamics with matrix-product states and polaron Hamiltonian methods.

Polariton Anomalous Hall Effect in Transition-Metal Dichalcogenides.

We analyze the properties of strongly coupled excitons and photons in systems made of semiconducting two-dimensional transition-metal dichalcogenides embedded in optical cavities. Through a detailed microscopic analysis of the coupling, we unveil novel, highly tunable features of the spectrum that result in polariton splitting and a breaking of light-matter selection rules. The dynamics of the composite polaritons is influenced by the Berry phase arising both from their constituents and from the confinement-enhanced coupling. We find that light-matter coupling emerges as a mechanism that enhances the Berry phase of polaritons well beyond that of its elementary constituents, paving the way to achieve a polariton anomalous Hall effect.

Angle resolved transmission through metal hole gratings.

We present the first angle resolved measurements of extraordinary optical transmission (EOT) through hole array gratings in a gold film. Varying the lattice spacing of the arrays and looking at higher diffraction orders, we retrieve the angular emission pattern of the constituent holes with better signal to noise ratio than with single-hole experiments. We present a method to determine separately the angular dependence of the direct and resonant contribution to EOT by using the spectral features of the diffraction orders together with an established model. The comparison of our results with the known angular transmission of a single hole in a metal film yields a good agreement for s-polarized light. Deviations are found for illumination with p-polarized light and we address the discrepancy with Coupled Mode Model calculations and Finite Difference Time Domain simulations. These measured deviations are currently not fully understood.

Scattering in the ultrastrong regime: nonlinear optics with one photon.

The scattering of a flying photon by a two-level system ultrastrongly coupled to a one-dimensional photonic waveguide is studied numerically. The photonic medium is modeled as an array of coupled cavities and the whole system is analyzed beyond the rotating wave approximation using matrix product states. It is found that the scattering is strongly influenced by the single- and multiphoton dressed bound states present in the system. In the ultrastrong coupling regime a new channel for inelastic scattering appears, where an incident photon deposits energy into the qubit, exciting a photon-bound state, and escaping with a lower frequency. This single-photon nonlinear frequency conversion process can reach up to 50% efficiency. Other remarkable features in the scattering induced by counterrotating terms are a blueshift of the reflection resonance and a Fano resonance due to long-lived excited states.

Theory of strong coupling between quantum emitters and propagating surface plasmons.

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.

Optimal light harvesting structures at optical and infrared frequencies.

One-dimensional light harvesting structures with a realistic geometry nano-patterned on an opaque metallic film are optimized to render high transmission efficiencies at optical and infrared frequencies. Simple design rules are developed for the particular case of a slit-groove array with a given number of grooves that are symmetrically distributed with respect to a central slit. These rules take advantage of the hybridization of Fabry-Perot modes in the slit and surface modes of the corrugated metal surface. Same design rules apply for optical and infrared frequencies. The parameter space of the groove array is also examined with a conjugate gradient optimization algorithm that used as a seed the geometries optimized following physical intuition. Both uniform and nonuniform groove arrays are considered. The largest transmission enhancement, with respect to a uniform array, is obtained for a chirped groove profile. Such relative enhancement is a function of the wavelength. It decreases from 39 % in the optical part of the spectrum to 15 % at the long wavelength infrared.

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.

Diffraction regimes of single holes.

We investigate both experimentally and theoretically the far-field diffraction patterns of single circular apertures as a function of their diameters d and at a given illumination wavelength λ. We observe the transition between the well-known pseudoscalar regime of large holes (d≫λ) and the less-known vectorial regime of subwavelength ones (d≪λ). Four different diffraction regimes are identified for different d/λ regions, each one with its polarization dependence. A thorough comparison with a theoretical model, which takes into account both finite hole size and the dielectric properties of the metal, allows us to explain and understand the physical processes leading to this behavior. Our results reveal the subtle interplay between two competing factors, one related to polarization symmetries associated with surface-plasmon excitations and the other originating in the coupling of the field to the waveguide mode of the aperture.

Mechanisms for extraordinary optical transmission through bull's eye structures.

We analyze both experimentally and theoretically the physical mechanisms that determine the optical transmission through deep sub-wavelength bull's eye structures (concentric annular grooves surrounding a circular hole). Our analysis focus on the transmission resonance as a function of the distance between the central hole and its nearest groove. We find that, for that resonance, each groove behaves almost independently, acting as an optical cavity that couples to incident radiation, and reflecting the surface plasmons radiated by the other side of the same cavity. It is the constructive contribution at the central hole of these standing waves emitted by independent grooves which ends up enhancing transmission. Also for each groove the coupling and reflection coefficients for surface plasmons are incorporated into a phenomenological Huygens-Fresnel model that gathers the main mechanisms to enhance transmission. Additionally, it is shown that the system presents a collective resonance in the electric field that does not lead to resonant transmission, because the fields radiated by the grooves do not interfere constructively at the central hole.

Waveguided spoof surface plasmons with deep-subwavelength lateral confinement.

We present a new type of waveguide scheme for terahertz circuitry based on the concept of spoof surface plasmons. This structure is composed of a one-dimensional array of L-shaped metallic elements horizontally attached to a metal surface. The dispersion relation of the surface electromagnetic modes supported by this system presents a very weak dependence with the lateral dimension and the modes are very deep-subwavelength confined with a long-enough propagation length.

Entanglement of two qubits mediated by one-dimensional plasmonic waveguides.

We investigate qubit-qubit entanglement mediated by plasmons supported by one-dimensional waveguides. We explore both the situation of spontaneous formation of entanglement from an unentangled state and the emergence of driven steady-state entanglement under continuous pumping. In both cases, we show that large values for the concurrence are attainable for qubit-qubit distances larger than the operating wavelength by using plasmonic waveguides that are currently available.

Anomalous band formation in arrays of terahertz nanoresonators.

We investigate band formation in one-dimensional periodic arrays of rectangular holes which have a nanoscale width but a length of 100 µm. These holes are tailored to work as resonators in the terahertz frequency regime. We study the evolution of the electromagnetic response with the period of the array, showing that this dependence is not monotonic due to both the oscillating behavior of the coupling between holes and its long-range character.

Holes with very acute angles: a new paradigm of extraordinary optical transmission through strongly localized modes.

It is shown that submicrometer holes with very acute angles present extraordinary optical transmission peaks associated to strongly localized modes. The positions of these peaks are: (i) strongly redshifted with respect to the peak position that could be expected if the considered hole were in a film made of perfect electric conductor, (ii) independent on the angle of incidence for a large range of angles and (iii) strongly dependent on the direction of the incident electric field. In addition, it is demonstrated that these properties are linked to the mechanisms leading to the existence of channel-plasmon-polaritons.

Optimization of bull's eye structures for transmission enhancement.

We present an exhaustive exploration of the parameter space defining the optical properties of a bull's eye structure, both experimentally and theoretically. By studying the resonance intensity variations associated with the different geometrical features, several parameters are seen to be interlinked and scale laws emerge. From the results it is possible to give a simple recipe to design a bull's eye structure with optimal transmission properties.

Domino plasmons for subwavelength terahertz circuitry.

A new approach for the spatial and temporal modulation of electromagnetic fields at terahertz frequencies is presented. The waveguiding elements are based on plasmonic and metamaterial notions and consist of an easy-to-manufacture periodic chain of metallic box-shaped elements protruding out of a metallic surface. It is shown that the dispersion relation of the corresponding electromagnetic modes is rather insensitive to the waveguide width, preserving tight confinement and reasonable absorption loss even when the waveguide transverse dimensions are well in the subwavelength regime. This property enables the simple implementation of key devices, such as tapers and power dividers. Additionally, directional couplers, waveguide bends, and ring resonators are characterized, demonstrating the flexibility of the proposed concept and the prospects for terahertz applications requiring high integration density.

Observation of enhanced transmission for s-polarized light through a subwavelength slit.

Enhanced optical transmission (EOT) through a single aperture is usually achieved by exciting surface plasmon polaritons with periodic grooves. Surface plasmon polaritons are only excited by p-polarized incident light, i.e. with the electric field perpendicular to the direction of the grooves. The present study experimentally investigates EOT for s-polarized light. A subwavelength slit surrounded on each side by periodic grooves has been fabricated in a gold film and covered by a thin dielectric layer. The excitation of s-polarized dielectric waveguide modes inside the dielectric film strongly increases the s-polarized transmission. A 25 fold increase is measured as compared to the case without the dielectric film. Transmission measurements are compared with a coupled mode method and show good qualitative agreement. Adding a waveguide can improve light transmission through subwavelength apertures, as both s and p-polarization can be efficiently transmitted.