It is shown that the ordinary semiclassical theory of the absorption of light by exciton states is not completely satisfactory (in contrast to the case of absorption due to interband transitions). A more complete theory is developed. It is shown that excitons are approximate bosons, and, in interaction with the electromagnetic field, the exciton field plays the role of the classical polarization field. The eigenstates of the system of crystal and radiation field are mixtures of photons and excitons. The ordinary one-quantum optical lifetime of an excitation is infinite. Absorption occurs only when "three-body" processes are introduced. The theory includes "local field" effects, leading to the Lorentz local field correction when it is applicable. A Smakula equation for the oscillator strength in terms of the integrated absorption constant is derived.

a Quantum-Mechanical Theory of the Contribution of Excitons to the Complex Dielectric Constant of Crystals.

In the regime of deep strong light–matter coupling, the coupling strength exceeds the transition energies of the material1–3, fundamentally changing its properties4,5; for example, the ground state of the system contains virtual photons and the internal electromagnetic field gets redistributed by photon self-interaction1,6. So far, no electronic excitation of a material has shown such strong coupling to free-space photons. Here we show that three-dimensional crystals of plasmonic nanoparticles can realize deep strong coupling under ambient conditions, if the particles are ten times larger than the interparticle gaps. The experimental Rabi frequencies (1.9 to 3.3 electronvolts) of face-centred cubic crystals of gold nanoparticles with diameters between 25 and 60 nanometres exceed their plasmon energy by up to 180 per cent. We show that the continuum of photons and plasmons hybridizes into polaritons that violate the rotating-wave approximation. The coupling leads to a breakdown of the Purcell effect—the increase of radiative damping through light–matter coupling—and increases the radiative polariton lifetime. The results indicate that metallic and semiconducting nanoparticles can be used as building blocks for an entire class of materials with extreme light–matter interaction, which will find application in nonlinear optics, the search for cooperative effects and ground states, polariton chemistry and quantum technology4,5. Photons and plasmons hybridize into polaritons in three-dimensional crystals of plasmonic nanoparticles, leading to deep strong light–matter coupling and the breakdown of the Purcell effect.

/pdf/deep-strong-light-matter-coupling-in-plasmonic-nanoparticle-mfm0jny4yp.pdf

Deep strong light–matter coupling in plasmonic nanoparticle crystals

We study a bipartite linear chain constituted by spherical metallic nanoparticles, where each nanoparticle supports a localized surface plasmon. The near-field dipolar interaction between the localized surface plasmons gives rise to collective plasmons, which are extended over the whole nanoparticle array. We derive analytically the spectrum and the eigenstates of the collective plasmonic excitations. At the edge of the Brillouin zone, the spectrum is of a pseudorelativistic nature similar to that present in the electronic band structure of polyacetylene. We find the effective Dirac Hamiltonian for the collective plasmons and show that the corresponding spinor eigenstates represent one-dimensional Dirac-like massive bosonic excitations. Therefore, the plasmonic lattice exhibits similar effects to those found for electrons in one-dimensional Dirac materials, such as the ability for transmission with highly suppressed backscattering due to Klein tunneling. We also show that the system is governed by a nontrivial Zak phase, which predicts the manifestation of edge states in the chain. When two dimerized chains with different topological phases are connected, we find the appearance of the bosonic version of a Jackiw-Rebbi midgap state. We further investigate the radiative and nonradiative lifetimes of the collective plasmonic excitations and comment on the challenges for experimental realization of the topological effects found theoretically.

Topological collective plasmons in bipartite chains of metallic nanoparticles

The assembly of plasmonic nanoparticles into ordered 2D- and 3D-superlattices could pave the way towards new tailored materials for plasmonic sensing, photocatalysis and manipulation of light on the nanoscale. The properties of such materials strongly depend on their geometry, and accordingly straightforward protocols to obtain precise plasmonic superlattices are highly desirable. Here, we synthesize large areas of crystalline mono-, bi- and multilayers of gold nanoparticles >20 nm with a small number of defects. The superlattices can be described as hexagonal crystals with standard deviations of the lattice parameter below 1%. The periodic arrangement within the superlattices leads to new well-defined collective plasmon-polariton modes. The general level of achieved superlattice quality will be of benefit for a broad range of applications, ranging from fundamental studies of light–matter interaction to optical metamaterials and substrates for surface-enhanced spectroscopies. Superlattices of nanoparticles promise new properties emerging from the periodic order. Here, the authors describe the synthesis of superlattices of plasmonic gold nanoparticles with high crystallinity and demonstrate how new plasmon-polariton modes appear in the structures.

/pdf/structural-order-in-plasmonic-superlattices-30vmofs4d1.pdf

Structural order in plasmonic superlattices.

Surface-enhanced vibrational spectroscopy strongly increases the cross section of Raman scattering and infrared absorption, overcoming the limited sensitivity and resolution of these two powerful analytic tools. While surface-enhanced setups with maximum enhancement have been studied widely in recent years, substrates with reproducible, uniform enhancement have received less attention although they are required in many applications. Here, we show that plasmonic supercrystals are an excellent platform for enhanced spectroscopy because they possess a high density of hotspots in the electric field. We describe the near field inside the supercrystal within the framework of plasmon polaritons that form due to strong light-matter interaction. From the polariton resonances we predict resonances in the far-field enhancement for Raman scattering and infrared absorption. We verify our predictions by measuring the vibrations of polystyrene molecules embedded in supercrystals of gold nanoparticles. The intensity of surface-enhanced Raman scattering is uniform within 10% across the crystal with a peak integrated enhancement of up to 300 and a peak hotspot enhancement of 105. The supercrystal polaritons induce pairs of incoming and outgoing resonances in the enhanced cross section as we demonstrate experimentally by measuring surface-enhanced Raman scattering with multiple laser wavelengths across the polariton resonance. The infrared absorption of polystyrene is likewise enhanced inside the supercrystals with a maximum enhancement of 400%. We show with a coupled oscillator model that the increase originates from the combined effects of hotspot formation and the excitation of standing polariton waves. Our work clearly relates the structural and optical properties of plasmonic supercrystals and shows that such crystals are excellent hosts and substrates for the uniform and predictable enhancement of vibrational spectra.

Surface-Enhanced Raman Scattering and Surface-Enhanced Infrared Absorption by Plasmon Polaritons in Three-Dimensional Nanoparticle Supercrystals.

We theoretically investigate plasmon polaritons in cubic lattices of spherical metallic nanoparticles. The nanoparticles, each supporting triply-degenerate localized surface plasmons, couple through the Coulomb dipole-dipole interaction, giving rise to collective plasmons that extend over the whole metamaterial. The latter hybridize with photons forming plasmon polaritons, which are the hybrid light-matter eigenmodes of the system. We derive general analytical expressions to evaluate both plasmon and plasmon-polariton dispersions and the corresponding eigenstates. These are obtained within a Hamiltonian formalism, which takes into account retardation effects in the dipolar interaction between the nanoparticles and considers the dielectric properties of the nanoparticles as well as their surrounding. Within this model we predict polaritonic splittings in the near-infrared to the visible range of the electromagnetic spectrum that depend on polarization, lattice symmetry, and wave-vector direction. Finally, we show that the predictions of our model are in excellent quantitative agreement with conventional finite-difference frequency-domain simulations, but with the advantages of analytical insight and significantly reduced computational cost.

/pdf/plasmon-polaritons-in-cubic-lattices-of-spherical-metallic-4hikh0mn90.pdf

Plasmon polaritons in cubic lattices of spherical metallic nanoparticles

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Plasmon polaritons in cubic lattices of spherical metallic nanoparticles