Theory of plasmon-polaritons in binary metallic supercrystals

We present a theory of optical excitations in binary plasmonic supercrystals that are made out of two types of metal nanoparticles. Compared to monodisperse supercrystals, binary crystals have a larger number of plasmonic bands. Their dispersion is governed by the lattice symmetry, unit cell parameters, and shape and material composition of the nanoparticle building blocks. We develop a quantum description of the plasmon polaritons in supercrystals that starts from the dipole and quadrupole excitations of the nanoparticles, their interaction, and their coupling to photons. We show how to use group theory to analyze the plasmon- and photon-induced supercrystal states and their interaction. Plasmon-polaritons of binary metallic supercrystals are in the regime of ultrastrong and deep strong light-matter interaction; i.e., the coupling strength is on the same order as the photon energy. One consequence of the strong interaction is that quadrupolar plasmon modes and photons with energies well above the plasmon energies have to be taken into account to calculate the polariton dispersion. A cesium chloride crystal of two nanoparticles with different dipole and quadrupole energies serves as the example structure to show how the plasmon-polariton dispersion depends on the properties of the nanoparticles and supercrystal structure. The tools presented here can be used to predict and analyze any type of optically active excitation in supercrystals. The results show how to differentiate the optical properties of binary nanoparticle supercrystals into properties that inflexibly depend on lattice symmetry and properties that can be finely tuned by choosing the nanoparticle composition and shape.