R. E. Noskov, D. A. Smirnova, N. S. Lapshina

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We consider nonlinear discrete modes in a two-dimensional lattice of metallic nanoparticles driven by optical radiation at a frequency close to the frequency of the surface plasmon resonance of an individual nanoparticle. We suppose that the particles are small enough and the interparticle distance is large enough to treat nanoparticle within point-dipole approximation. We also assume that nanoparticles are made of silver and possess an intrinsic nonlinear Kerr-type response. Since each particle acts as a resonantly excited oscillator with slow (in comparison with the light period) inertial response, we employ a slowly varying amplitude approach to describe dynamical behavior of particle polarizations. Following a standard linear stability analysis, we obtain areas of bistability and modulation instability for the homogeneous stationary solution of the corresponding dynamical system in the plane ‘intensity-frequency’. Based on these data, we present and analyze examples of generation of plasmonic Faraday waves, stable two-dimensional solitons, oscillons, and kinks (switching waves), which separate two different homogeneous states of particle polarizations. We also discuss realistic duration of the laser pulse which should be large enough to cause the formation of the considered nonlinear modes and small enough to prevent particle ablation.

Keywords: plasmonics, nanophotonics, metal nanoparticle, cubic susceptibility of silver nanoparticle , surface plasmon resonance, discrete localized mode, modulation instability, Faraday waves, soliton, oscillon, kink


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