Analytical study of nonlinear dynamics of laser beam interaction with metallic nanoparticle linear array in parallel propagation

In this article using a modified Drude model, which includes all dominant electron energy scattering mechanisms and interparticle interactions, the relativistic dynamics of a linear chain of spherical nanoparticle interacting with a laser beam propagating parallel to the orientation of nanoparticles array is investigated. In the point-dipole description of nanoparticles, taking into account interaction of two nearest neighbors, analytical solutions are obtained for the momentum equations of conducting electrons of nanoparticles related to the first, second and third harmonics of laser fields. Formulae are simplified for some asymptotic cases. Numerical analysis is carried out for a linear chain including 10 of 10nm radius Au nanoparticles. It is shown that the interparticle separation has a key role in the nonlinear dynamics of the system. Dipole-dipole interaction of nanoparticles causes a blueshift for the main and third harmonics plasmon resonance, whereas it leads to a redshift for the plasmon resonance of the second order longitudinal displacements of nanoparticles. Related to the different orders, linear and nonlinear polarization of each particle is obtained and permittivity, first and second order susceptibility, linear and nonlinear refractive index of each nanoparticle are analytically obtained which these findings can have direct application in nano-optics and nano-plasmonics.