Self-focusing of laser beam propagating through a dissipative suspension of metallic nanoparticles is studied. The impact of the imaginary part of nanoparticle polarizability on the optical force and consequently on the particles' rearrangement in the presence of laser fields with an initial Gaussian profile is considered. It is shown that the absorption of laser leads to the creation of optical force along the wave propagation direction which can cause longitudinal distribution of nanoparticles. Considering fifth order nonlinearity of wave amplitude that comes from the simultaneous considering of normal Kerr effect produced by the inhomogeneity of the refractive index resulted from the ponderomotive force acting on conducting electrons and artificial Kerr nonlinearity caused by the polarization optical force acting on electrically polarized particles, set of differential equations describing nonlinear steady-state evolution of laser beam is derived by using a non-paraxial method. Dynamics of laser for different frequencies is investigated and optimum frequency range for improving focusing property is determined. It is shown that the artificial Kerr effect causes localization of particles near the propagation axis that can substantially reduce the threshold power for occurring self-focusing in comparison with plasma and other rigid plasmonic systems.
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