In this paper, we study the effect of restoration force caused by the limited size of a small metallic nanoparticle (MNP) on its linear response to the electric field of incident light. In a semiclassical phenomenological Drude-like model for small MNP, we consider restoration force caused by the displacement of conduction electrons with respect to the ionic positive background taking into account a free coefficient as a function of diameter of nanoparticle (NP) in the force term obtained by the idealistic Thomson model in order to adjust the classical approach. All important mechanisms of the energy dissipation such as electron-electron, electron-phonon and electron-NP surface scatterings and radiation are included in the model. In addition a correction term added to the damping factor of mentioned mechanisms in order to rectify the deficiencies of theoretical approaches. For determining the free parameters of model, the experimental data of extinction cross section of gold NPs with different sizes doped in the glass host medium are used and a good agreement between experimental data and results of our model is observed. It is shown that by decreasing the diameter of NP, the restoration force becomes larger and classical confinement effect becomes more dominant in the interaction. According to experimental data, the best fitted parameter for the coefficient of restoration force is a third order negative powers function of diameter. The fitted function for the correction damping factor is proportional to the inverse squared wavelength and third order power series of NP diameter. Based on the model parameters, the real and imaginary parts of permittivity for different sizes of gold NPs are presented and it is seen that the imaginary part is more sensitive to the diameter variations. Increase in the NP diameter causes increase in the real part of permittivity (which is negative) and decrease in the imaginary part. :1912.11245v1 [cond-mat.mtrl-sci]
arXiv
The study of the dynamics of the interaction of intense electromagnetic fields with metallic nanoparticles is a great interest of some applied nonlinear phenomena in nano-optics and plasmonics. These phenomena include harmonics generation, nano-focusing, self-focusing, nonlinear modes and nano-waveguiding. Using a relativistic modified Drude model, we analytically solve the motion equations of conduction electrons of spherical nanoparticles in a linear chain interacting with a linearly-polarized laser propagating perpendicular to the symmetry axis of the chain. The mutual interaction of each particle with two adjacent neighbors has been considered in the dipole-dipole interaction regime. By means of a perturbative approach, the motion equations related to the first, second and third harmonics of electromagnetic fields are solved. Numerical studies are carried out for a linear chain including 10 of 10 nm radius gold nanoparticles. The effect of interparticle separation and laser polarization on the nonlinear dynamics of the system has been investigated. It is shown that the interaction of particles causes a blueshift for the plasmon resonance of the system for the polarization of laser where the electric field is perpendicular to the symmetry axis of the chain. In the parallel case of the laser electric field, plasmon resonance frequency experiences a redshift for the first and third harmonics displacements, whereas it blueshifts for the second harmonics due to the interparticle interactions. Also, the interaction of particles causes a decrease in the amplitude of the conduction electrons at the plasmon resonance region for the perpendicular state of laser polarization and its increase for the parallel state.
In this theoretical study, the problem of Second Harmonic Generation (SHG) in the interaction of laser beam with a Metallic Nanoparticle (MNP) dimer is considered. Using a classical electrodynamics approach, the nonlinear interaction of laser beam fields with Nanoparticles (NPs) is considered taking into account the dipole-dipole interparticle interactions. Analytical formulae are derived for the effect of dipole-dipole interaction on the Second Harmonic (SH) radiation power for two different polarizations of laser beam. It is found that the interaction causes the substantial enhancement of the SH radiation power while for the case when the laser beam field is parallel to the dimer axis, this enhancement is larger. Additionally, the dipole-dipole interaction of NPs leads to the redshift of the peak value with respect to the individual NP radiation. The resonance frequency displacement of the parallel case is more than that of the perpendicular one. The effect of particles size and interparticle separation on the SHG is studied.
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