Damping rates of surface plasmons for particles of size from nano- to micrometers; reduction of the nonradiative decay

Abstract

Damping rates of multipolar, localized surface plasmons (SP) of gold and silver nanospheres of radii up to 1000nm were found with the tools of classical electrodynamics. The significant increase in damping rates followed by noteworthy decrease for larger particles takes place along with substantial red-shift of plasmon resonance frequencies as a function of particle size. We also introduced interface damping into our modeling, which substantially modifies the plasmon damping rates of smaller particles. We demonstrate unexpected reduction of the multipolar SP damping rates in certain size ranges. This effect can be explained by the suppression of the nonradiative decay channel as a result of the lost competition with the radiative channel. We show that experimental dipole damping rates [H. Baida, et al., Nano Lett. 9(10) (2009) 3463, and C. Sönnichsen, et al., Phys. Rev. Lett. 88 (2002) 077402], and the resulting resonance quality factors can be described in a consistent and straightforward way within our modeling extended to particle sizes still unavailable experimentally.

A generalized non-local optical response theory for plasmonic nanostructures

“…Line broadening has been seen experimentally in the extinction of small particles [37][38][39][40][41] and EELS measurements on plasmons in thin nanowires and bow-tie antennas have also revealed plasmon losses exceeding the expectations based on bulk-damping parameters 42,43 . In the literature such line broadening has often been phenomenologically accounted for by a size-dependent damping rate [37][38][39][40][41] , but without placing it in the context of non-local semiclassical equations of motion. The phenomenology introduced by Kreibig 37,38 describes the linewidth broadening by introducing a size-dependent correction to the damping rate: g-g þ Au F /R.…”

Size Effect in Plasmon Resonance of Metallic Nanoparticles: RPA versus COMSOL

“…for- mula (1)), well explains the experimentally observed also irregular (i.e., not proportional to a 3 ) size effect for the red-shift. This Lorentz friction induced correction mixes, however, with the extrinsic size effect due to the multipole contributions, but rather for radii a > 60 nm (Au) significantly exceeding the previously suggested limiting 20 nm [10,11,13]. The quadrupole contribution (and the higher multipoles at larger radii) results in the deformation and larger broadening of the extinction fea-tures not allowing its Lorentzian form any longer (the higher energy quadrupole assistant broad peak occurs first at smaller wavelength in association to the dipole peak broadened and red-shifted by the Lorentz friction).…”

“…The extrinsic regime resolves itself in the Mie theory to the inclusion of the multipole mixing in e-m response. To obtain a coincidence with the experimentally observed size effect in the red-shift of plasmon resonance in larger nanospheres the irradiation corrections to the dielectric function have been introduced proportional to the number of electrons, thus ∼ a 3 [13]. This overestimates, however, the radiative damping.…”

Controllable Cobalt Oxide/Au Hierarchically Nanostructured Electrode for Nonenzymatic Glucose Sensing

“…The scattering contribution can then be calculated by subtracting the absorption coefficient from the total extinction value. Here the real part of the dielectric constant determines the position of the wavelength while the bandwidth, or time spent dephasing, is determined by the imaginary component [18,[30][31][32][33]. In general, for smaller nanoparticles, <40 nm, the optical extinction is dominated by absorption whereas scattering contributions increase as the diameter of the nanoparticle grows [21,33,34].…”

“…Tuning of the LSPR properties can be achieved through synthesis by exploiting differences in nanoparticle size, geometry, surface morphology, aggregation, aspect ratio, and the dielectric constant of the surrounding media [15,33,[35][36][37][38][39][40][41][42][43][44][45]. Since each application relies on a specific set of conditions for optimized efficiency, the structural parameters of the nanoparticles employed for use must be tailored accordingly.…”