Classical Theory of Optical Nonlinearity in Conducting Nanoparticles

Panasyuk, George Y.; Schotland, John C.; Markel, Vadim A.

doi:10.1103/physrevlett.100.047402

Cited by 35 publications

(33 citation statements)

References 12 publications

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“…In Ref. 15, we have argued the surface charge in a polarized metal nanoparticle can not be confined to an infinitely thin layer. When the width of this layer is not negligible (compared to the particle radius), a nonlinear correction to the particle polarizability is obtained.…”

Section: Magnitude Of the Nonlinear Effect And Comparison With Thementioning

confidence: 99%

Theoretical and numerical investigation of the size-dependent optical effects in metal nanoparticles

et al. 2011

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We further develop the theory of quantum finite-size effects in metallic nanoparticles, which was originally formulated by Hache, Ricard and Flytzanis [J. Opt. Soc. Am. B 3, 1647 (1986)] and (in a somewhat corrected form) by Rautian [Sov. Phys. JETP 85, 451 (1997)]. These references consider a metal nanoparticle as a degenerate Fermi gas of conduction electrons in an infinitely-high spherical potential well. This model (referred to as the HRFR model below) yields mathematical expressions for the linear and the third-order nonlinear polarizabilities of a nanoparticle in terms of infinite nested series. These series have not been evaluated numerically so far and, in the case of nonlinear polarizability, they can not be evaluated with the use of conventional computers due to the high computational complexity involved. Rautian has derived a set of remarkable analytical approximations to the series but direct numerical verification of Rautian's approximate formulas remained a formidable challenge. In this work, we derive an expression for the third-order nonlinear polarizability, which is exact within the HRFR model but amenable to numerical implementation. We then evaluate the expressions obtained by us numerically for both linear and nonlinear polarizabilities. We investigate the limits of applicability of Rautian's approximations and find that they are surprisingly accurate in a wide range of physical parameters. We also discuss the limits of small frequencies (comparable or below the Drude relaxation constant) and of large particle sizes (the bulk limit) and show that these limits are problematic for the HRFR model, irrespectively of any additional approximations used. Finally, we compare the HRFR model to the purely classical theory of nonlinear polarization of metal nanoparticles developed by us earlier [Phys. Rev. Lett. 100, 47402 (2008)].

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Section: Magnitude Of the Nonlinear Effect And Comparison With Thementioning

confidence: 99%

Theoretical and numerical investigation of the size-dependent optical effects in metal nanoparticles

et al. 2011

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“…In a series of papers [11][12][13][14][15] a quantum approach for the spin Hall conductivity had been discussed. In [16] a classical theory is proposed.…”

Section: Introductionmentioning

confidence: 99%

Thermally assisted spin Hall effect

Schulz

Trimper

2008

Physics Letters A

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The spin polarized charge transport is systematically analyzed as a thermally driven stochastic process. The approach is based on Kramers' equation describing the semiclassical motion under the inclusion of stochastic and damping forces. Due to the relativistic spin-orbit coupling the damping experiences a relativistic correction leading to an additional contribution within the spin Hall conductivity. A further contribution to the conductivity is originated from the averaged underlying crystal potential, the mean value of which depends significantly on the electric field. We derive an exact expression for the electrical conductivity. All corrections are estimated in lowest order of a relativistic approach and in the linear response regime.

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“…One profound theoretical question is related to the applicability of macroscopic theories when a particle has only few nanometers in size. While study of size and quantum effects and their influence on linear and nonlinear response on electromagnetic fields have a rather long history (see, for example, Refs [36][37][38][39][40]), systematic investigation of the role of these effects and its influence on thermal properties of small bodies took part only recently. In Refs.…”

Section: Introductionmentioning

confidence: 99%

Size effects in long-term quasistatic heat transport

Panasyuk

Yerkes

2013

Phys. Rev. E

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We consider finite size effects on heat transfer between thermal reservoirs mediated by a quantum system, where the number of modes in each reservoir is finite. Our approach is based on the generalized quantum Langevin equation and the thermal reservoirs are described as ensembles of oscillators within the DrudeUllersma model. A general expression for the heat current between the thermal reservoirs in the long-time quasi-static regime, when an observation time is of the order of ∆ −1 and ∆ is the mode spacing constant of a thermal reservoir, is obtained. The resulting equations that govern the long-time relaxation for the mode temperatures and the average temperatures of the reservoirs are derived and approximate analytical solutions are found. The obtained time dependences of the temperatures and the resulting heat current reveal peculiarities at t = 2πm/∆ with nonnegative integers m and the heat current vanishes non-monotonically when t → ∞. The validity of Fourier's law for a chain of finite-size macroscopic subsystems is considered. As is shown, for characteristic times of the order of ∆ −1 the temperatures of subsystems' modes deviate from each other and the validity of Fourier's law cannot be established. In a case when deviations of initial temperatures of the subsystems from their average value are small, t → ∞ asymptotic values for the mode temperatures do not depend on a mode's number and are the same as if Fourier's law were valid for all times.

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Classical Theory of Optical Nonlinearity in Conducting Nanoparticles

Abstract: We develop a classical theory of electron confinement in conducting nanoparticles. The theory is used to compute the nonlinear optical response of the nanoparticle to a harmonic external field.Comment: Page margins have been adjusted; otherwise, identical to the previous versio

Cited by 35 publications

References 12 publications

Theoretical and numerical investigation of the size-dependent optical effects in metal nanoparticles

Theoretical and numerical investigation of the size-dependent optical effects in metal nanoparticles

Thermally assisted spin Hall effect

Size effects in long-term quasistatic heat transport

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