Quantum hydrodynamic theory for plasmonics: Impact of the electron density tail

From the static polarization function of electrons in the random phase approximation, the quantum Bohm potential for the quantum hydrodynamic description of electrons and the density gradient correction to the Thomas–Fermi free energy at a finite temperature for the two‐ and one‐dimensional cases are derived. The behaviour of the Bohm potential and of the density gradient correction as a function of the degeneracy parameter is discussed. Based on recent developments in the fluid description of quantum plasmas, the Bohm potential for the high‐frequency domain is presented.

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“…The functional derivative of the leading term of the density gradient correction gives the Bohm potential of quantum hydrodynamics:

V_{B} = \frac{ℏ^{2}}{8 m_{e}} \frac{δ}{δ n} ((), true \int γ_{D} ((),, n, T) \frac{∣ \nabla n ((), r) ∣^{2}}{n ((), r)} d boldr) = prefix- 2 \frac{ℏ^{2}}{8 m_{e}} γ_{D} ((),, n, T) \frac{\nabla^{2} n}{n} + scriptO ((), {((), n_{1} true/ n_{0})}^{2}) .

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Section: Relation Between the Polarization Function In The Rpa And Thsupporting

confidence: 92%

“…The functional derivative of the leading term of the density gradient correction gives the Bohm potential of quantum hydrodynamics [27][28][29] :…”

Section: Relation Between the Polarization Function In The Rpa And Thmentioning

confidence: 99%

Gradient correction and Bohm potential for two‐ and one‐dimensional electron gases at a finite temperature

Moldabekov

Bönitz

Рамазанов

2017

Contrib. Plasma Phys

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“…In this respect, it was shown that the nonlocal correction and the spill‐out effects have counteracting influences (Figure d) . In the treatment of the spill‐out effects careful consideration should be given to the calculation of the spatial dependence of the equilibrium electron density, to which the results are very sensitive …”

Section: Free‐electron Dynamics In Plasmonic Nanostructuresmentioning

confidence: 99%

“…[39,40] In the treatment of the spill-out effects careful consideration should be given to the calculation of the spatial dependence of the equilibrium electron density, to which the results are very sensitive. [41] Other examples of linear nonlocal hydrodynamic effects include the modification of the molecular fluorescence [42] as well as the plasmonic field confinement and enhancement [43][44][45][46] , the latter effects lead to the re-evaluation of SERS efficiency [47] and are also important in the context of nonlinear optics. For a recent review on the linear nonlocal hydrodynamic phenomena we refer the reader to Ref.…”

Section: Linear Free-electron Dynamicsmentioning

confidence: 99%

Free‐electron Optical Nonlinearities in Plasmonic Nanostructures: A Review of the Hydrodynamic Description

Krasavin

Ginzburg

Zayats

2017

Laser & Photonics Reviews

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Requirements of integrated photonics and miniaturisation of optical devices demand efficient nonlinear components not constrained by conventional macroscopic nonlinear crystals. Intrinsic nonlinear response of free carriers in plasmonic materials provides opportunities to design both second-and third-order nonlinear optical properties of plasmonic nanostructures and control light with light using Kerr-type nonlinearities as well as achieve harmonic generation. This review summarises principles of free-carrier nonlinearities in the hydrodynamic description in both perturbative and non-perturbative regimes, considering also contribution of nonlocal effects. Engineering of harmonic generation, solitons, nonlinear refraction and ultrafast all-optical switching in plasmonic nanostructures and metamaterials are discussed. The full hydrodynamic consideration of nonlinear dynamics of free carriers reveals key contributions to the nonlinear effects defined by the interplay between a topology of the nanostructure and nonlinear response of the fermionic gas at the nanoscale, allowing design of high effective nonlinearities in a desired spectral range. Flexibility and unique features of free-electron nonlinearities are important for nonlinear plasmonic applications in free-space as well as integrated and quantum nanophotonic technologies.

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“…But when the sizes approach the nanoscale, the model is no longer able to explain experimentally observable phenomena like, for example, the blueshift of the resonance frequency of the localized surface plasmon (LSP) in metallic nanospheres [1]. An improved model that has been successful in describing the optical properties of metals on the nanoscale is the hydrodynamic Drude model (HDM) [2][3][4][5][6][7][8][9][10][11][12]. In this model, the polarization depends nonlocally on the electrical field, and the aforementioned blueshift appears as a size-dependent nonlocal effect [7,13,14].…”

Section: Introductionmentioning

confidence: 99%