Probing the ultimate limits of plasmonic enhancement

Abstract

Metals support surface plasmons at optical wavelengths and have the ability to localize light to subwavelength regions. The field enhancements that occur in these regions set the ultimate limitations on a wide range of nonlinear and quantum optical phenomena. We found that the dominant limiting factor is not the resistive loss of the metal, but rather the intrinsic nonlocality of its dielectric response. A semiclassical model of the electronic response of a metal places strict bounds on the ultimate field enhancement. To demonstrate the accuracy of this model, we studied optical scattering from gold nanoparticles spaced a few angstroms from a gold film. The bounds derived from the models and experiments impose limitations on all nanophotonic systems.

Fig. 1

Geometry of the film-coupled nanoparticle. Left: Schematic of the sample. Right: Cross-section of a single film-coupled nanosphere.

Fig. 2

Simulation of a single film-coupled nanoparticle. Left: Relative electron surface density showing the exited surface plasmon polariton propagating over the metal film. Right (top): A plane wave is incident at 75° from normal on the nanoparticle. Right (bottom): A close-up of the near-fields surrounding the nanosphere; note the large field amplitude directly below the sphere. Looking closer yet, it can be seen that the fields penetrate into the nanosphere a distance on the order of the Thomas-Fermi screening length.

Fig. 3

Behavior of the film-coupled nanosphere, assuming a local model and the nonlocal model with various values of β, as a function of gap distance. Calculations refer to a gold nanosphere of radius r = 30nm on a 300 nm thick film. (A) Position of the peak scattering intensity as a function of gap distance. (B) The corresponding field enhancement ratio. Note that in the absence of nonlocal effects, the peak scattering wavelength is extreme and the field enhancement grows to enormous values; nonlocality places a limit on the ultimate enhancement.

Fig. 4

Experimental confirmation of nonlocal contributions to surface plasmon scattering. (A) Schematic of NP-film gap system showing a gold NP separated from the film by an amine-terminated alkanethiol SAM. (B) Thickness of the SAM layers as a function of the number of carbon atoms. (C) Normalized dark-field measured spectra of ensembles of film-coupled NPs for SAM spacer layers of different numbers of carbon atoms. (D) Comparison of experimental measurements from both SAM and LBL type spacers with numerical results with β = 1.27×10⁶m/s.