General Properties of Local Plasmons in Metal Nanostructures

Under the quasistatic approximation, the characteristics of a local plasmon resonance of a metal nanostructure exhibit several general properties. The resonance frequency depends on the fraction of plasmon energy residing in the metal through the real dielectric function of the metal. For a given resonant frequency, the $Q$ factor of the resonance is determined only by the complex dielectric function of the metal material, independent of the nanostructure form or the dielectric environment. A simple result describing the effect of optical gain on the $Q$ factor is also obtained.

Figure 1

Plots of the ratios of plasmon energies in the metal nanostructure to that in the surrounding dielectric medium versus plasmon resonance frequency for metal materials of gold (dashed line), silver (dotted line), and ideal Drude free-electron metal (solid line). Results depend only on the dielectric functions of the metals but not on the specific nanostructure. Dielectric constants for gold and silver used in the calculation were obtained from Ref. 18. The bulk plasmon frequency of the Drude metal is chosen to be at 9 eV to facilitate comparison with silver and gold. The inset shows qualitatively the frequency dependence of the real dielectric constant of a typical metal below its bulk plasmon frequency.

Figure 2

Examples of field distribution affecting the plasmon resonance frequency of a metal nanostructure. (a) Metal spheres imbedded in different dielectric media, (b) metal nanoshells of different thicknesses with symmetric plasmon mode, (c) metal nanoshells of different thicknesses with antisymmetric plasmon mode, (d) metal nanorods of different aspect ratios with field polarization parallel to the rod, and (e) metal nanorods of different aspect ratios with field polarization perpendicular to the rod.

Figure 3

Quality factor versus resonance frequency for plasmon resonances in metal nanostructures. Results for gold (dashed line) and silver (dotted line) are displayed and they are independent of the shape and form of nanostructures.