What are localized surface plasmon resonances?

We have seen that surface plasmons are charge-density waves that propagate over the surfaces of metals. Because the wavelength is much smaller than that of light at the same frequency, surface plasmons can be difficult to excite, and once excited they do not radiate light. The surface plasmon waves will reflect from discontinuities in the electric permittivity, of either the metal or the overlying dielectric. If a metal film has two parallel boundaries, the surface plasmon waves will reflect, forming standing waves. This happens on the surfaces of metal particles - at particular frequencies the surface plasmons form standing waves on the metal surface. These are known as localized surface plasmon (LSP) resonances.

The image on the right shows a simulation of the vertical component of the electric field as a function of time for a LSP on a metal nanorod. Since the wavelength of the surface plasmons are small,the metal particles can be much smaller than the wavelength of light. Unlike metal films, there is no phase matching condition required and LSPs on metal nanoparticles can be directly excited by light. Furthermore, they will radiate light by the same mechanism.

The LSP resonances are the natural electric modes of the metal particle. Examples of natural resonant modes of a nanorod are shown opposite. When the nanoparticles are much smaller than the wavelength of light, the distribution of surface charge can be calculated using a simple electrostatic theory [1-3]. In the small size limit, the electric and magnetic fields decouple and Maxwell's equations describing the surface plasmons take the same form as in electrostatics, even though the fields are oscillating at the frequency of light. This results in a very nice eigenvalue problem that can be solved numerically for metal particles of any shape.

We have used this method extensively to describe the properties of metal nanoparticles, and in particular, their interactions. More importantly we have developed a simple theory of the interaction that enables complex plasmonic systems to be analysed mathematically. In many important cases, the mathematics can be done as simple "back of the envelope" calculations that avoid the need for complex numerical simulations. A discussion of this method is given on the following pages.

References

[1] F. Ouyang, M. Isaacson: "Surface plasmon excitation of objects with arbitrary shape and dielectric constant" Philosophical Magazine B 60, 481 -492 (1989); [2] I. D. Mayergoyz, D. R. Fredkin, Z. Zhang: "Electrostatic (plasmon) resonances in nanoparticles" Physical Review B 72, 155412 (2005); [3] D. J. Bergman: "Dielectric constant of a two-component granular composite: a practical scheme for calculating the pole spectrum" Physical Review B 19, 2359-2368 (1979)

The first three localized surface plasmon resonances of a metal rod. The surface plasmons form standing waves on the surfaces of the rods. In this simulation blue represents a positive charge and red represents a negative charge.

Copyright Tim Davis 2012