Resonant systems and Fano resonances

Localized surface plasmon resonances arise from the surface charge standing waves on metal nanoparticles. The resonances can be excited by light and, consequently, will re-radiate the light. Most of the radiation from nanoparticles is from their oscillating dipole moments, although there is a small contribution from the higher order moments. This means that a nanoparticle mode with a zero dipole moment will be a poor radiator of light and it will be difficult to excite it directly by applying light.

When two or more particles are in close proximity to one another, there is coupling between them mediated by the electric fields from the surface plasmons. This coupling leads to an exchange of energy, providing a mechanism to excite the non-radiating, or dark, modes of a nanoparticle. However, this has unusual consequences. The "dark" particle will absorb energy from the "bright" particle resulting in a decrease in the radiation from the "bright" particle. Some of the energy transferred onto the "dark" particle can be transferred back again to the "bright" particle. If the transfer is associated with a phase difference, there can be destructive interference between the resonances on the two particles such that it inhibits the "bright" particle from radiating. This is known as induced-transparency. The loss of energy into a "dark" state leads to a particular shape of the resonance curve (see graph) and is known as a Fano resonance, after U. Fano who studied such resonances in relation to neutrons [1].

A system exhibiting induced transparency (and a Fano resonance) was proposed and modelled by Zhang et al [2] and demonstrated experimentally by Liu et al [3]. In my group we developed a simple mathematical description of this interaction in the limit where the particles are much smaller than the wavelength of light [4].

The images above show the three-particle configuration that leads to the induced transparency effect associated with a Fano resonance. Light is polarized parallel to the top nanorod (3). The two parallel nanorods (1 & 2) are excited by LSP coupling. The excited mode is a quadrupole which is "dark". This absorbs energy from nanorod 3. The strengths of the excitations are given by the three mathematical expressions. The coupling leads to a shift in the resonance of nanorod 3.

References

[1] U. Fano: "Effects of Configuration Interaction on Intensities and Phase Shifts" Physical Review 124, 1866 (1961); [2] S. Zhang, D. A. Genov, Y. Wang, M. Liu, X. Zhang: "Plasmon-Induced Transparency in Metamaterials" Physical Review Letters 101, 47401 -47401 (2008); [3] N. Liu, L. Langguth, T. Weiss, J. Kostel, M. Fleischhauer, T. Pfau, H. Giessen: "Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit" Nature Materials 8, 758-762 (2009); [4] T. J. Davis, D. E. Gomez, K. C. Vernon: "Simple Model for the Hybridization of Surface Plasmon Resonances in Metallic Nanoparticles" Nano Letters 10, 2618-2625 (2010)

Copyright Tim Davis 2012