Resonance Behaviour of Plasmonic Nano-structures

Summary: We have analyzed the resonance response and the relevant field distributions of various nanoparticles at their resonant frequencies. The study of field patterns has been extended to combinations of rods in L,U,O particles, narrow-gap U particles, array of coupled rods and split rings. Resonance curves have been studied; the relations between the total length of the particle and the resonances have been examined. The nature of these resonances, whether plasmonic or an LC resonance, has been discussed.

We introduces a 'narrow-gap U particle' by closing the gap of the U parcile, and demonstrated that the plasmonic behaviour of this particle differs from that of the free rods; instead an infinite array of rods set along each other, ("coupled rods"), exhibits a similar behaviou. This occurs when the length of these coupled rods is the same as the total length of the narrow-gap U particle and distance between the rods is sthe same as the size of the gap of the U particle. In this case, the two systems show similar plasmonic behaviour including the same resonance behaviour and electric field distribution. 

We also discussed split rings and their equivalent LC circutis; we conclude that the round shape split-ring, and not the square-shaped U particle, has less losses and heat radiation. We derived the resonant frequencies of nano split rings analytically. In doing so we have discussed all the parameters invovled in the formulas, such as gap and surface capacitances, as well as kniteci and magnetic inductances, and in addtion we also have discussed the saturation of resonance frequency when the particles are scaled down in size; this was a very important case because all of our particles were in this regime of saturated resonant frequency.

Using numerical simulations, we have varied the gap from 60 nm down to 1 nm, at the same time keeping the overall length of the metallic path at 280 nm to observe the plasmonic resonances and to investigate the behaviour of the particles in different conditions. We could show graphically that the resonant frequency of all nano-particles we investigated, except for the free rod, react in the same way to changes in their gap sizes. 

Changing the gap of the nanostructures changes their capactiance and reaults in a change to their resonant frequency. In particular, this study showed that different nanoparticles that have common parameters but completely different shapes can have the same resonant behaviour, and we also showed how these resonance behaviours are related to each other.

We also emphasize that, as the size of a particle is scaled down, the field distributioin resembles more and more the plasmonic mode distribution.