Introduction

The purpose of this chapter is to further discuss the concept of the impedance of a nanoantenna. As highlighted in the previous chapter, at RF the impedance plays a key role in two respects: (i) the real part of the impedance is called radiation resistance and quantifies the amount of energy radiated by the antenna; (ii) the interaction between the antenna and the feeding circuit is analyzed using the impedance. The maximum power transmission occurs when an impedance matching condition is satisfied. It is of interest to analyze the light emission assisted by a nanoantenna in terms of impedance for the same reasons: how much power is emitted? What is the effect of the interaction between the source and its environment? When comparing the case of RF and the case of optical emission assisted by a nanoantenna, it is remarkable to realize that we deal with the same fundamental issue: electromagnetic wave emission by electrons. However, in optics we analyze photon emission using very different concepts such as density of states, Purcell factor, lifetime or decay rates.

The aim is twofold: (i) we wish to establish a connection between the two points of view; (ii) we wish to introduce the concept of impedance in optics as a practical tool to analyze the interaction between an antenna and a quantum emitter. Regarding the concept of impedance for nanoantennas, the cases of antennas consisting of two separate parts such as dimers or two rods has been extensively analyzed in the previous chapter and in Refs.