Quasi-1D Electromagnetic Resonators

We show that a long and narrow conducting sheet of finite length may behave as a one dimensional electromagnetic resonator. The induced current along the resonator is a standing wave, and it is solution of a one dimensional integro-differential equation with homogeneous boundary conditions. The corresponding charge distribution exhibits strong accumulation at the two ends of the resonator. As a consequence, the electric field scattered in proximity of the two ends undergoes a strong enhancement and may be exploited for sensing or light-matter applications. Eventually, an example of a quasi-one dimensional resonator based on graphene is discussed.