  An entirely analytical theory is provided for describing the resonance
properties of optical nanoantennas made of a stack of homogeneous discs, i.e.
circular patch nanoantennas. It consists in analytically calculating the phase
accumulation of surface plasmon polaritons across the resonator and an
additional contribution from the complex reflection coefficient at the antenna
termination. This makes the theory self-contained with no need for fitting
parameters. The very antenna resonances are then explained by a simple
Fabry-Perot resonator model. Predictions are compared to rigorous simulations
and show excellent agreement. Using this analytical model, circular antennas
can be tuned by varying the composition of the stack.
