A extremely thin Fabry-Perot resonator has been designed. It is based on a high permittivity artificial dielectric layer. An analytical model has been developed, which is useful to predict the transmission coefficient of the Fabry-Perot resonator from its geometrical parameters. The Fabry-Perot resonator has a thickness 74 times smaller than the free space wavelength at the lowest resonance frequency and its quality factor is Q ≈ 2.8 · 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> .