Design rules for a Fabry-Perot narrow band transmission filter containing a metamaterial negative-index defect

In this work, we theoretically study the optical properties of a multilayer Fabry-Perot narrow band transmission filter containing a metamaterial negative-index defect. As in the usual Fabry-Perot filter design, the negative-index defect is sandwiched by two quarter- wave dielectric mirrors. Some useful design rules on selecting value of the negative-index of the defect have been numerically elucidated. Such narrow band transmission filtering is achieved when the refractive index of defect is either a negative even integer if the thickness is taken as a quarter of design wavelength; or a negative odd integer if the thickness is taken as a half of design wavelength.