Plane wave analysis of bull's eye gratings

We investigated the transmittivity of a bull's eye grating using the plane wave expansion method. The parameters of the grating were optimized at 1550 nm. The grating has annular grooves with alternating layers of aluminum and air. The dispersion relation was obtained by expressing Maxwell's equations in cylindrical co-ordinates and solving the eigenvalue problem. We observe flat bands for frequencies below plasma frequency (ω
_p
). COMSOL simulations were used to validate the eigenfrequencies at k → 0 in the band diagram.