Perfect matching of concave diffraction grating with continuously circular Bragg mirrors on SOI platform

A concave diffraction grating (CDG), based on circular Bragg mirrors, was constructed on the 220 nm silicon-on-insulator (SOI) platform. This continuous and smooth dielectric mirror is employed to eliminate the extra scattering loss occurring at the connection with neighboring grating teeth. A perfect match between the Bragg condition and the grating condition was derived in order to determine the geometrical parameters of the grating profile. finite-difference time-domain (FDTD) simulation shows that the reflection of the designed Bragg mirror can be up to 99.7% over a broad bandwidth of 330 nm. And the grating with circular Bragg mirrors exhibits low insertion loss in a relatively high order of M 5 with some unwanted diffraction orders suppressed, thus creating a large dispersion while keeping compact structure.