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With transfer matrix theory, we study the transmission of a distributed Braggreflector (DBR) with two dielectric gratings on top and on the bottom. Owing tothe diffraction of the two gratings, the transmission shows a comb-likespectrum which red shifts with increasing the grating period during theforbidden band of the DBR. The number density of the comb peaks increases withincreasing the number of the DBR cells, while the ratio of the average fullwidth at half maximum (FWHM) of the transmission peaks in the transmission combto the corresponding average free spectral range, being about 0.04 and 0.02 forthe TE and TM incident waves, is almost invariant. The average FWHM of the TMwaves is about half of the TE waves, and both they could be narrower than 0.1nm. In addition, the transmission comb peaks of the TE and TM waves can befully separated during certain waveband. We further prove that the transmissioncomb is robust against the randomness of the heights of the DBR layers, evenwhen a 15\% randomness is added to their heights. Therefore, the proposedstructure is a candidate for a multichannel narrow-band filter or amultichannel polarizer.

Transmission comb of a distributed Bragg reflector induced by two surface dielectric gratings