Analysis of optical reflection in a chirped distributed bragg reflector

A theoretical analysis of optical reflection for a dielectric chirped distributed Bragg reflector (DBR) is presented. The chirped DBR is modeled by several sub-DBRs stacked successively with different values in the thickness ratio, ρ = d ₂/d ₁, where d ₂ and d ₁ are the thicknesses of two constituent dielectric layers. Reflection spectra are numerically calculated and analyzed by making use of the transfer matrix method in a stratified medium. The results show that such a chirped structure has a weak effect on the fundamental bandgap, but the higher order bandgaps are strongly affected. The second bandgap is apparently broadened due to the shift in its lower band edge. Results of spectra for both TE and TM waves at different incident angles are also given and discussed.