Effect of layer thickness variations on propagation delay andpenetration depth of a quarter-wave distributed Bragg reflector

The authors derive an analytical formula for the change of propagation delay and phase penetration depth of a quarter-wave distributed Bragg reflector (DBR) owing to thickness and/or composition variations. The analytical expression provides a very good estimate of change in penetration depth with arbitrary thickness perturbation in one or more layers of the DBR. For a Fabry-Perot cavity clad on both sides by two quarter-wave DBRs, the shift in the Fabry-Perot mode due to thickness variations in one or both of the DBRs can be simply obtained by calculation using the change in penetration depths of the corresponding DBR or both DBRs