EFFECT OF LAYER THICKNESS VARIATIONS ON PROPAGATION DELAY AND PENETRATION DEPTH OF A QUARTER-WAVE DISTRIBUTED-BRAGG-REFLECTOR

We present a derivation of an analytical formula for the change of pro pagation delay and phase penetration depth of a quarter-wave distribut ed Bragg reflector (DBR) owing to thickness and/or composition variati ons. 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 DBR's, the shift in the Fabry-Perot mode due to thic kness variations in one or both of the DBR's can be simply obtained by calculation using the change in penetration depths of the correspondi ng DBR or both DBR's.