Effect of layer thickness variations in a distributed-Bragg-reflector mirror on the phase of the reflected light.

We present an analytical derivation of the phase change of the reflection coefficient of a distributed-Bragg-reflector mirror when the thickness of a layer in the mirror changes. These phase changes are additive, as has been verified by an exact numerical calculation using transmission matrices. Such a phase change will affect the lasing wave-length of vertical-cavity surface-emitting lasers and the center wavelength of various integrated Bragg devices.