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.
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Weber et al. (1990) studied this question.