Electro-optic effect and birefringence in semiconductor vertical-cavity lasers

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Abstract
Semiconductor vertical-cavity surface-emitting lasers (VCSELs) are known to exhibit a small amount of birefringence. We present a model that enables us to estimate how much of this is due to the electro-optic effect produced by the inevitable internal electric field in working devices. Of vital importance for this model is the notion that the position-dependent changes in the refractive index should be weighted by the local optical intensity both in the spacer as well as in the distributed Bragg reflectors. Index variations in the optical nodes thus go unnoticed, whereas those in the antinodes can strongly affect the cavity resonance. This is related to the idea that the active quantum wells in a VCSEL should be positioned in optical antinodes to produce the highest modal gain. The results of our model calculation are compared with statistical data on the magnitude and orientation of the measured birefringence in planar proton-implanted VCSELs. These data show the presence of a systematic contribution to the birefringence, which can presumably be attributed to the electro-optic effect, and a random contribution, which we attribute to stress and strain.