Transverse pattern selection and spatio-temporal
dynamics in the competition among and superposition of first order
Gauss-Hermite modes in a quantum well VCSEL are sensitive to birefringence
and astigmatism. When modes of different spatial pattern and/or
polarization state are frequency degenerate, the only stable solutions are
those with doughnut intensity patterns. Patterns with orthogonal
polarizations for the two constituent spatial modes are far more stable
than plane polarized doughnuts. When there are weak anisotropies
(birefringence and/or dichroism) the pattern is stationary with a locally
time independent intensity (though the polarization state differs from
position to position). When the anisotropies are strong, the emission
becomes time dependent with two spectral components in the optical
spectrum, each with a different pattern and polarization.
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