  We present investigations on the coherence of the emission from the
polarization split fundamental mode of an AlGaInAs/GaAs quantum-dot microcavity
laser. Using polarization insensitive measurements of the first-order
field-correlation function $g^{(1)}(\tau)$ we determine the power-dependent
degree of polarization. Whereas the orthogonally-polarized components of the
fundamental mode exhibit comparable strength below the lasing threshold, a
degree of linear polarization of 0.99 is observed in the coherent regime. This
is also observed for increasing temperatures up to 77K. Furthermore, by
measuring $g^{(1)}(\tau)$ for both modes separately the stronger mode is found
to reveal a record coherence time of 20ns. Finally, based on a theoretical
model it is possible to fully characterize the cavity emission in terms of
first- and second-order coherence using auxiliary data from $g^{(2)}(\tau)$
measurements performed with a recently developed streak camera technique.
