  We classify and distinguish optically biaxial materials, which can have
triclinic, monoclinic or orthorhombic crystal symmetry, by the degeneracy of
the indices of refraction of their four singular optical axes (Windungsachsen)
in the absorption regime. We provide explicit analytical solutions for angular
orientations of the singular optical axes in monoclinic crystals and
orthorhombic crystals. As a model material we analyze monoclinic gallia
($\beta$-Ga$_2$O$_3$) and discuss in detail the dispersion (i.e. the spectral
variation of the angular position) of its singular optical axes. For a certain
energy range ($E \approx 7.23$-$7.33$ eV) we find quasi-uniaxial symmetry. At
two energies ($E \approx 8.14$ eV and $E \approx 8.37$ eV) we find triaxial
spectral points for which one regular optical axis and two singular optical
axes exist. Concurrently a Stokes analysis of the spectral dependence of the
electrical field eigenvectors is made and discussed for various crystal
orientations. For a singular optical axis $|S_3|=1$; for the two degenerate
singular axes at the triaxial point the Stokes vector is undefined. For a
certain energy ($E=6.59$ eV), the $\langle 010 \rangle$-orientation is close to
a singular optical axis, $|S_3|=0.977$. The analysis provided here is
prototypical for the treatment of the optical properties of optically biaxial
functional materials in the absorption and gain regimes.
