We present an analytic simplified form for the 4 x 4 propagation matrix of
a general homogeneous biaxial layer. The expression is applicable to any li
near homogeneous, absorbing, biaxial, gyrotropic, magneto-optic, arbitraril
y oriented anisotropic structure. Its simple form speeds up the calculation
of the optical properties of inhomogeneous anisotropic media and allows re
al-time analysis of ellipsometric experimental data. A simplified analytic
expression for the propagation matrix is also derived for the case of mode
degeneration such as for propagation at certain angles and for the isotropi
c case. Using this analytic method it is found that the time required for c
alculating the propagation matrix is shorter by a factor of two than that u
sing direct numerical calculation.