- We present an analytic simplified form for the 4 × 4 propagation matrix of a general homogeneous biaxial layer. The expression is applicable to any linear homogeneous, absorbing, biaxial, gyrotropic, magneto-optic, arbitrarily oriented anisotropic structure. Its simple form speeds up the calculation of the optical properties of inhomogeneous anisotropic media and allows real-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 isotropic case. Using this analytic method it is found that the time required for calculating the propagation matrix is shorter by a factor of two than that using direct numerical calculation.