  Birefringent crystals are extensively used to manipulate polarized light. The
generalized transfer matrix developed allows efficient calculation of the full
polarization state of light transmitted through and reflected by a stack of
arbitrarily-many discrete layers of isotropic and birefringent materials at any
frequency and angle of incidence. The matrix of a uniaxial birefringent crystal
with arbitrary rotation is calculated, along with its reduction to the matrix
of an isotropic medium. This method is of great practical importance where
tight control of systematic effects is needed in optical systems employing
birefringent crystals, one example being wave plates used by cosmic microwave
background polarimetry with wide field-of-view telescopes.
