  We investigate the linear propagation of a paraxial optical beam in
anisotropic media. We start from the eigenmode solution of the plane wave in
the media, then subsequently derive the wave equation for the beam propagating
along a general direction except the optic axes. The wave equation has a term
containing the second mixed partial derivative which originates from the
anisotropy, and this term can result in the rotation of the beam spot. The
rotation effect is investigated by solving analytically the wave equation with
an initial elliptical Gaussian beam for both uniaxial and biaxial media. For
both media, it is found that there exists a specific direction, which is
dependent on anisotropy of the media, on the cross-section perpendicular to
propagation direction to determine the rotation of the beam spot. When the
major axis of the elliptical spot of the input beam is parallel to or
perpendicular to the specific direction, the beam spot will not rotate during
propagation, otherwise, it will rotate with the direction and the velocity
determined by input parameters of the beam.
