  It is demonstrated that the orbital angular momentum (OAM) carried by the
elliptic beam without the phase-singularity can induce the anisotropic
diffraction (AD). The quantitative relation between the OAM and its induced AD
is analytically obtained by a comparison of two different kinds of
(1+2)-dimensional beam propagations: the linear propagations of the elliptic
beam without the OAM in an anisotropic medium and that with the OAM in an
isotropic one. In the former case, the optical beam evolves as the fundamental
mode of the eigenmodes when its ellipticity is the square root of the
anisotropic parameter defined in the paper; while in the latter case, the
fundamental mode exists only when the OAM carried by the optical beam equals a
specific one called a critical OAM. The OAM always enhances the beam-expanding
in the major-axis direction and weakens that in the minor-axis direction no
matter the sign of the OAM, and the larger the OAM, the stronger the AD induced
by it. Besides, the OAM can also make the elliptic beam rotate, and the
absolute value of the rotation angle is no larger than $\pi/2$ during the
propagation.
