  The exchange of orbital angular momentum (OAM) between paraxial optical
vortex and a Bose-Einstein condensate (BEC) of atomic gases is well known. In
this paper, we develop a theory for the microscopic interaction between matter
and an optical vortex beyond paraxial approximation. We show how superposition
of vortex states of BEC can be created with a focused optical vortex. Since,
the polarization or spin angular momentum (SAM) of the optical field is coupled
with OAM of the field, in this case, these angular momenta can be transferred
to the internal electronic and external center-of-mass (c.m.) motion of atoms
provided both the motions are coupled. We propose a scheme for producing the
superposition of matter-wave vortices using Gaussian and a focused
Laguerre-Gaussian (LG) beam. We study how two-photon Rabi frequencies of
stimulated Raman transitions vary with focusing angles for different
combinations of OAM and SAM of optical states. We demonstrate the formation of
vortex-antivortex structure and discuss interference of three vortex states in
a BEC.
