  With coupled Gross-Piteavskii equations we study excitation of
exciton-polariton vortices and antivortices in a pillar microcavity by a
Gaussian pump beam. The structure of vortices and antivortices shows a strong
dependence on the microcavity radius, pump geometry, and nonlinear
exciton-exciton interaction. Due to the nonlinear interaction the strong
Gaussian beam cannot excite more polariton vortices or antivortices with
respect to the weak one. The calculation demonstrates that the weak Gaussian
beam can excite vortex-antivortex pairs, vortices with high angular momentum,
and superposition states of vortex and antivortex with high opposite angular
momentum. The pump geometry for the Gaussian beam to excite these vortex
structures are analyzed in detail, which holds a potential application for
Sagnac interferometry and generating the optical beams with high angular
momentum.
