  We studied complex lasing pattern formations in a thin-slice solid-state
laser with wide-aperture laser-diode end-pumping. Radial and rectangular vortex
arrays were found to be formed in a controlled fashion with symmetric and
asymmetric pump beam profiles, respectively. Most of these vortices exhibited
single-frequency oscillations arising from a spontaneous process of transverse
mode locking of nearly degenerate modes assisted by the laser nonlinearity.
Single-frequency rectangular array beams consisting of a large number of
vortices, e.g., closely packed 36 or 46 vortex pixels, were generated,
originating from Ince-Gaussian modes excited by the asymmetric pumping.
