Spontaneous Generation of Vortex Array Beams from a Thin-Slice   Solid-State Laser with Wide-Aperture Laser-Diode Pumping
  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. 
Kenju Otsuka, Shu-Chun Chu