We report the first calculations of mode patterns of unstable-cavity lasers
with truly two-dimensional transverse geometries. A detailed account of nu
merical techniques, incorporating a nonorthogonal beam-propagation method,
and results for cavities with a range of transverse symmetries, such as reg
ular polygonal and rhomboid, are presented. In view of the beautiful comple
xity of the eigenmodes predicted, a novel kaleidoscope laser is proposed. (
C) 2000 Optical Society of America [S0740-3224(00)00803-1] OCIS codes: 030.
4070, 050.1940, 110.1220, 120.2040, 140.3410.