We conduct a comprehensive investigation of the lasing mechanism in a photo
nic crystal slab laser with a refractive index that is periodic in two dime
nsions. Experimental spectra of laser structures fabricated with organic ga
in media are presented. It is found that lasing frequencies can be explaine
d in terms of Van Hove singularities in the density of modes. We also obser
ve lasing spectra that cannot be obtained from structures with one-dimensio
nal periodicity, such as traditional distributed feedback lasers. Lasing fr
equencies an computed using numerical techniques.