Previous works on photorefractive self-organizing laser cavities were about lasers that oscillate, prior the self-organization process occurs, on a set of axial modes sharing the same transverse structure. In a well-designed broad-area laser diode extended cavity, we theoretically and experimentally demonstrate that the insertion of a photorefractive crystal can also affect the transverse modal structure to force the laser, initially oscillating on several transverse modes, to oscillate on a single transverse and axial mode. This spatial self-organization process leads to an enhancement of the single mode operating range of the laser.