The optimum
distribution for the laser pulse which drives the photoemission in a
photoinjector is a 3D-ellipsoid. Simulations show that the emittance
obtained for photo-electron beams generated from such distributions
can be as small as the "cathode emittance". Indeed no non-linear
space charge forces are generated and the emittance compensation works
perfectly well. We describe in which parameter range this applies. Producing
a laser beam contained in a 3D-ellipsoid is very difficult. However,
several concepts could lead to the solution. We review the challenges
presented by these different methods.