Phase-space quality factor for ultrashort pulsed beams.

We derive an expression for the lower bound of the phase-space beam quality factor M(2) of an ultrashort pulse. We show that the condition M(2)>or=1 does not, in general, hold for such pulsed beams. Rather, the minimum value of M(2) depends on the pulse spectrum. We also show that M(2) attains minimum only for pulsed beams whose spot size varies with frequency as omega(-1/2), and that the radial intensity profile of the best-quality pulsed beam can be non-Gaussian.