Abstract

We derive an expression for the lower bound of the phase-space beam quality factor ${\mathcal{M}}^2$ of an ultrashort pulse. We show that the condition ${\mathcal{M}}^2\ge 1$ does not, in general, hold for such pulsed beams. Rather, the minimum value of ${\mathcal{M}}^2$ depends on the pulse spectrum. We also show that ${\mathcal{M}}^2$ 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.

© 2008 Optical Society of America

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