Diffraction and focusing of extremely short optical pulses: generalizationof the Sommerfeld integral

The Sommerfeld diffraction theory is extended to the case of extremely shor t pulses. We show that in the far held the energy-density distribution of t he diffractional pattern is transformed into a Gaussian distribution, when the plane wave with uniform radial amplitude distribution and one oscillati on period falls upon the circular aperture. When one focuses the Gaussian b eam with one oscillation period, the energy-density distribution in the foc al plane differs from the Gaussian distribution. (C) 1999 Optical Society o f America.