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

摘要

The Sommerfeld diffraction theory is extended to the case of extremely short pulses. We show that in the far field the energy-density distribution of the diffractional pattern is transformed into a Gaussian distribution, when the plane wave with uniform radial amplitude distribution and one oscillation period falls upon the circular aperture. When one focuses the Gaussian beam with one oscillation period, the energy-density distribution in the focal plane differs from the Gaussian distribution.