Diffraction of short pulses with boundary diffraction wave theory.

The diffraction of short pulses is studied on the basis of the Miyamoto-Wolf theory of the boundary diffraction wave, which is a mathematical formulation of Young's idea about the nature of diffraction. It is pointed out that the diffracted field is given by the superposition of the boundary wave pulse (formed by interference of the elementary boundary diffraction waves) and the geometric (direct) pulse (governed by the laws of geometrical optics). The case of a circular aperture is treated in details. The diffracted field on the optical axis is calculated analytically (without any approximation) for an arbitrary temporal pulse shape. Because of the short pulse duration and the path difference the geometric and the boundary wave pulses appear separately, i.e., the boundary waves are manifested in themselves in the illuminated region (in the sense of geometrical optics). The properties of the boundary wave pulse is discussed. Its radial intensity distribution can be approximated by the Bessel function of zero order if the observation points are in the illuminated region and far from the plane of the aperture and close to the optical axis. Although the boundary wave pulse propagates on the optical axis at a speed exceeding c, it does not contradict the theory of relativity.