Diffraction of short pulses with boundary diffraction wave theory - art. no. 026601

The diffraction of short pulses is studied on the basis of the Miyamoto-Wol f theory of the boundary diffraction wave, which is a mathematical formulat ion 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 pu lse (formed by interference of the elementary boundary diffraction waves) a nd the geometric (direct) pulse (governed by the laws of geometrical optics ). The case of a circular aperture is treated in details. The diffracted fi eld on the optical axis is calculated analytically (without any approximati on) for an arbitrary temporal pulse shape. Because of the short pulse durat ion and the path difference the geometric and the boundary wave pulses appe ar separately, i.e., the boundary waves are manifested in themselves in the illuminated region tin the sense of geometrical optics). The properties of the boundary wave pulse is discussed. Its radial intensity distribution ca n be approximated by the Bessel function of zero order if the observation p oints 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, it does not contradict the theory of relativity.