Far-field analysis of ultrashort pulse through the tiled gratings

From the Huygens-Fresnel principle, an integral expression with the chromatic aberration was obtained of the field amplitude of a beam with a shape of a quarter of a circle. From the integral expression amplitude expressions of the coherent addition field of four such subbeams with different phase delay were acquired and a mathematic model of the field in the far field was set up. Numerical modulation was carried out for a 1 ps ultrashort pulse with a 10 cm aperture and 200 cm focal length. The far-field intensity distributions of three cases were given including single beam, four beams without phase delay and four beams with a phase delay of π between them. The conclusion is that the far-field pattern of a beam with a shape of a quarter of a circle is no more centrosymmetric but axis sym