Smoothing the side lobes of a focused pattern by spectral dispersion in the broadband laser

Starting from the Huygens-Fresnel diffraction integral, the propagation equations of a broadband laser passing through a dispersive lens and a dispersive wedge are derived. Smoothing effect on the side lobes of the focused pattern is achieved as the broadband laser passes through the lens because of the spectral dispersion of the lens. By inserting a dispersive wedge behind the lens, better smoothing effect is realized because a relative position shift between focused patterns of different frequency components is generated due to the spectral dispersion of the wedge. Smoothing effect on the side lobe is obtained even with small bandwidth of the broadband laser as the wedge is used.