A generalized analysis of femtosecond laser pulse broadening after angular dispersion

We derive a general analytical expression for the width of a femtosecond laser pulse after passing through an angular dispersion device, valid for the plane wave, spherical wave, and Gaussian beam models. This expression is a simple function of two effects: spectral lateral walkoff and group delay dispersion. Plane waves and spherical waves experience no spectral lateral walkoff, as the beams are not explicitly limited in space. The group delay dispersion (GDD) of a Gaussian beam is similar to that of a plane wave at distances much less than the Rayleigh length, and similar to that of the spherical wave at distances far exceeding the Rayleigh length. The GDD of the spherical wave and Gaussian beam approach a constant value at large distances, which is entirely determined by the dispersion parameters of the optical component and the distance between disperser and source point or beam waist. The width of a plane wave pulse always increases in proportion to the propagation distance. The width of a spherical wave or Gaussian beam pulse widens rapidly at first, but soon levels off to nearly constant value.