Unified theory of coherence and polarization of stationary beams is applied to pulsed light beams research. Partially coherent square flat-topped electromagnetic pulsed beams have been constructed, and analytical expressions for cross-spectral density matrix of a class of the pulsed light beams focused by a phase modulated lens have been derived. A detailed study on effects of phase distortion radii, phase distortion depth, phase modulated position and correlation length on spectral density in focused filed is carried on. It is shown that local phase modulation will produce another spectral density peak in the focused field, and correlation parameter of source and phase modulation parameters determine the value of intensity peak, and make it shift in some cases. Especially when parameters of correlation of the source are chosen to be some values, a focal switch phenomenon will occur. Change of spatial coherent length of the source produces the spatially focal shift and pulse time correlation length also produces spectral density peak shift on frequency.