Application of the Wigner function and matrix optics to describe variations in the shape of ultrashort laser pulses propagating through linear optical systems

The transformation of the shape of ultrashort laser pulses (USPs) in time can be described similarly to the process of image formation in space. It is shown that the wave description of imaging is simplified by using the Wigner function, this description in the quadratic approximation being identical to the use of the ABCD matrices. The transformation of USPs propagating through linear optical systems was described and these systems were classified by the methods of matrix optics.