Wigner Optics in the Time Domain

Abstract

The powerful mathematical apparatus of the Wigner distribution function allows us to describe the transformations of ultrashort laser pulses during their propagation through optically transparent media with dispersion and Kerr nonlinearity. Since in the quadratic approximation, the descriptions take the form of linear operators in matrix form, a linear theory of the rotation of laser pulses in phase space “time-frequency” and related theories (theory of time solitons, tomography of optical pulses, fractal Fourier transformations in the time domain) have been created by using the analogy with Wigner-optics in the space domain.