Propagation of Optical Pulses and Pulsed Beams in the Frequency Domain

The diffraction integral formulae in the temporal frequency domain and spatial-temporal frequency domain are derived by using a Fourier transform and tensor analysis method. Based on these formulae, the abcd law in the temporal frequency domain and the tensor ABCD law in the four-dimensional spatial-temporal frequency domain are derived. An application example of the derived formulae is provided.