Spectral and temporal properties of ultrashort light pulse in the far zone

The spectral and temporal properties of ultrashort pulses in the far zone are studied by using Rayleigh diffraction integrals. It is shown that the Fourier spectra of the pulse at an observation point in the far zone is different from the spectra in the initial plane. For ultrashort pulses there exists a spectral shift whose magnitude depends on the spectral linewidth, the effective spatial width, and the direction of observation. These results are more similar to that of a partially coherent light beam given by Dacic and Wolf [J. Opt. Sec. Am. A 5 (1988) 1118]. But the spectral shift presented here only arises from the frequency dependence of the propagator that characterizes the propagation of the Fourier monochromatic components of the pulsed field. The shift is remarkable for light pulses with several femtosecond duration, but the pulse shape in the far zone is nearly unchanged.