Far-field diffraction of pulsed optical beams in dispersive media

Propagation of a pulsed optical beam (a train of ultrashort optical pulses) inside a linear dispersive medium is studied in the far field without making the paraxial approximation. This approach permits us to obtain analytical results that are valid for relatively large diffraction angles. Pulse characteristics are found to be affected considerably by the combination of diffraction and dispersion. In a weakly dispersive medium, pulses wider than a few optical cycles maintain their shape but experience temporal and spectral shifts whose magnitude depends on the diffraction angle. When the effects of group-velocity dispersion are included, the pulse width depends not only on the diffraction angle but also on the nature of dispersion (normal versus anomalous). Much larger off-axis pulse widths are predicted in the case of anomalous dispersion.