A convenient approximate formula is proposed for the study of free-space propagation of spatial and temporal pulses with an identifiable carrier frequency. It does not contain a time derivative operation on the pulse’s temporal envelope explicitly. It is shown that once a short (for example, picosecond or subpicosecond) pulse is created with a spatial and a temporal structure, it does not last forever. The approximation discussed is valid over a certain distance as dictated by the wave equation. Beyond this distance, the spatial and temporal characteristics begin to influence each other significantly. Two examples are presented. The first example is that of a pulse with a factored form of a spatial envelope times a temporal envelope. The second example is that of a clear aperture with a grating, by which pulse stretching or temporal distortion is examined and the result is in agreement with that found in the literature.
© 1994 Optical Society of America
Arvind S. Marathay, "Propagation of optical pulses with spatial and temporal dependence," Appl. Opt. 33, 3139-3145 (1994)