A solution is presented for the field produced when an infinitely short pulse is focused by an infinite-aperture system. In contrast to the results obtained in the standard theory of focusing of monochromatic waves, it has proved possible to evaluate the propagation integrals in terms of known functions and generalized functions. The result provides a useful expression for the field in the focal region of small-f-number systems. The field is singular in certain space–time regions because the incident pulse was taken to be infinitely short. The singularities can be removed for pulses of finite duration by convolving the field with the time variation of the incident pulse.
© 1989 Optical Society of America
Original Manuscript: December 23, 1988
Manuscript Accepted: May 5, 1989
Published: September 1, 1989
George C. Sherman, "Short pulses in the focal region," J. Opt. Soc. Am. A 6, 1382-1387 (1989)