Abstract

The extensive theory available on the wavefield present in the focal region of optical systems deals exclusively with monochromatic waves. Since optical systems are now being utilized to focus very short optical pulses, it will be useful to extend the theory into the time domain. This paper presents an analytic approximation in the time domain for the wavefield in the focal region of a very small f/No. system valid when the pulse is very short. In contrast to the monochromatic case, it has proved possible to evaluate the propagation integrals in terms of known functions. The solution expresses the wavefield as a superimposition of one-half of a spherical pulse in front of the focal plane converging toward the focal point and a cylindrical pulse converging toward the optic axis for early time. At later time, there is one-half of a spherical pulse behind the focal plane diverging away from the focal point and a cylindrical pulse diverging from, the optic axis. On crossing the focal plane, the spherical waves pass to zero abruptly. The total field is continuous at the focal plane, however, because the cylindrical wave has a discontinuity there of equal magnitude with opposite sense.

© 1986 Optical Society of America