Generation of a Bessel—Gauss pulse from a moving disk source distribution

Assuming a moving disk source distribution, the Riemann method and Gegenbauer's addition theorem in a mixed coordinate-space-phase-space formulation have been used to derive a zeroth-order Bessel-Gauss pulse solution to the inhomogeneous wave equation. In the region where tau(2) greater than or similar to rho(eff)(2) + z(2), the total solution can be separated into a wave that attenuates quickly and a Bessel-Gauss pulse that exists only after a certain time and continues for long times. In the region where z(2) less than or equal to tau(2) less than or similar to rho(eff)(2) + z(2), only a short-time solution exists. (C) 1997 Optical Society of America.