Assuming a disk source distribution moving in a straight line along the z axis at some velocity slower than the speed of light, an approximate Bessel–Gauss pulse solution to the inhomogeneous wave equation has been determined. This approximate pulse propagates in a specific region of space–time and is a long-time duration or steady-state solution of the inhomogeneous wave equation. The localization properties of this approximate waveform depend on the normalized speed of the source distribution. For source speeds close to the speed of light, the waveform is highly localized. As the source speed decreases, the scalar wave becomes less localized along the direction of propagation.

© 1999 Optical Society of America

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