## Droplet-shaped waves: causal finite-support analogs of X-shaped waves |

JOSA A, Vol. 29, Issue 4, pp. 457-462 (2012)

http://dx.doi.org/10.1364/JOSAA.29.000457

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### Abstract

A model of steady-state X-shaped wave generation by a superluminal (supersonic) pointlike source infinitely moving along a straight line is extended to a more realistic causal scenario of a source pulse launched at time zero and propagating rectilinearly at a constant superluminal speed. In the case of an infinitely short (delta) pulse, the new model yields an analytical solution, corresponding to the propagation-invariant X-shaped wave clipped by a droplet-shaped support, which perpetually expands along the propagation and transversal directions, thus tending the droplet-shaped wave to the X-shaped one.

© 2012 Optical Society of America

**OCIS Codes**

(070.0070) Fourier optics and signal processing : Fourier optics and signal processing

(320.5550) Ultrafast optics : Pulses

(350.5500) Other areas of optics : Propagation

(350.5720) Other areas of optics : Relativity

(350.7420) Other areas of optics : Waves

(070.7345) Fourier optics and signal processing : Wave propagation

**ToC Category:**

Ultrafast Optics

**History**

Original Manuscript: November 9, 2011

Revised Manuscript: December 21, 2011

Manuscript Accepted: December 23, 2011

Published: March 15, 2012

**Citation**

Andrei B. Utkin, "Droplet-shaped waves: causal finite-support analogs of X-shaped waves," J. Opt. Soc. Am. A **29**, 457-462 (2012)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-29-4-457

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