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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Editor: Franco Gori
  • Vol. 29, Iss. 4 — Apr. 1, 2012
  • pp: 457–462

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

Andrei B. Utkin  »View Author Affiliations

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

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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

Original Manuscript: November 9, 2011
Revised Manuscript: December 21, 2011
Manuscript Accepted: December 23, 2011
Published: March 15, 2012

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

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