OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Franco Gori
  • Vol. 28, Iss. 4 — Apr. 1, 2011
  • pp: 534–540

Diffraction of spatiotemporally localized X-wave pulses from a screen containing two rectangular slits

A. M. Shaarawi, A. S. El-Halawani, and I. M. Besieris  »View Author Affiliations


JOSA A, Vol. 28, Issue 4, pp. 534-540 (2011)
http://dx.doi.org/10.1364/JOSAA.28.000534


View Full Text Article

Enhanced HTML    Acrobat PDF (626 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The diffraction of X-waves from a screen containing two slits is investigated. It is shown that when the peak of the incident X-wave hits the screen midway between the slits, two pulses are generated from each slit. These pulses follow laterally skewed trajectories relative to the direction of propagation of the incident X-wave along the central axis of the configuration. One of the two pulses converges on the central axis and the other diverges away from it. A geometrical construction explaining the behavior of these pulses is provided. It is shown that the trajectory of each radiated pulse can be deduced from the intersection of two curved wavefronts emanating from the two edges of each slit. The pulses converging on the central axis meet at a certain range, thus suggesting a novel focusing scheme.

© 2011 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(260.0260) Physical optics : Physical optics
(320.5550) Ultrafast optics : Pulses

ToC Category:
Ultrafast Optics

History
Original Manuscript: November 9, 2010
Manuscript Accepted: November 25, 2010
Published: March 9, 2011

Citation
A. M. Shaarawi, A. S. El-Halawani, and I. M. Besieris, "Diffraction of spatiotemporally localized X-wave pulses from a screen containing two rectangular slits," J. Opt. Soc. Am. A 28, 534-540 (2011)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-4-534


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. Y. Lu and J. F. Greenleaf, “Nondiffracting X waves—exact solutions to free space scalar wave equation and their finite aperture realization,” IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 39, 19–31 (1992). [CrossRef]
  2. J. Y. Lu and J. F. Greenleaf, “Experimental verification of nondiffracting X waves,” IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 39, 441–446 (1992). [CrossRef]
  3. R. W. Ziolkowski, I. M. Besieris, and A. M. Shaarawi, “Aperture realizations of the exact solutions to homogeneous-wave equations,” J. Opt. Soc. Am. A 10, 75–87 (1993). [CrossRef]
  4. P. Saari and K. Reivelt, “Evidence of X-shaped propagation-invariant localized light waves,” Phys. Rev. Lett. 79, 4135–4138(1997). [CrossRef]
  5. E. Recami, “On localized X-shaped superluminal solutions to Maxwell equations,” Physica A (Amsterdam) 252, 586–610(1998). [CrossRef]
  6. I. M. Besieris, M. Abdel-Rahman, A. M. Shaarawi, and A. Chatzipetros, “Two fundamental representations of localized pulse solutions to the scalar wave equation,” Prog. Electromagn. Res. PIER. 19, 1–48 (1998). [CrossRef]
  7. A. T. Friberg, J. Fagerholm, and M. M. Salomaa, “Space-frequency analysis of nondiffracting pulses,” Opt. Commun. 136, 207–212 (1997). [CrossRef]
  8. A. M. Shaarawi, I. M. Besieris, R. W. Ziolkowski, and S. M. Sedky, “Generation of approximate focus wave mode pulses from wide-band dynamic Gaussian aperture,” J. Opt. Soc. Am. A 12, 1954–1964 (1995). [CrossRef]
  9. M. Zamboni-Rached, K. Z. Nobrega, H. E. Hernàandez-Figueroa, and E. Recami, “Localized superluminal solutions to the wave equation in (vacuum or) dispersive media, for arbitrary frequencies and with adjustable bandwidth,” Opt. Commun. 226, 15–23 (2003). [CrossRef]
  10. H. Valtna-Lukner, K. Reivelt, and P. Saari, “Methods for generating wideband localized waves of superluminal group-velocity,” Opt. Commun. 278, 1–7 (2007). [CrossRef]
  11. J. Brittingham, “Focus wave modes in homogeneous Maxwell equations: transverse electric mode,” J. Appl. Phys. 54, 1179–1189 (1983). [CrossRef]
  12. R. W. Ziolkowski, “Exact solutions of the wave equation with complex source locations,” J. Mathe. Phys. 26, 861–863 (1985). [CrossRef]
  13. R. W. Ziolkowski, “Localized transmission of electromagnetic energy,” Phys. Rev. A 39, 2005–2033 (1989). [CrossRef] [PubMed]
  14. I. M. Besieris, A. M. Shaarawi, and R. W. Ziolkowski, “A bidirectional traveling plane wave representation of exact solutions of the scalar wave equation,” J. Mathe. Phys. 30, 1254–1269(1989). [CrossRef]
  15. R. Donnelly and R. Ziolkowski, “Designing localized waves,” Proc. R. Soc. A 440, 541–565 (1993). [CrossRef]
  16. P. L. Overfelt, “Bessel-Gauss pulses,” Phys. Rev. A 44, 3941–3947 (1991). [CrossRef] [PubMed]
  17. J. Y. Lu, M. Fatemi, and J. F. Greenleaf, “Pulsed-echo imaging with X wave,” Acoust. Imag. Hologr., P.Tortoli and L.Masotti, eds. 22, 191–196 (1996).
  18. P. Saari and K. Reivelt, “Generation and classification of localized waves by Lorentz transformations in Fourier space,” Phys. Rev. E 69, 036612 (2004).
  19. R. Grunwald, M. Bock, V. Kebbel, S. Huferath, U. Neumann, G. Steinmeyer, G. Stibenz, J.-L. Neron, and M. Piche, “Ultrashort-pulsed truncated polychromatic Bessel-Gauss beams,” Opt. Express 16, 1077–1089 (2008). [CrossRef] [PubMed]
  20. R. Grunwald, U. Griebner, F. Tschirschwitz, E. T. J. Nibbering, T. Elsaesser, V. Kebbel, H.-J. Hartmann, and W. Jupter, “Generation of femtosecond Bessel beams with mircroaxicon arrays,” Opt. Lett. 25, 981–983 (2000). [CrossRef]
  21. M. Zamboni-Rached, E. Recami, and H. E. Hernàndez-Figueroa, “New localized superluminal solutions to the wave equations with finite total energies and arbitrary frequencies,” Euro. Phys. J. D21, 217–228 (2002). [CrossRef]
  22. E. Recami, M. Zamboni-Rached, K. Z. Nobrega, C. A. Dartora, and H. E. Hernàndez-Figueroa, “On the localized superluminal solutions to the Maxwell equations,” IEEE J. Sel. Top. Quantum Electron. 9, 59–73 (2003). [CrossRef]
  23. A. M. Attiya, “Transverse electric X-wave: propagation, scattering, diffraction and generation problems,” Ph.D. dissertation (Cairo University, 2001).
  24. A. M. Attiya, E. El Diwany, A. M. Shaarawi, and I. M. Besieris, “Diffraction of transverse electric (TE) X-wave by conducting objects,” Prog. Electromagn. Res. PIER. 38, 167–198 (2002). [CrossRef]
  25. A. M. Shaarawi, I. M. Besieris, and R. W. Ziolkowski, “Diffraction of a nondispersive wave packet in the two slit interference experiment,” Phys. Lett. A 188, 218–224 (1994). [CrossRef]
  26. C. Conti, S. Trillo, P. Di Trapani, G. Valiulis, A. Piskarskas, O. Jedrkiewicz, and J. Trull, “Nonlinear electromagnetic X-waves,” Phys. Rev. Lett. 90, 170406 (2003). [CrossRef] [PubMed]
  27. P. Bowlan, H. Valtna-Lukner, M. Lõhmus, P. Piksarv, P. Saari, and R. Trebino, “Measuring the spatiotemporal field of ultrashort Bessel-X pulses,” Opt. Lett. 34, 2276–2278 (2009). [CrossRef] [PubMed]
  28. H. Valtna-Lukner, P. Bowlan, M. Lõhmus, P. Piksarv, R. Trebino, and P. Saari, “Direct spatiotemporal measurements of accelerating ultrashort Bessel-type light bullets,” Opt. Express 17, 14948–14955 (2009). [CrossRef] [PubMed]
  29. P. Saari, P. Bowlan, H. Valtna-Lukner, M. Lõhmus, P. Piksarv, and R. Trebino, “Basic diffraction phenomena in the time domain,” Opt. Express 18, 11083–11088 (2010). [CrossRef] [PubMed]
  30. M. Zamboni-Rached, “Analytical expressions for the longitudinal evolution of nondiffracting pulses truncated by finite apertures,” J. Opt. Soc. Am. A 23, 2166–2176 (2006). [CrossRef]
  31. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
  32. E. Hecht, Optics (Addison-Wesley, 1998).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited