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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 10, Iss. 1 — Jan. 1, 1993
  • pp: 75–87

Aperture realizations of exact solutions to homogeneous-wave equations

Richard W. Ziolkowski, Ioannis M. Besieris, and Amr M. Shaarawi  »View Author Affiliations

JOSA A, Vol. 10, Issue 1, pp. 75-87 (1993)

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Several new classes of localized solutions to the homogeneous scalar wave and Maxwell’s equations have been reported recently. Theoretical and experimental results have now clearly demonstrated that remarkably good approximations to these acoustic and electromagnetic localized-wave solutions can be achieved over extended near-field regions with finite-sized, independently addressable, pulse-driven arrays. We demonstrate that only the forward-propagating (causal) components of any homogeneous solution of the scalar-wave equation are actually recovered from either an infinite- or a finite-sized aperture in an open region. The backward-propagating (acausal) components result in an evanescent-wave superposition that plays no significant role in the radiation process. The exact, complete solution can be achieved only from specifying its values and its derivatives on the boundary of any closed region. By using those localized-wave solutions whose forward-propagating components have been optimized over the associated backward-propagating terms, one can recover the desirable properties of the localized-wave solutions over the extended near-field regions of a finite-sized, independently addressable, pulse-driven array. These results are illustrated with an extreme exampl—one dealing with the original solution, which is superluminal, and its finite aperture approximation, a slingshot pulse.

© 1993 Optical Society of America

Original Manuscript: January 21, 1992
Revised Manuscript: July 13, 1992
Manuscript Accepted: July 28, 1992
Published: January 1, 1993

Richard W. Ziolkowski, Ioannis M. Besieris, and Amr M. Shaarawi, "Aperture realizations of exact solutions to homogeneous-wave equations," J. Opt. Soc. Am. A 10, 75-87 (1993)

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  1. R. W. Ziolkowski, “Exact solutions of the wave equation with complex source locations,” J. Math. Phys. 26, 861–863 (1985). [CrossRef]
  2. R. W. Ziolkowski, “Localized transmission of electromagnetic energy,” Phys. Rev. A 39, 2005–2033 (1989). [CrossRef] [PubMed]
  3. I. M. Besieris, A. M. Shaarawi, R. W. Ziolkowski, “A bidirectional travelling plane wave representation of exact solutions of the scalar wave equation,” J. Math. Phys. 30, 1254–1269 (1989). [CrossRef]
  4. A. M. Shaarawi, I. M. Besieris, R. W. Ziolkowski, “Localized energy pulse trains launched from an open, semi-infinite, circular waveguide,” J. Appl. Phys. 65, 805–813 (1989). [CrossRef]
  5. J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987). [CrossRef] [PubMed]
  6. P. D. Einziger, S. Raz, “Wave solutions under complex space–time shifts,” J. Opt. Soc. Am. A 4, 3–10 (1987). [CrossRef]
  7. E. Heyman, L. B. Felsen, “Complex-source pulsed-beam fields,” J. Opt. Soc. Am. A 6, 806–817 (1989). [CrossRef]
  8. P. Hillion, “Spinor focus wave modes,” J. Math. Phys. 28, 1743–1748 (1987). [CrossRef]
  9. A. M. Shaarawi, I. M. Besieris, R. W. Ziolkowski, “A novel approach to the synthesis of nondispersive wave packet solutions to the Klein–Gordon and the Dirac equations,” J. Math. Phys. 31, 2511–2519 (1990). [CrossRef]
  10. A. M. Vengsarkar, I. M. Besieris, A. M. Shaarawi, R. W. Ziolkowski, “Closed-form, localized wave solutions in optical fiber waveguides,” J. Opt. Soc. Am. A 9, 937–949 (1992). [CrossRef]
  11. M. K. Tippett, R. W. Ziolkowski, “A bidirectional wave transformation of the cold plasma equations,” J. Math. Phys. 32, 488–492 (1991). [CrossRef]
  12. R. W. Ziolkowski, I. M. Besieris, A. M. Shaarawi, “Localized wave representations of acoustic and electromagnetic radiation,” Proc. IEEE 79, 1371–1378 (1991). [CrossRef]
  13. R. Donnelly, R. W. Ziolkowski, “A method for constructing solutions of homogeneous partial differential equations: localized waves,” Proc.R. Soc. London Ser. A 437, 673–692 (1992). [CrossRef]
  14. R. W. Ziolkowski, D. K. Lewis, B. D. Cook, “Experimental verification of the localized wave transmission effect,” Phys. Rev. Lett. 62, 147–150 (1989). [CrossRef] [PubMed]
  15. R. W. Ziolkowski, D. K. Lewis, “Verification of the localized wave transmission effect,” J. Appl. Phys. 68, 6083–6086 (1990). [CrossRef]
  16. E. Heyman, B. Z. Steinberg, L. B. Felsen, “Spectral analysis of focus wave modes,” J. Opt. Soc. Am. A 4, 2081–2091 (1987). [CrossRef]
  17. E. Heyman, “Focus wave modes: a dilemma with causality,” IEEE Trans. Antennas Propag. 37, 1604–1608 (1989). [CrossRef]
  18. G. C. Sherman, A. J. Devaney, L. Mandel, “Plane-wave expansions of the optical field,” Opt. Commun. 6, 115–118 (1972). [CrossRef]
  19. A. J. Devaney, G. C. Sherman, “Plane-wave representations for scalar wave fields,” SIAM Rev. 15, 765–786 (1973). [CrossRef]
  20. O. Yu. Zharii, “Relationship between traveling and inhomogeneous waves in the theory of transient wave processes,” Sov. Phys. Acoust. 36, 372–374 (1990) [Akust. Zh. 36, 659–664 (1990)].
  21. R. W. Ziolkowski, “Localized wave physics and engineering,” Phys. Rev. A 44, 3960–3984 (1991). [CrossRef] [PubMed]
  22. R. W. Ziolkowski, “Properties of electromagnetic beams generated by ultra-wide bandwidth pulse-driven arrays,” Trans.IEEE Antennas Propag. 40, 888–905 (1992). [CrossRef]
  23. P. Hillion, “Focus wave modes: remarks,” J. Opt. Soc. Am. A 8, 695 (1991). [CrossRef]
  24. D. S. Jones, The Theory of Electromagnetism (Pergamon, New York, 1964), pp. 38–42.
  25. L. B. Felsen, N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, New York, 1973).
  26. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965).
  27. J. B. Marion, Classical Electromagnetic Radiation (Academic, New York, 1965), Chap. 7.
  28. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1962), Chap. 14.
  29. J. A. Waak, J. H. Spencer, K. J. Johnston, R. S. Simon, “Superluminal resupply of a stationary hot spot in 3C 395?” Astron. J. 90, 1989–1991 (1985). [CrossRef]
  30. R. M. Bevensee, BOMA Enterprises, Alamo, California (personal communications, April1991).
  31. J. A. Kong, Electromagnetic Wave Theory (Wiley, New York, 1986).
  32. R. Donnelly, Department of Electrical Engineering, Memorial University, St. Johns, Newfoundland (personal communication, December1991).
  33. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980).

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