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

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  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).

2010 (1)

2009 (2)

2008 (1)

2007 (1)

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]

2006 (1)

2004 (1)

P. Saari and K. Reivelt, “Generation and classification of localized waves by Lorentz transformations in Fourier space,” Phys. Rev. E 69, 036612 (2004).

2003 (3)

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]

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]

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]

2002 (2)

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]

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]

2000 (1)

1998 (2)

E. Recami, “On localized X-shaped superluminal solutions to Maxwell equations,” Physica A (Amsterdam) 252, 586–610(1998).
[CrossRef]

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]

1997 (2)

A. T. Friberg, J. Fagerholm, and M. M. Salomaa, “Space-frequency analysis of nondiffracting pulses,” Opt. Commun. 136, 207–212 (1997).
[CrossRef]

P. Saari and K. Reivelt, “Evidence of X-shaped propagation-invariant localized light waves,” Phys. Rev. Lett. 79, 4135–4138(1997).
[CrossRef]

1995 (1)

1994 (1)

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]

1993 (2)

1992 (2)

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]

J. Y. Lu and J. F. Greenleaf, “Experimental verification of nondiffracting X waves,” IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 39, 441–446 (1992).
[CrossRef]

1991 (1)

P. L. Overfelt, “Bessel-Gauss pulses,” Phys. Rev. A 44, 3941–3947 (1991).
[CrossRef] [PubMed]

1989 (2)

R. W. Ziolkowski, “Localized transmission of electromagnetic energy,” Phys. Rev. A 39, 2005–2033 (1989).
[CrossRef] [PubMed]

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]

1985 (1)

R. W. Ziolkowski, “Exact solutions of the wave equation with complex source locations,” J. Mathe. Phys. 26, 861–863 (1985).
[CrossRef]

1983 (1)

J. Brittingham, “Focus wave modes in homogeneous Maxwell equations: transverse electric mode,” J. Appl. Phys. 54, 1179–1189 (1983).
[CrossRef]

Abdel-Rahman, M.

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]

Attiya, A. M.

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]

A. M. Attiya, “Transverse electric X-wave: propagation, scattering, diffraction and generation problems,” Ph.D. dissertation (Cairo University, 2001).

Besieris, I. M.

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]

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]

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]

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]

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]

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]

Bock, M.

Bowlan, P.

Brittingham, J.

J. Brittingham, “Focus wave modes in homogeneous Maxwell equations: transverse electric mode,” J. Appl. Phys. 54, 1179–1189 (1983).
[CrossRef]

Chatzipetros, A.

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]

Conti, C.

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]

Dartora, C. A.

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]

Di Trapani, P.

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]

Donnelly, R.

R. Donnelly and R. Ziolkowski, “Designing localized waves,” Proc. R. Soc. A 440, 541–565 (1993).
[CrossRef]

El Diwany, E.

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]

Elsaesser, T.

Fagerholm, J.

A. T. Friberg, J. Fagerholm, and M. M. Salomaa, “Space-frequency analysis of nondiffracting pulses,” Opt. Commun. 136, 207–212 (1997).
[CrossRef]

Fatemi, M.

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).

Friberg, A. T.

A. T. Friberg, J. Fagerholm, and M. M. Salomaa, “Space-frequency analysis of nondiffracting pulses,” Opt. Commun. 136, 207–212 (1997).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

Greenleaf, J. F.

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]

J. Y. Lu and J. F. Greenleaf, “Experimental verification of nondiffracting X waves,” IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 39, 441–446 (1992).
[CrossRef]

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).

Griebner, U.

Grunwald, R.

Hartmann,

Hecht, E.

E. Hecht, Optics (Addison-Wesley, 1998).

Hernàandez-Figueroa, H. E.

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]

Hernàndez-Figueroa, H. E.

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]

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]

Huferath, S.

Jedrkiewicz, O.

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]

Jupter, W.

Kebbel, V.

Lõhmus, M.

Lu, J. Y.

J. Y. Lu and J. F. Greenleaf, “Experimental verification of nondiffracting X waves,” IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 39, 441–446 (1992).
[CrossRef]

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]

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).

Neron, J.-L.

Neumann, U.

Nibbering, E. T. J.

Nobrega, K. Z.

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]

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]

Overfelt, P. L.

P. L. Overfelt, “Bessel-Gauss pulses,” Phys. Rev. A 44, 3941–3947 (1991).
[CrossRef] [PubMed]

Piche, M.

Piksarv, P.

Piskarskas, A.

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]

Recami, E.

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]

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]

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]

E. Recami, “On localized X-shaped superluminal solutions to Maxwell equations,” Physica A (Amsterdam) 252, 586–610(1998).
[CrossRef]

Reivelt, K.

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]

P. Saari and K. Reivelt, “Generation and classification of localized waves by Lorentz transformations in Fourier space,” Phys. Rev. E 69, 036612 (2004).

P. Saari and K. Reivelt, “Evidence of X-shaped propagation-invariant localized light waves,” Phys. Rev. Lett. 79, 4135–4138(1997).
[CrossRef]

Saari, P.

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]

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]

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]

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]

P. Saari and K. Reivelt, “Generation and classification of localized waves by Lorentz transformations in Fourier space,” Phys. Rev. E 69, 036612 (2004).

P. Saari and K. Reivelt, “Evidence of X-shaped propagation-invariant localized light waves,” Phys. Rev. Lett. 79, 4135–4138(1997).
[CrossRef]

Salomaa, M. M.

A. T. Friberg, J. Fagerholm, and M. M. Salomaa, “Space-frequency analysis of nondiffracting pulses,” Opt. Commun. 136, 207–212 (1997).
[CrossRef]

Sedky, S. M.

Shaarawi, A. M.

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]

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]

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]

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]

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]

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]

Steinmeyer, G.

Stibenz, G.

Trebino, R.

Trillo, S.

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]

Trull, J.

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]

Tschirschwitz, F.

Valiulis, G.

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]

Valtna-Lukner, H.

Zamboni-Rached, M.

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]

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]

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]

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]

Ziolkowski, R.

R. Donnelly and R. Ziolkowski, “Designing localized waves,” Proc. R. Soc. A 440, 541–565 (1993).
[CrossRef]

Ziolkowski, R. W.

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]

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]

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]

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]

R. W. Ziolkowski, “Localized transmission of electromagnetic energy,” Phys. Rev. A 39, 2005–2033 (1989).
[CrossRef] [PubMed]

R. W. Ziolkowski, “Exact solutions of the wave equation with complex source locations,” J. Mathe. Phys. 26, 861–863 (1985).
[CrossRef]

Euro. Phys. J. (1)

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]

IEEE J. Sel. Top. Quantum Electron. (1)

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]

IEEE Trans. Ultrason. Ferroelec. Freq. Contr. (2)

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]

J. Y. Lu and J. F. Greenleaf, “Experimental verification of nondiffracting X waves,” IEEE Trans. Ultrason. Ferroelec. Freq. Contr. 39, 441–446 (1992).
[CrossRef]

J. Appl. Phys. (1)

J. Brittingham, “Focus wave modes in homogeneous Maxwell equations: transverse electric mode,” J. Appl. Phys. 54, 1179–1189 (1983).
[CrossRef]

J. Mathe. Phys. (2)

R. W. Ziolkowski, “Exact solutions of the wave equation with complex source locations,” J. Mathe. Phys. 26, 861–863 (1985).
[CrossRef]

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]

J. Opt. Soc. Am. A (3)

Opt. Commun. (3)

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]

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]

A. T. Friberg, J. Fagerholm, and M. M. Salomaa, “Space-frequency analysis of nondiffracting pulses,” Opt. Commun. 136, 207–212 (1997).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Lett. A (1)

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]

Phys. Rev. (1)

P. Saari and K. Reivelt, “Generation and classification of localized waves by Lorentz transformations in Fourier space,” Phys. Rev. E 69, 036612 (2004).

Phys. Rev. A (2)

P. L. Overfelt, “Bessel-Gauss pulses,” Phys. Rev. A 44, 3941–3947 (1991).
[CrossRef] [PubMed]

R. W. Ziolkowski, “Localized transmission of electromagnetic energy,” Phys. Rev. A 39, 2005–2033 (1989).
[CrossRef] [PubMed]

Phys. Rev. Lett. (2)

P. Saari and K. Reivelt, “Evidence of X-shaped propagation-invariant localized light waves,” Phys. Rev. Lett. 79, 4135–4138(1997).
[CrossRef]

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]

Physica A (Amsterdam) (1)

E. Recami, “On localized X-shaped superluminal solutions to Maxwell equations,” Physica A (Amsterdam) 252, 586–610(1998).
[CrossRef]

Proc. R. Soc. A (1)

R. Donnelly and R. Ziolkowski, “Designing localized waves,” Proc. R. Soc. A 440, 541–565 (1993).
[CrossRef]

Prog. Electromagn. Res. PIER. (1)

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]

Prog. Electromagn. Res. PIER. (1)

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]

Other (4)

A. M. Attiya, “Transverse electric X-wave: propagation, scattering, diffraction and generation problems,” Ph.D. dissertation (Cairo University, 2001).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).

E. Hecht, Optics (Addison-Wesley, 1998).

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).

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Figures (7)

Fig. 1
Fig. 1

Geometry of the two slits on the screen.

Fig. 2
Fig. 2

Surface plot of the incident X-wave.

Fig. 3
Fig. 3

Schematic diagram showing the configuration of the setup under consideration.

Fig. 4
Fig. 4

(a) Surface plot of the radiated field at c t = 0.01 m and z 0 = 0.010001 m . (b) Contour plots at the same instant in time over an extended range.

Fig. 5
Fig. 5

(a) Geometric construction of the wavefronts radiated from the right slit. (b) Schematic illustrating the optical path differences between the instants in time at which each wavefront reaches the edges of the right slit.

Fig. 6
Fig. 6

Trajectories of the converging and diverging pulses radiated from Slit 1 and Slit 2. The inset shows the hyperbolic character of the trajectories near the aperture.

Fig. 7
Fig. 7

Contour plot of the diffracted field at c t = 0.03 m and z 0 = 0.030003 m .

Equations (18)

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ψ 1 ( ρ , z , t ) = a 1 + i γ ( z v t ) ( ρ 2 + [ a 1 + i γ ( z v t ) ] 2 ) 3 2 ,
ψ out ( x , y , z , t ) = n = 1 N A n 2 π R n [ z ψ in ] ,
t = t R n c .
v peak = c cos θ 0 .
Circle   1 R : ( x ( d 2 + w 2 ) ) 2 + z 2 = ( c τ ) 2 ,
Circle   2 R : ( x ( d 2 w 2 ) ) 2 + z 2 = ( c τ w sin θ 0 ) 2 ,
Circle   1 B : ( x ( d 2 w 2 ) ) 2 + z 2 = ( c τ d sin θ 0 ) 2 ,
Circle   2 B : ( x ( d 2 + w 2 ) ) 2 + z 2 = ( c τ ( d + w ) sin θ 0 ) 2 .
x = d 2 + w 2 sin 2 θ 0 c τ sin θ 0 ,
( c τ w 2 sin θ 0 ) 2 cos 2 θ 0 z 2 = w 2 4 cos 2 θ 0 ,
( x d 2 ) 2 cot 2 θ 0 z 2 = w 2 4 cos 2 θ 0 .
x = d 2 ( w 2 + d ) sin 2 θ 0 + c τ sin θ 0 .
( c τ ( w 2 + d ) sin θ 0 ) 2 cos 2 θ 0 z 2 = w 2 4 cos 2 θ 0 ,
( x d 2 ) 2 cot 2 θ 0 z 2 = w 2 4 cos 2 θ 0 .
x = d 2 w 2 sin 2 θ 0 + c τ sin θ 0 ,
x = d 2 + ( w 2 + d ) sin 2 θ 0 c τ sin θ 0 ,
( x + d 2 ) 2 cot 2 θ 0 z 2 = w 2 4 cos 2 θ 0 ,
z = 1 2 cot θ 0 d 2 w 2 sin θ 0 d 2 cot θ 0 .

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