Abstract

An X-shaped localized pulse based on a zero-order Mathieu function is obtained by a proper superposition of Mathieu beams, and some properties are analyzed.

© 2004 Optical Society of America

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  1. E. Recami, “On localized X-shaped superluminal solutions to Maxwell equations,” Physica A 252, 586–610 (1998).
    [CrossRef]
  2. R. W. Ziolkowski, “Localized transmission of electromagnetic energy,” Phys. Rev. A 39, 2005–2032 (1989).
    [CrossRef] [PubMed]
  3. J.-Y. Lu, J. F. Greenleaf, “Nondiffracting X-waves exact solutions to free space scalar wave equation and their finite aperture realization,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19–31 (1992).
    [CrossRef]
  4. R. W. Ziolkowski, I. M. Besieris, A. M. Shaarawi, “Aperture realizations of exact solutions to homogeneous-wave equations,” J. Opt. Soc. Am. A 10, 75–87 (1993).
    [CrossRef]
  5. A. M. Shaarawi, I. M. Besieris, “On the superluminal propagation of X-shaped localized waves,” J. Phys. A Math. Gen. 33, 7227–7254 (2000).
    [CrossRef]
  6. M. Zamboni-Rached, E. Recami, H. E. Hernández-Figueroa, “New localized superluminal solutions to the wave equations with finite total energies and arbitrary frequencies,” Eur. Phys. J. D 21, 217–228 (2002).
    [CrossRef]
  7. M. Zamboni-Rached, H. E. Hernández-Figueroa, “A rigorous analysis of localized wave propagation in optical fibers,” Opt. Commun. 191, 49–54 (2001).
    [CrossRef]
  8. M. Zamboni-Rached, E. Recami, F. Fontana, “Localized superluminal solutions to Maxwell equations propagating along a normal-sized waveguide,” Phys. Rev. E 64, 066603 (2001).
    [CrossRef]
  9. P. L. Overfelt, “Bessel-Gauss pulses,” Phys. Rev. A 44, 3941 (1991).
    [CrossRef] [PubMed]
  10. J.-Y. Lu, J. F. Greenleaf, “Experimental verification of nondiffracting X-waves,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 441–446 (1992).
    [CrossRef]
  11. P. Saari, K. Reivelt, “Evidence of X-shaped propagation invariant localized light waves,” Phys. Rev. Lett. 79, 4135–4138 (1997).
    [CrossRef]
  12. D. Mugnai, A. Ranfagni, R. Ruggeri, “Observation of superluminal behaviors in wave propagation,” Phys. Rev. Lett. 84, 4830–4833 (2000).
    [CrossRef] [PubMed]
  13. J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [CrossRef] [PubMed]
  14. J. Durnin, “Exact solutions for nondiffracting beams 1. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
    [CrossRef]
  15. S. Chavez-Cerda, G. S. McDonald, G. H. C. New, “Nondiffracting beams: travelling, standing, rotating and spiral waves,” Opt. Commun. 123, 225–233 (1996).
    [CrossRef]
  16. J. Rogel-Salazar, G. H. C. New, S. Chavez-Cerda, “Bessel–Gauss beam optical resonator,” Opt. Commun. 190, 117–122 (2001).
    [CrossRef]
  17. J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
    [CrossRef]
  18. M. Erdelyi, Z. L. Horvath, G. Szabo, ZsBor, F. K. Tittel, J. R. Carvalho, M. C. Smayling, “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15, 287–292 (1997).
    [CrossRef]
  19. H. Kim, H.-J. Kim, K. Kim, D.-Y. Park, “Partially coherent nondiffracting beams,” J. Korean Phys. Soc. 37, 713–719 (2000).
  20. J. Arlt, K. Dholakia, “Generation of high-order bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
    [CrossRef]
  21. J. C. GutierrezVega, M. D. Iturbe-Castillo, E. Tepichin, G. Ramirez, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, “New member in the family of propagation-invariant optical fields: Mathieu beams,” Opt. Photon. News, Dec.2000, pp. 37–38.
  22. J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, S. Chavez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25, 1493–1495 (2000).
    [CrossRef]
  23. C. A. Dartora, M. Zamboni-Rached, K. Z. Nóbrega, E. Recami, H. E. Hernández-Figueroa, “General formulation for the analysis of scalar diffraction-free beams using angular modulation: Mathieu and Bessel beams,” Opt. Commun. 222, 75–80 (2003).
    [CrossRef]
  24. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965).
  25. N. W. McLachlan, Theory and Application of Mathieu Functions (Clarendon, Oxford, UK, 1947).

2003 (1)

C. A. Dartora, M. Zamboni-Rached, K. Z. Nóbrega, E. Recami, H. E. Hernández-Figueroa, “General formulation for the analysis of scalar diffraction-free beams using angular modulation: Mathieu and Bessel beams,” Opt. Commun. 222, 75–80 (2003).
[CrossRef]

2002 (1)

M. Zamboni-Rached, E. Recami, H. E. Hernández-Figueroa, “New localized superluminal solutions to the wave equations with finite total energies and arbitrary frequencies,” Eur. Phys. J. D 21, 217–228 (2002).
[CrossRef]

2001 (4)

M. Zamboni-Rached, H. E. Hernández-Figueroa, “A rigorous analysis of localized wave propagation in optical fibers,” Opt. Commun. 191, 49–54 (2001).
[CrossRef]

M. Zamboni-Rached, E. Recami, F. Fontana, “Localized superluminal solutions to Maxwell equations propagating along a normal-sized waveguide,” Phys. Rev. E 64, 066603 (2001).
[CrossRef]

J. Rogel-Salazar, G. H. C. New, S. Chavez-Cerda, “Bessel–Gauss beam optical resonator,” Opt. Commun. 190, 117–122 (2001).
[CrossRef]

J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[CrossRef]

2000 (6)

H. Kim, H.-J. Kim, K. Kim, D.-Y. Park, “Partially coherent nondiffracting beams,” J. Korean Phys. Soc. 37, 713–719 (2000).

J. Arlt, K. Dholakia, “Generation of high-order bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[CrossRef]

J. C. GutierrezVega, M. D. Iturbe-Castillo, E. Tepichin, G. Ramirez, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, “New member in the family of propagation-invariant optical fields: Mathieu beams,” Opt. Photon. News, Dec.2000, pp. 37–38.

A. M. Shaarawi, I. M. Besieris, “On the superluminal propagation of X-shaped localized waves,” J. Phys. A Math. Gen. 33, 7227–7254 (2000).
[CrossRef]

D. Mugnai, A. Ranfagni, R. Ruggeri, “Observation of superluminal behaviors in wave propagation,” Phys. Rev. Lett. 84, 4830–4833 (2000).
[CrossRef] [PubMed]

J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, S. Chavez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25, 1493–1495 (2000).
[CrossRef]

1998 (1)

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

1997 (2)

M. Erdelyi, Z. L. Horvath, G. Szabo, ZsBor, F. K. Tittel, J. R. Carvalho, M. C. Smayling, “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15, 287–292 (1997).
[CrossRef]

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

1996 (1)

S. Chavez-Cerda, G. S. McDonald, G. H. C. New, “Nondiffracting beams: travelling, standing, rotating and spiral waves,” Opt. Commun. 123, 225–233 (1996).
[CrossRef]

1993 (1)

1992 (2)

J.-Y. Lu, J. F. Greenleaf, “Nondiffracting X-waves exact solutions to free space scalar wave equation and their finite aperture realization,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19–31 (1992).
[CrossRef]

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

1991 (1)

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

1989 (1)

R. W. Ziolkowski, “Localized transmission of electromagnetic energy,” Phys. Rev. A 39, 2005–2032 (1989).
[CrossRef] [PubMed]

1987 (2)

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

J. Durnin, “Exact solutions for nondiffracting beams 1. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[CrossRef]

Arlt, J.

J. Arlt, K. Dholakia, “Generation of high-order bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[CrossRef]

Besieris, I. M.

A. M. Shaarawi, I. M. Besieris, “On the superluminal propagation of X-shaped localized waves,” J. Phys. A Math. Gen. 33, 7227–7254 (2000).
[CrossRef]

R. W. Ziolkowski, I. M. Besieris, A. M. Shaarawi, “Aperture realizations of exact solutions to homogeneous-wave equations,” J. Opt. Soc. Am. A 10, 75–87 (1993).
[CrossRef]

Carvalho, J. R.

M. Erdelyi, Z. L. Horvath, G. Szabo, ZsBor, F. K. Tittel, J. R. Carvalho, M. C. Smayling, “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15, 287–292 (1997).
[CrossRef]

Chavez-Cerda, S.

J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[CrossRef]

J. Rogel-Salazar, G. H. C. New, S. Chavez-Cerda, “Bessel–Gauss beam optical resonator,” Opt. Commun. 190, 117–122 (2001).
[CrossRef]

J. C. GutierrezVega, M. D. Iturbe-Castillo, E. Tepichin, G. Ramirez, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, “New member in the family of propagation-invariant optical fields: Mathieu beams,” Opt. Photon. News, Dec.2000, pp. 37–38.

J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, S. Chavez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25, 1493–1495 (2000).
[CrossRef]

S. Chavez-Cerda, G. S. McDonald, G. H. C. New, “Nondiffracting beams: travelling, standing, rotating and spiral waves,” Opt. Commun. 123, 225–233 (1996).
[CrossRef]

Dartora, C. A.

C. A. Dartora, M. Zamboni-Rached, K. Z. Nóbrega, E. Recami, H. E. Hernández-Figueroa, “General formulation for the analysis of scalar diffraction-free beams using angular modulation: Mathieu and Bessel beams,” Opt. Commun. 222, 75–80 (2003).
[CrossRef]

Dholakia, K.

J. Arlt, K. Dholakia, “Generation of high-order bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[CrossRef]

Durnin, J.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

J. Durnin, “Exact solutions for nondiffracting beams 1. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[CrossRef]

Eberly, J. H.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Erdelyi, M.

M. Erdelyi, Z. L. Horvath, G. Szabo, ZsBor, F. K. Tittel, J. R. Carvalho, M. C. Smayling, “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15, 287–292 (1997).
[CrossRef]

Fontana, F.

M. Zamboni-Rached, E. Recami, F. Fontana, “Localized superluminal solutions to Maxwell equations propagating along a normal-sized waveguide,” Phys. Rev. E 64, 066603 (2001).
[CrossRef]

Gradshteyn, I. S.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965).

Greenleaf, J. F.

J.-Y. Lu, J. F. Greenleaf, “Nondiffracting X-waves exact solutions to free space scalar wave equation and their finite aperture realization,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19–31 (1992).
[CrossRef]

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

GutierrezVega, J. C.

J. C. GutierrezVega, M. D. Iturbe-Castillo, E. Tepichin, G. Ramirez, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, “New member in the family of propagation-invariant optical fields: Mathieu beams,” Opt. Photon. News, Dec.2000, pp. 37–38.

Gutierrez-Vega, J. C.

J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[CrossRef]

J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, S. Chavez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25, 1493–1495 (2000).
[CrossRef]

Hernández-Figueroa, H. E.

C. A. Dartora, M. Zamboni-Rached, K. Z. Nóbrega, E. Recami, H. E. Hernández-Figueroa, “General formulation for the analysis of scalar diffraction-free beams using angular modulation: Mathieu and Bessel beams,” Opt. Commun. 222, 75–80 (2003).
[CrossRef]

M. Zamboni-Rached, E. Recami, H. E. Hernández-Figueroa, “New localized superluminal solutions to the wave equations with finite total energies and arbitrary frequencies,” Eur. Phys. J. D 21, 217–228 (2002).
[CrossRef]

M. Zamboni-Rached, H. E. Hernández-Figueroa, “A rigorous analysis of localized wave propagation in optical fibers,” Opt. Commun. 191, 49–54 (2001).
[CrossRef]

Horvath, Z. L.

M. Erdelyi, Z. L. Horvath, G. Szabo, ZsBor, F. K. Tittel, J. R. Carvalho, M. C. Smayling, “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15, 287–292 (1997).
[CrossRef]

Iturbe-Castillo, M. D.

J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[CrossRef]

J. C. GutierrezVega, M. D. Iturbe-Castillo, E. Tepichin, G. Ramirez, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, “New member in the family of propagation-invariant optical fields: Mathieu beams,” Opt. Photon. News, Dec.2000, pp. 37–38.

J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, S. Chavez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25, 1493–1495 (2000).
[CrossRef]

Kim, H.

H. Kim, H.-J. Kim, K. Kim, D.-Y. Park, “Partially coherent nondiffracting beams,” J. Korean Phys. Soc. 37, 713–719 (2000).

Kim, H.-J.

H. Kim, H.-J. Kim, K. Kim, D.-Y. Park, “Partially coherent nondiffracting beams,” J. Korean Phys. Soc. 37, 713–719 (2000).

Kim, K.

H. Kim, H.-J. Kim, K. Kim, D.-Y. Park, “Partially coherent nondiffracting beams,” J. Korean Phys. Soc. 37, 713–719 (2000).

Lu, J.-Y.

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

J.-Y. Lu, J. F. Greenleaf, “Nondiffracting X-waves exact solutions to free space scalar wave equation and their finite aperture realization,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 39, 19–31 (1992).
[CrossRef]

McDonald, G. S.

S. Chavez-Cerda, G. S. McDonald, G. H. C. New, “Nondiffracting beams: travelling, standing, rotating and spiral waves,” Opt. Commun. 123, 225–233 (1996).
[CrossRef]

McLachlan, N. W.

N. W. McLachlan, Theory and Application of Mathieu Functions (Clarendon, Oxford, UK, 1947).

Miceli, J. J.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Mugnai, D.

D. Mugnai, A. Ranfagni, R. Ruggeri, “Observation of superluminal behaviors in wave propagation,” Phys. Rev. Lett. 84, 4830–4833 (2000).
[CrossRef] [PubMed]

New, G. H. C.

J. Rogel-Salazar, G. H. C. New, S. Chavez-Cerda, “Bessel–Gauss beam optical resonator,” Opt. Commun. 190, 117–122 (2001).
[CrossRef]

J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[CrossRef]

S. Chavez-Cerda, G. S. McDonald, G. H. C. New, “Nondiffracting beams: travelling, standing, rotating and spiral waves,” Opt. Commun. 123, 225–233 (1996).
[CrossRef]

Nóbrega, K. Z.

C. A. Dartora, M. Zamboni-Rached, K. Z. Nóbrega, E. Recami, H. E. Hernández-Figueroa, “General formulation for the analysis of scalar diffraction-free beams using angular modulation: Mathieu and Bessel beams,” Opt. Commun. 222, 75–80 (2003).
[CrossRef]

Overfelt, P. L.

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

Park, D.-Y.

H. Kim, H.-J. Kim, K. Kim, D.-Y. Park, “Partially coherent nondiffracting beams,” J. Korean Phys. Soc. 37, 713–719 (2000).

Ramirez, G.

J. C. GutierrezVega, M. D. Iturbe-Castillo, E. Tepichin, G. Ramirez, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, “New member in the family of propagation-invariant optical fields: Mathieu beams,” Opt. Photon. News, Dec.2000, pp. 37–38.

Ramirez, G. A.

J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[CrossRef]

Ranfagni, A.

D. Mugnai, A. Ranfagni, R. Ruggeri, “Observation of superluminal behaviors in wave propagation,” Phys. Rev. Lett. 84, 4830–4833 (2000).
[CrossRef] [PubMed]

Recami, E.

C. A. Dartora, M. Zamboni-Rached, K. Z. Nóbrega, E. Recami, H. E. Hernández-Figueroa, “General formulation for the analysis of scalar diffraction-free beams using angular modulation: Mathieu and Bessel beams,” Opt. Commun. 222, 75–80 (2003).
[CrossRef]

M. Zamboni-Rached, E. Recami, H. E. Hernández-Figueroa, “New localized superluminal solutions to the wave equations with finite total energies and arbitrary frequencies,” Eur. Phys. J. D 21, 217–228 (2002).
[CrossRef]

M. Zamboni-Rached, E. Recami, F. Fontana, “Localized superluminal solutions to Maxwell equations propagating along a normal-sized waveguide,” Phys. Rev. E 64, 066603 (2001).
[CrossRef]

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

Reivelt, K.

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

Rodriguez-Dagnino, R. M.

J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[CrossRef]

J. C. GutierrezVega, M. D. Iturbe-Castillo, E. Tepichin, G. Ramirez, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, “New member in the family of propagation-invariant optical fields: Mathieu beams,” Opt. Photon. News, Dec.2000, pp. 37–38.

Rogel-Salazar, J.

J. Rogel-Salazar, G. H. C. New, S. Chavez-Cerda, “Bessel–Gauss beam optical resonator,” Opt. Commun. 190, 117–122 (2001).
[CrossRef]

Ruggeri, R.

D. Mugnai, A. Ranfagni, R. Ruggeri, “Observation of superluminal behaviors in wave propagation,” Phys. Rev. Lett. 84, 4830–4833 (2000).
[CrossRef] [PubMed]

Ryzhik, I. M.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965).

Saari, P.

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

Shaarawi, A. M.

A. M. Shaarawi, I. M. Besieris, “On the superluminal propagation of X-shaped localized waves,” J. Phys. A Math. Gen. 33, 7227–7254 (2000).
[CrossRef]

R. W. Ziolkowski, I. M. Besieris, A. M. Shaarawi, “Aperture realizations of exact solutions to homogeneous-wave equations,” J. Opt. Soc. Am. A 10, 75–87 (1993).
[CrossRef]

Smayling, M. C.

M. Erdelyi, Z. L. Horvath, G. Szabo, ZsBor, F. K. Tittel, J. R. Carvalho, M. C. Smayling, “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15, 287–292 (1997).
[CrossRef]

Szabo, G.

M. Erdelyi, Z. L. Horvath, G. Szabo, ZsBor, F. K. Tittel, J. R. Carvalho, M. C. Smayling, “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15, 287–292 (1997).
[CrossRef]

Tepichin, E.

J. C. Gutierrez-Vega, M. D. Iturbe-Castillo, G. A. Ramirez, E. Tepichin, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, G. H. C. New, “Experimental demonstration of optical Mathieu beams,” Opt. Commun. 195, 35–40 (2001).
[CrossRef]

J. C. GutierrezVega, M. D. Iturbe-Castillo, E. Tepichin, G. Ramirez, R. M. Rodriguez-Dagnino, S. Chavez-Cerda, “New member in the family of propagation-invariant optical fields: Mathieu beams,” Opt. Photon. News, Dec.2000, pp. 37–38.

Tittel, F. K.

M. Erdelyi, Z. L. Horvath, G. Szabo, ZsBor, F. K. Tittel, J. R. Carvalho, M. C. Smayling, “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15, 287–292 (1997).
[CrossRef]

Zamboni-Rached, M.

C. A. Dartora, M. Zamboni-Rached, K. Z. Nóbrega, E. Recami, H. E. Hernández-Figueroa, “General formulation for the analysis of scalar diffraction-free beams using angular modulation: Mathieu and Bessel beams,” Opt. Commun. 222, 75–80 (2003).
[CrossRef]

M. Zamboni-Rached, E. Recami, H. E. Hernández-Figueroa, “New localized superluminal solutions to the wave equations with finite total energies and arbitrary frequencies,” Eur. Phys. J. D 21, 217–228 (2002).
[CrossRef]

M. Zamboni-Rached, E. Recami, F. Fontana, “Localized superluminal solutions to Maxwell equations propagating along a normal-sized waveguide,” Phys. Rev. E 64, 066603 (2001).
[CrossRef]

M. Zamboni-Rached, H. E. Hernández-Figueroa, “A rigorous analysis of localized wave propagation in optical fibers,” Opt. Commun. 191, 49–54 (2001).
[CrossRef]

Ziolkowski, R. W.

ZsBor,

M. Erdelyi, Z. L. Horvath, G. Szabo, ZsBor, F. K. Tittel, J. R. Carvalho, M. C. Smayling, “Generation of diffraction-free beams for applications in optical microlithography,” J. Vac. Sci. Technol. B 15, 287–292 (1997).
[CrossRef]

Eur. Phys. J. D (1)

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