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
PDF Article"; _cf_contextpath=""; _cf_ajaxscriptsrc="/CFIDE/scripts/ajax"; _cf_jsonprefix='//'; _cf_websocket_port=8577; _cf_flash_policy_port=1243; _cf_clientid='01F648DC7B64C6D668F8215DDFE46E1B';/* ]]> */
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
PDF Article
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]
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]
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]
E. Recami, “On localized X-shaped superluminal solutions to Maxwell equations,” Physica A 252, 586–610 (1998).
[CrossRef]
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]
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]
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]
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]
P. L. Overfelt, “Bessel-Gauss pulses,” Phys. Rev. A 44, 3941 (1991).
[CrossRef]
[PubMed]
R. W. Ziolkowski, “Localized transmission of electromagnetic energy,” Phys. Rev. A 39, 2005–2032 (1989).
[CrossRef]
[PubMed]
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]
J. Arlt, K. Dholakia, “Generation of high-order bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[CrossRef]
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]
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]
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]
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]
J. Arlt, K. Dholakia, “Generation of high-order bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[CrossRef]
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]
J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]
[PubMed]
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]
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]
I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965).
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]
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, 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]
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]
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]
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]
H. Kim, H.-J. Kim, K. Kim, D.-Y. Park, “Partially coherent nondiffracting beams,” J. Korean Phys. Soc. 37, 713–719 (2000).
H. Kim, H.-J. Kim, K. Kim, D.-Y. Park, “Partially coherent nondiffracting beams,” J. Korean Phys. Soc. 37, 713–719 (2000).
H. Kim, H.-J. Kim, K. Kim, D.-Y. Park, “Partially coherent nondiffracting beams,” J. Korean Phys. Soc. 37, 713–719 (2000).
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]
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]
N. W. McLachlan, Theory and Application of Mathieu Functions (Clarendon, Oxford, UK, 1947).
J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]
[PubMed]
D. Mugnai, A. Ranfagni, R. Ruggeri, “Observation of superluminal behaviors in wave propagation,” Phys. Rev. Lett. 84, 4830–4833 (2000).
[CrossRef]
[PubMed]
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]
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]
P. L. Overfelt, “Bessel-Gauss pulses,” Phys. Rev. A 44, 3941 (1991).
[CrossRef]
[PubMed]
H. Kim, H.-J. Kim, K. Kim, D.-Y. Park, “Partially coherent nondiffracting beams,” J. Korean Phys. Soc. 37, 713–719 (2000).
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, 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]
D. Mugnai, A. Ranfagni, R. Ruggeri, “Observation of superluminal behaviors in wave propagation,” Phys. Rev. Lett. 84, 4830–4833 (2000).
[CrossRef]
[PubMed]
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]
P. Saari, K. Reivelt, “Evidence of X-shaped propagation invariant localized light waves,” Phys. Rev. Lett. 79, 4135–4138 (1997).
[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]
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. Rogel-Salazar, G. H. C. New, S. Chavez-Cerda, “Bessel–Gauss beam optical resonator,” Opt. Commun. 190, 117–122 (2001).
[CrossRef]
D. Mugnai, A. Ranfagni, R. Ruggeri, “Observation of superluminal behaviors in wave propagation,” Phys. Rev. Lett. 84, 4830–4833 (2000).
[CrossRef]
[PubMed]
I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965).
P. Saari, K. Reivelt, “Evidence of X-shaped propagation invariant localized light waves,” Phys. Rev. Lett. 79, 4135–4138 (1997).
[CrossRef]
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]
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]
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]
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.
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]
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]
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]
R. W. Ziolkowski, “Localized transmission of electromagnetic energy,” Phys. Rev. A 39, 2005–2032 (1989).
[CrossRef]
[PubMed]
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]
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]
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]
H. Kim, H.-J. Kim, K. Kim, D.-Y. Park, “Partially coherent nondiffracting beams,” J. Korean Phys. Soc. 37, 713–719 (2000).
J. Durnin, “Exact solutions for nondiffracting beams 1. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
[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]
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]
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]
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]
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]
J. Arlt, K. Dholakia, “Generation of high-order bessel beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
[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]
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]
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]
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.
R. W. Ziolkowski, “Localized transmission of electromagnetic energy,” Phys. Rev. A 39, 2005–2032 (1989).
[CrossRef]
[PubMed]
P. L. Overfelt, “Bessel-Gauss pulses,” Phys. Rev. A 44, 3941 (1991).
[CrossRef]
[PubMed]
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]
P. Saari, K. Reivelt, “Evidence of X-shaped propagation invariant localized light waves,” Phys. Rev. Lett. 79, 4135–4138 (1997).
[CrossRef]
D. Mugnai, A. Ranfagni, R. Ruggeri, “Observation of superluminal behaviors in wave propagation,” Phys. Rev. Lett. 84, 4830–4833 (2000).
[CrossRef]
[PubMed]
J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef]
[PubMed]
E. Recami, “On localized X-shaped superluminal solutions to Maxwell equations,” Physica A 252, 586–610 (1998).
[CrossRef]
I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965).
N. W. McLachlan, Theory and Application of Mathieu Functions (Clarendon, Oxford, UK, 1947).
OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.
Alert me when this article is cited.