Abstract

The propagation and transmission of Bessel beams through nano-layered structures has been discussed recently. Within this framework we recognize the formation of unguided diffraction-free waves with the spot size approaching and occasionally surpassing the limit of a wavelength when a Bessel beam of any order n is launched onto a thin material slab with grazing incidence. On the basis of the plane-wave representation of cylindrical waves, a simple model is introduced providing an exact description of the transverse pattern of this type of diffraction-suppressed localized wave. Potential applications in surface science are put forward for consideration.

© 2010 Optical Society of America

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    [Crossref] [PubMed]

2009 (3)

D. Mugnai and P. Spalla, “Electromagnetic propagation of Bessel-like localized waves in the presence of absorbing media,” Opt. Commun. 282, 4668-4671 (2009).
[Crossref]

J. Hu and C. R. Menyuk, “Understanding leaky modes: slab waveguide revisited,” Adv. Opt. Photon. 1, 58-106 (2009).
[Crossref]

Z. Li, K. B. Alici, H. Caglayan, and E. Ozbay, “Generation of an axially asymmetric Bessel-like beam from a metallic subwavelength aperture,” Phys. Rev. Lett. 102, 143901 (2009).
[Crossref] [PubMed]

2008 (2)

2006 (3)

2005 (1)

2004 (3)

S. Longhi, K. Janner, and P. Laporta, “Propagating pulsed Bessel beams in periodic media,” J. Opt. B 6, 477-481 (2004).
[Crossref]

C. López-Mariscal, J. C. Gutiérrez-Vega, and S. Chávez-Cerda, “Production of high-order Bessel beams with a Mach-Zehnder interferometer,” Appl. Opt. 43, 5060-5063 (2004).
[Crossref] [PubMed]

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. D. Trapani, “Nonlinear unbalanced Bessel beams: Stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004).
[Crossref] [PubMed]

2003 (3)

J. Amako, D. Sawaki, and E. Fujii, “Microstructuring transparent materials by use of nondiffracting ultrashort pulse beams generated by diffractive optics,” J. Opt. Soc. Am. B 20, 2562-2568 (2003).
[Crossref]

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810-816 (2003).
[Crossref] [PubMed]

M. A. Porras, G. Valiulis, and P. D. Trapani, “Unified description of Bessel X waves with cone dispersion and tilted pulses,” Phys. Rev. E 68, 016613 (2003).
[Crossref]

2002 (5)

P. Pääkkönen, J. Tervo, P. Vahimaa, J. Turunen, and F. Gori, “General vectorial decomposition of electromagnetic fields with application to propagation-invariant and rotating fields,” Opt. Express 10, 949-959 (2002).
[PubMed]

K. Reivelt and P. Saari, “Optically realizable localized wave solutions of the homogeneous scalar wave equation,” Phys. Rev. E 65, 046622 (2002).
[Crossref]

K. Reivelt and P. Saari, “Experimental demonstration of realizability of optical focus wave modes,” Phys. Rev. E 66, 056611 (2002).
[Crossref]

M. Zamboni-Rached, K. Z. Nóbrega, E. Recami, and H. E. Hernández-Figueroa, “Superluminal X-shaped beams propagating without distortion along a coaxial guide,” Phys. Rev. E 66, 046617 (2002).
[Crossref]

C. J. R. Sheppard, “Generalized Bessel pulse beams,” J. Opt. Soc. Am. A 19, 2218-2222 (2002).
[Crossref]

2001 (1)

D. Mugnai, “Passage of a Bessel beam through a classically forbidden region,” Opt. Commun. 188, 17-24 (2001).
[Crossref]

2000 (4)

1998 (2)

Z. Bouchal, J. Bajer, and M. Bertolotti, “Vectorial spectral analysis of the nonstationary electromagnetic field,” J. Opt. Soc. Am. A 15, 2172-2181 (1998).
[Crossref]

S. Holm, “Bessel and conical beams and approximation with annular arrays,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 712-718 (1998).
[Crossref]

1997 (3)

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064-4075 (1997).
[Crossref]

Z. L. Horváth, M. Erdélyi, G. Szabó, Z. Bor, F. K. Tittel, and J. R. Cavallaro, “Generation of nearly nondiffracting Bessel beams with a Fabry-Perot interferometer,” J. Opt. Soc. Am. A 14, 3009-3013 (1997).
[Crossref]

B. Hafizi, E. Esarey, and P. Sprangle, “Laser-driven acceleration with Bessel beams,” Phys. Rev. E 55, 3539-3545 (1997).
[Crossref]

1995 (3)

R. Horák, J. Bajer, M. Bertolotti, and C. Sibilia, “Diffraction-free field in a planar nonlinear waveguide,” Phys. Rev. E 52, 4421-4429 (1995).
[Crossref]

J. F. McGilp, “Optical characterisation of semiconductor surfaces and interfaces,” Prog. Surf. Sci. 49, 1-106 (1995).
[Crossref]

Z. Bouchal and M. Olivik, “Non-diffracting vector Bessel beams,” J. Mod. Opt. 45, 1555-1566 (1995).
[Crossref]

1993 (1)

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70, 1401-1404 (1993).
[Crossref] [PubMed]

1992 (1)

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

1989 (2)

1987 (2)

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

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

Alici, K. B.

Z. Li, K. B. Alici, H. Caglayan, and E. Ozbay, “Generation of an axially asymmetric Bessel-like beam from a metallic subwavelength aperture,” Phys. Rev. Lett. 102, 143901 (2009).
[Crossref] [PubMed]

Amako, J.

Arfken, G. B.

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Academic, 2001).

Arlt, J.

J. Arlt, T. Hitomi, and K. Dholakia, “Atom guiding along Laguerre-Gaussian and Bessel light beams,” Appl. Phys. B 71, 549—554 (2000).
[Crossref]

J. Arlt and M. J. Padgett, “Generation of a beam with a dark focus surrounded by regions of higher intensity: the optical bottle beam,” Opt. Lett. 25, 191-193 (2000).
[Crossref]

Bajer, J.

Z. Bouchal, J. Bajer, and M. Bertolotti, “Vectorial spectral analysis of the nonstationary electromagnetic field,” J. Opt. Soc. Am. A 15, 2172-2181 (1998).
[Crossref]

R. Horák, J. Bajer, M. Bertolotti, and C. Sibilia, “Diffraction-free field in a planar nonlinear waveguide,” Phys. Rev. E 52, 4421-4429 (1995).
[Crossref]

Bertolotti, M.

Z. Bouchal, J. Bajer, and M. Bertolotti, “Vectorial spectral analysis of the nonstationary electromagnetic field,” J. Opt. Soc. Am. A 15, 2172-2181 (1998).
[Crossref]

R. Horák, J. Bajer, M. Bertolotti, and C. Sibilia, “Diffraction-free field in a planar nonlinear waveguide,” Phys. Rev. E 52, 4421-4429 (1995).
[Crossref]

Bor, Z.

Born, M.

M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge Univ. Press, 1999).

Bouchal, Z.

Caglayan, H.

Z. Li, K. B. Alici, H. Caglayan, and E. Ozbay, “Generation of an axially asymmetric Bessel-like beam from a metallic subwavelength aperture,” Phys. Rev. Lett. 102, 143901 (2009).
[Crossref] [PubMed]

Cavallaro, J. R.

Chávez-Cerda, S.

Christodoulides, D. N.

Dholakia, K.

J. Arlt, T. Hitomi, and K. Dholakia, “Atom guiding along Laguerre-Gaussian and Bessel light beams,” Appl. Phys. B 71, 549—554 (2000).
[Crossref]

Dubietis, A.

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. D. Trapani, “Nonlinear unbalanced Bessel beams: Stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004).
[Crossref] [PubMed]

Durnin, J.

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

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

Eberly, J. H.

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

Elsaesser, T.

Erdélyi, M.

Esarey, E.

B. Hafizi, E. Esarey, and P. Sprangle, “Laser-driven acceleration with Bessel beams,” Phys. Rev. E 55, 3539-3545 (1997).
[Crossref]

Faccio, D.

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. D. Trapani, “Nonlinear unbalanced Bessel beams: Stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004).
[Crossref] [PubMed]

Friberg, A. T.

Fujii, E.

Gori, F.

Gorshkov, V. N.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064-4075 (1997).
[Crossref]

Greenleaf, J. F.

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

Griebner, U.

Grier, D. G.

D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810-816 (2003).
[Crossref] [PubMed]

Grunwald, R.

Gutiérrez-Vega, J. C.

Hafizi, B.

B. Hafizi, E. Esarey, and P. Sprangle, “Laser-driven acceleration with Bessel beams,” Phys. Rev. E 55, 3539-3545 (1997).
[Crossref]

Hartmann, H.-J.

Heckenberg, N. R.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064-4075 (1997).
[Crossref]

Herminghaus, S.

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70, 1401-1404 (1993).
[Crossref] [PubMed]

Hernández-Figueroa, H. E.

M. Zamboni-Rached, K. Z. Nóbrega, E. Recami, and H. E. Hernández-Figueroa, “Superluminal X-shaped beams propagating without distortion along a coaxial guide,” Phys. Rev. E 66, 046617 (2002).
[Crossref]

Hitomi, T.

J. Arlt, T. Hitomi, and K. Dholakia, “Atom guiding along Laguerre-Gaussian and Bessel light beams,” Appl. Phys. B 71, 549—554 (2000).
[Crossref]

Holm, S.

S. Holm, “Bessel and conical beams and approximation with annular arrays,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 712-718 (1998).
[Crossref]

Horák, R.

R. Horák, J. Bajer, M. Bertolotti, and C. Sibilia, “Diffraction-free field in a planar nonlinear waveguide,” Phys. Rev. E 52, 4421-4429 (1995).
[Crossref]

Horváth, Z. L.

Hu, J.

Indebetouw, G.

Inoue, T.

Y. Matsuoka, Y. Kizuka, and T. Inoue, “The characteristics of laser micro drilling using a Bessel beam,” Appl. Phys. A 84, 423-430 (2006).
[Crossref]

Janner, K.

S. Longhi, K. Janner, and P. Laporta, “Propagating pulsed Bessel beams in periodic media,” J. Opt. B 6, 477-481 (2004).
[Crossref]

Jüptner, W.

Kebbel, V.

Kizuka, Y.

Y. Matsuoka, Y. Kizuka, and T. Inoue, “The characteristics of laser micro drilling using a Bessel beam,” Appl. Phys. A 84, 423-430 (2006).
[Crossref]

Laporta, P.

S. Longhi, K. Janner, and P. Laporta, “Propagating pulsed Bessel beams in periodic media,” J. Opt. B 6, 477-481 (2004).
[Crossref]

Li, Z.

Z. Li, K. B. Alici, H. Caglayan, and E. Ozbay, “Generation of an axially asymmetric Bessel-like beam from a metallic subwavelength aperture,” Phys. Rev. Lett. 102, 143901 (2009).
[Crossref] [PubMed]

Longhi, S.

S. Longhi, K. Janner, and P. Laporta, “Propagating pulsed Bessel beams in periodic media,” J. Opt. B 6, 477-481 (2004).
[Crossref]

López-Mariscal, C.

Love, J. D.

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

Lu, J.

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

Malos, J. T.

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064-4075 (1997).
[Crossref]

Manela, O.

Matsuoka, Y.

Y. Matsuoka, Y. Kizuka, and T. Inoue, “The characteristics of laser micro drilling using a Bessel beam,” Appl. Phys. A 84, 423-430 (2006).
[Crossref]

McGilp, J. F.

J. F. McGilp, “Optical characterisation of semiconductor surfaces and interfaces,” Prog. Surf. Sci. 49, 1-106 (1995).
[Crossref]

Menyuk, C. R.

Miceli, J. J.

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

Miret, J. J.

Mugnai, D.

D. Mugnai and P. Spalla, “Electromagnetic propagation of Bessel-like localized waves in the presence of absorbing media,” Opt. Commun. 282, 4668-4671 (2009).
[Crossref]

D. Mugnai, “Passage of a Bessel beam through a classically forbidden region,” Opt. Commun. 188, 17-24 (2001).
[Crossref]

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

Nibbering, E. T. J.

Nóbrega, K. Z.

M. Zamboni-Rached, K. Z. Nóbrega, E. Recami, and H. E. Hernández-Figueroa, “Superluminal X-shaped beams propagating without distortion along a coaxial guide,” Phys. Rev. E 66, 046617 (2002).
[Crossref]

Olivik, M.

Z. Bouchal and M. Olivik, “Non-diffracting vector Bessel beams,” J. Mod. Opt. 45, 1555-1566 (1995).
[Crossref]

Ozbay, E.

Z. Li, K. B. Alici, H. Caglayan, and E. Ozbay, “Generation of an axially asymmetric Bessel-like beam from a metallic subwavelength aperture,” Phys. Rev. Lett. 102, 143901 (2009).
[Crossref] [PubMed]

Pääkkönen, P.

Padgett, M. J.

Parola, A.

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. D. Trapani, “Nonlinear unbalanced Bessel beams: Stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004).
[Crossref] [PubMed]

Porras, M. A.

C. J. Zapata-Rodríguez, M. A. Porras, and J. J. Miret, “Free-space delay lines and resonances with ultraslow pulsed Bessel beams,” J. Opt. Soc. Am. A 25, 2758-2763 (2008).
[Crossref]

C. J. Zapata-Rodríguez and M. A. Porras, “X-wave bullets with negative group velocity in vacuum,” Opt. Lett. 31, 3532-3534 (2006).
[Crossref] [PubMed]

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. D. Trapani, “Nonlinear unbalanced Bessel beams: Stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004).
[Crossref] [PubMed]

M. A. Porras, G. Valiulis, and P. D. Trapani, “Unified description of Bessel X waves with cone dispersion and tilted pulses,” Phys. Rev. E 68, 016613 (2003).
[Crossref]

Ranfagni, A.

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

Recami, E.

M. Zamboni-Rached, K. Z. Nóbrega, E. Recami, and H. E. Hernández-Figueroa, “Superluminal X-shaped beams propagating without distortion along a coaxial guide,” Phys. Rev. E 66, 046617 (2002).
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[Crossref]

K. Reivelt and P. Saari, “Experimental demonstration of realizability of optical focus wave modes,” Phys. Rev. E 66, 056611 (2002).
[Crossref]

K. Reivelt and P. Saari, “Linear-optical generation of localized waves” in Localized Waves, H.E.Hernández-Figueroa, M.Zamboni-Rached, and E.Recami, eds.(Wiley, 2008), pp. 185-213.
[Crossref]

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

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K. Reivelt and P. Saari, “Experimental demonstration of realizability of optical focus wave modes,” Phys. Rev. E 66, 056611 (2002).
[Crossref]

K. Reivelt and P. Saari, “Optically realizable localized wave solutions of the homogeneous scalar wave equation,” Phys. Rev. E 65, 046622 (2002).
[Crossref]

K. Reivelt and P. Saari, “Linear-optical generation of localized waves” in Localized Waves, H.E.Hernández-Figueroa, M.Zamboni-Rached, and E.Recami, eds.(Wiley, 2008), pp. 185-213.
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[Crossref]

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D. Mugnai and P. Spalla, “Electromagnetic propagation of Bessel-like localized waves in the presence of absorbing media,” Opt. Commun. 282, 4668-4671 (2009).
[Crossref]

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B. Hafizi, E. Esarey, and P. Sprangle, “Laser-driven acceleration with Bessel beams,” Phys. Rev. E 55, 3539-3545 (1997).
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M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064-4075 (1997).
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[Crossref]

Zapata-Rodríguez, C. J.

Adv. Opt. Photon. (1)

Appl. Opt. (1)

Appl. Phys. A (1)

Y. Matsuoka, Y. Kizuka, and T. Inoue, “The characteristics of laser micro drilling using a Bessel beam,” Appl. Phys. A 84, 423-430 (2006).
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S. Longhi, K. Janner, and P. Laporta, “Propagating pulsed Bessel beams in periodic media,” J. Opt. B 6, 477-481 (2004).
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J. Opt. Soc. Am. A (8)

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D. G. Grier, “A revolution in optical manipulation,” Nature 424, 810-816 (2003).
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Opt. Commun. (2)

D. Mugnai, “Passage of a Bessel beam through a classically forbidden region,” Opt. Commun. 188, 17-24 (2001).
[Crossref]

D. Mugnai and P. Spalla, “Electromagnetic propagation of Bessel-like localized waves in the presence of absorbing media,” Opt. Commun. 282, 4668-4671 (2009).
[Crossref]

Opt. Express (1)

Opt. Lett. (4)

Phys. Rev. A (1)

M. S. Soskin, V. N. Gorshkov, M. V. Vasnetsov, J. T. Malos, and N. R. Heckenberg, “Topological charge and angular momentum of light beams carrying optical vortices,” Phys. Rev. A 56, 4064-4075 (1997).
[Crossref]

Phys. Rev. E (6)

R. Horák, J. Bajer, M. Bertolotti, and C. Sibilia, “Diffraction-free field in a planar nonlinear waveguide,” Phys. Rev. E 52, 4421-4429 (1995).
[Crossref]

M. Zamboni-Rached, K. Z. Nóbrega, E. Recami, and H. E. Hernández-Figueroa, “Superluminal X-shaped beams propagating without distortion along a coaxial guide,” Phys. Rev. E 66, 046617 (2002).
[Crossref]

M. A. Porras, G. Valiulis, and P. D. Trapani, “Unified description of Bessel X waves with cone dispersion and tilted pulses,” Phys. Rev. E 68, 016613 (2003).
[Crossref]

K. Reivelt and P. Saari, “Optically realizable localized wave solutions of the homogeneous scalar wave equation,” Phys. Rev. E 65, 046622 (2002).
[Crossref]

K. Reivelt and P. Saari, “Experimental demonstration of realizability of optical focus wave modes,” Phys. Rev. E 66, 056611 (2002).
[Crossref]

B. Hafizi, E. Esarey, and P. Sprangle, “Laser-driven acceleration with Bessel beams,” Phys. Rev. E 55, 3539-3545 (1997).
[Crossref]

Phys. Rev. Lett. (5)

T. Wulle and S. Herminghaus, “Nonlinear optics of Bessel beams,” Phys. Rev. Lett. 70, 1401-1404 (1993).
[Crossref] [PubMed]

M. A. Porras, A. Parola, D. Faccio, A. Dubietis, and P. D. Trapani, “Nonlinear unbalanced Bessel beams: Stationary conical waves supported by nonlinear losses,” Phys. Rev. Lett. 93, 153902 (2004).
[Crossref] [PubMed]

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D. Mugnai, A. Ranfagni, and R. Ruggeri, “Observation of superluminal behaviors in wave propagation,” Phys. Rev. Lett. 84, 4830-4833 (2000).
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Other (7)

J. J. Miret and C. J. Zapata-Rodríguez, “Surface-assisted ultralocalization in nondiffracting beams,” arXiv:1001.3204 [physics. optics](2010).

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Chapman and Hall, 1983).

M. Born and E. Wolf, Principles of Optics, 7th ed.(Cambridge Univ. Press, 1999).

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

J. A. Stratton, Electromagnetic Theory (McGraw-Hill, 1941).

G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Academic, 2001).

K. Reivelt and P. Saari, “Linear-optical generation of localized waves” in Localized Waves, H.E.Hernández-Figueroa, M.Zamboni-Rached, and E.Recami, eds.(Wiley, 2008), pp. 185-213.
[Crossref]

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Figures (7)

Fig. 1
Fig. 1

Normalized amplitude (upper row) and complex argument (lower row) of the wave function U n ( x , y ) for κ = 9.07 μ m 1 and indices (a), (b) n = 0 , (c), (d) n = 1 , and (e), (f) n = 2 .

Fig. 2
Fig. 2

(a) Schematic geometry of the planar-layer-based medium. In (b) we represent the wave fields in regions established by interfaces at y = ± L 2 . Perfect matching ε c = ε leads to wave fields U ± = F ± = R ± . .

Fig. 3
Fig. 3

Wave function U n + ( x , y ) associated with Bessel beams of Fig. 1. As before, normalized amplitude is represented in the upper row and complex argument is plotted in the lower row.

Fig. 4
Fig. 4

Transverse distribution of Bessel-excited wave field e x ( x , y ) inside a thin slab of width L = 100 μ m made of a material with relative dielectric constant δ = 10 2 . Again | e x | is plotted in the upper row and its complex argument is shown in the lower row.

Fig. 5
Fig. 5

Ray tracing representation of the Bessel-like beams shown in Fig. 4. Dual parallel axes at y = ± 0.25 μ m (and x = 0 ) set the confinement region of the nondiffracting beam. Spherical aberration drawing the envelope of the refracted rays gives rise to a bilateral-symmetric caustic.

Fig. 6
Fig. 6

Resultant field e x ( x , y ) for different Bessel indices n in the vicinities of a thin slab with L = 0.5 μ m and δ = 10 . Subfigures in the upper row account for amplitudes; associated complex arguments are depicted below.

Fig. 7
Fig. 7

Electric field e x ( x , y ) given in Eq. (14) for L = 0.5 μ m and δ = 1 . For a given Bessel index n the field amplitude is represented above and its complex argument below.

Equations (19)

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E ( x , y , z , t ) = e ( x , y ) exp ( i β z i ω t ) ,
H ( x , y , z , t ) = h ( x , y ) exp ( i β z i ω t ) ,
2 U x 2 + 2 U y 2 + ( k 2 β 2 ) U = 0 ,
ε c = ε ( 1 + δ )
J n ( ρ ) = i n 2 π π π exp ( i ρ cos φ + i n φ ) d φ .
U n = i n 2 π ( π 0 + 0 π ) exp [ i n α + i κ ( x cos α + y sin α ) ] d α .
U n ± ( x , y ) = 1 2 π κ κ U ̃ n ± ( k x ) exp ( ± i k y y ) exp ( i k x x ) d k x ,
U ̃ n ± ( k x ) = i n ( k x ± i k y ) n k y κ n ,
U n ( x , y ) = ( 1 ) n [ U n + ( x , y ) ] * ,
U n + ( x , y ) = 1 2 m = sinc [ ( m n ) 2 ] U m ( x , y ) ,
F n ± ( x , y ) = 1 2 π κ κ F ̃ n ± ( k x ) exp ( ± i k c , y y ) exp ( i k x x ) d k x .
R n ± ( x , y ) = 1 2 π κ κ R ̃ n ± ( k x ) exp ( ± i k y y ) exp ( i k x x ) d k x
[ R ̃ n ± F ̃ n ± ] = [ A B C D ] [ U ̃ n ± U ̃ n ] ,
A = 4 k c , y k y exp [ i ( k c , y k y ) L ] ( k c , y + k y ) 2 ( k c , y k y ) 2 exp ( 2 i k c , y L ) ,
B = 2 i ( k c , y 2 k y 2 ) sin ( k c , y L ) exp [ i ( k c , y k y ) L ] ( k c , y + k y ) 2 ( k c , y k y ) 2 exp ( 2 i k c , y L ) ,
C = 2 k y ( k c , y + k y ) exp [ i ( k c , y k y ) L 2 ] ( k c , y + k y ) 2 ( k c , y k y ) 2 exp ( 2 i k c , y L ) ,
D = 2 k y ( k c , y k y ) exp ( i k c , y L ) exp [ i ( k c , y k y ) L 2 ] ( k c , y + k y ) 2 ( k c , y k y ) 2 exp ( 2 i k c , y L ) .
e x ( x , y ) = { U n + ( x , y ) + R n ( x , y ) , if y < L 2 ; F n + ( x , y ) + F n ( x , y ) , if | y | < L 2 ; U n ( x , y ) + R n + ( x , y ) , if y > L 2 ; }
R n ± ( x , y ) = U n ( x , y ± L ) ,

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