Abstract

The focusing capabilities of an inward cylindrical traveling wave aperture distribution and the non-diffractive behaviour of its radiated field are analyzed. The wave dynamics of the infinite aperture radiated field is clearly unveiled by means of closed form expressions, based on incomplete Hankel functions, and their ray interpretation. The non-diffractive behaviour is also confirmed for finite apertures up to a defined limited range. A radial waveguide made by metallic gratings over a ground plane and fed by a coaxial feed is used to validate numerically the analytical results. The proposed system and accurate analysis of non-diffractive Bessel beams launched by inward waves opens new opportunities for planar, low profile beam generators at microwaves, Terahertz and optics.

© 2014 Optical Society of America

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References

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  1. J. Durnin, “Exact solutions for nondiffracting beams. I. The scalar theory,” J. Opt. Soc. Am. A 4, 651–654 (1987).
    [CrossRef]
  2. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499 (1987).
    [CrossRef] [PubMed]
  3. M. Lapointe, “Review of non-diffracting Bessel beam experiments,” Opt. Laser Technol. 24, 315–321 (1992).
    [CrossRef]
  4. J. Arlt and K. Dholakia, “Generation of high-order Bessel-beams by use of an axicon,” Opt. Commun. 177, 297–301 (2000).
    [CrossRef]
  5. R. M. Herman and T. A. Wiggins, “Production and uses of diffracionless beams,” J. Opt. Soc. Am. A 8, 932–942 (1991).
    [CrossRef]
  6. 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]
  7. W. B. Williams and J. B. Pendry, “Generating Bessel beams by use of localized modes,” J. Opt. Soc. Am. A 22, 992–997 (2005).
    [CrossRef]
  8. A. Mazzinghi, M. Balma, D. Devona, G. Guarnieri, G. Mauriello, M. Albani, and A. Freni, “Large depth of field pseudo-Bessel beam generation with a RLSA antenna,” IEEE Trans. Antennas Propag. (to be published).
  9. J. C. Gutiérrez-Vega, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Alternative formulation for invariant optical fields: Mathieu beams,” Opt. Lett. 25, 1493–1495 (2000).
    [CrossRef]
  10. J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, “Unified description of nondiffracting X and Y waves,” Phys. Rev. A 62, 4261 (2000).
  11. M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Near field diffraction of Hankel beams,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2006), paper JSuA36.
    [CrossRef]
  12. M. Ettorre and A. Grbic, “Generation of propagating Bessel beams using leaky-wave modes,” IEEE Trans. Antennas Propag. 60, 3605–3613 (2012).
    [CrossRef]
  13. M. Ettorre, S. M. Rudolph, and A. Grbic, “Generation of propagating Bessel beams using leaky-wave modes: experimental validation,” IEEE Trans. Antennas Propag. 60, 2645–2653 (2012).
    [CrossRef]
  14. M. F. Inami and A. Grbic, “Generating Bessel beams using an electrically-large annular slot,” in Proceedings of IEEE AP-S/URSI-USNC Symposium (IEEE2013).
  15. S. Chávez-Cerda, “A new approach to Bessel beams,” J. Mod. Opt. 46, 923–930 (1999).
  16. S. Chávez-Cerda and G. H. C. New, “Evaluation of focused Hankel waves and Bessel beams,” Opt. Commun. 181, 369–377 (2000).
    [CrossRef]
  17. J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Fornel, and F. Capasso, “Cosine-Gauss plasmon beam: a localized long-range nondiffracting surface wave,” Phys. Rev. Lett. 109, 093904 (2012).
    [CrossRef] [PubMed]
  18. L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves, Series on Electromagnetic Wave Theory (IEEE Press, 1994).
    [CrossRef]
  19. R. Cicchetti and A. Faraone, “Incomplete Hankel and modified Bessel functions: a class of special functions for electromagnetics,” IEEE Trans. Antennas Propag. 52, 3373–3389 (2004).
    [CrossRef]
  20. M. Albani, A. Mazzinghi, and A. Freni, “Automatic design of CP-RLSA antennas,” IEEE Trans. Antennas Propag. 60, 5538–5547 (2012).
    [CrossRef]
  21. M. Ettorre, M. Casaletti, G. Valerio, R. Sauleau, L. Le Coq, S. C. Pavone, and M. Albani, “On the near-field shaping and focusing capability of a radial line slot array,” IEEE Trans. Antennas Propag. 62, 1991–1999 (2014).
    [CrossRef]

2014 (1)

M. Ettorre, M. Casaletti, G. Valerio, R. Sauleau, L. Le Coq, S. C. Pavone, and M. Albani, “On the near-field shaping and focusing capability of a radial line slot array,” IEEE Trans. Antennas Propag. 62, 1991–1999 (2014).
[CrossRef]

2012 (4)

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Fornel, and F. Capasso, “Cosine-Gauss plasmon beam: a localized long-range nondiffracting surface wave,” Phys. Rev. Lett. 109, 093904 (2012).
[CrossRef] [PubMed]

M. Albani, A. Mazzinghi, and A. Freni, “Automatic design of CP-RLSA antennas,” IEEE Trans. Antennas Propag. 60, 5538–5547 (2012).
[CrossRef]

M. Ettorre and A. Grbic, “Generation of propagating Bessel beams using leaky-wave modes,” IEEE Trans. Antennas Propag. 60, 3605–3613 (2012).
[CrossRef]

M. Ettorre, S. M. Rudolph, and A. Grbic, “Generation of propagating Bessel beams using leaky-wave modes: experimental validation,” IEEE Trans. Antennas Propag. 60, 2645–2653 (2012).
[CrossRef]

2009 (1)

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]

2005 (1)

2004 (1)

R. Cicchetti and A. Faraone, “Incomplete Hankel and modified Bessel functions: a class of special functions for electromagnetics,” IEEE Trans. Antennas Propag. 52, 3373–3389 (2004).
[CrossRef]

2000 (4)

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

J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, “Unified description of nondiffracting X and Y waves,” Phys. Rev. A 62, 4261 (2000).

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

S. Chávez-Cerda and G. H. C. New, “Evaluation of focused Hankel waves and Bessel beams,” Opt. Commun. 181, 369–377 (2000).
[CrossRef]

1999 (1)

S. Chávez-Cerda, “A new approach to Bessel beams,” J. Mod. Opt. 46, 923–930 (1999).

1992 (1)

M. Lapointe, “Review of non-diffracting Bessel beam experiments,” Opt. Laser Technol. 24, 315–321 (1992).
[CrossRef]

1991 (1)

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 (1987).
[CrossRef] [PubMed]

Albani, M.

M. Ettorre, M. Casaletti, G. Valerio, R. Sauleau, L. Le Coq, S. C. Pavone, and M. Albani, “On the near-field shaping and focusing capability of a radial line slot array,” IEEE Trans. Antennas Propag. 62, 1991–1999 (2014).
[CrossRef]

M. Albani, A. Mazzinghi, and A. Freni, “Automatic design of CP-RLSA antennas,” IEEE Trans. Antennas Propag. 60, 5538–5547 (2012).
[CrossRef]

A. Mazzinghi, M. Balma, D. Devona, G. Guarnieri, G. Mauriello, M. Albani, and A. Freni, “Large depth of field pseudo-Bessel beam generation with a RLSA antenna,” IEEE Trans. Antennas Propag. (to be published).

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]

Anguiano-Morales, M.

M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Near field diffraction of Hankel beams,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2006), paper JSuA36.
[CrossRef]

Arlt, J.

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

Balma, M.

A. Mazzinghi, M. Balma, D. Devona, G. Guarnieri, G. Mauriello, M. Albani, and A. Freni, “Large depth of field pseudo-Bessel beam generation with a RLSA antenna,” IEEE Trans. Antennas Propag. (to be published).

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]

Capasso, F.

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Fornel, and F. Capasso, “Cosine-Gauss plasmon beam: a localized long-range nondiffracting surface wave,” Phys. Rev. Lett. 109, 093904 (2012).
[CrossRef] [PubMed]

Casaletti, M.

M. Ettorre, M. Casaletti, G. Valerio, R. Sauleau, L. Le Coq, S. C. Pavone, and M. Albani, “On the near-field shaping and focusing capability of a radial line slot array,” IEEE Trans. Antennas Propag. 62, 1991–1999 (2014).
[CrossRef]

Chávez-Cerda, S.

S. Chávez-Cerda and G. H. C. New, “Evaluation of focused Hankel waves and Bessel beams,” Opt. Commun. 181, 369–377 (2000).
[CrossRef]

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

S. Chávez-Cerda, “A new approach to Bessel beams,” J. Mod. Opt. 46, 923–930 (1999).

M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Near field diffraction of Hankel beams,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2006), paper JSuA36.
[CrossRef]

Cicchetti, R.

R. Cicchetti and A. Faraone, “Incomplete Hankel and modified Bessel functions: a class of special functions for electromagnetics,” IEEE Trans. Antennas Propag. 52, 3373–3389 (2004).
[CrossRef]

Cluzel, B.

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Fornel, and F. Capasso, “Cosine-Gauss plasmon beam: a localized long-range nondiffracting surface wave,” Phys. Rev. Lett. 109, 093904 (2012).
[CrossRef] [PubMed]

de Fornel, F.

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Fornel, and F. Capasso, “Cosine-Gauss plasmon beam: a localized long-range nondiffracting surface wave,” Phys. Rev. Lett. 109, 093904 (2012).
[CrossRef] [PubMed]

Dellinger, J.

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Fornel, and F. Capasso, “Cosine-Gauss plasmon beam: a localized long-range nondiffracting surface wave,” Phys. Rev. Lett. 109, 093904 (2012).
[CrossRef] [PubMed]

Devona, D.

A. Mazzinghi, M. Balma, D. Devona, G. Guarnieri, G. Mauriello, M. Albani, and A. Freni, “Large depth of field pseudo-Bessel beam generation with a RLSA antenna,” IEEE Trans. Antennas Propag. (to be published).

Dholakia, K.

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

Durnin, J.

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 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

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

Ettorre, M.

M. Ettorre, M. Casaletti, G. Valerio, R. Sauleau, L. Le Coq, S. C. Pavone, and M. Albani, “On the near-field shaping and focusing capability of a radial line slot array,” IEEE Trans. Antennas Propag. 62, 1991–1999 (2014).
[CrossRef]

M. Ettorre, S. M. Rudolph, and A. Grbic, “Generation of propagating Bessel beams using leaky-wave modes: experimental validation,” IEEE Trans. Antennas Propag. 60, 2645–2653 (2012).
[CrossRef]

M. Ettorre and A. Grbic, “Generation of propagating Bessel beams using leaky-wave modes,” IEEE Trans. Antennas Propag. 60, 3605–3613 (2012).
[CrossRef]

Fagerholm, J.

J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, “Unified description of nondiffracting X and Y waves,” Phys. Rev. A 62, 4261 (2000).

Faraone, A.

R. Cicchetti and A. Faraone, “Incomplete Hankel and modified Bessel functions: a class of special functions for electromagnetics,” IEEE Trans. Antennas Propag. 52, 3373–3389 (2004).
[CrossRef]

Felsen, L. B.

L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves, Series on Electromagnetic Wave Theory (IEEE Press, 1994).
[CrossRef]

Freni, A.

M. Albani, A. Mazzinghi, and A. Freni, “Automatic design of CP-RLSA antennas,” IEEE Trans. Antennas Propag. 60, 5538–5547 (2012).
[CrossRef]

A. Mazzinghi, M. Balma, D. Devona, G. Guarnieri, G. Mauriello, M. Albani, and A. Freni, “Large depth of field pseudo-Bessel beam generation with a RLSA antenna,” IEEE Trans. Antennas Propag. (to be published).

Friberg, A. T.

J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, “Unified description of nondiffracting X and Y waves,” Phys. Rev. A 62, 4261 (2000).

Genevet, P.

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Fornel, and F. Capasso, “Cosine-Gauss plasmon beam: a localized long-range nondiffracting surface wave,” Phys. Rev. Lett. 109, 093904 (2012).
[CrossRef] [PubMed]

Grbic, A.

M. Ettorre, S. M. Rudolph, and A. Grbic, “Generation of propagating Bessel beams using leaky-wave modes: experimental validation,” IEEE Trans. Antennas Propag. 60, 2645–2653 (2012).
[CrossRef]

M. Ettorre and A. Grbic, “Generation of propagating Bessel beams using leaky-wave modes,” IEEE Trans. Antennas Propag. 60, 3605–3613 (2012).
[CrossRef]

M. F. Inami and A. Grbic, “Generating Bessel beams using an electrically-large annular slot,” in Proceedings of IEEE AP-S/URSI-USNC Symposium (IEEE2013).

Guarnieri, G.

A. Mazzinghi, M. Balma, D. Devona, G. Guarnieri, G. Mauriello, M. Albani, and A. Freni, “Large depth of field pseudo-Bessel beam generation with a RLSA antenna,” IEEE Trans. Antennas Propag. (to be published).

Gutiérrez-Vega, J. C.

Herman, R. M.

Inami, M. F.

M. F. Inami and A. Grbic, “Generating Bessel beams using an electrically-large annular slot,” in Proceedings of IEEE AP-S/URSI-USNC Symposium (IEEE2013).

Iturbe-Castillo, M. D.

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

M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Near field diffraction of Hankel beams,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2006), paper JSuA36.
[CrossRef]

Lapointe, M.

M. Lapointe, “Review of non-diffracting Bessel beam experiments,” Opt. Laser Technol. 24, 315–321 (1992).
[CrossRef]

Le Coq, L.

M. Ettorre, M. Casaletti, G. Valerio, R. Sauleau, L. Le Coq, S. C. Pavone, and M. Albani, “On the near-field shaping and focusing capability of a radial line slot array,” IEEE Trans. Antennas Propag. 62, 1991–1999 (2014).
[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]

Lin, J.

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Fornel, and F. Capasso, “Cosine-Gauss plasmon beam: a localized long-range nondiffracting surface wave,” Phys. Rev. Lett. 109, 093904 (2012).
[CrossRef] [PubMed]

Marcuvitz, N.

L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves, Series on Electromagnetic Wave Theory (IEEE Press, 1994).
[CrossRef]

Mauriello, G.

A. Mazzinghi, M. Balma, D. Devona, G. Guarnieri, G. Mauriello, M. Albani, and A. Freni, “Large depth of field pseudo-Bessel beam generation with a RLSA antenna,” IEEE Trans. Antennas Propag. (to be published).

Mazzinghi, A.

M. Albani, A. Mazzinghi, and A. Freni, “Automatic design of CP-RLSA antennas,” IEEE Trans. Antennas Propag. 60, 5538–5547 (2012).
[CrossRef]

A. Mazzinghi, M. Balma, D. Devona, G. Guarnieri, G. Mauriello, M. Albani, and A. Freni, “Large depth of field pseudo-Bessel beam generation with a RLSA antenna,” IEEE Trans. Antennas Propag. (to be published).

Méndez-Otero, M. M.

M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Near field diffraction of Hankel beams,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2006), paper JSuA36.
[CrossRef]

Miceli, J. J.

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

New, G. H. C.

S. Chávez-Cerda and G. H. C. New, “Evaluation of focused Hankel waves and Bessel beams,” Opt. Commun. 181, 369–377 (2000).
[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]

Pavone, S. C.

M. Ettorre, M. Casaletti, G. Valerio, R. Sauleau, L. Le Coq, S. C. Pavone, and M. Albani, “On the near-field shaping and focusing capability of a radial line slot array,” IEEE Trans. Antennas Propag. 62, 1991–1999 (2014).
[CrossRef]

Pendry, J. B.

Rudolph, S. M.

M. Ettorre, S. M. Rudolph, and A. Grbic, “Generation of propagating Bessel beams using leaky-wave modes: experimental validation,” IEEE Trans. Antennas Propag. 60, 2645–2653 (2012).
[CrossRef]

Salo, J.

J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, “Unified description of nondiffracting X and Y waves,” Phys. Rev. A 62, 4261 (2000).

Salomaa, M. M.

J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, “Unified description of nondiffracting X and Y waves,” Phys. Rev. A 62, 4261 (2000).

Sauleau, R.

M. Ettorre, M. Casaletti, G. Valerio, R. Sauleau, L. Le Coq, S. C. Pavone, and M. Albani, “On the near-field shaping and focusing capability of a radial line slot array,” IEEE Trans. Antennas Propag. 62, 1991–1999 (2014).
[CrossRef]

Valerio, G.

M. Ettorre, M. Casaletti, G. Valerio, R. Sauleau, L. Le Coq, S. C. Pavone, and M. Albani, “On the near-field shaping and focusing capability of a radial line slot array,” IEEE Trans. Antennas Propag. 62, 1991–1999 (2014).
[CrossRef]

Wiggins, T. A.

Williams, W. B.

IEEE Trans. Antennas Propag. (5)

M. Ettorre and A. Grbic, “Generation of propagating Bessel beams using leaky-wave modes,” IEEE Trans. Antennas Propag. 60, 3605–3613 (2012).
[CrossRef]

M. Ettorre, S. M. Rudolph, and A. Grbic, “Generation of propagating Bessel beams using leaky-wave modes: experimental validation,” IEEE Trans. Antennas Propag. 60, 2645–2653 (2012).
[CrossRef]

R. Cicchetti and A. Faraone, “Incomplete Hankel and modified Bessel functions: a class of special functions for electromagnetics,” IEEE Trans. Antennas Propag. 52, 3373–3389 (2004).
[CrossRef]

M. Albani, A. Mazzinghi, and A. Freni, “Automatic design of CP-RLSA antennas,” IEEE Trans. Antennas Propag. 60, 5538–5547 (2012).
[CrossRef]

M. Ettorre, M. Casaletti, G. Valerio, R. Sauleau, L. Le Coq, S. C. Pavone, and M. Albani, “On the near-field shaping and focusing capability of a radial line slot array,” IEEE Trans. Antennas Propag. 62, 1991–1999 (2014).
[CrossRef]

J. Mod. Opt. (1)

S. Chávez-Cerda, “A new approach to Bessel beams,” J. Mod. Opt. 46, 923–930 (1999).

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

Opt. Commun. (2)

S. Chávez-Cerda and G. H. C. New, “Evaluation of focused Hankel waves and Bessel beams,” Opt. Commun. 181, 369–377 (2000).
[CrossRef]

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

Opt. Laser Technol. (1)

M. Lapointe, “Review of non-diffracting Bessel beam experiments,” Opt. Laser Technol. 24, 315–321 (1992).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (1)

J. Salo, J. Fagerholm, A. T. Friberg, and M. M. Salomaa, “Unified description of nondiffracting X and Y waves,” Phys. Rev. A 62, 4261 (2000).

Phys. Rev. Lett. (3)

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

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]

J. Lin, J. Dellinger, P. Genevet, B. Cluzel, F. de Fornel, and F. Capasso, “Cosine-Gauss plasmon beam: a localized long-range nondiffracting surface wave,” Phys. Rev. Lett. 109, 093904 (2012).
[CrossRef] [PubMed]

Other (4)

L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves, Series on Electromagnetic Wave Theory (IEEE Press, 1994).
[CrossRef]

A. Mazzinghi, M. Balma, D. Devona, G. Guarnieri, G. Mauriello, M. Albani, and A. Freni, “Large depth of field pseudo-Bessel beam generation with a RLSA antenna,” IEEE Trans. Antennas Propag. (to be published).

M. Anguiano-Morales, M. M. Méndez-Otero, M. D. Iturbe-Castillo, and S. Chávez-Cerda, “Near field diffraction of Hankel beams,” in Frontiers in Optics, OSA Technical Digest (CD) (Optical Society of America, 2006), paper JSuA36.
[CrossRef]

M. F. Inami and A. Grbic, “Generating Bessel beams using an electrically-large annular slot,” in Proceedings of IEEE AP-S/URSI-USNC Symposium (IEEE2013).

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Figures (8)

Fig. 1
Fig. 1

Schematic view of the considered configuration. The aperture field distribution is a cylindrical inward wave with radial propagation constant kρa. The non-diffractive zone is limited by the cone with angle θa = sin−1(kρa/k), where k is the free space wavenumber.

Fig. 2
Fig. 2

Ray interpretation of the GO field for an infinite aperture. (a) Inward Hankel aperture distribution: the GO field comprises an inward Hankel beam ray (in red), present throughout the space, and an outward Hankel beam ray (in green) bounded inside the cone θ < θa; the superposition of the two rays inside the cone (yellow area) creates a Bessel beam. (b) Outward Hankel aperture distribution: the GO field comprises only an outward Hankel beam ray (in green) bounded outside the cone θ < θa.

Fig. 3
Fig. 3

Electric field radiated by an infinite aperture. |Ez| (1st column), |Eρ| (2nd column) and total electric field amplitude |E| (3rd column). Standard Bessel beam reference field (1st row), field radiated by an inward Hankel distribution (2nd row), and field radiated by an outward Hankel distribution (3rd row). The axes are normalized with respect to the wavelength (λ) at the operating frequency f. The dashed line marks the GO boundary θ = θa.

Fig. 4
Fig. 4

Electric field radiated by an finite aperture with radius of a = 7λ. |Ez| (1st column), |Eρ| (2nd column) and total electric field amplitude |E| (3rd column). Standard Bessel beam reference field (1st row), and field radiated by an inward Hankel distribution (2nd row). The axes are normalized with respect to the wavelength (λ) at the operating frequency f. The dashed line marks the GO boundaries.

Fig. 5
Fig. 5

Ray interpretation of the GO field for an finite aperture. The dashed lines indicated the GO boundaries. The GO contribution is limited in a triangular region with a side corresponding to the finite aperture. The GO field comprises an inward Hankel beam ray (in red), present throughout this triangular region, and an outward Hankel beam ray (in green) bounded inside the cone θ < θa; the superposition of the two rays creates a Bessel beam inside a zone with rhomboidal cross section (yellow area).

Fig. 6
Fig. 6

Radial waveguide loaded with metallic gratings and fed by a coaxial fed.

Fig. 7
Fig. 7

Electric field radiated by the launcher prototype in Fig. 6, calculated using COMSOL Multiphysics. From left to right, |Ez|, |Eρ| and |E|. The axes are normalized with respect to the wavelength (λ) at the operating frequency f = 10 GHz. The dashed line marks the GO boundaries and the dotted line refers to the field scan shown in Fig. 8.

Fig. 8
Fig. 8

Normalized |Ez| component of the electric field at z = 4.667λ for the structure in Fig. 6 simulated with COMSOL Multiphysics. The field radiated by a truncated inward Hankel distribution is shown for comparison.

Tables (1)

Tables Icon

Table 1 Geometrical sizes of the Bessel beam launcher: radial positions (ρi) and widths (wi) of the annular slots. The PPW is filled with a dielectric with permittivity 2.2 and thickness h1 = 3.175 mm.

Equations (24)

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E ( ρ , z ) = 1 4 π e j π + [ k ρ k z H 0 ( 2 ) ( k ρ ρ ) z ^ + j H 1 ( 2 ) ( k ρ ρ ) ρ ^ ] E ˜ t ( k ρ ) e j k z z k ρ d k ρ ,
E ˜ t ( k ρ ) = 2 π j 0 + E t ( ρ , z = 0 ) J 1 ( k ρ ρ ) ρ d ρ ,
E ˜ t ( k ρ ) = 4 k ρ k ρ a ( k ρ 2 k ρ a 2 ) .
E ( r ) = E G O ( r ) + E S W ( r ) ,
E G O ( r ) = 2 [ k ρ a j k z a J 0 ( k ρ a ρ ) z ^ + J 1 ( k ρ a ρ ) ρ ^ ] e j k z a z U ( θ a θ ) + [ k ρ a j k z a H 0 ( 1 ) ( k ρ a ρ ) z ^ + H 1 ( 1 ) ( k ρ a ρ ) ρ ^ ] e j k z a z U ( θ θ a ) ,
E S W ( r ) = k ρ a j k z a [ sgn ( w 0 ) H 0 ( 2 ) ( k ρ a ρ , | w 0 | ) e j k z a z H 0 ( 2 ) ( k ρ a ρ , w 0 + ) e j k z a z ] z ^ [ sgn ( w 0 ) H 1 ( 2 ) ( k ρ a ρ , | w 0 | ) e j k z a z + H 1 ( 2 ) ( k ρ a ρ , w 0 + ) e j k z a z ] ρ ^ 2 j π k ρ a ( z ^ + cot θ ρ ^ ) e j k r r ~ 2 sin θ j π k ρ a ( cos 2 θ cos 2 θ a ) e j k r r θ ^ .
E G O ( r ) = [ k ρ a j k z a H 0 ( 2 ) ( k ρ a ρ ) z ^ + H 1 ( 2 ) ( k ρ a ρ ) ρ ^ ] e j k z a z U ( θ θ a ) ,
E ˜ t ( k ρ ) = 4 k ρ 2 k ρ a 2 [ k ρ k ρ a + π a 2 j ( k ρ H 1 ( 1 ) ( k ρ a a ) J 0 ( k ρ a ) k ρ a H 0 ( 1 ) ( k ρ a a ) J 1 ( k ρ a ) ) ] .
E ( r ) = [ ( k 2 + 2 z 2 ) z ^ + 2 ρ z ρ ^ ] S ( r )
S ( r ) = 1 4 π e j π + E ˜ t ( k ρ ) H 0 ( 2 ) ( k ρ ρ ) e j k z z k z d k ρ .
1 k ρ 2 k ρ a 2 = 1 2 j k z a ( 0 e j ( k z k z a ) ζ d ζ 0 e j ( k z + k z a ) ζ d ζ ) ,
1 2 π 1 4 j k ρ k z H 0 ( 2 ) ( k ρ ρ ) e j k z z d k ρ = e j k ρ 2 + z 2 4 π ρ 2 + z 2 ,
S ( r ) = 4 k ρ a k z a ( 0 e j k z a ζ e j k ρ 2 + ( z ζ ) 2 4 π ρ 2 + ( z ζ ) 2 d ζ 0 e j k z a ζ e j k ρ 2 + ( z ζ ) 2 4 π ρ 2 + ( z ζ ) 2 d ζ ) .
w = sinh 1 ( z ζ ρ ) tanh 1 ( k z a k )
S ( r ) = 1 j π k ρ a k z a [ H 0 ( 2 ) ( k ρ a ρ , w 0 ) e j k z a z H 0 ( 2 ) ( k ρ a ρ , w 0 + ) e j k z a z ] ,
H 0 ( 2 ) ( Ω , w 0 ) = j π w 0 + e j Ω cosh w d w ,
w 0 ± = tanh 1 cos θ ± tanh 1 cos θ a ,
S ( r ) = 1 j π k ρ a k z a [ 2 J 0 ( k ρ a ρ , w 0 ) e j k z a z H 0 ( 2 ) ( k ρ a ρ , w 0 ) e j k z a z + H 0 ( 2 ) ( k ρ a ρ , w 0 + ) e j k z a z ] .
H 0 ( 2 ) ( Ω , w 0 ) = H 0 ( 2 ) ( Ω ) U ( w 0 ) + sgn ( w 0 ) H 0 ( 2 ) ( Ω , | w 0 | ) , w 0 R
S ( r ) = S GO ( r ) + S SW ( r ) ,
S GO ( r ) = 1 j k ρ a k z a [ 2 J 0 ( k ρ a ρ ) U ( θ a θ ) + H 0 ( 1 ) ( k ρ a ρ ) U ( θ θ a ) ] e j k z a z ,
S SW ( r ) = 1 j k ρ a k z a [ sgn ( w 0 ) H 0 ( 2 ) ( k ρ a ρ , | w 0 | ) e j k z a z H 0 ( 2 ) ( k ρ a ρ , w 0 + ) e j k z a z ] .
H 0 ( 2 ) ( Ω , w 0 ) ~ e j Ω cosh w 0 π Ω sinh w 0 , ( Ω , w 0 > 0 )
S SW ( r ) ~ 2 j π k 3 sin θ a ( cos 2 θ cos 2 θ a ) e j k r r , ( k ρ a ρ , θ θ a ) .

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