Abstract

Diffraction patterns formed by axicons with different tip (vertex) angles are analytically and numerically investigated. Results show that the axicon (or tapered dielectric probe) can form an extended axial light beam, a compact evanescent field, a hollow beam, and a collimated beam, depending on the vertex angle. Two-dimensional and three-dimensional models of a tapered dielectric probe show that, with small changes to the vertex angle, light transmitted by the probe is scattered rather than focused, and vice versa. Angle meanings corresponded to boundary transitions have a quantum character and densify as the angle approaches zero. These features should be taken into consideration when manufacturing microaxicons intended for various applications.

© 2017 Optical Society of America

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References

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  32. S. N. Khonina and D. A. Savelyev, “High-aperture binary axicons for the formation of the longitudinal electric field component on the optical axis for linear and circular polarizations of the illuminating beam,” J. Exp. Theor. Phys. 117(4), 623–630 (2013).
    [Crossref]
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    [Crossref]

2015 (1)

A. V. Ustinov, S. A. Degtyarev, and S. N. Khonina, “Diffraction by a conical axicon considering multiple internal reflections,” Comput. Opt. 39(4), 500–507 (2015).
[Crossref]

2014 (3)

2013 (2)

S. N. Khonina and D. A. Savelyev, “High-aperture binary axicons for the formation of the longitudinal electric field component on the optical axis for linear and circular polarizations of the illuminating beam,” J. Exp. Theor. Phys. 117(4), 623–630 (2013).
[Crossref]

A. A. Kuchmizhak, Y. N. Kulchin, O. B. Vitrik, A. G. Savchuk, S. V. Makarov, S. I. Kudryashov, and A. A. Ionin, “Optical apertureless fiber micro-probe for surface laser modification of metal films with sub-100 nm resolution,” Opt. Commun. 308, 125–129 (2013).
[Crossref]

2012 (5)

H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, “Nanofocusing in a metal–insulator–metal gap plasmon waveguide with a three-dimensional linear taper,” Nat. Photonics 6(12), 838–844 (2012).
[Crossref]

S. Berweger, J. M. Atkin, R. L. Olmon, and M. B. Raschke, “Light on the tip of a needle: plasmonic nanofocusing for spectroscopy on the nanoscale,” J. Phys. Chem. Lett. 3(7), 945–952 (2012).
[Crossref] [PubMed]

A. V. Ustinov and S. N. Khonina, “Calculating the complex transmission function of refractive axicons,” Opt. Mem. Neural. Networks 21(3), 133–144 (2012).
[Crossref]

B. Zhu, J. Stiens, V. Matvejev, and R. Vounckx, “Inexpensive and easy fabrication of multi-mode tapered dielectric circular probes at millimeter wave frequencies,” Prog. Electromagnetics Res. 126, 237–254 (2012).
[Crossref]

A. V. Ustinov and S. N. Khonina, “Calculating the complex transmission function of refractive axicons,” Opt. Mem. Neural. Networks 21(3), 133–144 (2012).
[Crossref]

2010 (1)

I. Alexeev, K.-H. Leitz, A. Otto, and M. Schmidt, “Application of Bessel beams for ultrafast laser volume structuring of non transparent media,” Phys. Procedia 5, 533–540 (2010).
[Crossref]

2009 (2)

2008 (2)

S. K. Mohanty, K. S. Mohanty, and M. W. Berns, “Organization of microscale objects using a microfabricated optical fiber,” Opt. Lett. 33(18), 2155–2157 (2008).
[Crossref] [PubMed]

T. Grosjean, A. Fahys, M. Suarez, D. Charraut, R. Salut, and D. Courjon, “Annular nanoantenna on fibre micro-axicon,” J. Microsc. 229(2), 354–364 (2008).
[Crossref] [PubMed]

2007 (3)

2006 (2)

B. P. S. Ahluwalia, X.-C. Yuan, S. H. Tao, W. C. Cheong, L. S. Zhang, and H. Wang, “Micromanipulation of high and low indices microparticles using a microfabricated double axicon,” J. Appl. Phys. 99(11), 113104 (2006).
[Crossref]

Y. J. Yu, H. Noh, M. H. Hong, H. R. Noh, Y. Arakawa, and W. Jhe, “Focusing characteristics of optical fiber axicon microlens for near-field spectroscopy: dependence of tip apex angle,” Opt. Commun. 267(1), 264–270 (2006).
[Crossref]

2005 (2)

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005).
[Crossref]

Z. Jaroszewicz, A. Burvall, and A. T. Friberg, “Axicon – the Most Important Optical Element,” Opt. Photonics News 16(4), 34–39 (2005).
[Crossref]

2004 (1)

A. De and G. V. Attimarad, “Numerical analysis of two dimensional tapered dielectric waveguide,” Prog. Electromagnetics Res. 44, 131–142 (2004).
[Crossref]

2001 (1)

R. Müller and C. Lienau, “Three-dimensional analysis of light propagation through uncoated near-field fibre probes,” J. Microsc. 202(2), 339–346 (2001).
[Crossref] [PubMed]

2000 (1)

A. J. Babadjanyan, N. L. Margaryan, and K. V. Nerkararyan, “Superfocusing of surface polaritons in the conical structure,” J. Appl. Phys. 87(8), 3785–3788 (2000).
[Crossref]

1999 (2)

R. M. Stöckle, N. Schaller, V. Deckert, C. Fokas, and R. Zenobi, “Brighter near-field optical probes by means of improving the optical destruction threshold,” J. Microsc. 194(2), 378–382 (1999).
[Crossref] [PubMed]

R. Stöckle, C. Fokas, V. Deckert, R. Zenobi, B. Sick, B. Hecht, and U. P. Wild, “High-quality near-field optical probes by tube etching,” Appl. Phys. Lett. 75(2), 160–162 (1999).
[Crossref]

1998 (1)

1991 (1)

W. Denk and D. W. Pohl, “Near-field optics: microscopy with nanometer-size fields,” J. Vac. Sci. Technol. B 9(2), 510–513 (1991).
[Crossref]

1987 (1)

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

1954 (1)

Ahluwalia, B. P. S.

B. P. S. Ahluwalia, X.-C. Yuan, S. H. Tao, W. C. Cheong, L. S. Zhang, and H. Wang, “Micromanipulation of high and low indices microparticles using a microfabricated double axicon,” J. Appl. Phys. 99(11), 113104 (2006).
[Crossref]

Alexeev, I.

I. Alexeev, K.-H. Leitz, A. Otto, and M. Schmidt, “Application of Bessel beams for ultrafast laser volume structuring of non transparent media,” Phys. Procedia 5, 533–540 (2010).
[Crossref]

Alferov, S. V.

Antosiewicz, T. J.

Arakawa, Y.

Y. J. Yu, H. Noh, M. H. Hong, H. R. Noh, Y. Arakawa, and W. Jhe, “Focusing characteristics of optical fiber axicon microlens for near-field spectroscopy: dependence of tip apex angle,” Opt. Commun. 267(1), 264–270 (2006).
[Crossref]

Atkin, J. M.

S. Berweger, J. M. Atkin, R. L. Olmon, and M. B. Raschke, “Light on the tip of a needle: plasmonic nanofocusing for spectroscopy on the nanoscale,” J. Phys. Chem. Lett. 3(7), 945–952 (2012).
[Crossref] [PubMed]

Attimarad, G. V.

A. De and G. V. Attimarad, “Numerical analysis of two dimensional tapered dielectric waveguide,” Prog. Electromagnetics Res. 44, 131–142 (2004).
[Crossref]

Babadjanyan, A. J.

A. J. Babadjanyan, N. L. Margaryan, and K. V. Nerkararyan, “Superfocusing of surface polaritons in the conical structure,” J. Appl. Phys. 87(8), 3785–3788 (2000).
[Crossref]

Berns, M. W.

Berweger, S.

S. Berweger, J. M. Atkin, R. L. Olmon, and M. B. Raschke, “Light on the tip of a needle: plasmonic nanofocusing for spectroscopy on the nanoscale,” J. Phys. Chem. Lett. 3(7), 945–952 (2012).
[Crossref] [PubMed]

Bokor, J.

H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, “Nanofocusing in a metal–insulator–metal gap plasmon waveguide with a three-dimensional linear taper,” Nat. Photonics 6(12), 838–844 (2012).
[Crossref]

Burvall, A.

Z. Jaroszewicz, A. Burvall, and A. T. Friberg, “Axicon – the Most Important Optical Element,” Opt. Photonics News 16(4), 34–39 (2005).
[Crossref]

Cabrini, S.

H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, “Nanofocusing in a metal–insulator–metal gap plasmon waveguide with a three-dimensional linear taper,” Nat. Photonics 6(12), 838–844 (2012).
[Crossref]

Chang, H. C.

A. V. Goncharenko, H. C. Chang, and J. K. Wang, “Electric near-field enhancing properties of a finite-size metal conical nano-tip,” Ultramicroscopy 107(2-3), 151–157 (2007).
[Crossref] [PubMed]

Charraut, D.

Cheong, W. C.

B. P. S. Ahluwalia, X.-C. Yuan, S. H. Tao, W. C. Cheong, L. S. Zhang, and H. Wang, “Micromanipulation of high and low indices microparticles using a microfabricated double axicon,” J. Appl. Phys. 99(11), 113104 (2006).
[Crossref]

Choo, H.

H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, “Nanofocusing in a metal–insulator–metal gap plasmon waveguide with a three-dimensional linear taper,” Nat. Photonics 6(12), 838–844 (2012).
[Crossref]

Courjon, D.

T. Grosjean, A. Fahys, M. Suarez, D. Charraut, R. Salut, and D. Courjon, “Annular nanoantenna on fibre micro-axicon,” J. Microsc. 229(2), 354–364 (2008).
[Crossref] [PubMed]

De, A.

A. De and G. V. Attimarad, “Numerical analysis of two dimensional tapered dielectric waveguide,” Prog. Electromagnetics Res. 44, 131–142 (2004).
[Crossref]

Deckert, V.

R. M. Stöckle, N. Schaller, V. Deckert, C. Fokas, and R. Zenobi, “Brighter near-field optical probes by means of improving the optical destruction threshold,” J. Microsc. 194(2), 378–382 (1999).
[Crossref] [PubMed]

R. Stöckle, C. Fokas, V. Deckert, R. Zenobi, B. Sick, B. Hecht, and U. P. Wild, “High-quality near-field optical probes by tube etching,” Appl. Phys. Lett. 75(2), 160–162 (1999).
[Crossref]

Degtyarev, S. A.

A. V. Ustinov, S. A. Degtyarev, and S. N. Khonina, “Diffraction by a conical axicon considering multiple internal reflections,” Comput. Opt. 39(4), 500–507 (2015).
[Crossref]

Denk, W.

W. Denk and D. W. Pohl, “Near-field optics: microscopy with nanometer-size fields,” J. Vac. Sci. Technol. B 9(2), 510–513 (1991).
[Crossref]

Dholakia, K.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005).
[Crossref]

Durnin, J.

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Eberly, J. H.

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Fahys, A.

T. Grosjean, A. Fahys, M. Suarez, D. Charraut, R. Salut, and D. Courjon, “Annular nanoantenna on fibre micro-axicon,” J. Microsc. 229(2), 354–364 (2008).
[Crossref] [PubMed]

Fokas, C.

R. Stöckle, C. Fokas, V. Deckert, R. Zenobi, B. Sick, B. Hecht, and U. P. Wild, “High-quality near-field optical probes by tube etching,” Appl. Phys. Lett. 75(2), 160–162 (1999).
[Crossref]

R. M. Stöckle, N. Schaller, V. Deckert, C. Fokas, and R. Zenobi, “Brighter near-field optical probes by means of improving the optical destruction threshold,” J. Microsc. 194(2), 378–382 (1999).
[Crossref] [PubMed]

Friberg, A. T.

Z. Jaroszewicz, A. Burvall, and A. T. Friberg, “Axicon – the Most Important Optical Element,” Opt. Photonics News 16(4), 34–39 (2005).
[Crossref]

Golub, I.

Goncharenko, A. V.

A. V. Goncharenko, H. C. Chang, and J. K. Wang, “Electric near-field enhancing properties of a finite-size metal conical nano-tip,” Ultramicroscopy 107(2-3), 151–157 (2007).
[Crossref] [PubMed]

Grosjean, T.

Gurbatov, S.

Hecht, B.

R. Stöckle, C. Fokas, V. Deckert, R. Zenobi, B. Sick, B. Hecht, and U. P. Wild, “High-quality near-field optical probes by tube etching,” Appl. Phys. Lett. 75(2), 160–162 (1999).
[Crossref]

Heitz, J.

Hong, M. H.

Y. J. Yu, H. Noh, M. H. Hong, H. R. Noh, Y. Arakawa, and W. Jhe, “Focusing characteristics of optical fiber axicon microlens for near-field spectroscopy: dependence of tip apex angle,” Opt. Commun. 267(1), 264–270 (2006).
[Crossref]

Ibrahim, I. A.

Ionin, A. A.

A. A. Kuchmizhak, Y. N. Kulchin, O. B. Vitrik, A. G. Savchuk, S. V. Makarov, S. I. Kudryashov, and A. A. Ionin, “Optical apertureless fiber micro-probe for surface laser modification of metal films with sub-100 nm resolution,” Opt. Commun. 308, 125–129 (2013).
[Crossref]

Jaroszewicz, Z.

Z. Jaroszewicz, A. Burvall, and A. T. Friberg, “Axicon – the Most Important Optical Element,” Opt. Photonics News 16(4), 34–39 (2005).
[Crossref]

Jhe, W.

Y. J. Yu, H. Noh, M. H. Hong, H. R. Noh, Y. Arakawa, and W. Jhe, “Focusing characteristics of optical fiber axicon microlens for near-field spectroscopy: dependence of tip apex angle,” Opt. Commun. 267(1), 264–270 (2006).
[Crossref]

Karpeev, S. V.

Khonina, S. N.

A. V. Ustinov, S. A. Degtyarev, and S. N. Khonina, “Diffraction by a conical axicon considering multiple internal reflections,” Comput. Opt. 39(4), 500–507 (2015).
[Crossref]

S. V. Alferov, S. N. Khonina, and S. V. Karpeev, “Study of polarization properties of fiber-optics probes with use of a binary phase plate,” J. Opt. Soc. Am. A 31(4), 802–807 (2014).
[Crossref] [PubMed]

S. N. Khonina and D. A. Savelyev, “High-aperture binary axicons for the formation of the longitudinal electric field component on the optical axis for linear and circular polarizations of the illuminating beam,” J. Exp. Theor. Phys. 117(4), 623–630 (2013).
[Crossref]

A. V. Ustinov and S. N. Khonina, “Calculating the complex transmission function of refractive axicons,” Opt. Mem. Neural. Networks 21(3), 133–144 (2012).
[Crossref]

A. V. Ustinov and S. N. Khonina, “Calculating the complex transmission function of refractive axicons,” Opt. Mem. Neural. Networks 21(3), 133–144 (2012).
[Crossref]

Kim, M.-K.

H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, “Nanofocusing in a metal–insulator–metal gap plasmon waveguide with a three-dimensional linear taper,” Nat. Photonics 6(12), 838–844 (2012).
[Crossref]

Kuchmizhak, A.

Kuchmizhak, A. A.

A. A. Kuchmizhak, Y. N. Kulchin, O. B. Vitrik, A. G. Savchuk, S. V. Makarov, S. I. Kudryashov, and A. A. Ionin, “Optical apertureless fiber micro-probe for surface laser modification of metal films with sub-100 nm resolution,” Opt. Commun. 308, 125–129 (2013).
[Crossref]

Kudryashov, S. I.

A. A. Kuchmizhak, Y. N. Kulchin, O. B. Vitrik, A. G. Savchuk, S. V. Makarov, S. I. Kudryashov, and A. A. Ionin, “Optical apertureless fiber micro-probe for surface laser modification of metal films with sub-100 nm resolution,” Opt. Commun. 308, 125–129 (2013).
[Crossref]

Kulchin, Y.

Kulchin, Y. N.

A. A. Kuchmizhak, Y. N. Kulchin, O. B. Vitrik, A. G. Savchuk, S. V. Makarov, S. I. Kudryashov, and A. A. Ionin, “Optical apertureless fiber micro-probe for surface laser modification of metal films with sub-100 nm resolution,” Opt. Commun. 308, 125–129 (2013).
[Crossref]

Lambelet, P.

Leitz, K.-H.

I. Alexeev, K.-H. Leitz, A. Otto, and M. Schmidt, “Application of Bessel beams for ultrafast laser volume structuring of non transparent media,” Phys. Procedia 5, 533–540 (2010).
[Crossref]

Lienau, C.

R. Müller and C. Lienau, “Three-dimensional analysis of light propagation through uncoated near-field fibre probes,” J. Microsc. 202(2), 339–346 (2001).
[Crossref] [PubMed]

Makarov, S. V.

A. A. Kuchmizhak, Y. N. Kulchin, O. B. Vitrik, A. G. Savchuk, S. V. Makarov, S. I. Kudryashov, and A. A. Ionin, “Optical apertureless fiber micro-probe for surface laser modification of metal films with sub-100 nm resolution,” Opt. Commun. 308, 125–129 (2013).
[Crossref]

Margaryan, N. L.

A. J. Babadjanyan, N. L. Margaryan, and K. V. Nerkararyan, “Superfocusing of surface polaritons in the conical structure,” J. Appl. Phys. 87(8), 3785–3788 (2000).
[Crossref]

Marquis-Weible, F.

Matvejev, V.

B. Zhu, J. Stiens, V. Matvejev, and R. Vounckx, “Inexpensive and easy fabrication of multi-mode tapered dielectric circular probes at millimeter wave frequencies,” Prog. Electromagnetics Res. 126, 237–254 (2012).
[Crossref]

McGloin, D.

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005).
[Crossref]

McLeod, J. H.

Miceli, J.

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Mohanty, K. S.

Mohanty, S. K.

Müller, R.

R. Müller and C. Lienau, “Three-dimensional analysis of light propagation through uncoated near-field fibre probes,” J. Microsc. 202(2), 339–346 (2001).
[Crossref] [PubMed]

Nepomniaschii, A.

Nerkararyan, K. V.

A. J. Babadjanyan, N. L. Margaryan, and K. V. Nerkararyan, “Superfocusing of surface polaritons in the conical structure,” J. Appl. Phys. 87(8), 3785–3788 (2000).
[Crossref]

Noh, H.

Y. J. Yu, H. Noh, M. H. Hong, H. R. Noh, Y. Arakawa, and W. Jhe, “Focusing characteristics of optical fiber axicon microlens for near-field spectroscopy: dependence of tip apex angle,” Opt. Commun. 267(1), 264–270 (2006).
[Crossref]

Noh, H. R.

Y. J. Yu, H. Noh, M. H. Hong, H. R. Noh, Y. Arakawa, and W. Jhe, “Focusing characteristics of optical fiber axicon microlens for near-field spectroscopy: dependence of tip apex angle,” Opt. Commun. 267(1), 264–270 (2006).
[Crossref]

Olmon, R. L.

S. Berweger, J. M. Atkin, R. L. Olmon, and M. B. Raschke, “Light on the tip of a needle: plasmonic nanofocusing for spectroscopy on the nanoscale,” J. Phys. Chem. Lett. 3(7), 945–952 (2012).
[Crossref] [PubMed]

Otto, A.

I. Alexeev, K.-H. Leitz, A. Otto, and M. Schmidt, “Application of Bessel beams for ultrafast laser volume structuring of non transparent media,” Phys. Procedia 5, 533–540 (2010).
[Crossref]

Pfeffer, M.

Philipona, C.

Piquerey, V.

Pohl, D. W.

W. Denk and D. W. Pohl, “Near-field optics: microscopy with nanometer-size fields,” J. Vac. Sci. Technol. B 9(2), 510–513 (1991).
[Crossref]

Raschke, M. B.

S. Berweger, J. M. Atkin, R. L. Olmon, and M. B. Raschke, “Light on the tip of a needle: plasmonic nanofocusing for spectroscopy on the nanoscale,” J. Phys. Chem. Lett. 3(7), 945–952 (2012).
[Crossref] [PubMed]

Saleh, S. S.

Salut, R.

T. Grosjean, A. Fahys, M. Suarez, D. Charraut, R. Salut, and D. Courjon, “Annular nanoantenna on fibre micro-axicon,” J. Microsc. 229(2), 354–364 (2008).
[Crossref] [PubMed]

Sandoz, P.

Savchuk, A. G.

A. A. Kuchmizhak, Y. N. Kulchin, O. B. Vitrik, A. G. Savchuk, S. V. Makarov, S. I. Kudryashov, and A. A. Ionin, “Optical apertureless fiber micro-probe for surface laser modification of metal films with sub-100 nm resolution,” Opt. Commun. 308, 125–129 (2013).
[Crossref]

Savelyev, D. A.

S. N. Khonina and D. A. Savelyev, “High-aperture binary axicons for the formation of the longitudinal electric field component on the optical axis for linear and circular polarizations of the illuminating beam,” J. Exp. Theor. Phys. 117(4), 623–630 (2013).
[Crossref]

Sayah, A.

Schaller, N.

R. M. Stöckle, N. Schaller, V. Deckert, C. Fokas, and R. Zenobi, “Brighter near-field optical probes by means of improving the optical destruction threshold,” J. Microsc. 194(2), 378–382 (1999).
[Crossref] [PubMed]

Schmidt, M.

I. Alexeev, K.-H. Leitz, A. Otto, and M. Schmidt, “Application of Bessel beams for ultrafast laser volume structuring of non transparent media,” Phys. Procedia 5, 533–540 (2010).
[Crossref]

Schuck, P. J.

H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, “Nanofocusing in a metal–insulator–metal gap plasmon waveguide with a three-dimensional linear taper,” Nat. Photonics 6(12), 838–844 (2012).
[Crossref]

Seok, T. J.

H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, “Nanofocusing in a metal–insulator–metal gap plasmon waveguide with a three-dimensional linear taper,” Nat. Photonics 6(12), 838–844 (2012).
[Crossref]

Sick, B.

R. Stöckle, C. Fokas, V. Deckert, R. Zenobi, B. Sick, B. Hecht, and U. P. Wild, “High-quality near-field optical probes by tube etching,” Appl. Phys. Lett. 75(2), 160–162 (1999).
[Crossref]

Staffaroni, M.

H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, “Nanofocusing in a metal–insulator–metal gap plasmon waveguide with a three-dimensional linear taper,” Nat. Photonics 6(12), 838–844 (2012).
[Crossref]

Stiens, J.

B. Zhu, J. Stiens, V. Matvejev, and R. Vounckx, “Inexpensive and easy fabrication of multi-mode tapered dielectric circular probes at millimeter wave frequencies,” Prog. Electromagnetics Res. 126, 237–254 (2012).
[Crossref]

Stöckle, R.

R. Stöckle, C. Fokas, V. Deckert, R. Zenobi, B. Sick, B. Hecht, and U. P. Wild, “High-quality near-field optical probes by tube etching,” Appl. Phys. Lett. 75(2), 160–162 (1999).
[Crossref]

Stöckle, R. M.

R. M. Stöckle, N. Schaller, V. Deckert, C. Fokas, and R. Zenobi, “Brighter near-field optical probes by means of improving the optical destruction threshold,” J. Microsc. 194(2), 378–382 (1999).
[Crossref] [PubMed]

Suarez, M.

T. Grosjean, A. Fahys, M. Suarez, D. Charraut, R. Salut, and D. Courjon, “Annular nanoantenna on fibre micro-axicon,” J. Microsc. 229(2), 354–364 (2008).
[Crossref] [PubMed]

Suarez, M. A.

Szoplik, T.

Tao, S. H.

B. P. S. Ahluwalia, X.-C. Yuan, S. H. Tao, W. C. Cheong, L. S. Zhang, and H. Wang, “Micromanipulation of high and low indices microparticles using a microfabricated double axicon,” J. Appl. Phys. 99(11), 113104 (2006).
[Crossref]

Ustinov, A. V.

A. V. Ustinov, S. A. Degtyarev, and S. N. Khonina, “Diffraction by a conical axicon considering multiple internal reflections,” Comput. Opt. 39(4), 500–507 (2015).
[Crossref]

A. V. Ustinov and S. N. Khonina, “Calculating the complex transmission function of refractive axicons,” Opt. Mem. Neural. Networks 21(3), 133–144 (2012).
[Crossref]

A. V. Ustinov and S. N. Khonina, “Calculating the complex transmission function of refractive axicons,” Opt. Mem. Neural. Networks 21(3), 133–144 (2012).
[Crossref]

Vitrik, O.

Vitrik, O. B.

A. A. Kuchmizhak, Y. N. Kulchin, O. B. Vitrik, A. G. Savchuk, S. V. Makarov, S. I. Kudryashov, and A. A. Ionin, “Optical apertureless fiber micro-probe for surface laser modification of metal films with sub-100 nm resolution,” Opt. Commun. 308, 125–129 (2013).
[Crossref]

Vounckx, R.

B. Zhu, J. Stiens, V. Matvejev, and R. Vounckx, “Inexpensive and easy fabrication of multi-mode tapered dielectric circular probes at millimeter wave frequencies,” Prog. Electromagnetics Res. 126, 237–254 (2012).
[Crossref]

Wang, H.

B. P. S. Ahluwalia, X.-C. Yuan, S. H. Tao, W. C. Cheong, L. S. Zhang, and H. Wang, “Micromanipulation of high and low indices microparticles using a microfabricated double axicon,” J. Appl. Phys. 99(11), 113104 (2006).
[Crossref]

Wang, J. K.

A. V. Goncharenko, H. C. Chang, and J. K. Wang, “Electric near-field enhancing properties of a finite-size metal conical nano-tip,” Ultramicroscopy 107(2-3), 151–157 (2007).
[Crossref] [PubMed]

Wild, U. P.

R. Stöckle, C. Fokas, V. Deckert, R. Zenobi, B. Sick, B. Hecht, and U. P. Wild, “High-quality near-field optical probes by tube etching,” Appl. Phys. Lett. 75(2), 160–162 (1999).
[Crossref]

Wróbel, P.

Wu, M. C.

H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, “Nanofocusing in a metal–insulator–metal gap plasmon waveguide with a three-dimensional linear taper,” Nat. Photonics 6(12), 838–844 (2012).
[Crossref]

Yablonovitch, E.

H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, “Nanofocusing in a metal–insulator–metal gap plasmon waveguide with a three-dimensional linear taper,” Nat. Photonics 6(12), 838–844 (2012).
[Crossref]

Yakunin, S.

Yu, Y. J.

Y. J. Yu, H. Noh, M. H. Hong, H. R. Noh, Y. Arakawa, and W. Jhe, “Focusing characteristics of optical fiber axicon microlens for near-field spectroscopy: dependence of tip apex angle,” Opt. Commun. 267(1), 264–270 (2006).
[Crossref]

Yuan, X.-C.

B. P. S. Ahluwalia, X.-C. Yuan, S. H. Tao, W. C. Cheong, L. S. Zhang, and H. Wang, “Micromanipulation of high and low indices microparticles using a microfabricated double axicon,” J. Appl. Phys. 99(11), 113104 (2006).
[Crossref]

Zenobi, R.

R. Stöckle, C. Fokas, V. Deckert, R. Zenobi, B. Sick, B. Hecht, and U. P. Wild, “High-quality near-field optical probes by tube etching,” Appl. Phys. Lett. 75(2), 160–162 (1999).
[Crossref]

R. M. Stöckle, N. Schaller, V. Deckert, C. Fokas, and R. Zenobi, “Brighter near-field optical probes by means of improving the optical destruction threshold,” J. Microsc. 194(2), 378–382 (1999).
[Crossref] [PubMed]

Zhang, L. S.

B. P. S. Ahluwalia, X.-C. Yuan, S. H. Tao, W. C. Cheong, L. S. Zhang, and H. Wang, “Micromanipulation of high and low indices microparticles using a microfabricated double axicon,” J. Appl. Phys. 99(11), 113104 (2006).
[Crossref]

Zhu, B.

B. Zhu, J. Stiens, V. Matvejev, and R. Vounckx, “Inexpensive and easy fabrication of multi-mode tapered dielectric circular probes at millimeter wave frequencies,” Prog. Electromagnetics Res. 126, 237–254 (2012).
[Crossref]

Appl. Opt. (4)

Appl. Phys. Lett. (1)

R. Stöckle, C. Fokas, V. Deckert, R. Zenobi, B. Sick, B. Hecht, and U. P. Wild, “High-quality near-field optical probes by tube etching,” Appl. Phys. Lett. 75(2), 160–162 (1999).
[Crossref]

Comput. Opt. (1)

A. V. Ustinov, S. A. Degtyarev, and S. N. Khonina, “Diffraction by a conical axicon considering multiple internal reflections,” Comput. Opt. 39(4), 500–507 (2015).
[Crossref]

Contemp. Phys. (1)

D. McGloin and K. Dholakia, “Bessel beams: diffraction in a new light,” Contemp. Phys. 46(1), 15–28 (2005).
[Crossref]

J. Appl. Phys. (2)

B. P. S. Ahluwalia, X.-C. Yuan, S. H. Tao, W. C. Cheong, L. S. Zhang, and H. Wang, “Micromanipulation of high and low indices microparticles using a microfabricated double axicon,” J. Appl. Phys. 99(11), 113104 (2006).
[Crossref]

A. J. Babadjanyan, N. L. Margaryan, and K. V. Nerkararyan, “Superfocusing of surface polaritons in the conical structure,” J. Appl. Phys. 87(8), 3785–3788 (2000).
[Crossref]

J. Exp. Theor. Phys. (1)

S. N. Khonina and D. A. Savelyev, “High-aperture binary axicons for the formation of the longitudinal electric field component on the optical axis for linear and circular polarizations of the illuminating beam,” J. Exp. Theor. Phys. 117(4), 623–630 (2013).
[Crossref]

J. Microsc. (3)

R. M. Stöckle, N. Schaller, V. Deckert, C. Fokas, and R. Zenobi, “Brighter near-field optical probes by means of improving the optical destruction threshold,” J. Microsc. 194(2), 378–382 (1999).
[Crossref] [PubMed]

R. Müller and C. Lienau, “Three-dimensional analysis of light propagation through uncoated near-field fibre probes,” J. Microsc. 202(2), 339–346 (2001).
[Crossref] [PubMed]

T. Grosjean, A. Fahys, M. Suarez, D. Charraut, R. Salut, and D. Courjon, “Annular nanoantenna on fibre micro-axicon,” J. Microsc. 229(2), 354–364 (2008).
[Crossref] [PubMed]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Phys. Chem. Lett. (1)

S. Berweger, J. M. Atkin, R. L. Olmon, and M. B. Raschke, “Light on the tip of a needle: plasmonic nanofocusing for spectroscopy on the nanoscale,” J. Phys. Chem. Lett. 3(7), 945–952 (2012).
[Crossref] [PubMed]

J. Vac. Sci. Technol. B (1)

W. Denk and D. W. Pohl, “Near-field optics: microscopy with nanometer-size fields,” J. Vac. Sci. Technol. B 9(2), 510–513 (1991).
[Crossref]

Nat. Photonics (1)

H. Choo, M.-K. Kim, M. Staffaroni, T. J. Seok, J. Bokor, S. Cabrini, P. J. Schuck, M. C. Wu, and E. Yablonovitch, “Nanofocusing in a metal–insulator–metal gap plasmon waveguide with a three-dimensional linear taper,” Nat. Photonics 6(12), 838–844 (2012).
[Crossref]

Opt. Commun. (2)

A. A. Kuchmizhak, Y. N. Kulchin, O. B. Vitrik, A. G. Savchuk, S. V. Makarov, S. I. Kudryashov, and A. A. Ionin, “Optical apertureless fiber micro-probe for surface laser modification of metal films with sub-100 nm resolution,” Opt. Commun. 308, 125–129 (2013).
[Crossref]

Y. J. Yu, H. Noh, M. H. Hong, H. R. Noh, Y. Arakawa, and W. Jhe, “Focusing characteristics of optical fiber axicon microlens for near-field spectroscopy: dependence of tip apex angle,” Opt. Commun. 267(1), 264–270 (2006).
[Crossref]

Opt. Express (2)

Opt. Lett. (2)

Opt. Mem. Neural. Networks (2)

A. V. Ustinov and S. N. Khonina, “Calculating the complex transmission function of refractive axicons,” Opt. Mem. Neural. Networks 21(3), 133–144 (2012).
[Crossref]

A. V. Ustinov and S. N. Khonina, “Calculating the complex transmission function of refractive axicons,” Opt. Mem. Neural. Networks 21(3), 133–144 (2012).
[Crossref]

Opt. Photonics News (1)

Z. Jaroszewicz, A. Burvall, and A. T. Friberg, “Axicon – the Most Important Optical Element,” Opt. Photonics News 16(4), 34–39 (2005).
[Crossref]

Phys. Procedia (1)

I. Alexeev, K.-H. Leitz, A. Otto, and M. Schmidt, “Application of Bessel beams for ultrafast laser volume structuring of non transparent media,” Phys. Procedia 5, 533–540 (2010).
[Crossref]

Phys. Rev. Lett. (1)

J. Durnin, J. Miceli, and J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58(15), 1499–1501 (1987).
[Crossref] [PubMed]

Prog. Electromagnetics Res. (2)

B. Zhu, J. Stiens, V. Matvejev, and R. Vounckx, “Inexpensive and easy fabrication of multi-mode tapered dielectric circular probes at millimeter wave frequencies,” Prog. Electromagnetics Res. 126, 237–254 (2012).
[Crossref]

A. De and G. V. Attimarad, “Numerical analysis of two dimensional tapered dielectric waveguide,” Prog. Electromagnetics Res. 44, 131–142 (2004).
[Crossref]

Ultramicroscopy (1)

A. V. Goncharenko, H. C. Chang, and J. K. Wang, “Electric near-field enhancing properties of a finite-size metal conical nano-tip,” Ultramicroscopy 107(2-3), 151–157 (2007).
[Crossref] [PubMed]

Other (1)

L. Novotny and D. Hecht, Principles of Nano-Optics (Cambridge: New York, 2006).

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Figures (8)

Fig. 1
Fig. 1 Path of the rays focused using the axicon if total internal reflection does not occur.
Fig. 2
Fig. 2 Axicon angle α 0 , range and associated light beams.
Fig. 3
Fig. 3 Results of calculations performed using the two-dimensional axicon model ( α 0 20 ° ).
Fig. 4
Fig. 4 Results of calculations performed using the two-dimensional axicon model ( 8 ° α 0 < 20 ° ).
Fig. 5
Fig. 5 Behavior of the laser beam as a function of the angle of the axicon.
Fig. 6
Fig. 6 Focusing of the Gaussian beam at α0 = 60°: (a) Meep, (b) COMSOL, and at α0 = 47°: (c) Meep, (d) COMSOL.
Fig. 7
Fig. 7 Focusing of a Gaussian beam at: if (а) α0 = 27°, (b) α0 = 25°, (c) α0 = 23°, (d) α0 = 21°, (e) α0 = 19°, (f) α0 = 17°, (g) α0 = 15°, (h) α0 = 13°, (i) α0 = 11°.
Fig. 8
Fig. 8 Passage of radiation through an axicon with a small angle at the vertex.

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

N A = sin β
α 0 α t i r = arc cos ( 1 n a x )
N A lim = sin ( α t i r ) = sin [ arc cos ( 1 n a x ) ]
α h a l o = 30 + 1 3 arc sin ( 1 n a x )
sin α v e r + n ( 4 cos 3 α v e r 3 cos α v e r ) = 0
n a x cos [ ( 2 p + 1 ) α c o l p ] = cos ( α c o l p ) , p 1
α c o l 1 = arc cos ( 1 2 1 n a x + 3 ) , α c o l 2 = arc cos ( 5 + 5 + 4 / n a x 8 ) .
n a x cos [ ( 2 p 1 ) α t i r p ] = 1 , p 2
α t i r p = ( 2 p 1 ) 1 arc cos ( 1 n a x ) , p 2
α t i r p + 1 < α 0 < α c o l p , p 1
α c o l p + 1 < α 0 < α t i r p + 1 , p 1
N A = ( 2 h / D ) ( n a x 1 + ( 1 n a x 2 ) ( 2 h / D ) 2 ) 1 + ( 2 h / D ) 2 ,

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