Abstract

The focal performance of the micro-axicon and the Fresnel axicon (fraxicon) are investigated, for the first time, by the rigorous electromagnetic theory and boundary element method. The micro-axicon with different angle of apex and the fraxicon with various period and angle of apex are investigated. The dark segments of the fraxicon are explored numerically. Rigorous results of focal performance of the micro-axicon and the fraxicon are different from the results given by the approximation of geometrical optics and the scalar diffraction theory. The scattering effects are dominant in the fraxicon with small size of feature. It is expected that our study can provides very useful information in analyzing the axicon in optical trapping systems.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  22. B. P. S. Ahluwalia, W. C. Cheong, X.-C. Yuan, L.-S. Zhang, S.-H. Tao, J. Bu, and H. Wang, "Design and fabrication of a double-axicon for generation of tailorable self-imaged three-dimensional intensity voids," Opt. Lett. 31, 987-989 (2006).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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2008 (1)

2007 (1)

2006 (3)

2005 (3)

C. J. Zapata-Rodríguez, and F. E. Hernńndez, "Focal squeeze in axicons," Opt. Commun. 254, 3-9 (2005).
[CrossRef]

W. C. Cheong, B. P. S. Ahluwalia, X.-C. Yuan, L.-S. Zhang, H. B. Niu, and X. Peng, "Fabrication of efficient microaxicon by direct electron-beam lithography for long nondiffracting distance of Bessel beams for optical manipulation," Appl. Phys. Lett. 87, 024104-1-3 (2005).
[CrossRef]

D. Mcgloin and K. Dholakia, "Bessel beams: diffraction in a new light," Contemp. Phys. 46, 15-28 (2005).
[CrossRef]

2004 (3)

2002 (1)

2000 (3)

D. J. Fischer, C. J. Harkrider, and D. T. Moore, "Design and manufacture of a gradient-index axicon," Appl. Opt. 39, 2687-2694 (2000).
[CrossRef]

T. Tanaka and S. Yamamoto, "Comparison of aberration between axicon and lens," Opt. Commun. 184, 113-118 (2000).
[CrossRef]

J. Fan, E. Parra, and H. M. Milchberg, "Resonant self-trapping and absorption of intense Bessel beams," Phys. Rev. Lett. 84, 3085-3088 (2000).
[CrossRef] [PubMed]

1996 (1)

1994 (1)

L. Lin, S. Lee, K. Pister, and M. C. Wu, "Three-dimensional micro-Fresnel optical elements fabricated by micromachining technique," Electron. Lett. 30, 448-449 (1994).
[CrossRef]

1992 (1)

1990 (1)

1989 (1)

M. Florjanczyk and R. Tremblay, "Guiding of atoms in a travelling-wave laser trap formed by the axicon," Opt. Commun. 74, 448-450 (1989).
[CrossRef]

1985 (1)

K. Yashiro and S. Ohkawa, "Boundary element method for electromagnetic scattering from cylinders," IEEE Trans. Antennas Propag. AP-33, 383-389 (1985).
[CrossRef]

1978 (1)

1960 (1)

1954 (1)

Ahluwalia, B. P. S.

B. P. S. Ahluwalia, W. C. Cheong, X.-C. Yuan, L.-S. Zhang, S.-H. Tao, J. Bu, and H. Wang, "Design and fabrication of a double-axicon for generation of tailorable self-imaged three-dimensional intensity voids," Opt. Lett. 31, 987-989 (2006).
[CrossRef] [PubMed]

W. C. Cheong, B. P. S. Ahluwalia, X.-C. Yuan, L.-S. Zhang, H. B. Niu, and X. Peng, "Fabrication of efficient microaxicon by direct electron-beam lithography for long nondiffracting distance of Bessel beams for optical manipulation," Appl. Phys. Lett. 87, 024104-1-3 (2005).
[CrossRef]

Arimoto, R.

Bélanger, P.-A.

Brzobohatý, O.

Bu, J.

Burvall, A.

Chen, Z.

Cheong, W. C.

B. P. S. Ahluwalia, W. C. Cheong, X.-C. Yuan, L.-S. Zhang, S.-H. Tao, J. Bu, and H. Wang, "Design and fabrication of a double-axicon for generation of tailorable self-imaged three-dimensional intensity voids," Opt. Lett. 31, 987-989 (2006).
[CrossRef] [PubMed]

W. C. Cheong, B. P. S. Ahluwalia, X.-C. Yuan, L.-S. Zhang, H. B. Niu, and X. Peng, "Fabrication of efficient microaxicon by direct electron-beam lithography for long nondiffracting distance of Bessel beams for optical manipulation," Appl. Phys. Lett. 87, 024104-1-3 (2005).
[CrossRef]

Cižmár, T

Davis, J. A.

Dholakia, K.

D. Mcgloin and K. Dholakia, "Bessel beams: diffraction in a new light," Contemp. Phys. 46, 15-28 (2005).
[CrossRef]

Ding, Z.

Fan, J.

J. Fan, E. Parra, and H. M. Milchberg, "Resonant self-trapping and absorption of intense Bessel beams," Phys. Rev. Lett. 84, 3085-3088 (2000).
[CrossRef] [PubMed]

Fischer, D. J.

Florjanczyk, M.

M. Florjanczyk and R. Tremblay, "Guiding of atoms in a travelling-wave laser trap formed by the axicon," Opt. Commun. 74, 448-450 (1989).
[CrossRef]

Friberg, A.

Furlan, W.

Furlan, W. D.

J. A. Monsoriu, C. J. Zapata-Rodrıguez, and W. D. Furlan, "Fractal axicons," Opt. Commun. 263, 1-5 (2006).
[CrossRef]

Gaylord, T. K.

Glytsis, E. N.

Golub, I.

Harkrider, C. J.

Hernnndez, F.E.

C. J. Zapata-Rodríguez, and F. E. Hernńndez, "Focal squeeze in axicons," Opt. Commun. 254, 3-9 (2005).
[CrossRef]

Hirayama, K.

Kawata, S.

Kotlyar, V. V.

Kovalev, A. A.

Lee, S.

L. Lin, S. Lee, K. Pister, and M. C. Wu, "Three-dimensional micro-Fresnel optical elements fabricated by micromachining technique," Electron. Lett. 30, 448-449 (1994).
[CrossRef]

Lin, L.

L. Lin, S. Lee, K. Pister, and M. C. Wu, "Three-dimensional micro-Fresnel optical elements fabricated by micromachining technique," Electron. Lett. 30, 448-449 (1994).
[CrossRef]

Martinsson, P.

Mcgloin, D.

D. Mcgloin and K. Dholakia, "Bessel beams: diffraction in a new light," Contemp. Phys. 46, 15-28 (2005).
[CrossRef]

McLeod, J. H.

Milchberg, H. M.

J. Fan, E. Parra, and H. M. Milchberg, "Resonant self-trapping and absorption of intense Bessel beams," Phys. Rev. Lett. 84, 3085-3088 (2000).
[CrossRef] [PubMed]

Monsoriu, J.

Monsoriu, J. A.

J. A. Monsoriu, C. J. Zapata-Rodrıguez, and W. D. Furlan, "Fractal axicons," Opt. Commun. 263, 1-5 (2006).
[CrossRef]

Moore, D. T.

Nelson, J. S.

Niu, H. B.

W. C. Cheong, B. P. S. Ahluwalia, X.-C. Yuan, L.-S. Zhang, H. B. Niu, and X. Peng, "Fabrication of efficient microaxicon by direct electron-beam lithography for long nondiffracting distance of Bessel beams for optical manipulation," Appl. Phys. Lett. 87, 024104-1-3 (2005).
[CrossRef]

Ohkawa, S.

K. Yashiro and S. Ohkawa, "Boundary element method for electromagnetic scattering from cylinders," IEEE Trans. Antennas Propag. AP-33, 383-389 (1985).
[CrossRef]

Parra, E.

J. Fan, E. Parra, and H. M. Milchberg, "Resonant self-trapping and absorption of intense Bessel beams," Phys. Rev. Lett. 84, 3085-3088 (2000).
[CrossRef] [PubMed]

Peng, X.

W. C. Cheong, B. P. S. Ahluwalia, X.-C. Yuan, L.-S. Zhang, H. B. Niu, and X. Peng, "Fabrication of efficient microaxicon by direct electron-beam lithography for long nondiffracting distance of Bessel beams for optical manipulation," Appl. Phys. Lett. 87, 024104-1-3 (2005).
[CrossRef]

Pister, K.

L. Lin, S. Lee, K. Pister, and M. C. Wu, "Three-dimensional micro-Fresnel optical elements fabricated by micromachining technique," Electron. Lett. 30, 448-449 (1994).
[CrossRef]

Qian, Y.

Ren, H.

Rioux, M.

Saavedra, G.

Saloma, C.

Soifer, V. A.

Tanaka, T.

Tao, S.-H.

Tremblay, R.

I. Golub and R. Tremblay, "Light focusing and guiding by an axicon-pair-generated tubular light beam," J. Opt. Soc. Am. B 7, 1264-1267 (1990).
[CrossRef]

M. Florjanczyk and R. Tremblay, "Guiding of atoms in a travelling-wave laser trap formed by the axicon," Opt. Commun. 74, 448-450 (1989).
[CrossRef]

Tuvey, C. S.

Wang, H.

Wang, Y. Z.

Wilson, D. W.

Wu, M. C.

L. Lin, S. Lee, K. Pister, and M. C. Wu, "Three-dimensional micro-Fresnel optical elements fabricated by micromachining technique," Electron. Lett. 30, 448-449 (1994).
[CrossRef]

Yamamoto, S.

T. Tanaka and S. Yamamoto, "Comparison of aberration between axicon and lens," Opt. Commun. 184, 113-118 (2000).
[CrossRef]

Yashiro, K.

K. Yashiro and S. Ohkawa, "Boundary element method for electromagnetic scattering from cylinders," IEEE Trans. Antennas Propag. AP-33, 383-389 (1985).
[CrossRef]

Yuan, X.-C.

B. P. S. Ahluwalia, W. C. Cheong, X.-C. Yuan, L.-S. Zhang, S.-H. Tao, J. Bu, and H. Wang, "Design and fabrication of a double-axicon for generation of tailorable self-imaged three-dimensional intensity voids," Opt. Lett. 31, 987-989 (2006).
[CrossRef] [PubMed]

W. C. Cheong, B. P. S. Ahluwalia, X.-C. Yuan, L.-S. Zhang, H. B. Niu, and X. Peng, "Fabrication of efficient microaxicon by direct electron-beam lithography for long nondiffracting distance of Bessel beams for optical manipulation," Appl. Phys. Lett. 87, 024104-1-3 (2005).
[CrossRef]

Zapata-Rodr’iguez, C. J.

J. A. Monsoriu, C. J. Zapata-Rodrıguez, and W. D. Furlan, "Fractal axicons," Opt. Commun. 263, 1-5 (2006).
[CrossRef]

Zapata-Rodríguez, C.J.

C. J. Zapata-Rodríguez, and F. E. Hernńndez, "Focal squeeze in axicons," Opt. Commun. 254, 3-9 (2005).
[CrossRef]

Zemánek, P.

Zhang, L.-S.

B. P. S. Ahluwalia, W. C. Cheong, X.-C. Yuan, L.-S. Zhang, S.-H. Tao, J. Bu, and H. Wang, "Design and fabrication of a double-axicon for generation of tailorable self-imaged three-dimensional intensity voids," Opt. Lett. 31, 987-989 (2006).
[CrossRef] [PubMed]

W. C. Cheong, B. P. S. Ahluwalia, X.-C. Yuan, L.-S. Zhang, H. B. Niu, and X. Peng, "Fabrication of efficient microaxicon by direct electron-beam lithography for long nondiffracting distance of Bessel beams for optical manipulation," Appl. Phys. Lett. 87, 024104-1-3 (2005).
[CrossRef]

Zhao, Y.

Appl. Opt. (3)

Appl. Phys. Lett. (1)

W. C. Cheong, B. P. S. Ahluwalia, X.-C. Yuan, L.-S. Zhang, H. B. Niu, and X. Peng, "Fabrication of efficient microaxicon by direct electron-beam lithography for long nondiffracting distance of Bessel beams for optical manipulation," Appl. Phys. Lett. 87, 024104-1-3 (2005).
[CrossRef]

Chin. Opt. Lett. (1)

Contemp. Phys. (1)

D. Mcgloin and K. Dholakia, "Bessel beams: diffraction in a new light," Contemp. Phys. 46, 15-28 (2005).
[CrossRef]

Electron. Lett. (1)

L. Lin, S. Lee, K. Pister, and M. C. Wu, "Three-dimensional micro-Fresnel optical elements fabricated by micromachining technique," Electron. Lett. 30, 448-449 (1994).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

K. Yashiro and S. Ohkawa, "Boundary element method for electromagnetic scattering from cylinders," IEEE Trans. Antennas Propag. AP-33, 383-389 (1985).
[CrossRef]

J. Opt. Soc. Am. (2)

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

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

Opt. Commun. (4)

M. Florjanczyk and R. Tremblay, "Guiding of atoms in a travelling-wave laser trap formed by the axicon," Opt. Commun. 74, 448-450 (1989).
[CrossRef]

J. A. Monsoriu, C. J. Zapata-Rodrıguez, and W. D. Furlan, "Fractal axicons," Opt. Commun. 263, 1-5 (2006).
[CrossRef]

T. Tanaka and S. Yamamoto, "Comparison of aberration between axicon and lens," Opt. Commun. 184, 113-118 (2000).
[CrossRef]

C. J. Zapata-Rodríguez, and F. E. Hernńndez, "Focal squeeze in axicons," Opt. Commun. 254, 3-9 (2005).
[CrossRef]

Opt. Express (3)

Opt. Lett. (4)

Phys. Rev. Lett. (1)

J. Fan, E. Parra, and H. M. Milchberg, "Resonant self-trapping and absorption of intense Bessel beams," Phys. Rev. Lett. 84, 3085-3088 (2000).
[CrossRef] [PubMed]

Other (1)

M. Bass, E. W. Van Stryland, D. R. Williams, and W. L. Wolfe, "Handbooks of Optics, Vol. 2: Devices, Measurements and Properties," (McGraw-Hill, New York, 1995).

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Figures (5)

Fig. 1.
Fig. 1.

A schematic diagram of axicons. (a) The bulk axicon, and (b) the Fresnel axicon with same angle of apex as given in (a).

Fig. 2.
Fig. 2.

The focal performance of 2D micro axicon with diameter D = 50.0 μm and angle of apex θ = 170°. (a) The gray-level intensity distributions in region S 2, (b) The lateral intensity distribution on different observation planes (solid curve for y = -100.0 μm and dashed curve for y = -40.0 μm, respectively), and (c) the intensity distribution along the axis of the micro-axicon.

Fig. 3.
Fig. 3.

Focal performance of the axicon with different angle of apex: (a) and (b) represent the field intensity distributions of the axicon with θ = 160° and 150° in the region S 2, respectively, and (c) displays the intensity profiles along y-axis.

Fig. 4.
Fig. 4.

(a) Normalized intensity distributions on observation plane y = -100.0 μm, and (b) the axial intensity distributions for different kinds of axicon. Curves a (black solid), b (red solid) and c (black dashed) describe the focal characteristics of the fraxicon with T = 5.0 μm, T = 2.5 μm and the bulk axicon, respectively.

Fig. 5.
Fig. 5.

The axial intensity distribution of T = 5.0 μm the fraxicon with different angle of apex. (a), (b), (c) and (d) are for θ = 170°, 160°, 150° and 140°, respectively. The red arrows mark the positions of dark segments.

Equations (1)

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E ( r ) = Γ [ E Γ ( r Γ ) G 2 ( r , r Γ ) n ̂ G 2 ( r , r Γ ) E Γ ( r Γ ) n ̂ ] d l ,

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