Abstract

We investigated the process of focusing a radially polarized (RP) light beam through a sub-wavelength annular aperture (SAA). We found that the result was a non-diffraction doughnut-shaped light beam which propagates in free space. After analyzing the electric field component of the focus generated by the SAA structure, we identified the relationship between the focal field generated by the SAA. We then compared it to a case with a traditional objective lens. From our findings, we propose that a SAA structure can be viewed as a continuous numerical aperture optical element.

© 2009 Optical Society of America

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  1. W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
    [CrossRef] [PubMed]
  2. H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
    [CrossRef] [PubMed]
  3. Z. W. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Letters 5, 1726–1729 (2005).
    [CrossRef] [PubMed]
  4. D. Z. Lin, C. H. Chen, C. K. Chang, T. D. Cheng, C. S. Yeh, and C. K. Lee, “Subwavelength nondiffraction beam generated by a plasmonic lens,” Appl. Phys. Lett. 92, 3 (2008).
  5. J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
    [CrossRef] [PubMed]
  6. Y. Mushiake, K. Matsumura, and N. Nakajima, “Generation of radially polarized optical beam mode by laser oscillation,” Proceedings of the IEEE 60, 1107–1109 (1972).
    [CrossRef]
  7. N. Passilly, R. de Saint Denis, K. Ait-Ameur, F. Treussart, R. Hierle, and J.-F. Roch, “Simple interferometric technique for generation of a radially polarized light beam,” Journal of the Optical Society of America A: Optics and Image Science, and Vision 22, 984–991 (2005).
    [CrossRef]
  8. M. Stalder, “Active and passive optical components using liquid crystals,” (SPIE -International Society for Optical Engineering, Bellingham WA, WA 98227–0010, USA, San Jose, CA, USA, 1996), pp. 30–39.
  9. M. Stalder and M. Schadt, “Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters,” Optics Letters 21, 1948 (1996).
    [CrossRef] [PubMed]
  10. C. Lopez-Mariscal, J. C. Gutierrez-Vega, and S. Chavez-Cerda, “Production of high-order Bessel beams with a Mach-Zehnder interferometer,” Appl. Optics 43, 5060–5063 (2004).
    [CrossRef]
  11. B. Hao and J. Leger, “Experimental measurement of longitudinal component in the vicinity of focused radially polarized beam,” Optics Express 15, 3550–3556 (2007).
    [CrossRef] [PubMed]
  12. Q. Zhan and J. R. Leger, “Focus shaping using cylindrical vector beams,” Optics Express 10, 324–331 (2002).
    [PubMed]
  13. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Optics Express 7, 77–87 (2000).
    [CrossRef] [PubMed]

2008 (1)

D. Z. Lin, C. H. Chen, C. K. Chang, T. D. Cheng, C. S. Yeh, and C. K. Lee, “Subwavelength nondiffraction beam generated by a plasmonic lens,” Appl. Phys. Lett. 92, 3 (2008).

2007 (1)

B. Hao and J. Leger, “Experimental measurement of longitudinal component in the vicinity of focused radially polarized beam,” Optics Express 15, 3550–3556 (2007).
[CrossRef] [PubMed]

2005 (2)

N. Passilly, R. de Saint Denis, K. Ait-Ameur, F. Treussart, R. Hierle, and J.-F. Roch, “Simple interferometric technique for generation of a radially polarized light beam,” Journal of the Optical Society of America A: Optics and Image Science, and Vision 22, 984–991 (2005).
[CrossRef]

Z. W. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Letters 5, 1726–1729 (2005).
[CrossRef] [PubMed]

2004 (1)

C. Lopez-Mariscal, J. C. Gutierrez-Vega, and S. Chavez-Cerda, “Production of high-order Bessel beams with a Mach-Zehnder interferometer,” Appl. Optics 43, 5060–5063 (2004).
[CrossRef]

2003 (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

2002 (2)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

Q. Zhan and J. R. Leger, “Focus shaping using cylindrical vector beams,” Optics Express 10, 324–331 (2002).
[PubMed]

2000 (1)

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Optics Express 7, 77–87 (2000).
[CrossRef] [PubMed]

1996 (1)

M. Stalder and M. Schadt, “Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters,” Optics Letters 21, 1948 (1996).
[CrossRef] [PubMed]

1987 (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

1972 (1)

Y. Mushiake, K. Matsumura, and N. Nakajima, “Generation of radially polarized optical beam mode by laser oscillation,” Proceedings of the IEEE 60, 1107–1109 (1972).
[CrossRef]

Ait-Ameur, K.

N. Passilly, R. de Saint Denis, K. Ait-Ameur, F. Treussart, R. Hierle, and J.-F. Roch, “Simple interferometric technique for generation of a radially polarized light beam,” Journal of the Optical Society of America A: Optics and Image Science, and Vision 22, 984–991 (2005).
[CrossRef]

Barnes, W. L.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Brown, T. G.

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Optics Express 7, 77–87 (2000).
[CrossRef] [PubMed]

Chang, C. K.

D. Z. Lin, C. H. Chen, C. K. Chang, T. D. Cheng, C. S. Yeh, and C. K. Lee, “Subwavelength nondiffraction beam generated by a plasmonic lens,” Appl. Phys. Lett. 92, 3 (2008).

Chavez-Cerda, S.

C. Lopez-Mariscal, J. C. Gutierrez-Vega, and S. Chavez-Cerda, “Production of high-order Bessel beams with a Mach-Zehnder interferometer,” Appl. Optics 43, 5060–5063 (2004).
[CrossRef]

Chen, C. H.

D. Z. Lin, C. H. Chen, C. K. Chang, T. D. Cheng, C. S. Yeh, and C. K. Lee, “Subwavelength nondiffraction beam generated by a plasmonic lens,” Appl. Phys. Lett. 92, 3 (2008).

Cheng, T. D.

D. Z. Lin, C. H. Chen, C. K. Chang, T. D. Cheng, C. S. Yeh, and C. K. Lee, “Subwavelength nondiffraction beam generated by a plasmonic lens,” Appl. Phys. Lett. 92, 3 (2008).

de Saint Denis, R.

N. Passilly, R. de Saint Denis, K. Ait-Ameur, F. Treussart, R. Hierle, and J.-F. Roch, “Simple interferometric technique for generation of a radially polarized light beam,” Journal of the Optical Society of America A: Optics and Image Science, and Vision 22, 984–991 (2005).
[CrossRef]

Degiron, A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

Dereux, A.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Devaux, E.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[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]

Ebbesen, T. W.

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Garcia-Vidal, F. J.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

Gutierrez-Vega, J. C.

C. Lopez-Mariscal, J. C. Gutierrez-Vega, and S. Chavez-Cerda, “Production of high-order Bessel beams with a Mach-Zehnder interferometer,” Appl. Optics 43, 5060–5063 (2004).
[CrossRef]

Hao, B.

B. Hao and J. Leger, “Experimental measurement of longitudinal component in the vicinity of focused radially polarized beam,” Optics Express 15, 3550–3556 (2007).
[CrossRef] [PubMed]

Hierle, R.

N. Passilly, R. de Saint Denis, K. Ait-Ameur, F. Treussart, R. Hierle, and J.-F. Roch, “Simple interferometric technique for generation of a radially polarized light beam,” Journal of the Optical Society of America A: Optics and Image Science, and Vision 22, 984–991 (2005).
[CrossRef]

Lee, C. K.

D. Z. Lin, C. H. Chen, C. K. Chang, T. D. Cheng, C. S. Yeh, and C. K. Lee, “Subwavelength nondiffraction beam generated by a plasmonic lens,” Appl. Phys. Lett. 92, 3 (2008).

Leger, J.

B. Hao and J. Leger, “Experimental measurement of longitudinal component in the vicinity of focused radially polarized beam,” Optics Express 15, 3550–3556 (2007).
[CrossRef] [PubMed]

Leger, J. R.

Q. Zhan and J. R. Leger, “Focus shaping using cylindrical vector beams,” Optics Express 10, 324–331 (2002).
[PubMed]

Lezec, H. J.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

Lin, D. Z.

D. Z. Lin, C. H. Chen, C. K. Chang, T. D. Cheng, C. S. Yeh, and C. K. Lee, “Subwavelength nondiffraction beam generated by a plasmonic lens,” Appl. Phys. Lett. 92, 3 (2008).

Linke, R. A.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

Liu, Z. W.

Z. W. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Letters 5, 1726–1729 (2005).
[CrossRef] [PubMed]

Lopez-Mariscal, C.

C. Lopez-Mariscal, J. C. Gutierrez-Vega, and S. Chavez-Cerda, “Production of high-order Bessel beams with a Mach-Zehnder interferometer,” Appl. Optics 43, 5060–5063 (2004).
[CrossRef]

Martin-Moreno, L.

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

Matsumura, K.

Y. Mushiake, K. Matsumura, and N. Nakajima, “Generation of radially polarized optical beam mode by laser oscillation,” Proceedings of the IEEE 60, 1107–1109 (1972).
[CrossRef]

Miceli, J. J.

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Mushiake, Y.

Y. Mushiake, K. Matsumura, and N. Nakajima, “Generation of radially polarized optical beam mode by laser oscillation,” Proceedings of the IEEE 60, 1107–1109 (1972).
[CrossRef]

Nakajima, N.

Y. Mushiake, K. Matsumura, and N. Nakajima, “Generation of radially polarized optical beam mode by laser oscillation,” Proceedings of the IEEE 60, 1107–1109 (1972).
[CrossRef]

Passilly, N.

N. Passilly, R. de Saint Denis, K. Ait-Ameur, F. Treussart, R. Hierle, and J.-F. Roch, “Simple interferometric technique for generation of a radially polarized light beam,” Journal of the Optical Society of America A: Optics and Image Science, and Vision 22, 984–991 (2005).
[CrossRef]

Pikus, Y.

Z. W. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Letters 5, 1726–1729 (2005).
[CrossRef] [PubMed]

Roch, J.-F.

N. Passilly, R. de Saint Denis, K. Ait-Ameur, F. Treussart, R. Hierle, and J.-F. Roch, “Simple interferometric technique for generation of a radially polarized light beam,” Journal of the Optical Society of America A: Optics and Image Science, and Vision 22, 984–991 (2005).
[CrossRef]

Schadt, M.

M. Stalder and M. Schadt, “Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters,” Optics Letters 21, 1948 (1996).
[CrossRef] [PubMed]

Srituravanich, W.

Z. W. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Letters 5, 1726–1729 (2005).
[CrossRef] [PubMed]

Stalder, M.

M. Stalder and M. Schadt, “Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters,” Optics Letters 21, 1948 (1996).
[CrossRef] [PubMed]

M. Stalder, “Active and passive optical components using liquid crystals,” (SPIE -International Society for Optical Engineering, Bellingham WA, WA 98227–0010, USA, San Jose, CA, USA, 1996), pp. 30–39.

Steele, J. M.

Z. W. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Letters 5, 1726–1729 (2005).
[CrossRef] [PubMed]

Sun, C.

Z. W. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Letters 5, 1726–1729 (2005).
[CrossRef] [PubMed]

Treussart, F.

N. Passilly, R. de Saint Denis, K. Ait-Ameur, F. Treussart, R. Hierle, and J.-F. Roch, “Simple interferometric technique for generation of a radially polarized light beam,” Journal of the Optical Society of America A: Optics and Image Science, and Vision 22, 984–991 (2005).
[CrossRef]

Yeh, C. S.

D. Z. Lin, C. H. Chen, C. K. Chang, T. D. Cheng, C. S. Yeh, and C. K. Lee, “Subwavelength nondiffraction beam generated by a plasmonic lens,” Appl. Phys. Lett. 92, 3 (2008).

Youngworth, K. S.

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Optics Express 7, 77–87 (2000).
[CrossRef] [PubMed]

Zhan, Q.

Q. Zhan and J. R. Leger, “Focus shaping using cylindrical vector beams,” Optics Express 10, 324–331 (2002).
[PubMed]

Zhang, X.

Z. W. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Letters 5, 1726–1729 (2005).
[CrossRef] [PubMed]

Appl. Optics (1)

C. Lopez-Mariscal, J. C. Gutierrez-Vega, and S. Chavez-Cerda, “Production of high-order Bessel beams with a Mach-Zehnder interferometer,” Appl. Optics 43, 5060–5063 (2004).
[CrossRef]

Journal of the Optical Society of America A: Optics and Image Science, and Vision (1)

N. Passilly, R. de Saint Denis, K. Ait-Ameur, F. Treussart, R. Hierle, and J.-F. Roch, “Simple interferometric technique for generation of a radially polarized light beam,” Journal of the Optical Society of America A: Optics and Image Science, and Vision 22, 984–991 (2005).
[CrossRef]

Nano Letters (1)

Z. W. Liu, J. M. Steele, W. Srituravanich, Y. Pikus, C. Sun, and X. Zhang, “Focusing surface plasmons with a plasmonic lens,” Nano Letters 5, 1726–1729 (2005).
[CrossRef] [PubMed]

Nature (1)

W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength optics,” Nature 424, 824–830 (2003).
[CrossRef] [PubMed]

Optics Express (3)

B. Hao and J. Leger, “Experimental measurement of longitudinal component in the vicinity of focused radially polarized beam,” Optics Express 15, 3550–3556 (2007).
[CrossRef] [PubMed]

Q. Zhan and J. R. Leger, “Focus shaping using cylindrical vector beams,” Optics Express 10, 324–331 (2002).
[PubMed]

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Optics Express 7, 77–87 (2000).
[CrossRef] [PubMed]

Optics Letters (1)

M. Stalder and M. Schadt, “Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters,” Optics Letters 21, 1948 (1996).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

J. Durnin, J. J. Miceli, and J. H. Eberly, “Diffraction-Free Beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Proceedings of the IEEE (1)

Y. Mushiake, K. Matsumura, and N. Nakajima, “Generation of radially polarized optical beam mode by laser oscillation,” Proceedings of the IEEE 60, 1107–1109 (1972).
[CrossRef]

Science (1)

H. J. Lezec, A. Degiron, E. Devaux, R. A. Linke, L. Martin-Moreno, F. J. Garcia-Vidal, and T. W. Ebbesen, “Beaming light from a subwavelength aperture,” Science 297, 820–822 (2002).
[CrossRef] [PubMed]

Subwavelength nondiffraction beam generated by a plasmonic lens (1)

D. Z. Lin, C. H. Chen, C. K. Chang, T. D. Cheng, C. S. Yeh, and C. K. Lee, “Subwavelength nondiffraction beam generated by a plasmonic lens,” Appl. Phys. Lett. 92, 3 (2008).

Other (1)

M. Stalder, “Active and passive optical components using liquid crystals,” (SPIE -International Society for Optical Engineering, Bellingham WA, WA 98227–0010, USA, San Jose, CA, USA, 1996), pp. 30–39.

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Figures (14)

Fig. 1.
Fig. 1.

SAA structure: (a) top view and (b) side view.

Fig. 2.
Fig. 2.

(a) Experimental set-up (b) polarization after passage through LC polarizer (c) image of the RP beam focused with a 5X objective lens.

Fig. 3.
Fig. 3.

The structure of liquid crystal polariz

Fig. 4.
Fig. 4.

Images obtained at different distances above the exiting surface. (Note: the focal spot is a doughnut shape)

Fig. 5.
Fig. 5.

Z cross-section intensity profile at the smallest central spot size

Fig. 6.
Fig. 6.

Maximum intensity measured at different distances above the exit surface for SAAs with different diameters.

Fig. 7.
Fig. 7.

Generalized cylindrically polarized beam with ϕ 0 rotation from radial direction

Fig. 8.
Fig. 8.

Light beam intensity when generalized cylindrically polarized beam incidence: (a) ϕ 0=25.56° (b) ϕ 0=45° (c) ϕ 0=63.43°

Fig. 9.
Fig. 9.

Shapes of the focal spots imaged at different focal planes: (a) z=4µm, (b) z=9µm, and (c) z=16µm.

Fig. 10.
Fig. 10.

SAA structure light beam intensity: (a) r component and (b) z component.

Fig. 11.
Fig. 11.

Comparison of the intensity distribution of the axial and radial components at the focus position. (Note: using objective lens and SAA structure with diameters of 6µm, 9µm, and 12µm)

Fig. 12.
Fig. 12.

RP beam incident into objective lens from a certain angle.

Fig. 13.
Fig. 13.

Using Matlab to calculate the focal pattern when the RP beam is incident into SAA structure with an annular aperture: (a) NA=0.342, (b) NA=0.5, and (c) NA=0.766.

Fig. 14.
Fig. 14.

Comparison of the intensity distribution of the r and z components at the focus position. (Note: using objective lens and SAA structure with diameter of 12µm)

Equations (5)

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

E ( r , φ ) = P ( c o s ϕ 0 e r + s i n ϕ 0 e φ )
E ( r , ϕ ) = e r .
E r ( r , z ) = A θ min θ max c o s 1 2 ( θ ) P ( θ ) sin θ cos θ J 1 ( kr sin θ ) d θ
E z ( r , z ) = A θ min θ max cos 1 2 ( θ ) P ( θ ) sin 2 θ J 0 ( kr sin θ ) d θ
P ( θ ) = exp [ β 0 2 ( sin θ sin θ ma x ) 2 ] J 1 [ 2 β 0 sin θ sin θ ma x ]

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