Abstract

When the pupil filters are used to improve the performance of the imaging system, the conversion efficiency is a critical characteristic for real applications. Here, in order to take full advantage of the subwavelength focusing property of the radially polarized higher-order Laguerre-Gaussian (LG) beam, we introduce the multi-zone binary phase pupil filters into the imaging system to deal with the problem that the focal spot is split along the z axis for the small size parameter of the incident LG beam. We provide an easy-to-perform procedure for the design of multi-zone binary phase pupil filters, where the zone numbers of π phase are uncertain when the optimizing procedure starts. Based on this optimizing procedure, we successfully find the set of optimum structures of a seventeen-belt binary phase pupil filters and generate the excellent focal spot, where the depth of focus, the focal spot transverse size, the Strehl ratio, and the sidelobe intensity are 9.53λ, 0.41λ, 41.75% and 16.35% in vacuum, respectively. Most importantly, even allowing the power loss of the incident LG beam truncated by the pupil of the imaging system, the conversion efficiency is still as high as 37.3%. Theoretical calculations show that we succeed to have sufficient conversion efficiency while utilizing the pupil filters to decrease the focal spot and extend the depth of focus.

© 2013 OSA

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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  25. T. G. Jabbour and S. M. Kuebler, “Vector diffraction analysis of high numerical aperture focused beams modified by two- and three-zone annular multi-phase plates,” Opt. Express14(3), 1033–1043 (2006).
    [CrossRef] [PubMed]

2012 (3)

2011 (3)

2010 (1)

2009 (3)

2008 (1)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2(8), 501–505 (2008).
[CrossRef]

2007 (3)

2006 (3)

2005 (1)

2004 (3)

2003 (1)

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett.91(23), 233901 (2003).
[CrossRef] [PubMed]

2001 (1)

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett.86(23), 5251–5254 (2001).
[CrossRef] [PubMed]

2000 (1)

1959 (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 358–379 (1959).
[CrossRef]

April, A.

Araki, T.

Beversluis, M. R.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett.86(23), 5251–5254 (2001).
[CrossRef] [PubMed]

Brown, T. G.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett.86(23), 5251–5254 (2001).
[CrossRef] [PubMed]

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express7(2), 77–87 (2000).
[CrossRef] [PubMed]

Bu, J.

Chen, J.

Chong, C. T.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2(8), 501–505 (2008).
[CrossRef]

Choudhury, A.

Dehez, H.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett.91(23), 233901 (2003).
[CrossRef] [PubMed]

Feurer, T.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process.86(3), 329–334 (2007).
[CrossRef]

Gao, B. Z.

Guo, H.

Hao, X.

Y. Ku, C. Kuang, X. Hao, Y. Xue, H. Li, and X. Liu, “Superenhanced three-dimensional confinement of light by compound metal-dielectric microspheres,” Opt. Express20(15), 16981–16991 (2012).
[CrossRef]

C. Kuang, X. Hao, X. Liu, T. Wang, and Y. Ku, “Formation of sub-half-wavelength focal spot with ultra long depth of focus,” Opt. Commun.284(7), 1766–1769 (2011).
[CrossRef]

Hashimoto, M.

Hashimoto, N.

Hayazawa, N.

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett.85(25), 6239–6241 (2004).
[CrossRef]

Hibi, T.

Horanai, H.

Jabbour, T. G.

Kano, H.

Kawata, S.

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett.85(25), 6239–6241 (2004).
[CrossRef]

Kim, W. C.

Kitamura, K.

Kozawa, Y.

Ku, Y.

Y. Ku, C. Kuang, X. Hao, Y. Xue, H. Li, and X. Liu, “Superenhanced three-dimensional confinement of light by compound metal-dielectric microspheres,” Opt. Express20(15), 16981–16991 (2012).
[CrossRef]

C. Kuang, X. Hao, X. Liu, T. Wang, and Y. Ku, “Formation of sub-half-wavelength focal spot with ultra long depth of focus,” Opt. Commun.284(7), 1766–1769 (2011).
[CrossRef]

Kuang, C.

Y. Ku, C. Kuang, X. Hao, Y. Xue, H. Li, and X. Liu, “Superenhanced three-dimensional confinement of light by compound metal-dielectric microspheres,” Opt. Express20(15), 16981–16991 (2012).
[CrossRef]

C. Kuang, X. Hao, X. Liu, T. Wang, and Y. Ku, “Formation of sub-half-wavelength focal spot with ultra long depth of focus,” Opt. Commun.284(7), 1766–1769 (2011).
[CrossRef]

Kuebler, S. M.

Kurihara, M.

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett.91(23), 233901 (2003).
[CrossRef] [PubMed]

Li, H.

Liu, D.

Liu, L.

Liu, X.

Y. Ku, C. Kuang, X. Hao, Y. Xue, H. Li, and X. Liu, “Superenhanced three-dimensional confinement of light by compound metal-dielectric microspheres,” Opt. Express20(15), 16981–16991 (2012).
[CrossRef]

C. Kuang, X. Hao, X. Liu, T. Wang, and Y. Ku, “Formation of sub-half-wavelength focal spot with ultra long depth of focus,” Opt. Commun.284(7), 1766–1769 (2011).
[CrossRef]

Lukyanchuk, B.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2(8), 501–505 (2008).
[CrossRef]

Meier, M.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process.86(3), 329–334 (2007).
[CrossRef]

Moh, K. J.

Nemoto, T.

Noda, S.

Novotny, L.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett.86(23), 5251–5254 (2001).
[CrossRef] [PubMed]

Park, K. S.

Park, N. C.

Park, Y. P.

Piché, M.

Pu, J.

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett.91(23), 233901 (2003).
[CrossRef] [PubMed]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 358–379 (1959).
[CrossRef]

Romano, V.

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process.86(3), 329–334 (2007).
[CrossRef]

Ryosuke, K.

Saito, Y.

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett.85(25), 6239–6241 (2004).
[CrossRef]

Sakai, K.

Sato, A.

Sato, S.

Sheppard, C.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2(8), 501–505 (2008).
[CrossRef]

Sheppard, C. J. R.

Shi, L.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2(8), 501–505 (2008).
[CrossRef]

Sun, J.

Terakado, G.

Tian, B.

Wang, H.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2(8), 501–505 (2008).
[CrossRef]

Wang, T.

C. Kuang, X. Hao, X. Liu, T. Wang, and Y. Ku, “Formation of sub-half-wavelength focal spot with ultra long depth of focus,” Opt. Commun.284(7), 1766–1769 (2011).
[CrossRef]

Watanabe, K.

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 358–379 (1959).
[CrossRef]

Xue, Y.

Yokoyama, H.

Yoon, Y. J.

Yoshiki, K.

Youngworth, K. S.

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett.86(23), 5251–5254 (2001).
[CrossRef] [PubMed]

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express7(2), 77–87 (2000).
[CrossRef] [PubMed]

Yuan, X. C.

Yun, M.

Zhan, Q.

Zhu, S. W.

Zhuang, S.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

N. Hayazawa, Y. Saito, and S. Kawata, “Detection and characterization of longitudinal field for tip-enhanced Raman spectroscopy,” Appl. Phys. Lett.85(25), 6239–6241 (2004).
[CrossRef]

Appl. Phys., A Mater. Sci. Process. (1)

M. Meier, V. Romano, and T. Feurer, “Material processing with pulsed radially and azimuthally polarized laser radiation,” Appl. Phys., A Mater. Sci. Process.86(3), 329–334 (2007).
[CrossRef]

J. Opt. Soc. Am. A (4)

Nat. Photonics (1)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photonics2(8), 501–505 (2008).
[CrossRef]

Opt. Commun. (1)

C. Kuang, X. Hao, X. Liu, T. Wang, and Y. Ku, “Formation of sub-half-wavelength focal spot with ultra long depth of focus,” Opt. Commun.284(7), 1766–1769 (2011).
[CrossRef]

Opt. Express (8)

H. Dehez, A. April, and M. Piché, “Needles of longitudinally polarized light: guidelines for minimum spot size and tunable axial extent,” Opt. Express20(14), 14891–14905 (2012).
[CrossRef] [PubMed]

Y. Kozawa, T. Hibi, A. Sato, H. Horanai, M. Kurihara, N. Hashimoto, H. Yokoyama, T. Nemoto, and S. Sato, “Lateral resolution enhancement of laser scanning microscopy by a higher-order radially polarized mode beam,” Opt. Express19(17), 15947–15954 (2011).
[CrossRef] [PubMed]

T. G. Jabbour and S. M. Kuebler, “Vector diffraction analysis of high numerical aperture focused beams modified by two- and three-zone annular multi-phase plates,” Opt. Express14(3), 1033–1043 (2006).
[CrossRef] [PubMed]

K. Kitamura, K. Sakai, and S. Noda, “Sub-wavelength focal spot with long depth of focus generated by radially polarized, narrow-width annular beam,” Opt. Express18(5), 4518–4525 (2010).
[CrossRef] [PubMed]

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express7(2), 77–87 (2000).
[CrossRef] [PubMed]

H. Guo, J. Chen, and S. Zhuang, “Vector plane wave spectrum of an arbitrary polarized electromagnetic wave,” Opt. Express14(6), 2095–2100 (2006).
[CrossRef] [PubMed]

Y. Ku, C. Kuang, X. Hao, Y. Xue, H. Li, and X. Liu, “Superenhanced three-dimensional confinement of light by compound metal-dielectric microspheres,” Opt. Express20(15), 16981–16991 (2012).
[CrossRef]

Q. Zhan, “Trapping metallic Rayleigh particles with radial polarization,” Opt. Express12(15), 3377–3382 (2004).
[CrossRef] [PubMed]

Opt. Lett. (4)

Phys. Rev. Lett. (2)

L. Novotny, M. R. Beversluis, K. S. Youngworth, and T. G. Brown, “Longitudinal field modes probed by single molecules,” Phys. Rev. Lett.86(23), 5251–5254 (2001).
[CrossRef] [PubMed]

R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett.91(23), 233901 (2003).
[CrossRef] [PubMed]

Proc. R. Soc. Lond. A Math. Phys. Sci. (1)

B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems II. Structure of the image field in an aplanatic system,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 358–379 (1959).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Focusing diagram of a radially polarized beam transmitting through the multi-zone binary phase pupil filters and an aplanatic system L.

Fig. 2
Fig. 2

Diagram of multi-zone binary phase pupil filters viewed as the N rectangular belts (a) before and (b) after adding phase π for ease of analysis. The blue rectangular denotes the phase π.

Fig. 3
Fig. 3

Intensity profiles along (a) the transverse axis (r) at the focal plane ( z=0 ) and (b) the z axis for various size parameters β 0 of the radially polarized LG 5,1 beam. The intensity profiles are normalized by the intensity of the focal point ( x=y=z=0 ).

Fig. 4
Fig. 4

Relations between the intensity of the focal point ( x=y=z=0 ) (blue solid curve), the effective power of the incident beam (green dashed curve), and the size parameters β 0 of the radially polarized LG 5,1 beam.

Fig. 5
Fig. 5

Cross section of the focal spot in the rz plane after the multi-zone binary phase pupil filters are used. (a) Total intensity distribution. (b) Transverse component. (c) Longitudinal component. (d) Total intensity distribution of the focal spot along the r (red dashed curve) and z (blue solid curve) axes. (e) The optimization transmission function T(θ) of the multi-zone binary phase pupil filters.

Equations (6)

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

E r (r,φ,z)=A 0 α cos 1 2 θsin(2θ) l 0 (θ)T(θ) J 1 (krsinθ)exp(jkzcosθ)dθ,
E z (r,φ,z)=j2A 0 α cos 1 2 θ sin 2 θ l 0 (θ)T(θ) J 0 (krsinθ)exp(jkzcosθ)dθ,
l 0 (θ)= β 0 2 sinθ sin 2 α exp( β 0 2 sin 2 θ sin 2 α ) L p 1 ( 2 β 0 2 sin 2 θ sin 2 α ),
F(m+1,M, n min m+1 , n max m+1 ,)=F(m,M, n c m +1, n max m +1,),
θ 1 =14.36, θ 2 =19.15, θ 3 =22.74, θ 4 =23.95, θ 5 =28.72, θ 6 =29.92, θ 7 =32.31, θ 8 =33.51, θ 9 =39.49, θ 10 =40.69, θ 11 =43.08, θ 12 =47.87, θ 13 =52.66, θ 14 =57.44, θ 15 =58.64, θ 16 =59.84.
r 1 =0.2611, r 2 =0.3453, r 3 =0.4069, r 4 =0.4271, r 5 =0.5059, r 6 =0.525, r 7 =0.5627, r 8 =0.5811, r 9 =0.6695, r 10 =0.6863, r 11 =0.719, r 12 =0.7807, r 13 =0.8369, r 14 =0.8872, r 15 =0.8989, r 16 =0.9101.

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