Abstract

An axially super-resolved quasi-spherical focal spot can be generated by focusing an amplitude-modulated radially polarized beam through a high numerical aperture objective. A method based on the unique depolarization pro perties of a circular focus is proposed to design the amplitude modulation. The generated focal spot shows a ratio of xyz=111.48 for the normalized FWHM in three dimensions, compared to that of xyz=10.741.72 under linear polarization (in the x direction) illumination. Moreover, the focusable light efficiency of the designed amplitude-modulated beam is 65%, which is more than 3 times higher than the optimized case under linear polarization and thus make the amplitude-modulated radial polarization beam more suitable for a wide range of applications.

© 2011 Optical Society of America

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2010 (3)

2009 (3)

2008 (1)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

2006 (1)

M. T. Caballero, C. Ibáñez-López, and M. Martínez-Corral, Opt. Eng. 45, 098003 (2006).
[CrossRef]

2005 (2)

C. Ibáñez-López, G. Saavedra, and G. Boyer, Opt. Express 13, 6168 (2005).
[CrossRef] [PubMed]

N. Fukuchi, Y. E. Biqing, Y. Igasaki, N. Yoshida, Y. Kobayashi, and T. Hara, Opt. Rev. 12, 372 (2005).
[CrossRef]

2004 (1)

2003 (2)

2001 (1)

C. M. Blanca, J. Bewersdorf, and S. W. Hell, Appl. Phys. Lett. 79, 2321 (2001).
[CrossRef]

1999 (2)

C. J. R. Sheppard, Opt. Lett. 24, 505 (1999).
[CrossRef]

M. Gu, Advanced Optical Imaging Theory (Springer, 1999).

1997 (1)

Abeysinghe, D. C.

W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, Nano Lett. 9, 4320 (2009).
[CrossRef] [PubMed]

Bewersdorf, J.

C. M. Blanca, J. Bewersdorf, and S. W. Hell, Appl. Phys. Lett. 79, 2321 (2001).
[CrossRef]

Biqing, Y. E.

N. Fukuchi, Y. E. Biqing, Y. Igasaki, N. Yoshida, Y. Kobayashi, and T. Hara, Opt. Rev. 12, 372 (2005).
[CrossRef]

Blanca, C. M.

C. M. Blanca, J. Bewersdorf, and S. W. Hell, Appl. Phys. Lett. 79, 2321 (2001).
[CrossRef]

Boyer, G.

Caballero, M. T.

M. T. Caballero, C. Ibáñez-López, and M. Martínez-Corral, Opt. Eng. 45, 098003 (2006).
[CrossRef]

M. Martínez-Corral, C. Ibáñez-López, G. Saavedra, and M. T. Caballero, Opt. Express 11, 1740 (2003).
[CrossRef] [PubMed]

Chen, W.

W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, Nano Lett. 9, 4320 (2009).
[CrossRef] [PubMed]

Chong, C. T.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Ding, Z.

Dorn, R.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Fan, Z.

Fukuchi, N.

N. Fukuchi, Y. E. Biqing, Y. Igasaki, N. Yoshida, Y. Kobayashi, and T. Hara, Opt. Rev. 12, 372 (2005).
[CrossRef]

Gu, M.

Hara, T.

N. Fukuchi, Y. E. Biqing, Y. Igasaki, N. Yoshida, Y. Kobayashi, and T. Hara, Opt. Rev. 12, 372 (2005).
[CrossRef]

Hell, S. W.

C. M. Blanca, J. Bewersdorf, and S. W. Hell, Appl. Phys. Lett. 79, 2321 (2001).
[CrossRef]

Huang, K.

Ibáñez-López, C.

Igasaki, Y.

N. Fukuchi, Y. E. Biqing, Y. Igasaki, N. Yoshida, Y. Kobayashi, and T. Hara, Opt. Rev. 12, 372 (2005).
[CrossRef]

Jia, B.

Kang, H.

Kang, X.

Kobayashi, Y.

N. Fukuchi, Y. E. Biqing, Y. Igasaki, N. Yoshida, Y. Kobayashi, and T. Hara, Opt. Rev. 12, 372 (2005).
[CrossRef]

Leuchs, G.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Li, J.

H. Kang, B. Jia, J. Li, D. Morrish, and M. Gu, Appl. Phys. Lett. 96, 065702 (2010).

B. Jia, H. Kang, J. Li, and M. Gu, Opt. Lett. 34, 1918 (2009).
[CrossRef] [PubMed]

Li, Y.

Lukyanchuk, B.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Martínez-Corral, M.

M. T. Caballero, C. Ibáñez-López, and M. Martínez-Corral, Opt. Eng. 45, 098003 (2006).
[CrossRef]

M. Martínez-Corral, C. Ibáñez-López, G. Saavedra, and M. T. Caballero, Opt. Express 11, 1740 (2003).
[CrossRef] [PubMed]

Morrish, D.

H. Kang, B. Jia, J. Li, D. Morrish, and M. Gu, Appl. Phys. Lett. 96, 065702 (2010).

Nelson, R. L.

W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, Nano Lett. 9, 4320 (2009).
[CrossRef] [PubMed]

Quabis, S.

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Saavedra, G.

Sheppard, C.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Sheppard, C. J. R.

Shi, L.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Shi, P.

Wang, G.

Wang, H.

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Wang, Z.

Yoshida, N.

N. Fukuchi, Y. E. Biqing, Y. Igasaki, N. Yoshida, Y. Kobayashi, and T. Hara, Opt. Rev. 12, 372 (2005).
[CrossRef]

Zhan, Q.

Zhang, X.

Adv. Opt. Photon. (1)

Appl. Opt. (1)

Appl. Phys. Lett. (2)

C. M. Blanca, J. Bewersdorf, and S. W. Hell, Appl. Phys. Lett. 79, 2321 (2001).
[CrossRef]

H. Kang, B. Jia, J. Li, D. Morrish, and M. Gu, Appl. Phys. Lett. 96, 065702 (2010).

Nano Lett. (1)

W. Chen, D. C. Abeysinghe, R. L. Nelson, and Q. Zhan, Nano Lett. 9, 4320 (2009).
[CrossRef] [PubMed]

Nat. Photonics (1)

H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, Nat. Photonics 2, 501 (2008).
[CrossRef]

Opt. Eng. (1)

M. T. Caballero, C. Ibáñez-López, and M. Martínez-Corral, Opt. Eng. 45, 098003 (2006).
[CrossRef]

Opt. Express (4)

Opt. Lett. (3)

Opt. Rev. (1)

N. Fukuchi, Y. E. Biqing, Y. Igasaki, N. Yoshida, Y. Kobayashi, and T. Hara, Opt. Rev. 12, 372 (2005).
[CrossRef]

Phys. Rev. Lett. (1)

R. Dorn, S. Quabis, and G. Leuchs, Phys. Rev. Lett. 91, 233901 (2003).
[CrossRef] [PubMed]

Other (2)

Http://www.arcoptix.com/.

M. Gu, Advanced Optical Imaging Theory (Springer, 1999).

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Figures (4)

Fig. 1
Fig. 1

(a) Schematic of experiment setup of an SLM-assisted confocal microscope system under radially polarized beam illumination. L, lens; M, mirror; HWP, half-wave plate; LP, linear polarizer; RPC, radial polarization converter; WS, wavefront sensor; BS, beam splitter; O, objective ( NA = 1.4 ). (b) Schematic of a radially polarized wave focused by a high NA objective. (c) Schematic of a three-zone amplitude modulation pattern.

Fig. 2
Fig. 2

(a) Ratio of the peak intensity of the radial and longitudinal components versus the normalized effective NA. The dashed line marks | E r | 2 max = | E z | 2 max when the effective NA is 0.61. (b) The axial size W z of the focal spot versus R 2 . (c) Dependence of the aspect ratio (α) and the axial resolution enhancement (β) on the transmission of zone 2 (T). (d) Dependence of the focusable light efficiency (η) and the ratio of sidelobe strength (ε) on the transmission of zone 2 (T).

Fig. 3
Fig. 3

(a), (b) Calculated electric field density distributions in the focus for unmodulated and amplitude-modulated radially polarized beams. (c) Cross sections of the focal spots in the axial direction as marked in (a) and (b) with the white lines. r and z are coordinates normalized by the wavelength of the incident beam.

Fig. 4
Fig. 4

Measured axial responses for unmodulated (UM) and amplidute-modulated (AM) radially polarized beams. Inset a: Designed amplitude modulation pattern. Inset b: Measured intensity distribution of the generated amplitude modulation measured by a wavefront sensor.

Equations (3)

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E z ( r , z ) = 0 θ max P ( θ ) ( 1 cos ( 2 θ ) ) J 0 ( n k r sin θ ) exp ( i n k z cos θ ) d θ ,
E r ( r , z ) = 0 θ max P ( θ ) sin ( 2 θ ) J 1 ( n k r sin θ ) exp ( i n k z cos θ ) d θ ,
P ( R ) = { 1 R R 1 0.18 R 1 R R 2 1 R 2 R R 0 .

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