Abstract

We compare generation of a dark spot using focusing of beams with azimuthal polarizion, radial polarization with a vortex, and a circular polarization with either a first or second order vortex. By optimization of the amplitude-phase pupil, it is ascertained that azimuthal polarization is the most suitable one to obtain the diffraction bounded dark spot per se whose scalar approximation limit has FWHM=0.29λ. Consequently, for dark spot generation, this polarization plays the role of the radial polarization in creation of the diffraction-limited bright spot. Using azimuthal polarization, it is shown that an amplitude-phase filter allows generation of a subdiffractive dark spot in a prescribed finite area.

© 2012 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2011 (3)

2010 (1)

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt. 12, 115707 (2010).
[CrossRef]

2009 (2)

S. Sato and Y. Kozawa, “Hollow vortex beams,” J. Opt. Soc. Am. A 26, 142–146 (2009).
[CrossRef]

F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Letters 9, 1249–1254 (2009).
[CrossRef]

2008 (2)

2007 (5)

2006 (3)

2005 (1)

2004 (2)

C. J. R. Sheppard and A. Choudhury, “Annular pupils, radial polarization, and superresolution,” Appl. Opt. 43, 4322–4327 (2004).
[CrossRef]

S. F. Pereira and A. S. van de Nes, “Superresolution by means of polarization, phase and amplitude pupil masks,” Opt. Commun. 234, 119–124 (2004).
[CrossRef]

2003 (2)

D. Gamic, X. Gan, and M. Gu, “Focusing of doughnut laser beams by a high numerical-aperture objective in a free space,” Opt. Express 11, 2747–2752 (2003).
[CrossRef]

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

2000 (1)

1997 (1)

1994 (1)

1992 (1)

1959 (1)

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

1952 (1)

G. Toraldo di Francia, “Super-gain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426–427 (1952).
[CrossRef]

Alonso, M. A.

Artl, J.

Bainier, C.

Bara Viñas, S.

Biss, D. P.

Bokor, N.

Borghi, R.

Brent, R. P.

R. P. Brent, “Algorithms for minimization without derivatives” (Prentice-Hall, 1973), pp. 195.

Brown, T. G.

Choudhury, A.

Courjon, D.

Daigoku, K.

N. Bokor, Y. Iketabi, T. Watanabe, K. Daigoku, N. Davidson, and M. Fujii, “On polarization effects in fluorescence depletion microscopy,” Opt. Commun. 272, 263–268 (2007).
[CrossRef]

Davidson, N.

N. Bokor, Y. Iketabi, T. Watanabe, K. Daigoku, N. Davidson, and M. Fujii, “On polarization effects in fluorescence depletion microscopy,” Opt. Commun. 272, 263–268 (2007).
[CrossRef]

N. Bokor and N. Davidson, “Generation of a hollow dark spherical spot by 4π focusing of a radially polarized Laguerre-Gaussian beam,” Opt. Lett. 31, 149–151 (2006).
[CrossRef]

Dorn, R.

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

Fujii, M.

N. Bokor, Y. Iketabi, T. Watanabe, K. Daigoku, N. Davidson, and M. Fujii, “On polarization effects in fluorescence depletion microscopy,” Opt. Commun. 272, 263–268 (2007).
[CrossRef]

Y. Iketaki, T. Watanabe, N. Bokor, and M. Fujii, “Investigation of the center intensity of first and second-order Laguerre-Gaussian beams with linear and circular polarization,” Opt. Lett. 32, 2357–2359 (2007).
[CrossRef]

Gamic, D.

Gan, X.

Golub, I.

Grosjean, T.

Gu, M.

Hao, X.

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt. 12, 115707 (2010).
[CrossRef]

Hell, S. W.

Helseth, L. E.

L. E. Helseth, “Smallest focal hole,” Opt. Commun. 257, 1–8 (2006).
[CrossRef]

Huang, F. M.

F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Letters 9, 1249–1254 (2009).
[CrossRef]

Iketabi, Y.

N. Bokor, Y. Iketabi, T. Watanabe, K. Daigoku, N. Davidson, and M. Fujii, “On polarization effects in fluorescence depletion microscopy,” Opt. Commun. 272, 263–268 (2007).
[CrossRef]

Iketaki, Y.

Jaroszewicz, Z.

Kalosha, V.

Khonina, S. N.

Kolodziejczyk, A.

Kozawa, Y.

Kuang, C.

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt. 12, 115707 (2010).
[CrossRef]

Lerman, G. M.

Leuchs, G.

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

Levy, V.

Liu, X.

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt. 12, 115707 (2010).
[CrossRef]

Makris, K. G.

Morris, G. M.

Padgett, M. J.

Pereira, S. F.

S. F. Pereira and A. S. van de Nes, “Superresolution by means of polarization, phase and amplitude pupil masks,” Opt. Commun. 234, 119–124 (2004).
[CrossRef]

Psaltis, D.

Pu, J.

Quabis, S.

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

Richards, B.

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

Sales, T. R. M.

Santarsiero, M.

Sato, S.

Sheppard, C. J. R.

Sypek, M.

Tian, B.

Toraldo di Francia, G.

G. Toraldo di Francia, “Super-gain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426–427 (1952).
[CrossRef]

van de Nes, A. S.

S. F. Pereira and A. S. van de Nes, “Superresolution by means of polarization, phase and amplitude pupil masks,” Opt. Commun. 234, 119–124 (2004).
[CrossRef]

Wang, T.

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt. 12, 115707 (2010).
[CrossRef]

Watanabe, T.

N. Bokor, Y. Iketabi, T. Watanabe, K. Daigoku, N. Davidson, and M. Fujii, “On polarization effects in fluorescence depletion microscopy,” Opt. Commun. 272, 263–268 (2007).
[CrossRef]

Y. Iketaki, T. Watanabe, N. Bokor, and M. Fujii, “Investigation of the center intensity of first and second-order Laguerre-Gaussian beams with linear and circular polarization,” Opt. Lett. 32, 2357–2359 (2007).
[CrossRef]

Wichmann, J.

Wolf, E.

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

Youngworth, K. S.

Zheludev, N. I.

F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Letters 9, 1249–1254 (2009).
[CrossRef]

Appl. Opt. (3)

J. Opt. (1)

X. Hao, C. Kuang, T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt. 12, 115707 (2010).
[CrossRef]

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

Nano Letters (1)

F. M. Huang and N. I. Zheludev, “Super-resolution without evanescent waves,” Nano Letters 9, 1249–1254 (2009).
[CrossRef]

Nuovo Cimento (1)

G. Toraldo di Francia, “Super-gain antennas and optical resolving power,” Nuovo Cimento Suppl. 9, 426–427 (1952).
[CrossRef]

Opt. Commun. (3)

S. F. Pereira and A. S. van de Nes, “Superresolution by means of polarization, phase and amplitude pupil masks,” Opt. Commun. 234, 119–124 (2004).
[CrossRef]

N. Bokor, Y. Iketabi, T. Watanabe, K. Daigoku, N. Davidson, and M. Fujii, “On polarization effects in fluorescence depletion microscopy,” Opt. Commun. 272, 263–268 (2007).
[CrossRef]

L. E. Helseth, “Smallest focal hole,” Opt. Commun. 257, 1–8 (2006).
[CrossRef]

Opt. Express (2)

Opt. Lett. (10)

S. N. Khonina and I. Golub, “Optimization of focusing of linearly polarized light,” Opt. Lett. 36, 352–354 (2011).
[CrossRef]

J. Artl and M. J. Padgett, “Generation of a beam with a dark focus surrounded by regions of higher intensity: the optical bottle beam,” Opt. Lett. 25, 191–193 (2000).
[CrossRef]

S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated-emission-depletion fluorescence microscopy,” Opt. Lett. 19, 780–782 (1994).
[CrossRef]

V. Kalosha and I. Golub, “Toward the subdiffraction focusing limit of optical superresolution,” Opt. Lett. 32, 3540–3542 (2007).
[CrossRef]

T. Grosjean, D. Courjon, and C. Bainier, “Smallest lithographic marks generated by optical focusing systems,” Opt. Lett. 32, 976–978 (2007).
[CrossRef]

B. Tian and J. Pu, “Tight focusing of a double-ring-shaped, azimuthally polarized beam,” Opt. Lett. 36, 2014–2016 (2011).
[CrossRef]

N. Bokor and N. Davidson, “Generation of a hollow dark spherical spot by 4π focusing of a radially polarized Laguerre-Gaussian beam,” Opt. Lett. 31, 149–151 (2006).
[CrossRef]

Y. Iketaki, T. Watanabe, N. Bokor, and M. Fujii, “Investigation of the center intensity of first and second-order Laguerre-Gaussian beams with linear and circular polarization,” Opt. Lett. 32, 2357–2359 (2007).
[CrossRef]

Y. Kozawa and S. Sato, “Dark spot formation by vector beams,” Opt. Lett. 33, 2326–2329 (2008).
[CrossRef]

K. G. Makris and D. Psaltis, “Superoscillatory diffraction-free beams,” Opt. Lett. 36, 4335–4357 (2011).
[CrossRef]

Phys. Rev. Lett. (1)

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

Proc. R. Soc. London Ser. A (1)

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

Other (1)

R. P. Brent, “Algorithms for minimization without derivatives” (Prentice-Hall, 1973), pp. 195.

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Tables (4)

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Table 1. Intensity Distribution in the Focus for Four Different Polarizationsa

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Table 2. Coefficients of Third Order Polynomial Used for Optimization of Dark Spot Generation for Four Different Polarizations

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Table 3. Intensity Distribution in the Focus for Azimuthal Polarization Using Different Parameters: τ , Secondary/Main Lobe Ratio Within a Radius ρ (the Intensity Distribution in Focus for the Last Two Cases is on a Logarithmic Scale to Make the Weak Lobes Visible)

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Table 4. Coefficients of Third Order Polynomial Used for Dark Spot Generation for the Four Cases Described in Table 3

Equations (6)

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| E 0 ( ρ ) | 2 | 0 R J 0 ( k r ρ f ) r d r | 2 f 2 R 2 k 2 ρ 2 J 1 2 ( k ρ R f ) .
| E 0 ( ρ ) | 2 | R δ R J 0 ( k r ρ f ) r d r | 2 R 2 δ 2 J 0 2 ( k ρ R f ) .
| E 1 ( ρ ) | 2 | 0 R J 1 ( k r ρ f ) r d r | 2 .
| E 1 ( ρ ) | 2 | R δ R J 1 ( k r ρ f ) r d r | 2 R 2 δ 2 J 1 2 ( k ρ R f ) ,
B m ( θ , ϕ ) = exp ( i m ϕ ) s = 0 S c s sin s θ .
Φ { | E m ( ρ ) | 2 ; T ( ρ ) } c s min ,

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