Abstract

We theoretically demonstrate that the doughnut focal spot can continuously be manipulated by synthetically using various beam modulation techniques. Comparatively, a more evident effect can be expected by different orders of phase modulation, while accurate manipulation stems from changing the phase diversity between two arms in an image inverting interferometer (III). The size of central dark spot can thus be continuously adjusted in a theoretically infinite scale, although it may actually be limited by resolution of Spatial Light Modulator (SLM). This approach brings additional flexibility to many applications, such as optical tweezers.

© 2012 OSA

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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2012

C. Kuang, Y. Liu, X. Hao, D. Luo, and X. Liu, “Creating attoliter detection volume by microsphere photonic nanojet and fluorescence depletion,” Opt. Commun.285(4), 402–406 (2012).
[CrossRef]

X. Hao, C. Kuang, Y. Li, and X. Liu, “Manipulation of doughnut focal spot by image inverting interferometry,” Opt. Lett.37(5), 821–823 (2012).
[CrossRef] [PubMed]

2011

D. Weigel, R. Foerster, H. Babovsky, A. Kiessling, and R. Kowarschik, “Enhanced resolution of microscopic objects by image inversion interferometry,” Opt. Express19(27), 26451–26462 (2011).
[CrossRef] [PubMed]

L. P. Du, G. H. Yuan, D. Y. Tang, and X. C. Yuan, “Tightly Focused Radially Polarized Beam for Propagating Surface Plasmon-Assisted Gap-Mode Raman Spectroscopy,” Plasmonics6(4), 651–657 (2011).
[CrossRef]

C. J. R. Sheppard, W. Gong, and K. Si, “Polarization effects in 4Pi microscopy,” Micron42(4), 353–359 (2011).
[CrossRef] [PubMed]

2010

2009

Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon.1(1), 1–57 (2009).
[CrossRef]

K. Wicker, S. Sindbert, and R. Heintzmann, “Characterisation of a resolution enhancing image inversion interferometer,” Opt. Express17(18), 15491–15501 (2009).
[CrossRef] [PubMed]

N. Sandeau, L. Wawrezinieck, P. Ferrand, H. Giovannini, and H. Rigneault, “Increasing the lateral resolution of scanning microscopes by a factor of two using 2-Image microscopy,” J. Eur. Opt. Soc. Rapid Pub. 4 (2009).

2008

H. F. Wang, L. P. 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]

C. L. Zhao, Y. J. Cai, F. Wang, X. H. Lu, and Y. Z. Wang, “Generation of a high-quality partially coherent dark hollow beam with a multimode fiber,” Opt. Lett.33(12), 1389–1391 (2008).
[CrossRef] [PubMed]

2007

S. R. Mishra, S. K. Tiwari, S. P. Ram, and S. C. Mehendale, “Generation of hollow conic beams using a metal axicon mirror,” Opt. Eng.46(8), 084002 (2007).
[CrossRef]

2006

K. I. Willig, R. R. Kellner, R. Medda, B. Hein, S. Jakobs, and S. W. Hell, “Nanoscale resolution in GFP-based microscopy,” Nat. Methods3(9), 721–723 (2006).
[CrossRef] [PubMed]

N. Sandeau and H. Giovannini, “Increasing the lateral resolution of 4Pi fluorescence microscopes,” J. Opt. Soc. Am. A23(5), 1089–1095 (2006).
[CrossRef] [PubMed]

2004

2003

2002

2000

1992

1959

B. Richards and E. Wolf, “Electromagnetic Diffraction in Optical Systems. 2. Structure of the Image Field in an Aplanatic System,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 358–379 (1959).
[CrossRef]

1835

G. B. Airy, “On the Diffraction of an Object-glass with Circular Aperture,” Trans. Cambridge Philos. Soc.5, 283–291 (1835).

Airy, G. B.

G. B. Airy, “On the Diffraction of an Object-glass with Circular Aperture,” Trans. Cambridge Philos. Soc.5, 283–291 (1835).

Babovsky, H.

Brown, T. G.

Cai, Y. J.

Cheng, Y.

Chong, C. T.

H. F. Wang, L. P. 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.

Deng, S. H.

Du, L. P.

L. P. Du, G. H. Yuan, D. Y. Tang, and X. C. Yuan, “Tightly Focused Radially Polarized Beam for Propagating Surface Plasmon-Assisted Gap-Mode Raman Spectroscopy,” Plasmonics6(4), 651–657 (2011).
[CrossRef]

Ferrand, P.

N. Sandeau, L. Wawrezinieck, P. Ferrand, H. Giovannini, and H. Rigneault, “Increasing the lateral resolution of scanning microscopes by a factor of two using 2-Image microscopy,” J. Eur. Opt. Soc. Rapid Pub. 4 (2009).

Foerster, R.

Giovannini, H.

N. Sandeau, L. Wawrezinieck, P. Ferrand, H. Giovannini, and H. Rigneault, “Increasing the lateral resolution of scanning microscopes by a factor of two using 2-Image microscopy,” J. Eur. Opt. Soc. Rapid Pub. 4 (2009).

N. Sandeau and H. Giovannini, “Increasing the lateral resolution of 4Pi fluorescence microscopes,” J. Opt. Soc. Am. A23(5), 1089–1095 (2006).
[CrossRef] [PubMed]

Gong, W.

C. J. R. Sheppard, W. Gong, and K. Si, “Polarization effects in 4Pi microscopy,” Micron42(4), 353–359 (2011).
[CrossRef] [PubMed]

Hao, X.

C. Kuang, Y. Liu, X. Hao, D. Luo, and X. Liu, “Creating attoliter detection volume by microsphere photonic nanojet and fluorescence depletion,” Opt. Commun.285(4), 402–406 (2012).
[CrossRef]

X. Hao, C. Kuang, Y. Li, and X. Liu, “Manipulation of doughnut focal spot by image inverting interferometry,” Opt. Lett.37(5), 821–823 (2012).
[CrossRef] [PubMed]

Hao, X. A.

X. A. Hao, C. F. Kuang, T. T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt.12(11), 115707 (2010).
[CrossRef]

Hein, B.

K. I. Willig, R. R. Kellner, R. Medda, B. Hein, S. Jakobs, and S. W. Hell, “Nanoscale resolution in GFP-based microscopy,” Nat. Methods3(9), 721–723 (2006).
[CrossRef] [PubMed]

Heintzmann, R.

Hell, S.

Hell, S. W.

K. I. Willig, R. R. Kellner, R. Medda, B. Hein, S. Jakobs, and S. W. Hell, “Nanoscale resolution in GFP-based microscopy,” Nat. Methods3(9), 721–723 (2006).
[CrossRef] [PubMed]

Jakobs, S.

K. I. Willig, R. R. Kellner, R. Medda, B. Hein, S. Jakobs, and S. W. Hell, “Nanoscale resolution in GFP-based microscopy,” Nat. Methods3(9), 721–723 (2006).
[CrossRef] [PubMed]

Kellner, R. R.

K. I. Willig, R. R. Kellner, R. Medda, B. Hein, S. Jakobs, and S. W. Hell, “Nanoscale resolution in GFP-based microscopy,” Nat. Methods3(9), 721–723 (2006).
[CrossRef] [PubMed]

Kiessling, A.

Kowarschik, R.

Kuang, C.

C. Kuang, Y. Liu, X. Hao, D. Luo, and X. Liu, “Creating attoliter detection volume by microsphere photonic nanojet and fluorescence depletion,” Opt. Commun.285(4), 402–406 (2012).
[CrossRef]

X. Hao, C. Kuang, Y. Li, and X. Liu, “Manipulation of doughnut focal spot by image inverting interferometry,” Opt. Lett.37(5), 821–823 (2012).
[CrossRef] [PubMed]

Kuang, C. F.

X. A. Hao, C. F. Kuang, T. T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt.12(11), 115707 (2010).
[CrossRef]

Leger, J. R.

Li, R. X.

Li, X. Y.

Li, Y.

Liu, L.

Liu, X.

X. Hao, C. Kuang, Y. Li, and X. Liu, “Manipulation of doughnut focal spot by image inverting interferometry,” Opt. Lett.37(5), 821–823 (2012).
[CrossRef] [PubMed]

C. Kuang, Y. Liu, X. Hao, D. Luo, and X. Liu, “Creating attoliter detection volume by microsphere photonic nanojet and fluorescence depletion,” Opt. Commun.285(4), 402–406 (2012).
[CrossRef]

X. A. Hao, C. F. Kuang, T. T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt.12(11), 115707 (2010).
[CrossRef]

Liu, Y.

C. Kuang, Y. Liu, X. Hao, D. Luo, and X. Liu, “Creating attoliter detection volume by microsphere photonic nanojet and fluorescence depletion,” Opt. Commun.285(4), 402–406 (2012).
[CrossRef]

Lu, X. H.

Lukyanchuk, B.

H. F. Wang, L. P. 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]

Luo, D.

C. Kuang, Y. Liu, X. Hao, D. Luo, and X. Liu, “Creating attoliter detection volume by microsphere photonic nanojet and fluorescence depletion,” Opt. Commun.285(4), 402–406 (2012).
[CrossRef]

Medda, R.

K. I. Willig, R. R. Kellner, R. Medda, B. Hein, S. Jakobs, and S. W. Hell, “Nanoscale resolution in GFP-based microscopy,” Nat. Methods3(9), 721–723 (2006).
[CrossRef] [PubMed]

Mehendale, S. C.

S. R. Mishra, S. K. Tiwari, S. P. Ram, and S. C. Mehendale, “Generation of hollow conic beams using a metal axicon mirror,” Opt. Eng.46(8), 084002 (2007).
[CrossRef]

Mishra, S. R.

S. R. Mishra, S. K. Tiwari, S. P. Ram, and S. C. Mehendale, “Generation of hollow conic beams using a metal axicon mirror,” Opt. Eng.46(8), 084002 (2007).
[CrossRef]

Ram, S. P.

S. R. Mishra, S. K. Tiwari, S. P. Ram, and S. C. Mehendale, “Generation of hollow conic beams using a metal axicon mirror,” Opt. Eng.46(8), 084002 (2007).
[CrossRef]

Richards, B.

B. Richards and E. Wolf, “Electromagnetic Diffraction in Optical Systems. 2. Structure of the Image Field in an Aplanatic System,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 358–379 (1959).
[CrossRef]

Rigneault, H.

N. Sandeau, L. Wawrezinieck, P. Ferrand, H. Giovannini, and H. Rigneault, “Increasing the lateral resolution of scanning microscopes by a factor of two using 2-Image microscopy,” J. Eur. Opt. Soc. Rapid Pub. 4 (2009).

Sandeau, N.

N. Sandeau, L. Wawrezinieck, P. Ferrand, H. Giovannini, and H. Rigneault, “Increasing the lateral resolution of scanning microscopes by a factor of two using 2-Image microscopy,” J. Eur. Opt. Soc. Rapid Pub. 4 (2009).

N. Sandeau and H. Giovannini, “Increasing the lateral resolution of 4Pi fluorescence microscopes,” J. Opt. Soc. Am. A23(5), 1089–1095 (2006).
[CrossRef] [PubMed]

Shen, F.

Sheppard, C.

H. F. Wang, L. P. 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. P.

H. F. Wang, L. P. 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]

Si, K.

C. J. R. Sheppard, W. Gong, and K. Si, “Polarization effects in 4Pi microscopy,” Micron42(4), 353–359 (2011).
[CrossRef] [PubMed]

Sindbert, S.

Stelzer, E. H. K.

Tang, D. Y.

L. P. Du, G. H. Yuan, D. Y. Tang, and X. C. Yuan, “Tightly Focused Radially Polarized Beam for Propagating Surface Plasmon-Assisted Gap-Mode Raman Spectroscopy,” Plasmonics6(4), 651–657 (2011).
[CrossRef]

Tiwari, S. K.

S. R. Mishra, S. K. Tiwari, S. P. Ram, and S. C. Mehendale, “Generation of hollow conic beams using a metal axicon mirror,” Opt. Eng.46(8), 084002 (2007).
[CrossRef]

Wang, F.

Wang, H. F.

H. F. Wang, L. P. 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. T.

X. A. Hao, C. F. Kuang, T. T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt.12(11), 115707 (2010).
[CrossRef]

Wang, X. H.

Wang, Y. Z.

Wawrezinieck, L.

N. Sandeau, L. Wawrezinieck, P. Ferrand, H. Giovannini, and H. Rigneault, “Increasing the lateral resolution of scanning microscopes by a factor of two using 2-Image microscopy,” J. Eur. Opt. Soc. Rapid Pub. 4 (2009).

Weigel, D.

Wicker, K.

Willig, K. I.

K. I. Willig, R. R. Kellner, R. Medda, B. Hein, S. Jakobs, and S. W. Hell, “Nanoscale resolution in GFP-based microscopy,” Nat. Methods3(9), 721–723 (2006).
[CrossRef] [PubMed]

Wolf, E.

B. Richards and E. Wolf, “Electromagnetic Diffraction in Optical Systems. 2. Structure of the Image Field in an Aplanatic System,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 358–379 (1959).
[CrossRef]

Xu, Z. Z.

Youngworth, K. S.

Yuan, G. H.

L. P. Du, G. H. Yuan, D. Y. Tang, and X. C. Yuan, “Tightly Focused Radially Polarized Beam for Propagating Surface Plasmon-Assisted Gap-Mode Raman Spectroscopy,” Plasmonics6(4), 651–657 (2011).
[CrossRef]

Yuan, X. C.

L. P. Du, G. H. Yuan, D. Y. Tang, and X. C. Yuan, “Tightly Focused Radially Polarized Beam for Propagating Surface Plasmon-Assisted Gap-Mode Raman Spectroscopy,” Plasmonics6(4), 651–657 (2011).
[CrossRef]

D. W. Zhang and X. C. Yuan, “Optical doughnut for optical tweezers,” Opt. Lett.28(9), 740–742 (2003).
[CrossRef] [PubMed]

Zhan, Q.

Zhan, Q. W.

Zhang, D. W.

Zhao, C. L.

Zheng, Y.

Adv. Opt. Photon.

Appl. Opt.

J. Eur. Opt. Soc. Rapid Pub.

N. Sandeau, L. Wawrezinieck, P. Ferrand, H. Giovannini, and H. Rigneault, “Increasing the lateral resolution of scanning microscopes by a factor of two using 2-Image microscopy,” J. Eur. Opt. Soc. Rapid Pub. 4 (2009).

J. Opt.

X. A. Hao, C. F. Kuang, T. T. Wang, and X. Liu, “Effects of polarization on the de-excitation dark focal spot in STED microscopy,” J. Opt.12(11), 115707 (2010).
[CrossRef]

J. Opt. Soc. Am. A

Micron

C. J. R. Sheppard, W. Gong, and K. Si, “Polarization effects in 4Pi microscopy,” Micron42(4), 353–359 (2011).
[CrossRef] [PubMed]

Nat. Methods

K. I. Willig, R. R. Kellner, R. Medda, B. Hein, S. Jakobs, and S. W. Hell, “Nanoscale resolution in GFP-based microscopy,” Nat. Methods3(9), 721–723 (2006).
[CrossRef] [PubMed]

Nat. Photonics

H. F. Wang, L. P. 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.

C. Kuang, Y. Liu, X. Hao, D. Luo, and X. Liu, “Creating attoliter detection volume by microsphere photonic nanojet and fluorescence depletion,” Opt. Commun.285(4), 402–406 (2012).
[CrossRef]

Opt. Eng.

S. R. Mishra, S. K. Tiwari, S. P. Ram, and S. C. Mehendale, “Generation of hollow conic beams using a metal axicon mirror,” Opt. Eng.46(8), 084002 (2007).
[CrossRef]

Opt. Express

Opt. Lett.

Plasmonics

L. P. Du, G. H. Yuan, D. Y. Tang, and X. C. Yuan, “Tightly Focused Radially Polarized Beam for Propagating Surface Plasmon-Assisted Gap-Mode Raman Spectroscopy,” Plasmonics6(4), 651–657 (2011).
[CrossRef]

Proc. R. Soc. Lond. A Math. Phys. Sci.

B. Richards and E. Wolf, “Electromagnetic Diffraction in Optical Systems. 2. Structure of the Image Field in an Aplanatic System,” Proc. R. Soc. Lond. A Math. Phys. Sci.253(1274), 358–379 (1959).
[CrossRef]

Trans. Cambridge Philos. Soc.

G. B. Airy, “On the Diffraction of an Object-glass with Circular Aperture,” Trans. Cambridge Philos. Soc.5, 283–291 (1835).

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Figures (4)

Fig. 1
Fig. 1

The configuration of system. QWP, quarter-wave plate; BSM, beam shape modulator; BS, beam splitter; IIO, image inverting optics; OL, objective lens; I1, typical vortex phase masks; I2, 3D structure of a double Porro prism and the corresponding optical path.

Fig. 2
Fig. 2

The central dark area size s versus the phase diversity α and the order of vortex phase modulation N. The dot lines are the standard cases generated by different N’s.

Fig. 3
Fig. 3

4Pi structure. (a) The configuration. QWP, quarter-wave plate; BSM, beam shape modulator; BS, beam splitter; IIO, image inverting optics; OL, objective lens; S, switcher. (b) The interval of each order N. The solid rectangles in the figure are the dark spot sizes obtained in standard case, while the error bars are the corresponding intervals by 4Pi (blue) and forward (red) structures.

Fig. 4
Fig. 4

The comparison between the focal spots generated by using 4Pi and forward structures. (a) The focal spots generated by forward (left) and 4Pi (right) structures when vortex 0~8π phase modulation is utilized. (b) The uniformity versus order N in 4Pi (blue) and forward (red) structures.

Tables (2)

Tables Icon

Table 1 Sizes of Doughnut Focal Spots Generated by Different Orders of Vortex Phase Modulation

Tables Icon

Table 2 Manipulation Scale of Central Dark Area Size s

Equations (8)

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

E ( r 2 , φ 2 , z 2 )=iC Ω sin(θ) A 0 (θ,φ) A 1 (θ,φ) A 2 (θ,φ) P (θ,φ) e iΔβ(θ,φ) e ikn( z 2 cosθ+ r 2 sinθcos(φ φ 2 )) dθdφ iC Ω F (θ,φ) e iΔβ(θ,φ) dθdφ
Δβ(θ,φ)=Nφ
E ( r 2 , φ 2 , z 2 )= I 1 E noninverted ( r 2 , φ 2 , z 2 )+ I 2 E inverted ( r 2 , φ 2 , z 2 ) =iC Ω F (θ,φ)[ I 1 e iNφ + I 2 e i(αNφ) ] dθdφ
{ A 0 (θ,φ)=1 A 1 (θ,φ)= e ( sinθ sin θ max ) 2 A 2 (θ,φ)= cosθ V(θ,φ)
A 1 (θ,φ)= e γ 0 2 ( sinθ sin θ max ) 2 J 1 (2 γ 0 sinθ sin θ max )
E '( r 2 , φ 2 , z 2 )= I 1 E noninverted ( r 2 , φ 2 , z 2 )+ I 2 E noninverted ( r 2 , φ 2 , z 2 )
U=1 | I max_x I max_y | I max_x + I max_y
F =2π R 3 ε 1 c ( ε 2 ε 1 ε 2 +2 ε 1 )I

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