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Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 12 — Jun. 4, 2012
  • pp: 12692–12698
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Continuous manipulation of doughnut focal spot in a large scale

Xiang Hao, Cuifang Kuang, Yanghui Li, and Xu Liu  »View Author Affiliations


Optics Express, Vol. 20, Issue 12, pp. 12692-12698 (2012)
http://dx.doi.org/10.1364/OE.20.012692


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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

1. Introduction

Since the vectorial diffraction theory was proposed, humans have gradually realized that it is not precise to describe the focal spot of a collimated beam as an Airy disk [1

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

] when the numerical aperture (NA) of objective lens utilized is high enough. Multiple aspects, including the phase [2

2. 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. Photonics 2(8), 501–505 (2008). [CrossRef]

], beam shape [3

3. C. J. R. Sheppard and A. Choudhury, “Annular pupils, radial polarization, and superresolution,” Appl. Opt. 43(22), 4322–4327 (2004). [CrossRef] [PubMed]

], polarization of incident light [4

4. C. J. R. Sheppard, W. Gong, and K. Si, “Polarization effects in 4Pi microscopy,” Micron 42(4), 353–359 (2011). [CrossRef] [PubMed]

] and aberration [5

5. S. H. Deng, L. Liu, Y. Cheng, R. X. Li, and Z. Z. Xu, “Effects of primary aberrations on the fluorescence depletion patterns of STED microscopy,” Opt. Express 18(2), 1657–1666 (2010). [CrossRef] [PubMed]

] can potentially change the shape of focal spot. This natural property of light, although makes it more difficult to forecast the focal phenomenon, indeed brings additional flexibility in optical design. Based on the explicit design to the whole system, some special, but useful focal spot patterns are created, and the corresponding design methods are proposed. However, once all devices in the optical path are fixed, it is not easy to adjust the final pattern.

Doughnut focal spot, with a dark center surrounded by a high-intensity ring, is widely used in many research domains: such as nonlinear optics [6

6. K. I. Willig, R. R. Kellner, R. Medda, B. Hein, S. Jakobs, and S. W. Hell, “Nanoscale resolution in GFP-based microscopy,” Nat. Methods 3(9), 721–723 (2006). [CrossRef] [PubMed]

], bio-optics [7

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

] and excitation of surface wave [8

8. 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,” Plasmonics 6(4), 651–657 (2011). [CrossRef]

]. It is not surprising that the performance of corresponding system highly relies on the intensity distribution of doughnut focal spot, especially the size of central dark area. Generally, the doughnut focal spot can be generated by using incident beam phase-encoded by a vortex 0~2π phase plate [6

6. K. I. Willig, R. R. Kellner, R. Medda, B. Hein, S. Jakobs, and S. W. Hell, “Nanoscale resolution in GFP-based microscopy,” Nat. Methods 3(9), 721–723 (2006). [CrossRef] [PubMed]

], azimuthally polarized beam [9

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

], or some micro/nano-structures [10

10. 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]

]. To any of the current approaches, changing the size of central dark area is a task hard to achieve, which severely limits the flexibility in practical applications. This problem can partially be solved by using high-order vortex phase plate [11

11. 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]

]. However, because a perfect doughnut focal spot can only be expected when the value of order is even, it is still impossible to continuously manipulate the size of central dark area. Theoretical simulation has confirmed that if the incident light is elliptically polarized, the size can continuously be manipulated in one direction by changing the ellipticility of polarization [12

12. 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]

]. However, a following question is that the uniformity of intensity around the central dark area will be destroyed. By using a hollow incident beam and defocusing the objective plane, Du et al. [8

8. 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,” Plasmonics 6(4), 651–657 (2011). [CrossRef]

] proposed a simple way to create the doughnut spot, and the size of central dark area can readily be manipulated in a large scale by modifying the defocusing distance. However, the diffractive effect makes it is unrealistic to shrink the size to subwavelength scale, otherwise, the central intensity can never maintain at zero.

Recently, Hao et al. [11

11. 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]

] represented a method to solve this problem. Based on image inverting interference (III), combined with 0~2π vortex phase modulation, they theoretically demonstrated that the doughnut focal spot could readily be manipulated, and either shrinkage or expansion of size of central dark area is possible in a scale of 0.555λ-0.830λ, where λ is the wavelength of incident beam. Although the continuous manipulation of the doughnut focal spot has been realized, the manipulation scale is still small. In practical system, such as optical tweezers, a larger manipulation scale will result in more optimized performance by supplying the capability to trap particles with diverse sizes or weights.

2. Theory

A straightforward way to modify the shape of focal spot is introducing the Spatial Light Modulator (SLM), or the phase plate, into the optical path. Generally, the doughnut focal spot can be attained by vortex phase modulation, and the corresponding phase delay parameter can be expressed as:
Δβ(θ,φ)=Nφ
(2)
where N is the order number, and N = 2, 4, 6… By substituting Eq. (2) into Eq. (1), the amplitude distribution of doughnut focal spot can be calculated without difficulty. A larger doughnut focal spot will stem from higher order of vortex phase modulation, and the detailed data is listed in Table 1

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

table-icon
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. The utilization of the image inverting interference (III) makes the distribution a bit more complex. The scheme of an III [14

14. D. Weigel, R. Foerster, H. Babovsky, A. Kiessling, and R. Kowarschik, “Enhanced resolution of microscopic objects by image inversion interferometry,” Opt. Express 19(27), 26451–26462 (2011). [CrossRef] [PubMed]

] is a two-beam interferometer with an image inverting optics included in one of the arms. In this situation, the amplitude distribution of final focal spot will be the interference result of the two spots independently generated by the noninverted and inverted beams, respectively, and can be written as:
E(r2,φ2,z2)=I1Enoninverted(r2,φ2,z2)+I2Einverted(r2,φ2,z2)=iCΩF(θ,φ)[I1eiNφ+I2ei(αNφ)]dθdφ
(3)
where I1 and I2 are intensity weights of noninverted and inverted beams, respectively, and I1+I2=1. α is the phase diversity between two arms.

3. Results and discussion

To realize the continuous manipulation of doughnut focal spot in a large scale, we set up a system as shown in 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.
. After radiated from the laser source, the incident beam will propagate through the Beam Shape Modulator (BSM), SLM and III, and finally be focused by the high NA objective lens to generate a doughnut focal spot. The function of BSM will be explicitly discussed in later sections. Many forthcoming devices are available to realize image inverting, such as 4f telescope [15

15. N. Sandeau and H. Giovannini, “Increasing the lateral resolution of 4Pi fluorescence microscopes,” J. Opt. Soc. Am. A 23(5), 1089–1095 (2006). [CrossRef] [PubMed]

], confocal concave mirror pairs [13

13. 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]

], double Porro prism [14

14. D. Weigel, R. Foerster, H. Babovsky, A. Kiessling, and R. Kowarschik, “Enhanced resolution of microscopic objects by image inversion interferometry,” Opt. Express 19(27), 26451–26462 (2011). [CrossRef] [PubMed]

], UZ-interferometer [16

16. K. Wicker, S. Sindbert, and R. Heintzmann, “Characterisation of a resolution enhancing image inversion interferometer,” Opt. Express 17(18), 15491–15501 (2009). [CrossRef] [PubMed]

], or modified Michelson one [17

17. 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).

]. It should be emphasized that the mirror based solutions, especially the double Porro prism, is probably very essential to the system working with femtosecond lasers, because it is simple and more compact, while the phase diversity between two arms can be modulated by adjusting the gap between two single prisms along the optical axis. Furthermore, the flat mirror is very insensitive to chromatic dispersion. To simplify the discussion, some conditions are listed as the premises without loss of generality. The incident light is a collimated beam with Gauss intensity distribution and circular polarization. The objective lens is aberration-free [18

18. C. J. R. Sheppard, “Validity of the Debye approximation,” Opt. Lett. 25(22), 1660–1662 (2000). [CrossRef] [PubMed]

] and oil-immersed, with NA = 1.4. The detection plane is placed exactly at the ideal foci of objective lens. Based on the assumptions above, all parameters in Eq. (1) can thus be clarified, that
{A0(θ,φ)=1A1(θ,φ)=e(sinθsinθmax)2A2(θ,φ)=cosθV(θ,φ)
(4)
where θmax=arcsin(NA/n), and n is the refractive index of immersion oil. V(θ,φ) is the conversion matrix of the polarization from the object field to the image field.

Considering the optimization to final focal spot, we make the intensity ratio between two arms of III as I1:I2 = 1:1, although it may not be the unique option. Thus, N and α will be the only variable parameters which can influence the amplitude distribution of focal spot. By substituting Eq. (4) into Eq. (3), the amplitude distribution can be derived, and the intensity can further be calculated by the formula I=|E|2. If defining the size of central dark spot s as the distance between two intensity peaks along the radial direction, s versus N and α can thus be presented as shown in 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.
, and the manipulation scales are concisely summarized in Table 2

Table 2. Manipulation Scale of Central Dark Area Size s

table-icon
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. Comparatively, a more evident effect can be expected by different orders of phase modulation (we name these values as the “Standard Cases”), while changing the phase diversity between two arms in III can modify the size s in both positive and negative directions around the “Standard Case”, and a finite manipulation interval can thus be created. Hence, a whole manipulation scale will be the mosaic result of the all intervals, and can be created by comprehensively adjusting two values. The whole system works like a transmission in a road-going vehicle, that the “gear” is decided by the order of vortex phase plate, while the “throttle” is the phase diversity between two arms of III. However, it is notable that although it is very small and can even be neglected, a gap indeed exists between two adjacent intervals, which make the whole manipulation actually discontinuous.

To overcome this defect, it is necessary to supply additional parameters to improve the manipulation flexibility, and that is the reason why BSM is used. The BSM includes two separate optical paths and can be switched to either one by the rotatable mirrors. The beam can either maintain the Gauss intensity distribution in cross section, or be reshaped as the hollow one. The hollow beam can simply be generated by making the incident beam propagating through an annular aperture, or by using some specific devices like axicon [19

19. 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]

], adaptive optics [20

20. Y. Zheng, X. H. Wang, F. Shen, and X. Y. Li, “Generation of dark hollow beam via coherent combination based on adaptive optics,” Opt. Express 18(26), 26946–26958 (2010). [CrossRef] [PubMed]

] or optical fiber [21

21. 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]

]. The hollow distribution in cross section can approximately be described as the Bessel-Gauss function [22

22. K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000). [CrossRef] [PubMed]

], that
A1(θ,φ)=eγ02(sinθsinθmax)2J1(2γ0sinθsinθmax)
(5)
where γ0 is the ratio of the pupil radius and the beam waist. To locate the intensity peak exactly at the edge of incident beam, let γ0 = 0.5. The utilization of Bessel-Gauss beam will expand the lower limit of each interval, and the calculation results are also shown in Table 2. Compared with the data of using Gauss Beam alone, the gap between two intervals can now be filled by switching the optical paths of BSM when necessary.

By using the method mentioned above, the expansion of size of central dark area is theoretically infinite in upper limit. A larger size stems from a higher order of vortex phase modulation. However, in practical experiment, the limited resolution of SLM will confine the acquisition of high order vortex phase modulation, which indirectly limits the attainable maximum size. Moreover, BSM can be abandoned if the 4Pi [23

23. S. Hell and E. H. K. Stelzer, “Properties of a 4pi Confocal Fluorescence Microscope,” J. Opt. Soc. Am. A 9(12), 2159–2166 (1992). [CrossRef]

] structure can be utilized. In a 4Pi structure, what is different from the forward structure mentioned above is that two opposing objective lenses which both are focused to the same geometrical location are introduced. The inverted and non-inverted arm of STED beam will propagate along opposite directions and be focused by two objective lenses, as shown in Fig. 3(a)
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.
. The amplitude distribution around the ideal foci can be expressed as
E'(r2,φ2,z2)=I1Enoninverted(r2,φ2,z2)+I2Enoninverted(r2,φ2,z2)
(6)
When all other aspects maintain the same, the size of central dark area generated by 4Pi structure will be smaller than that by forward one, as shown in Fig. 3(b). In this case, the overlap can be achieved by switching between the forward and 4Pi structures.

However, even we deliberately ignore the additional cost and complexity induced, the introduction of 4Pi structure will worsen the intensity uniformity around the central dark area of focal spot (as shown in Fig. 4(a)
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.
), and this situation becomes more severe when the order N is enlarged. To give a quantitative evaluation, we define the uniformity parameter as
U=1|Imax_xImax_y|Imax_x+Imax_y
(7)
where Imax_x and Imax_y are the maximum intensities of focal spot along x and y directions, respectively. The results are illustrated in Fig. 4(b). The curve presents an apparent downward trend of uniformity following with the increasing of N when 4Pi is used. On the other hand, similar influence can never be detected in the forward structure.

As mentioned above, the doughnut focal spot possesses a lot of potential applications, while the variable size of central dark area will brings additional flexibility to them. Taking the optical tweezers for example, the origin of the trapping force is the gradient of field intensity. Generally, the gradient can be expressed as [24

24. Q. W. Zhan and J. R. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10(7), 324–331 (2002). [PubMed]

]:
F=2πR3ε1c(ε2ε1ε2+2ε1)I
(8)
where R is the radius of particle, c is the speed of light in vacuum, ∇I is the gradient of the intensity, and ε1 and ε2 are the dielectric constants of the solvent and particle, respectively. As the size of central dark area and the gradient of intensity will change synchronously, it is convenient to introduce this system into the optical tweezers to trap diverse particles with different sizes and/or weights.

4. Conclusion

In conclusion, this paper proposes a new approach to expand the continuous manipulation scale of doughnut focal spot. This target is achieved by synthetically using various beam modulation techniques, including intensity and phase modulation of incident beam, and III. The whole system works like a transmission in a road-going vehicle, that the “gear” is decided by the order of vortex phase modulation, and the “throttle” is the phase diversity between two arms of III. The manipulation gaps of size between two adjacent orders cannot be overlaid unless the beam shape is switched between Gaussian and Bessel-Gaussian modes. The result is simulated based on the vectorial diffraction theory. Although in theory the continuous manipulation scale can infinitely be broadened by this method, but the actual upper limit will be decided by the resolution of SLM. The introduction of 4Pi will optimize the performance of system by increasing the overlap of manipulation scale between orders of vortex, but at the expense of the worse intensity uniformity. This method will significantly enhance the performance of optical tweezers by enabling trapping a large variety of particles in the same optical system.

Acknowledgment

This work was financially supported by grants from the Qianjiang Talent Project (Grant No.2011R10010), the Doctoral Fund of Ministry of Education of China (Grant No.20110101120061), the Scholarship Award for Excellent Doctoral Student granted by Ministry of Education, and the Fundamental Research Funds for the Central Universities (Grant No.2012FZA5004).

References and links

1.

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

2.

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. Photonics 2(8), 501–505 (2008). [CrossRef]

3.

C. J. R. Sheppard and A. Choudhury, “Annular pupils, radial polarization, and superresolution,” Appl. Opt. 43(22), 4322–4327 (2004). [CrossRef] [PubMed]

4.

C. J. R. Sheppard, W. Gong, and K. Si, “Polarization effects in 4Pi microscopy,” Micron 42(4), 353–359 (2011). [CrossRef] [PubMed]

5.

S. H. Deng, L. Liu, Y. Cheng, R. X. Li, and Z. Z. Xu, “Effects of primary aberrations on the fluorescence depletion patterns of STED microscopy,” Opt. Express 18(2), 1657–1666 (2010). [CrossRef] [PubMed]

6.

K. I. Willig, R. R. Kellner, R. Medda, B. Hein, S. Jakobs, and S. W. Hell, “Nanoscale resolution in GFP-based microscopy,” Nat. Methods 3(9), 721–723 (2006). [CrossRef] [PubMed]

7.

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

8.

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,” Plasmonics 6(4), 651–657 (2011). [CrossRef]

9.

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

10.

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]

11.

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]

12.

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]

13.

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]

14.

D. Weigel, R. Foerster, H. Babovsky, A. Kiessling, and R. Kowarschik, “Enhanced resolution of microscopic objects by image inversion interferometry,” Opt. Express 19(27), 26451–26462 (2011). [CrossRef] [PubMed]

15.

N. Sandeau and H. Giovannini, “Increasing the lateral resolution of 4Pi fluorescence microscopes,” J. Opt. Soc. Am. A 23(5), 1089–1095 (2006). [CrossRef] [PubMed]

16.

K. Wicker, S. Sindbert, and R. Heintzmann, “Characterisation of a resolution enhancing image inversion interferometer,” Opt. Express 17(18), 15491–15501 (2009). [CrossRef] [PubMed]

17.

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).

18.

C. J. R. Sheppard, “Validity of the Debye approximation,” Opt. Lett. 25(22), 1660–1662 (2000). [CrossRef] [PubMed]

19.

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]

20.

Y. Zheng, X. H. Wang, F. Shen, and X. Y. Li, “Generation of dark hollow beam via coherent combination based on adaptive optics,” Opt. Express 18(26), 26946–26958 (2010). [CrossRef] [PubMed]

21.

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]

22.

K. S. Youngworth and T. G. Brown, “Focusing of high numerical aperture cylindrical-vector beams,” Opt. Express 7(2), 77–87 (2000). [CrossRef] [PubMed]

23.

S. Hell and E. H. K. Stelzer, “Properties of a 4pi Confocal Fluorescence Microscope,” J. Opt. Soc. Am. A 9(12), 2159–2166 (1992). [CrossRef]

24.

Q. W. Zhan and J. R. Leger, “Focus shaping using cylindrical vector beams,” Opt. Express 10(7), 324–331 (2002). [PubMed]

OCIS Codes
(050.1960) Diffraction and gratings : Diffraction theory
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(350.4855) Other areas of optics : Optical tweezers or optical manipulation

ToC Category:
Physical Optics

History
Original Manuscript: March 23, 2012
Revised Manuscript: May 16, 2012
Manuscript Accepted: May 17, 2012
Published: May 21, 2012

Virtual Issues
Vol. 7, Iss. 8 Virtual Journal for Biomedical Optics

Citation
Xiang Hao, Cuifang Kuang, Yanghui Li, and Xu Liu, "Continuous manipulation of doughnut focal spot in a large scale," Opt. Express 20, 12692-12698 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-12-12692


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References

  1. G. B. Airy, “On the Diffraction of an Object-glass with Circular Aperture,” Trans. Cambridge Philos. Soc.5, 283–291 (1835).
  2. 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]
  3. C. J. R. Sheppard and A. Choudhury, “Annular pupils, radial polarization, and superresolution,” Appl. Opt.43(22), 4322–4327 (2004). [CrossRef] [PubMed]
  4. C. J. R. Sheppard, W. Gong, and K. Si, “Polarization effects in 4Pi microscopy,” Micron42(4), 353–359 (2011). [CrossRef] [PubMed]
  5. S. H. Deng, L. Liu, Y. Cheng, R. X. Li, and Z. Z. Xu, “Effects of primary aberrations on the fluorescence depletion patterns of STED microscopy,” Opt. Express18(2), 1657–1666 (2010). [CrossRef] [PubMed]
  6. 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]
  7. D. W. Zhang and X. C. Yuan, “Optical doughnut for optical tweezers,” Opt. Lett.28(9), 740–742 (2003). [CrossRef] [PubMed]
  8. 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]
  9. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon.1(1), 1–57 (2009). [CrossRef]
  10. 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]
  11. 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]
  12. 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]
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  14. 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]
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