Abstract

Circular Dammann grating (CDG) under high numerical aperture (NA) focusing is described based on Richards–Wolf vectorial diffraction theory in this paper. Several CDGs are presented under the condition of NA=0.9 with the illumination of circularly polarized plane-wave laser beams. Numerical results show that the sizes of these circular patterns with equal-intensity are in the wavelength scale, and doughnut-shaped central spots and dark rings are in the subwavelength width. To verify this kind of CDG, a binary pure-phase three-order CDG is fabricated to produce a dark center pattern surrounded by three concentric bright rings. The corresponding intensity distribution of the pattern on the focal plane of a high-NA objective (NA=0.9) is measured, and the results agree well with theoretical simulations. This kind of CDG with annular patterns of equal-intensity in the wavelength scale should be highly interesting for its potential applications in optical trapping, stimulated emission depletion (STED) microscopy, and the study of singular optics, as well as annular array illumination.

© 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]
  6. F. J. Wen and P. S. Chung, “A new circular Dammann grating using a Hankel transform,” J. Opt. A 10, 075306 (2008).
    [CrossRef]
  7. F. J. Wen and P. S. Chung, “Use of the circular Dammann grating in angle measurement,” Appl. Opt. 47, 5197–5200 (2008).
    [CrossRef]
  8. F. J. Wen, Z. Chen, and P. S. Chung, “Area measurement at long-distance using a circular Dammann grating,” Appl. Opt. 49, 648–652 (2010).
    [CrossRef]
  9. S. Zhao, J. F. Wen, and P. S. Chung, “Simple focal-length measurement technique with a circular Dammann grating,” Appl. Opt. 46, 44–49 (2007).
    [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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    [CrossRef]
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    [CrossRef]
  21. W. Wang, C. Zhou, and W. Jia, “High-fidelity replication of Dammann gratings using soft lithography,” Appl. Opt. 47, 1427–1429 (2008).
    [CrossRef]
  22. J. Yu, C. Zhou, and W. Jia, “Transverse superresolution with extended depth of focus using binary phase filters for optical storage system,” Opt. Commun. 283, 4171–4177 (2010).
    [CrossRef]
  23. J. Yu, C. Zhou, W. Jia, and A. Hu, “Focal shift and axial dispersion of binary pure-phase filters in focusing systems,” Proc. SPIE 7848, 784815 (2010).
    [CrossRef]
  24. H. Luo, C. Zhou, and H. Zou, “Highly sensitive wave-front sensor with a non-zero-order phase plate,” Appl. Opt. 44, 4654–4658 (2005).
    [CrossRef]

2011

2010

U. Levy, B. Desiatov, I. Goykhman, T. Nachmias, A. Ohayon, and S. E. Meltzer, “Design, fabrication, and characterization of circular Dammann gratings based on grayscale lithography,” Opt. Lett. 35, 880–882 (2010).
[CrossRef]

F. J. Wen, Z. Chen, and P. S. Chung, “Area measurement at long-distance using a circular Dammann grating,” Appl. Opt. 49, 648–652 (2010).
[CrossRef]

J. Yu, C. Zhou, and W. Jia, “Transverse superresolution with extended depth of focus using binary phase filters for optical storage system,” Opt. Commun. 283, 4171–4177 (2010).
[CrossRef]

J. Yu, C. Zhou, W. Jia, and A. Hu, “Focal shift and axial dispersion of binary pure-phase filters in focusing systems,” Proc. SPIE 7848, 784815 (2010).
[CrossRef]

2009

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
[CrossRef]

K. B. Doh, K. Dobson, T.-C. Poon, and P. S. Chung, “Optical image coding with a circular Dammann grating,” Appl. Opt. 48, 134–139 (2009).
[CrossRef]

2008

A. N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photon. 2, 365–370 (2008).
[CrossRef]

F. J. Wen and P. S. Chung, “A new circular Dammann grating using a Hankel transform,” J. Opt. A 10, 075306 (2008).
[CrossRef]

F. J. Wen and P. S. Chung, “Use of the circular Dammann grating in angle measurement,” Appl. Opt. 47, 5197–5200 (2008).
[CrossRef]

W. Wang, C. Zhou, and W. Jia, “High-fidelity replication of Dammann gratings using soft lithography,” Appl. Opt. 47, 1427–1429 (2008).
[CrossRef]

2007

2006

2005

2004

2003

1995

1994

1993

R. Kant, “An analytical solution of vector diffraction for focusing optical systems,” J. Mod. Opt. 40, 337–347(1993).
[CrossRef]

1977

H. Dammann and E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

1959

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

Bowman, C. N.

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
[CrossRef]

Chen, Z.

Chung, P. S.

Dai, H.

Dammann, H.

H. Dammann and E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Demir, H.

Desiatov, B.

Dickinson, M. R.

A. N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photon. 2, 365–370 (2008).
[CrossRef]

Diehl, D. W.

Dobson, K.

Doh, K. B.

Goykhman, I.

Grigorenko, A. N.

A. N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photon. 2, 365–370 (2008).
[CrossRef]

Hell, S. W.

Hu, A.

J. Yu, C. Zhou, W. Jia, and A. Hu, “Focal shift and axial dispersion of binary pure-phase filters in focusing systems,” Proc. SPIE 7848, 784815 (2010).
[CrossRef]

Jia, J.

Jia, W.

J. Yu, C. Zhou, and W. Jia, “Transverse superresolution with extended depth of focus using binary phase filters for optical storage system,” Opt. Commun. 283, 4171–4177 (2010).
[CrossRef]

J. Yu, C. Zhou, W. Jia, and A. Hu, “Focal shift and axial dispersion of binary pure-phase filters in focusing systems,” Proc. SPIE 7848, 784815 (2010).
[CrossRef]

W. Wang, C. Zhou, and W. Jia, “High-fidelity replication of Dammann gratings using soft lithography,” Appl. Opt. 47, 1427–1429 (2008).
[CrossRef]

Kant, R.

R. Kant, “An analytical solution of vector diffraction for focusing optical systems,” J. Mod. Opt. 40, 337–347(1993).
[CrossRef]

Klotz, E.

H. Dammann and E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Kowalski, B. A.

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
[CrossRef]

Law, S. Y.

Levy, U.

Liu, J.-P.

Liu, L.

Luo, D.

Luo, H.

McLeod, R. R.

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
[CrossRef]

Meltzer, S. E.

Nachmias, T.

Ohayon, A.

Poon, T.-C.

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. A 253, 358–379 (1959).
[CrossRef]

Roberts, N. W.

A. N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photon. 2, 365–370 (2008).
[CrossRef]

Scott, T. F.

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
[CrossRef]

Shinoda, Y.

Sullivan, A. C.

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
[CrossRef]

Sun, X.

Visser, T. D.

Wang, W.

Wen, F. J.

Wen, J. F.

Wichmann, J.

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. A 253, 358–379 (1959).
[CrossRef]

Yu, J.

J. Yu, C. Zhou, and W. Jia, “Transverse superresolution with extended depth of focus using binary phase filters for optical storage system,” Opt. Commun. 283, 4171–4177 (2010).
[CrossRef]

J. Yu, C. Zhou, W. Jia, and A. Hu, “Focal shift and axial dispersion of binary pure-phase filters in focusing systems,” Proc. SPIE 7848, 784815 (2010).
[CrossRef]

Zhang, Y.

A. N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photon. 2, 365–370 (2008).
[CrossRef]

Zhao, S.

Zhou, C.

Zhou, X.

Zou, H.

Appl. Opt.

C. Zhou and L. Liu, “Numerical study of Dammann array illuminators,” Appl. Opt. 34, 5961–5969 (1995).
[CrossRef]

S. Zhao, J. F. Wen, and P. S. Chung, “Simple focal-length measurement technique with a circular Dammann grating,” Appl. Opt. 46, 44–49 (2007).
[CrossRef]

F. J. Wen, S. Y. Law, and P. S. Chung, “Design of circular Dammann gratings by employing the circular spot rotation method,” Appl. Opt. 46, 5452–5455 (2007).
[CrossRef]

W. Wang, C. Zhou, and W. Jia, “High-fidelity replication of Dammann gratings using soft lithography,” Appl. Opt. 47, 1427–1429 (2008).
[CrossRef]

F. J. Wen and P. S. Chung, “Use of the circular Dammann grating in angle measurement,” Appl. Opt. 47, 5197–5200 (2008).
[CrossRef]

K. B. Doh, K. Dobson, T.-C. Poon, and P. S. Chung, “Optical image coding with a circular Dammann grating,” Appl. Opt. 48, 134–139 (2009).
[CrossRef]

F. J. Wen, Z. Chen, and P. S. Chung, “Area measurement at long-distance using a circular Dammann grating,” Appl. Opt. 49, 648–652 (2010).
[CrossRef]

H. Luo, C. Zhou, and H. Zou, “Highly sensitive wave-front sensor with a non-zero-order phase plate,” Appl. Opt. 44, 4654–4658 (2005).
[CrossRef]

Y. Shinoda, J.-P. Liu, P. S. Chung, K. Dobson, X. Zhou, and T.-C. Poon, “Three-dimensional complex image coding using a circular Dammann grating,” Appl. Opt. 50, B38–B45(2011).
[CrossRef]

D. Luo, X. Sun, H. Dai, and H. Demir, “Polarization-dependent circular Dammann grating made of azo-dye-doped liquid crystals,” Appl. Opt. 50, 2316–2321 (2011).
[CrossRef]

J. Mod. Opt.

R. Kant, “An analytical solution of vector diffraction for focusing optical systems,” J. Mod. Opt. 40, 337–347(1993).
[CrossRef]

J. Opt. A

F. J. Wen and P. S. Chung, “A new circular Dammann grating using a Hankel transform,” J. Opt. A 10, 075306 (2008).
[CrossRef]

J. Opt. Soc. Am. A

Nat. Photon.

A. N. Grigorenko, N. W. Roberts, M. R. Dickinson, and Y. Zhang, “Nanometric optical tweezers based on nanostructured substrates,” Nat. Photon. 2, 365–370 (2008).
[CrossRef]

Opt. Acta

H. Dammann and E. Klotz, “Coherent optical generation and inspection of two-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977).
[CrossRef]

Opt. Commun.

J. Yu, C. Zhou, and W. Jia, “Transverse superresolution with extended depth of focus using binary phase filters for optical storage system,” Opt. Commun. 283, 4171–4177 (2010).
[CrossRef]

S. Zhao and P. S. Chung, “Collimation testing using a circular Dammann grating,” Opt. Commun. 279, 51–56 (2007).
[CrossRef]

Opt. Lett.

Proc. R. Soc. A

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

Proc. SPIE

J. Yu, C. Zhou, W. Jia, and A. Hu, “Focal shift and axial dispersion of binary pure-phase filters in focusing systems,” Proc. SPIE 7848, 784815 (2010).
[CrossRef]

Science

T. F. Scott, B. A. Kowalski, A. C. Sullivan, C. N. Bowman, and R. R. McLeod, “Two-color single-photon photoinitiation and photoinhibition for subdiffraction photolithography,” Science 324, 913–917 (2009).
[CrossRef]

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Figures (5)

Fig. 1.
Fig. 1.

Schematic of the high-NA focusing system with a CDG.

Fig. 2.
Fig. 2.

Numerical simulations of the normalized transverse two-dimensional intensity distribution of several CDGs. (a) One-order CDG with single ring; (b) one-order CDG with single ring and an equal-intensity bright center; (c) two-order CDG with two rings; (d) two-order CDG with two rings and an equal-intensity bright center; (e) three-order CDG with three rings. The units of x and y axes are in wavelength.

Fig. 3.
Fig. 3.

Numerical normalized intensity profile along the radial axis of a three-order CDG under high-NA focusing, where the solid line (green) denotes the total intensity profile, the dashed line (red) denotes the longitudinal component, and the dotted line (blue) denotes the transverse component of the normalized intensity.

Fig. 4.
Fig. 4.

Illustration of the experiment setup. The pupil stop is 4 mm in diameter, and it is located before the CDG sample to make sure its pupil aperture is equal to that of the focusing objective. The oil-objective (NA=1.25, 100×) is used for magnifying the focused field, and a CCD camera with a pixel size of 5.2 μm is employed for capturing the intensity distribution of the focused pattern.

Fig. 5.
Fig. 5.

Experimental results: (a) intensity pattern on the focal plane of the focusing system with a three-order CDG. The scale bar is 1 μm in length. (b) Cross-section profile along the white line through the center of (a).

Tables (1)

Tables Icon

Table 1. Optimized Solutions of Binary-Phase (0,π) CDGs Under High-NA Focusing (NA=0.9)

Equations (7)

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Ex(ρ,ϕ,z)=A{q2sin(2ϕ)+i[q0+q2cos(2ϕ)]},Ey(ρ,ϕ,z)=A[q0q2cos(2ϕ)iq2sin(2ϕ)],Ez(ρ,ϕ,z)=2Aq1(cosϕ+isinϕ),
q0=0αT(θ)L(θ)sinθcosθ(1+cosθ)J0(kρsinθ)exp(ikzcosθ)dθq1=0αT(θ)L(θ)sin2θcosθJ1(kρsinθ)exp(ikzcosθ)dθq2=0αT(θ)L(θ)sinθcosθ(1cosθ)J2(kρsinθ)exp(ikzcosθ)dθ,
It(ρ,ϕ,z)=ExEx*+EyEy*=2A2(q02+q22).
q0=0αT(θ)sinθcosθ(1+cosθ)J0(kρsinθ)dθ,q1=0αT(θ)sin2θcosθJ1(kρsinθ)dθ,q2=0αT(θ)sinθcosθ(1cosθ)J2(kρsinθ)dθ.
T(θ)={1θ2n1<θ<θ2nexp(iπ)θ2n<θ<θ2n+1n=1,2,,
unif=max(In)min(In)max(In)+min(In),
η=n=0NIn,

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