OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 51, Iss. 10 — Apr. 1, 2012
  • pp: 1619–1630

Three-dimensional Dammann array

Junjie Yu, Changhe Zhou, Wei Jia, Wugang Cao, Shaoqing Wang, Jianyong Ma, and Hongchao Cao  »View Author Affiliations

Applied Optics, Vol. 51, Issue 10, pp. 1619-1630 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (1181 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We demonstrate a scheme that can produce a three-dimensional (3D) focus spot array in a 3D lattice structure, called a 3D Dammann array, in focal region of an objective. This 3D Dammann array is generated by using two separate micro-optical elements, a Dammann zone plate (DZP) that produces a series of coaxial focus spots and a conventional two-dimensional (2D) Dammann grating (DG). A simple, fast, and clear method is presented to design this binary pure-phase ( 0 , π ) DZP in vectorial Debye theory regime. Based on this kind of DZP, one can always obtain a 3D Dammann array both for low and high numerical aperture (NA) focusing objectives. For experimental demonstration, an arrangement combining a DZP, a 2D DG, and a pair of opposing lenses is proposed to generate a 5 × 5 × 5 Dammann array in focal region of an objective with NA = 0.127 and another 6 × 6 × 7 Dammann array for an objective of NA = 0.66 . It is shown that this arrangement makes it possible to achieve 3D Dammann arrays with micrometer-sized focus spots and focus spacings of tens of micrometers for various practical applications, such as 3D parallel micro- and nanomachining, 3D simultaneous optical manipulation, 3D optical data storage, and multifocal fluorescence microscope, etc.

© 2012 Optical Society of America

OCIS Codes
(050.1970) Diffraction and gratings : Diffractive optics
(140.3300) Lasers and laser optics : Laser beam shaping
(220.4000) Optical design and fabrication : Microstructure fabrication
(230.1360) Optical devices : Beam splitters
(220.4241) Optical design and fabrication : Nanostructure fabrication
(050.6875) Diffraction and gratings : Three-dimensional fabrication

ToC Category:
Diffraction and Gratings

Original Manuscript: December 19, 2011
Manuscript Accepted: January 6, 2012
Published: March 30, 2012

Virtual Issues
Vol. 7, Iss. 6 Virtual Journal for Biomedical Optics

Junjie Yu, Changhe Zhou, Wei Jia, Wugang Cao, Shaoqing Wang, Jianyong Ma, and Hongchao Cao, "Three-dimensional Dammann array," Appl. Opt. 51, 1619-1630 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. S. Maruo and K. Ikuta, “Three-dimensional microfabrication by use of single-photon-absorbed polymerization,” Appl. Phys. Lett. 76, 2656–2658 (2000). [CrossRef]
  2. R. R. Gattass and E. Mazur, “Femtosecond laser micromachining in transparent materials,” Nat. Photon. 2, 219–225(2008). [CrossRef]
  3. M. Deubel, M. Wegener, S. Linden, G. von Freymann, and S. John, “3D-2D-3D photonic crystal heterostructures fabricated by direct laser writing,” Opt. Lett. 31, 805–807(2006). [CrossRef]
  4. M. Thiel, J. Fischer, G. von Freymann, and M. Wegener, “Direct laser writing of three-dimensional submicron structures using a continuous-wave laser at 532 nm,” Appl. Phys. Lett. 97, 221102 (2010). [CrossRef]
  5. L. J. Li, R. R. Gattass, E. Gershgoren, H. Hwang, and J. T. Fourkas, “Achieving lambda/20 resolution by one-color initiation and deactivation of polymerization,” Science 324, 910–913 (2009). [CrossRef]
  6. J. Kato, N. Takeyasu, Y. Adachi, H. Sun, and S. Kawata, “Multiple-spot parallel processing for laser micronanofabrication,” Appl. Phys. Lett. 86, 044102 (2005). [CrossRef]
  7. Y. Lin, M. H. Hong, T. C. Chong, C. S. Lim, G. X. Chen, L. S. Tan, Z. B. Wang, and L. P. Shi, “Ultrafast-laser-induced parallel phase-change nanolithography,” Appl. Phys. Lett. 89, 041108 (2006). [CrossRef]
  8. H. Lin, B. Jia, and M. Gu, “Dynamic generation of Debye diffraction-limited multifocal arrays for direct laser printing nanofabrication,” Opt. Lett. 36, 406–408 (2011). [CrossRef]
  9. H. Dammann and E. Klotz, “Coherent optical generation and inspection of 2-dimensional periodic structures,” Opt. Acta 24, 505–515 (1977). [CrossRef]
  10. C. Zhou and L. Liu, “Numerical study of Dammann array illuminators,” Appl. Opt. 34, 5961–5969 (1995). [CrossRef]
  11. A. W. Lohmann and J. A. Thomas, “Making an array illuminator based on the Talbot effect,” Appl. Opt. 29, 4337–4340 (1990). [CrossRef]
  12. C. Zhou, W. Wang, E. Dai, and L. Liu, “Simple principles of the Talbot effect,” Opt. Photon. News 15(11), 46–50 (2004). [CrossRef]
  13. C. Zhou, S. Stankovic, and T. Tschudi, “Analytic phase-factor equations for Talbot array illuminations,” Appl. Opt. 38, 284–290 (1999). [CrossRef]
  14. Y. Lu, C. Zhou, S. Wang, and B. Wang, “Polarization-dependent Talbot effect,” J. Opt. Soc. Am. A 23, 2154–2160 (2006). [CrossRef]
  15. J. Zheng, C. Zhou, and B. Wang, “Phase interpretation for polarization-dependent near-field images of high-density gratings,” Opt. Commun. 281, 3254–3259 (2008). [CrossRef]
  16. J. Davis, I. Moreno, J. Martínez, T. Hernandez, and D. Cottrell “Creating 3D lattice patterns using programmable Dammann gratings,” Appl. Opt. 50, 3653–3657 (2011). [CrossRef]
  17. I. Moreno, J. A. Davis, D. M. Cottrell, N. Zhang, and X.-C. Yuan, “Encoding generalized phase functions on Dammann gratings,” Opt. Lett. 35, 1536–1538 (2010). [CrossRef]
  18. C. Zhou and J. Yu, “Dammann zone plate,” Chinese invention patent, application 201010585480.4 (2010).
  19. B. Richards and E. Wolf, “Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplantic system,” Proc. R. Soc. London Ser. A 253, 358–379 (1959). [CrossRef]
  20. M. Leutenegger, R. Rao, R. A. Leitgeb, and T. Lasser, “Fast focus field calculations,” Opt. Express 14, 11277–11291(2006). [CrossRef]
  21. C. W. McCutchen, “Generalized aperture and the three-dimensional diffraction image,” J. Opt. Soc. Am. 54, 240–242(1964). [CrossRef]
  22. J. A. Davis, C. S. Tuvey, O. López-Coronado, J. Campos, M. J. Yzuel, and C. Iemmi, “Tailoring the depth of focus for optical imaging systems using a Fourier transform approach,” Opt. Lett. 32, 844–846 (2007). [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. C. Zhou, J. Jia, and L. Liu, “Circular Dammann grating,” Opt. Lett. 28, 2174–2176 (2003). [CrossRef]
  25. R. Dorn, S. Quabis, and G. Leuchs, “Sharper focus for a radially polarized light beam,” Phys. Rev. Lett. 91, 233901 (2003). [CrossRef]
  26. Q. Zhan, “Cylindrical vector beams: from mathematical concepts to applications,” Adv. Opt. Photon. 1, 1–57 (2009). [CrossRef]
  27. H. Wang, L. Shi, B. Lukyanchuk, C. Sheppard, and C. T. Chong, “Creation of a needle of longitudinally polarized light in vacuum using binary optics,” Nat. Photon. 2, 501–505 (2008). [CrossRef]
  28. W. Wang, C. Zhou, and W. Jia, “High-fidelity replication of Dammann gratings using soft lithography,” Appl. Opt. 47, 1427–1429 (2008). [CrossRef]
  29. M. Martínez-Corral, L. Muñoz-Escrivá, and A. Pons, “Three-dimensional behavior of apodized nontelecentric focusing systems,” Appl. Opt. 40, 3164–3168 (2001). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

Supplementary Material

» Media 1: AVI (6972 KB)     

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited