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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 5 — Feb. 27, 2012
  • pp: 4903–4920

Talbot images of wavelength-scale amplitude gratings

Myun-Sik Kim, Toralf Scharf, Christoph Menzel, Carsten Rockstuhl, and Hans Peter Herzig  »View Author Affiliations

Optics Express, Vol. 20, Issue 5, pp. 4903-4920 (2012)

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By means of experiment and simulation, we achieve unprecedented insights into the formation of Talbot images to be observed in transmission for light diffracted at wavelength-scale amplitude gratings. Emphasis is put on disclosing the impact and the interplay of various diffraction orders to the formation of Talbot images. They can be manipulated by selective filtering in the Fourier plane. Experiments are performed with a high-resolution interference microscope that measures the amplitude and phase of fields in real-space. Simulations have been performed using rigorous diffraction theory. Specific phase features, such as singularities found in the Talbot images, are discussed. This detailed analysis helps to understand the response of fine gratings. It provides moreover new insights into the fundamental properties of gratings that often find use in applications such as, e.g., lithography, sensing, and imaging.

© 2012 OSA

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(050.1960) Diffraction and gratings : Diffraction theory
(070.0070) Fourier optics and signal processing : Fourier optics and signal processing
(070.6110) Fourier optics and signal processing : Spatial filtering
(070.6760) Fourier optics and signal processing : Talbot and self-imaging effects
(180.3170) Microscopy : Interference microscopy

ToC Category:
Diffraction and Gratings

Original Manuscript: December 14, 2011
Revised Manuscript: February 3, 2012
Manuscript Accepted: February 3, 2012
Published: February 13, 2012

Myun-Sik Kim, Toralf Scharf, Christoph Menzel, Carsten Rockstuhl, and Hans Peter Herzig, "Talbot images of wavelength-scale amplitude gratings," Opt. Express 20, 4903-4920 (2012)

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  1. F. Talbot, “Facts relating to optical science. No. IV,” Philos. Mag.9, 401–407 (1836).
  2. L. Rayleigh, “On copying diffraction gratings and some phenomena connected therewith,” Philos. Mag.11, 196–205 (1881).
  3. R. F. Edgar, “The Fresnel diffraction images of periodic structures,” J. Mod. Opt.16, 281–287 (1969).
  4. J. T. Winthrop and C. R. Worthington, “Theory of Fresnel images. I. Plane periodic objects in monochromatic light,” J. Opt. Soc. Am.55(4), 373–381 (1965). [CrossRef]
  5. A. Kołodziejczyk, “Realization of Fourier images without using a lens by sampling the optical object,” J. Mod. Opt.32, 74–746 (1985).
  6. Y.-S. Cheng and R.-C. Chang, “Theory of image formation using the Talbot effect,” Appl. Opt.33(10), 1863–1874 (1994). [CrossRef] [PubMed]
  7. S. Teng, Y. Tan, and C. Cheng, “Quasi-Talbot effect of the high-density grating in near field,” J. Opt. Soc. Am. A25(12), 2945–2951 (2008). [CrossRef] [PubMed]
  8. M. Berry and S. Klein, “Integer, fractional and fractal Talbot effects,” J. Mod. Opt.43(10), 2139–2164 (1996). [CrossRef]
  9. E. Noponen and J. Turunen, “Electromagnetic theory of Talbot imaging,” Opt. Commun.98(1-3), 132–140 (1993). [CrossRef]
  10. Y. Lu, C. Zhou, and H. Luo, “Talbot effect of a grating with different kinds of flaws,” J. Opt. Soc. Am. A22(12), 2662–2667 (2005). [CrossRef] [PubMed]
  11. F. J. Torcal-Milla, L. M. Sanchez-Brea, and J. Vargas, “Effect of aberrations on the self-imaging phenomenon,” J. Lightwave Technol.29(7), 1051–1057 (2011). [CrossRef]
  12. O. Bryngdahl, “Image formation using self-imaging techniques,” J. Opt. Soc. Am.63(4), 416–419 (1973). [CrossRef]
  13. J. C. Bhattacharya, “Measurement of the refractive index using the Talbot effect and a moire technique,” Appl. Opt.28(13), 2600–2604 (1989). [CrossRef] [PubMed]
  14. G. Spagnolo, D. Ambrosini, and D. Paoletti, “Displacement measurement using the Talbot effect with a Ronchi grating,” J. Opt. A: Pure Appl. Opt4(6), S376–S380 (2002). [CrossRef]
  15. A. Isoyan, F. Jiang, Y. C. Cheng, F. Cerrina, P. Wachulak, L. Urbanski, J. Rocca, C. Menoni, and M. Marconi, “Talbot lithography: self-imaging of complex structures,” J. Vac. Sci. Technol. B27(6), 2931–2937 (2009). [CrossRef]
  16. L. Stuerzebecher, T. Harzendorf, U. Vogler, U. D. Zeitner, and R. Voelkel, “Advanced mask aligner lithography: fabrication of periodic patterns using pinhole array mask and Talbot effect,” Opt. Express18(19), 19485–19494 (2010). [CrossRef] [PubMed]
  17. A. W. Lohmann and J. A. Thomas, “Making an array illuminator based on the talbot effect,” Appl. Opt.29(29), 4337–4340 (1990). [CrossRef] [PubMed]
  18. F. Huang, N. Zheludev, Y. Chen, and F. de Abajo, “Focusing of light by a nanohole array,” Appl. Phys. Lett.90(9), 091119 (2007). [CrossRef]
  19. M. Berry, I. Marzoli, and W. Schleich, “Quantum carpets, carpets of light,” Phys. World 39–46 (June 2001)
  20. X.-B. Song, H.-B. Wang, J. Xiong, K. Wang, X. Zhang, K.-H. Luo, and L.-A. Wu, “Experimental observation of quantum Talbot effects,” Phys. Rev. Lett.107(3), 033902 (2011). [CrossRef] [PubMed]
  21. M. S. Chapman, C. R. Ekstrom, T. D. Hammond, J. Schmiedmayer, B. E. Tannian, S. Wehinger, and D. E. Pritchard, “Near-field imaging of atom diffraction gratings: The atomic Talbot effect,” Phys. Rev. A51(1), R14–R17 (1995). [CrossRef] [PubMed]
  22. S. Nowak, Ch. Kurtsiefer, T. Pfau, and C. David, “High-order Talbot fringes for atomic matter waves,” Opt. Lett.22(18), 1430–1432 (1997). [CrossRef] [PubMed]
  23. P. Cloetens, J. P. Guigay, C. De Martino, J. Baruchel, and M. Schlenker, “Fractional Talbot imaging of phase gratings with hard x rays,” Opt. Lett.22(14), 1059–1061 (1997). [CrossRef] [PubMed]
  24. B. J. McMorran and A. D. Cronin, “An electron Talbot interferometer,” New J. Phys.11(3), 033021 (2009). [CrossRef]
  25. M. R. Dennis, N. I. Zheludev, and F. J. García de Abajo, “The plasmon Talbot effect,” Opt. Express15(15), 9692–9700 (2007). [CrossRef] [PubMed]
  26. S. Cherukulappurath, D. Heinis, J. Cesario, N. F. van Hulst, S. Enoch, and R. Quidant, “Local observation of plasmon focusingin Talbot carpets,” Opt. Express17(26), 23772–23784 (2009). [CrossRef] [PubMed]
  27. A. Nesci, R. Dändliker, M. Salt, and H. P. Herzig, “Measuring amplitude and phase distribution of fields generated by gratings with sub-wavelength resolution,” Opt. Commun.205(4-6), 229–238 (2002). [CrossRef]
  28. D. Goldstein, Understanding the Light Microscope: A Computer-Aided Introduction (Academic Press, 1999), Chap. 1.
  29. D. Malacara, Optical Shop Testing (Wiley, 2007), 3rd ed., Chap. 16.
  30. M.-S. Kim, T. Scharf, and H. P. Herzig, “Amplitude and phase measurements of highly focused light in optical data storage systems,” Jpn. J. Appl. Phys.49(8), 08KA03 (2010). [CrossRef]
  31. M.-S. Kim, T. Scharf, and H. P. Herzig, “Small-size microlens characterization by multiwavelength high-resolution interference microscopy,” Opt. Express18(14), 14319–14329 (2010). [CrossRef] [PubMed]
  32. M.-S. Kim, T. Scharf, S. Mühlig, C. Rockstuhl, and H. P. Herzig, “Engineering photonic nanojets,” Opt. Express19(11), 10206–10220 (2011). [CrossRef] [PubMed]
  33. M.-S. Kim, T. Scharf, M. T. Haq, W. Nakagawa, and H. P. Herzig, “Subwavelength-size solid immersion lens,” Opt. Lett.36(19), 3930–3932 (2011). [CrossRef] [PubMed]
  34. C. Rockstuhl, I. Märki, T. Scharf, M. Salt, H. P. Herzig, and R. Dändliker, “High resolution interference microscopy: a tool for probing optical waves in the far-field on a nanometric length scale,” Curr. Nanosci.2(4), 337–350 (2006). [CrossRef]
  35. J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, and K. Merkel, “Digital wave-front measuring interferometry: some systematic error sources,” Appl. Opt.22(21), 3421–3432 (1983). [CrossRef] [PubMed]
  36. P. Hariharan, B. F. Oreb, and T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt.26(13), 2504–2506 (1987). [CrossRef] [PubMed]
  37. M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999).
  38. E. Abbe, “Beiträge zur theorie des mikroskops und der mikroskopischen wahrnehmung,” Arch. Mikrosc. Anat. Entwicklungsmech9(1), 413–418 (1873). [CrossRef]
  39. H. Köhler, “On Abbe’s theory of image formation in the microscope,” Opt. Acta (Lond.)28(12), 1691–1701 (1981). [CrossRef]
  40. H. Gross, H. Zugge, M. Peschka, and F. Blechinger, Handbook of Optical Systems (Wiley, 2007), Vol. 3, p. 126.
  41. J. W. Goodman, Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005), Chap. 6.
  42. H. Gundlach, “From the history of microscopy: Abbe’s diffraction trials,” Innovation, The Magazine from Carl Zeiss15, 18–23 (2005).
  43. L. Li, “New formulation of the Fourier modal method for crossed surface-relief gratings,” J. Opt. Soc. Am. A14(10), 2758–2767 (1997). [CrossRef]
  44. T. Paul, C. Rockstuhl, and F. Lederer, “Integrating cold plasma equations into the Fourier modal method to analyze second harmonic generation at metallic nanostructures,” J. Mod. Opt.58(5-6), 438–448 (2011). [CrossRef]
  45. E. P. Goodwin and J. C. Wyant, Field Guide to Interferometric Optical Testing (SPIE, 2006).
  46. S. Yokozeki, “Moiré fringes,” Opt. Lasers Eng.3(1), 15–27 (1982). [CrossRef]
  47. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College Publishing, 1976), Chap. 6.
  48. R. G. Griggers, Encyclopedia of Optical Engineering (CRC Press, 2003), p. 1928.

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