Abstract

Talbot and Talbot-Lau effects are frequently used in lensless imaging applications with light, ultrasound, x-rays, atoms and molecules – generally in situations where refractive optical elements are non-existent or not suitable. We here show an experimental visualization of the intriguing wave patterns that are associated with near-field interferometry behind a single periodic diffraction grating under plane wave illumination and which are often referred to as Talbot carpets or quantum carpets. We also show the patterns behind two separated diffraction gratings under nearly-monochromatic but spatially incoherent illumination that illustrate the nature of Talbot-Lau carpets.

© 2009 Optical Society of America

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History
Original Manuscript: September 10, 2009
Manuscript Accepted: October 28, 2009
Revised Manuscript: October 16, 2009
Published: November 2, 2009

References

1. H. F. Talbot, "Facts Relating to Optical Science," Philos. Mag. 9, 401-407 (1836).
2. E. Lau, "Beugungserscheinungen an Doppelrastern," Ann. Phys. 6, 417 (1948). [CrossRef]
3. L. Rayleigh, "On Copying Diffraction-Gratings, and some Phenomena Connected Therewith," Philos. Mag. 11, 196 (1881).
4. W. Montgomery, "Self-imaging objects of infinite aperture," J. Opt. Soc. Am. 57(6), 772-775 (1967). [CrossRef]
5. K. Patorski, "Incoherent Superposition ofMultiple Self-imaging Lau Effect andMoire Fringe Explanation," Opt. Acta 30, 745-758 (1983).
6. G. J. Swanson and E. N. Leith, "Analysis of the Lau Effect and Generalized Grating Imaging," J. Opt. Soc. Am. A 2, 789-793 (1985). [CrossRef]
7. L. Liu, "Talbot and Lau effects on incident beams of arbitrary wavefront, and their use," Appl. Opt. 28(21), 4668-4678 (1989). [CrossRef]
8. K. Patorski, "Self-Imaging and its Applications," in Progress in Optics XXVII, E. Wolf, ed., (Elsevier Science Publishers B. V., Amsterdam, 1989), pp. 2-108.
9. K. Banaszek, K. Wodkiewicz, and W. P. Schleich, "Fractional Talbot effect in Phase Space: A Compact Summation Formula," Opt. Express 2, 169 - 172 (1998). [CrossRef]
10. O. Friesch, W. Schleich, and I. Marzoli, "Quantum carpets woven by Wigner functions," New J. Phys. 2(1), 4 (2000).
11. S. Mirza and C. Shakher, "Surface profiling using phase shifting Talbot interferometric technique," Optical Engineering 44, 013,601 (2004).
12. M. Thakur, C. Tay, and C. Quan, "Surface profiling of a transparent object by use of phase-shifting Talbot interferometry," Appl. Opt. 44(13), 2541-2545 (2005). [CrossRef]
13. J. Bhattacharya, "Measurement of the refractive index using the Talbot effect and a moire technique," Appl. Opt. 28(13), 2600-2604 (1989). [CrossRef]
14. S. Prakash, S. Singh, and A. Verma, "A low cost technique for automated measurement of focal length using Lau effect combined with Moire readout," J. Mod. Opt. 53(14), 2033-2042 (2006). [CrossRef]
15. P. Singh, M. Faridi, and C. Shakher, "Measurement of temperature of an axisymmetric flame using shearing interferometry and Fourier fringe analysis technique," Opt. Eng. 43, 387 (2004). [CrossRef]
16. G. Spagnolo, D. Ambrosini, and D. Paoletti, "Displacement measurement using the Talbot effect with a Ronchi grating," J. Opt. A 4(6), 376-380 (2002).
17. F. Huang, N. Zheludev, Y. Chen, and F. de Abajo, "Focusing of light by a nanohole array," Appl. Phys. Lett. 90, 091,119 (2007).
18. M. Dennis, N. Zheludev, and F. García de Abajo, "The plasmon Talbot effect," Opt. Express 15(15), 9692-9700 (2007). [CrossRef]
19. P. Cloetens, J. 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]
20. F. Pfeiffer, T. Weitkamp, O. Bunk and C. David, "Phase retrieval and differential phase-contrast imaging with low-brilliance X-ray sources," Nature 2, 258-261 (2006).
21. J. F. Clauser and S. Li, "‘Heisenberg Microscope’ Decoherence Atom Interferometry," Phys. Rev. A 50, 2430 (1994). [CrossRef]
22. 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. A 51, R14 (1995). [CrossRef]
23. S. Nowak, C. Kurtsiefer, T. Pfau, and C. David, "High-Order Talbot Fringes for Atomic Matter Waves," Opt. Lett. 22, 1430-32 (1997). [CrossRef]
24. S. B. Cahn, A. Kumarakrishnan, U. Shim, T. Sleator, P. R. Berman, and B. Dubetsky, "Time-Domain de Broglie Wave Interferometry," Phys. Rev. Lett. 79, 784-787 (1997). [CrossRef]
25. L. Deng, E. W. Hagley, J. Wen, M. Trippenbach, Y. Band, P. S. Julienne, J. E. Simsarian, K. Helmerson, S. L. Rolston, and W. D. Phillips, "Four-wave mixing with matter waves," Nature 398(6724), 218 (1999). [CrossRef]
26. B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, "Matter-Wave Interferometer for Large Molecules," Phys. Rev. Lett. 88, 100,404 (2002). [CrossRef]
27. S. Gerlich, L. Hackermüller, K. Hornberger, A. Stibor, H. Ulbricht, M. Gring, F. Goldfarb, T. Savas, M. Müri, M. Mayor, and M. Arndt, "A Kapitza-Dirac-Talbot-Lau interferometer for highly polarizable molecules," Nat. Phys. 3, 711 - 715 (2007). [CrossRef]
28. B. J. McMorran and A. D. Cronin, "An electron Talbot interferometer," New J. Phys. 11, 033,021 (2009). [CrossRef]
29. I. Marzoli, A. Kaplan, F. Saif, and W. Schleich, "Quantum carpets of a slightly relativistic particle," Fortschr. Phys. 56(10) (2008). [CrossRef]
30. M. Berry, I. Marzoli, and W. Schleich, "Quantum Carpets, Carpets of Light," Phys. World1-6 (2001).
31. M. Berry and S. Klein, "Integer, Fractional and Fractal Talbot Effects" J. Mod. Opt. 43, 2139-2164 (1996).
32. J. F. Clauser, "Factoring Integers with Youngs N-Slit Interferometer," Phys. Rev. A 53, 4587-4590 (1996). [CrossRef]
33. S. Wölk, W. P. Schleich, "Quantum carpets: Factorization with degeneracies," Proceedings of the Middleton Festival, Princeton, in print (2009).
34. J. Yeazell and C. Stroud, "Observation of fractional revivals in the evolution of a Rydberg atomic wave packet," Phys. Rev. A 43(9), 5153-5156 (1991). [CrossRef]
35. M. Vrakking, D. Villeneuve, A. Stolow, "Observation of fractional revivals of a molecular wave packet," Phys. Rev. A 54(1), 37 (1996). [CrossRef]
36. J. H. Hannay, M. V. Berry, "Quantization of linear maps on a torus-fresnel diffraction by a periodic grating," Physica 1D267-290 (1980).

Author Affiliations

Sarayut Deachapunya

Burapha University, Department of Physics, Faculty of Science

Mathias Tomandl

Faculty of Physics, University of Vienna

William B. Case

Grinnell College

Markus Arndt

University of Vienna, Faculty of Physics

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