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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Editor: Henry van Driel
  • Vol. 28, Iss. 2 — Feb. 1, 2011
  • pp: 275–280

Theory of nonlinear Talbot effect

Jianming Wen, Yong Zhang, Shi-Ning Zhu, and Min Xiao  »View Author Affiliations

JOSA B, Vol. 28, Issue 2, pp. 275-280 (2011)

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The nonlinear Talbot effect, in which self-images are formed by generated parametric light from the nonlinear optical process, is presented in this paper. The comparison is made between the conventional Talbot effect and the newly observed nonlinear case. The essence of such nonlinear self-images is provided and future work on this effect is also discussed. The conceptional extension achieved here not only opens a door for broader scopes of applications in imaging techniques but also offers a way for other research fields such as visualizing various ferric domains and subwavelength lithography.

© 2011 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(070.6760) Fourier optics and signal processing : Talbot and self-imaging effects
(190.4410) Nonlinear optics : Nonlinear optics, parametric processes
(260.1960) Physical optics : Diffraction theory

ToC Category:
Nonlinear Optics

Original Manuscript: August 30, 2010
Revised Manuscript: November 20, 2010
Manuscript Accepted: November 22, 2010
Published: January 19, 2011

Jianming Wen, Yong Zhang, Shi-Ning Zhu, and Min Xiao, "Theory of nonlinear Talbot effect," J. Opt. Soc. Am. B 28, 275-280 (2011)

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  1. H. F. Talbot, “Facts relating to optical science,” Philos. Mag. 9, 401–407 (1836).
  2. L. Rayleigh, “On copying diffraction gratings and on some phenomenon connected therewith,” Philos. Mag. 11, 196–205(1881).
  3. A. Winkelmann, “Uber einige Erscheinungen, die bei der Beugung des Lichtes durch Gitter Auftreten,” Ann. Phys. (Leipzig) 332, 905–954 (1908). [CrossRef]
  4. H. Weisel, “Uber die nach Fresnelscher Art Beobachteten Beugungserscheninungen der Gitter,” Ann. Phys. (Leipzig) 338, 995–1031 (1910). [CrossRef]
  5. M. Wolfke, “Uber die Abbildung eines Gitters Auβerhald der Einstellebene,” Ann. Phys. (Leipzig) 345, 194–200 (1913). [CrossRef]
  6. J. M. Cowley and A. F. Moodie, “Fourier images,” Proc. Phys. Soc. London Sect. B 70, 486–513 (1957). [CrossRef]
  7. G. L. Rogers, “Calculations of intermediate Fourier images of a finite line grating on a digital computer,” Br. J. Appl. Phys. 14, 657–661 (1963). [CrossRef]
  8. G. L. Rogers, “Interesting paradox in Fourier images,” J. Opt. Soc. Am. 62, 917–918 (1972). [CrossRef]
  9. J. T. Winthrop and C. R. Worthington, “Theory of Fresnel images. I. Plane periodic objects in monochromatic light,” J. Opt. Soc. Am. 55, 373–381 (1965). [CrossRef]
  10. W. D. Montgomery, “Self-imaging objects of infinite aperture,” J. Opt. Soc. Am. 57, 772–778 (1967). [CrossRef]
  11. K. Patorski, “The self-imaging phenomenon and its applications,” in Progress in Optics, E.Wolf, ed. (North-Holland, 1989), Vol. 27, pp. 1–108. [CrossRef]
  12. A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, “Optics and interferometry with atoms and molecules,” Rev. Mod. Phys. 81, 1051–1129 (2009). [CrossRef]
  13. C. Leichtle, I. S. Averbukh, and W. P. Schleich, “Generic structure of multilevel quantum beats,” Phys. Rev. Lett. 77, 3999–4002 (1996). [CrossRef] [PubMed]
  14. M. V. Berry and J. Goldberg, “Renormalisation of curlicues,” Nonlinearity 1, 1–26 (1988). [CrossRef]
  15. M. V. Berry and S. Klein, “Integer, fractional and fractal Talbot effects,” J. Mod. Opt. 43, 2139–2164 (1996). [CrossRef]
  16. M. V. Berry, I. Marzoli, and W. P. Schleich, “Quantum carpets, carpets of light,” Phys. World 14, 39–44 (2001).
  17. H. Mack, M. Bienert, F. Haug, M. Freyberger, and W. P. Schleich, “Wave packets can factorize numbers,” Phys. Status Solidi B 233, 408–415 (2002). [CrossRef]
  18. K. -H. Luo, J. -M. Wen, X. -H. Chen, Q. Liu, M. Xiao, and L. -A. Wu, “Second-order Talbot effect with entangled photon pairs,” Phys. Rev. A 80, 043820 (2009). [CrossRef]
  19. T. B. Pittman, Y. -H. Shih, D. V. Strekalov, and A. V. Sergienko, “Optical imaging by means of two-photon quantum entanglement,” Phys. Rev. A 52, R3429–R3432 (1995). [CrossRef] [PubMed]
  20. M. H. Rubin, “Transverse correlation in optical spontaneous parametric down-conversion,” Phys. Rev. A 54, 5349–5460 (1996). [CrossRef] [PubMed]
  21. R. Iwanow, D. A. May-Arrioja, D. N. Christodoulides, G. I. Stegeman, Y. Min, and W. Sohler, “Discrete Talbot effect in waveguide arrays,” Phys. Rev. Lett. 95, 053902 (2005). [CrossRef] [PubMed]
  22. T. Weitkamp, B. Nöhammer, A. Diaz, and C. David, “X-ray wavefront analysis and optics characterization with a grating interferometer,” Appl. Phys. Lett. 86, 054101 (2005). [CrossRef]
  23. Y. Zhang, J. -M. Wen, S. -N. Zhu, and M. Xiao, “Nonlinear Talbot effect,” Phys. Rev. Lett. 104, 183901 (2010). [CrossRef] [PubMed]
  24. M. Fiebig, Th. Lottemoser, D. Fröhlich, A. V. Goltsev, and R. V. Pisarev, “Observation of coupled magnetic and electric domains,” Nature (London) 419, 818–820 (2002). [CrossRef]
  25. C. -S. Guo, X. Yin, L. -W. Zhu, and Z. -P. Hong, “Analytical expression for phase distribution of a hexagonal array at fractional Talbot planes,” Opt. Lett. 32, 2079–2081 (2007). [CrossRef] [PubMed]
  26. M. Paturzo, P. De Natale, S. De Nicola, P. Ferraro, S. Mailis, R. W. Eason, G. Coppola, M. Iodice, and M. Gioffrè, “Tunable two-dimensional hexagonal phase array in domain-engineered Z-cut lithium niobate crystal,” Opt. Lett. 31, 3164–3166 (2006). [CrossRef] [PubMed]
  27. S. Szapiel and K. Patorski, “Fresnel diffraction images of periodic objects under Gaussian beam illumination,” Opt. Acta 26, 439–446 (1979). [CrossRef]
  28. H. Jin and P. Xu, Department of Physics, National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China, email pingxu520@nju.edu.cn. (personal communication, 2010).
  29. M. V. Berry and E. Bodenschatz, “Caustics, multiply reconstructed by Talbot interference,” J. Mod. Opt. 46, 349–365 (1999). [CrossRef]

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