OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 21, Iss. 12 — Dec. 1, 2004
  • pp: 2366–2374

Asymptotic focusing properties of a sinusoidal phase grating

Bernd Rohwedder and Pablo Barberis-Blostein  »View Author Affiliations


JOSA A, Vol. 21, Issue 12, pp. 2366-2374 (2004)
http://dx.doi.org/10.1364/JOSAA.21.002366


View Full Text Article

Enhanced HTML    Acrobat PDF (688 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The lensing behavior of sinusoidal phase gratings is studied in the limit of large phase amplitudes Φ. The resulting asymptotic expressions are compared with the exact results and are shown to represent excellent approximations even for moderate values of Φ. They are well suited to a quantitative description of focusing imperfections caused by the strong spherical aberrations encountered in this type of microlens array.

© 2004 Optical Society of America

OCIS Codes
(050.1950) Diffraction and gratings : Diffraction gratings
(070.6760) Fourier optics and signal processing : Talbot and self-imaging effects
(080.1510) Geometric optics : Propagation methods
(110.2760) Imaging systems : Gradient-index lenses

History
Original Manuscript: March 12, 2004
Revised Manuscript: June 30, 2004
Manuscript Accepted: June 30, 2004
Published: December 1, 2004

Citation
Bernd Rohwedder and Pablo Barberis-Blostein, "Asymptotic focusing properties of a sinusoidal phase grating," J. Opt. Soc. Am. A 21, 2366-2374 (2004)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-21-12-2366


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. O. Nomoto, “Über eine neue Sichtbarmachungsmethode stehender Ultraschallwellen in Flüssigkeiten,” Proc. Phys. Math. Soc. Jpn. 18, 402–424 (1936).
  2. N. S. Nagendra Nath, “The visibility of ultrasonic waves and its periodic variations,” Proc. Indian Acad. Sci., Sect. A 4, 262–274 (1936).
  3. E. Hiedemann, E. Schreuer, “Zur Periodizität der Abbildung von Ultraschallwellen,” Z. Phys. 107, 463–473 (1937). [CrossRef]
  4. K. G. H. Baldwin, “Experiments in atom optics,” Aust. J. Phys. 49, 855–897 (1996). [CrossRef]
  5. S. Gupta, A. E. Leanhardt, A. D. Cronin, D. E. Pritchard, “Coherent manipulation of atoms with standing light waves,” C. R. Acad. Sci. Paris 2(IV), 479–495 (2001).
  6. D. Meschede, H. Metcalf, “Atomic nanofabrication: atomic deposition and lithography by laser and magnetic forces,” J. Phys. D 36, R17–R38 (2003). [CrossRef]
  7. B. Rohwedder, “Atom optical elements based on near-field grating sequences,” Fortschr. Phys. 47, 883–911 (1999). [CrossRef]
  8. M. Leibscher, I. Sh. Averbukh, “Squeezing of atoms in a pulsed optical lattice,” Phys. Rev. A 65, 053816 (2002). [CrossRef]
  9. D. V. Strekalov, A. Turlapov, A. Kumarakrishnan, T. Sleator, “Periodic structures generated in a cloud of cold atoms,” Phys. Rev. A 66, 023601 (2002). [CrossRef]
  10. P. Barberis, B. Rohwedder, “Spherical correction lens array for atom nanofabrication,” Phys. Rev. A 67, 033604 (2003). [CrossRef]
  11. J. S. Darlin, P. Senthilkumaran, S. Bhattacharya, M. P. Kothiyal, R. S. Sirohi, “Fabrication of an array illuminator using tandem Michelson interferometers,” Opt. Commun. 123, 1–4 (1996). [CrossRef]
  12. K. Patorski, “Optical testing of ultrasonic phase gratings using a Fresnel diffraction method,” Ultrasonics 19, 169–172 (1981). [CrossRef]
  13. S. P. Trainoff, D. S. Cannell, “Physical optics treatment of the shadowgraph,” Phys. Fluids 14, 1340–1363 (2002). [CrossRef]
  14. M. V. Berry, S. Klein, “Integer, fractional, and fractal Talbot effects,” J. Mod. Opt. 43, 2139–2164 (1996). [CrossRef]
  15. A. Reichelt, E. Storck, U. Wolff, “Near field diffraction pattern behind a sinusoidal phase grating,” Opt. Commun. 3, 169–172 (1971). [CrossRef]
  16. N. G. De Bruijn, Asymptotic Methods in Analysis (North-Holland, Amsterdam, 1958), Chap. 4 (“Laplace Method”) and 5 (“Saddle-Point Method”).
  17. Strictly speaking, the exponentially small contribution of these “distant” saddles must be consistently included to obtain a convergent asymptotic series. For the details, see M. V. Berry, C. J. Howls, “Hyperasymptotics for integrals with saddles,” Proc. R. Soc. London Ser. A 434, 657–675 (1999). [CrossRef]
  18. M. V. Berry, E. Bodenschatz, “Caustics, multiply reconstructed by Talbot interference,” J. Mod. Opt. 46, 349–365 (1999). [CrossRef]
  19. T. Pearcey, “The structure of an electromagnetic field in the neighbourhood of a cusp of a caustic,” Philos. Mag. 37, 311–317 (1946).
  20. J. L. Cohen, B. Dubetsky, P. R. Berman, “Atom focusing by far-detuned and resonant standing wave fields: thin-lens regime,” Phys. Rev. A 60, 4886–4901 (1999). [CrossRef]
  21. J. Primot, “Theoretical description of Shack-Hartmann wave-front sensor,” Opt. Commun. 222, 81–92 (2003). [CrossRef]
  22. K. K. Berggren, M. Prentiss, G. L. Timp, R. E. Behringer, “Calculation of atomic positions in nanometer-scale direct-write optical lithography with an optical standing wave,” J. Opt. Soc. Am. B 11, 1166–1176 (1994). [CrossRef]
  23. J. J. McClelland, “Atom-optical properties of a standing-wave light field,” J. Opt. Soc. Am. B 12, 1761–1767 (1995). [CrossRef]
  24. K. Okamoto, Y. Inouye, S. Kawata, “Atomic-beam propagation in a two-dimensional standing wave of light: a numerical analysis based on a particle-optics,” Jpn. J. Appl. Phys., Part 1 40, 609–613 (2001). [CrossRef]
  25. C. J. Lee, “Quantum-mechanical analysis of atom lithography,” Phys. Rev. A 61, 063604 (2000). [CrossRef]
  26. S. J. H. Petra, K. A. H. van Leeuwen, L. Feenstra, W. Hogervorst, W. Vassen, “Numerical simulations on the motion of atoms travelling through a standing-wave light field,” Eur. Phys. J. D 27, 83–91 (2003). [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.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited