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

  • Editor: Franco Gori
  • Vol. 30, Iss. 12 — Dec. 1, 2013
  • pp: 2561–2571

Reflection of Laguerre–Gaussian beams carrying orbital angular momentum: a full Taylor expanded solution

Jun Ou, Yuesong Jiang, Jiahua Zhang, and Yuntao He  »View Author Affiliations


JOSA A, Vol. 30, Issue 12, pp. 2561-2571 (2013)
http://dx.doi.org/10.1364/JOSAA.30.002561


View Full Text Article

Enhanced HTML    Acrobat PDF (901 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

Partial reflection of linearly polarized Laguerre–Gaussian beams incident at a dielectric interface are studied beyond the paraxial regime. Based on the angular spectrum method and Taylor series expansion, we derive exact analytical expressions for the reflected electric field. This result holds in both the paraxial and nonparaxial regimes. The result is then extended to beams of arbitrary polarization and used to analytically calculate the transverse and longitudinal shifts of the beams’ center of gravity. Finally, several numerical examples are performed to verify the analytical formulas we derived near the Brewster angle.

© 2013 Optical Society of America

OCIS Codes
(120.5700) Instrumentation, measurement, and metrology : Reflection
(120.7000) Instrumentation, measurement, and metrology : Transmission
(260.2110) Physical optics : Electromagnetic optics

ToC Category:
Physical Optics

History
Original Manuscript: August 20, 2013
Revised Manuscript: October 21, 2013
Manuscript Accepted: October 21, 2013
Published: November 15, 2013

Citation
Jun Ou, Yuesong Jiang, Jiahua Zhang, and Yuntao He, "Reflection of Laguerre–Gaussian beams carrying orbital angular momentum: a full Taylor expanded solution," J. Opt. Soc. Am. A 30, 2561-2571 (2013)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-30-12-2561


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. F. Goos and H. Hanchen, “Ein neuer und fundamentaler Versuch zur total reflexion,” Ann. Phys. 436, 333–346 (1947). [CrossRef]
  2. F. I. Fedorov, “K teorii polnovo otrazenija,” Dokl. Akad. Nauk SSSR 105, 465–467 (1955).
  3. C. Imbert, “Calculation and experimental proof of the transverse shift induced by total internal reflection of a circularly polarized light beam,” Phys. Rev. D 5, 787–796 (1972). [CrossRef]
  4. K. Y. Bliokh and Y. P. Bliokh, “Polarization, transverse shifts, and angular momentum conservation laws in partial reflection and refraction of an electromagnetic wave packet,” Phys. Rev. E 75, 066609 (2007). [CrossRef]
  5. A. Aiello and J. P. Woerdman, “Role of beam propagation in Goos-Hanchen and Imbert-Fedorov shifts,” Opt. Lett. 33, 1437–1439 (2008). [CrossRef]
  6. M. Merano, A. Aiello, M. P. van Exter, and J. P. Woerdman, “Observing angular deviations in the specular reflection of a light beam,” Nat. Photonics 3, 337–340 (2009). [CrossRef]
  7. K. Y. Bliokh and Y. P. Bliokh, “Conservation of angular momentum, transverse shift, and spin Hall effect in reflection and refraction of an electromagnetic wave packet,” Phys. Rev. Lett. 96, 073903 (2006). [CrossRef]
  8. O. Hosten and P. Kwiat, “Observation of the spin Hall effect of light via weak measurements,” Science 319, 787–790 (2008). [CrossRef]
  9. L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, “Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes,” Phys. Rev. A 45, 8185–8189 (1992). [CrossRef]
  10. L. Allen, M. J. Padgett, and M. Babiker, “The orbital angular momentum of light,” in Progress in Optics, E. Wolf, ed., Vol. 39 (Elsevier, 1999), pp. 291–372.
  11. V. G. Fedoseyev, “Spin-independent transverse shift of the centre of gravity of a reflected and of a refracted light beam,” Opt. Commun. 193, 9–18 (2001). [CrossRef]
  12. R. Dasgupta and P. K. Gupta, “Experimental observation of spin-independent transverse shift of the centre of gravity of a reflected Laguerre-Gaussian light beam,” Opt. Commun. 257, 91–96 (2006). [CrossRef]
  13. H. Okuda and H. Sasada, “Huge transverse deformation in nonspecular reflection of a light beam possessing orbital angular momentum near critical incidence,” Opt. Express 14, 8393–8402 (2006). [CrossRef]
  14. H. Okuda and H. Sasada, “Significant deformations and propagation variations of Laguerre–Gaussian beams reflected and transmitted at a dielectric interface,” J. Opt. Soc. Am. A 25, 881–890 (2008). [CrossRef]
  15. M. Merano, N. Hermosa, and J. P. Woerdman, “How orbital angular momentum affects beam shifts in optical reflection,” Phys. Rev. A 82, 023817 (2010). [CrossRef]
  16. N. Hermosa, M. Merano, A. Aiello, and J. P. Woerdman, “Orbital angular momentum induced beam shifts,” Proc. SPIE 7950, 79500F (2011).
  17. N. Hermosa, A. Aiello, and J. P. Woerdman, “Radial mode dependence of optical beam shifts,” Opt. Lett. 37, 1044–1046 (2012). [CrossRef]
  18. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, 1996).
  19. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th ed. (Academic, 2007).
  20. M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975). [CrossRef]
  21. G. P. Agrawal and D. N. Pattanayak, “Gaussian beam propagation beyond the paraxial approximation,” J. Opt. Soc. Am. A 69, 575–578 (1979). [CrossRef]
  22. F. W. J. Olver and L. C. Maximon, “Bessel functions,” in NIST Handbook of Mathematical Functions, F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark, eds. (Cambridge University, 2010), p. 265.
  23. A. Cerjan and C. Cerjan, “Orbital angular momentum of Laguerre-Gaussian beams beyond the paraxial approximation,” J. Opt. Soc. Am. A 28, 2253–2260 (2011). [CrossRef]
  24. A. Aiello and J. P. Woerdman, “Theory of angular Goos-Hanchen shift near Brewster incidence,” arXiv:0903.3730v2 (2009).
  25. W. H. Carter, “Electromagnetic field of a Gaussian beam with an elliptical cross section,” J. Opt. Soc. Am. 62, 1195–1201 (1972). [CrossRef]
  26. K. Y. Bliokh, I. V. Shadrivov, and Y. S. Kivshar, “Goos-Hanchen and Imbert-Fedorov shifts of polarized vortex beams,” Opt. Lett. 34, 389–391 (2009). [CrossRef]
  27. M. Merano, N. Hermosa, A. Aiello, and J. P. Woerdman, “Demonstration of a quasi-scalar angular Goos-Hanchen effect,” Opt. Lett. 35, 3562–3564 (2010). [CrossRef]
  28. J. Ou, Y. Jiang, F. Li, and L. Liu, “Shift of beam centroid of Laguerre-Gaussian beams reflected and refracted at a dielectric interface,” Acta Phys. Sin. 60, 114203 (2011) (in Chinese).
  29. L. Kong, X. Wang, S. Li, Y. Li, J. Chen, B. Gu, and H. Wang, “Spin Hall effect of reflected light from an air-glass interface around the Brewster’s angle,” Appl. Phys. Lett. 100, 071109 (2012). [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