## Orbital angular momentum of Laguerre–Gaussian beams beyond the paraxial approximation

JOSA A, Vol. 28, Issue 11, pp. 2253-2260 (2011)

http://dx.doi.org/10.1364/JOSAA.28.002253

Enhanced HTML Acrobat PDF (171 KB)

### Abstract

We derive a full field solution for Laguerre–Gaussian beams consistent with the Helmholtz equation using the angular spectrum method. Field components are presented as an order expansion in the ratio of the wave length to the beam waist,

© 2011 Optical Society of America

**OCIS Codes**

(000.4430) General : Numerical approximation and analysis

(050.1960) Diffraction and gratings : Diffraction theory

(070.2590) Fourier optics and signal processing : ABCD transforms

**ToC Category:**

Diffraction and Gratings

**History**

Original Manuscript: June 7, 2011

Revised Manuscript: August 22, 2011

Manuscript Accepted: September 9, 2011

Published: October 11, 2011

**Citation**

Alexander Cerjan and Charles Cerjan, "Orbital angular momentum of Laguerre–Gaussian beams beyond the paraxial approximation," J. Opt. Soc. Am. A **28**, 2253-2260 (2011)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-28-11-2253

Sort: Year | Journal | Reset

### References

- 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] [PubMed]
- R. A. Beth, “Mechanical detection and measurement of the angular momentum of light,” Phys. Rev. 50, 115–125 (1936). [CrossRef]
- A. T. O’Neil, I. MacVicar, L. Allen, and M. J. Padgett, “Intrinsic and extrinsic nature of the orbital angular momentum of a light beam,” Phys. Rev. Lett. 88, 053601–053604 (2002). [CrossRef] [PubMed]
- S. M. Barnett, “Optical angular-momentum flux,” J. Opt. B: Quantum Semiclass. Opt. 4, S7–S16 (2002). [CrossRef]
- M. V. Berry, “Optical currents,” J. Opt. A: Pure Appl. Opt. 11, 094001 (2009). [CrossRef]
- K. Y. Bliokh, M. A. Alonso, E. A. Ostrovskaya, and A. Aiello, “Angular momentum and spin–orbit interaction of nonparaxial light in free space,” Phys. Rev. A 82, 063825 (2010). [CrossRef]
- C. F. Li, “Spin and orbital angular momentum of a class of nonparaxial light beams having a globally defined polarization,” Phys. Rev. A 80, 063814 (2009). [CrossRef]
- C. J. Bouwkamp, “Diffraction theory,” Rep. Prog. Phys. 17, 32–100 (1950).
- P. C. Clemmow, The Plane Wave Spectrum Representations of Electromagnetic Fields (Pergamon, 1966).
- J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1968).
- G. P. Agrawal and D. N. Pattanayak, “Gaussian beam propagation beyond the paraxial approximation,” J. Opt. Soc. Am. 69, 575–578 (1979). [CrossRef]
- L. Cicchitelli, H. Hora, and R. Postle, “Longitudinal field components for laser beams in vacuum,” Phys. Rev. A 41, 3727–3732(1990). [CrossRef] [PubMed]
- B. Quesnel and P. Mora, “Theory and simulation of the interaction of ultraintense laser pulses with electrons in vacuum,” Phys. Rev. E 58, 3719–3732 (1998). [CrossRef]
- C. G. Chen, P. T. Konkola, J. Ferrera, R. K. Heilmann, and M. L. Schattenburg, “Analyses of vector Gaussian beam propagation and the validity of paraxial and spherical approximations,” J. Opt. Soc. Am. A 19, 404–412 (2002). [CrossRef]
- M. Lax, W. H. Louisell, and W. B. McKnight, “From Maxwell to paraxial wave optics,” Phys. Rev. A 11, 1365–1370 (1975). [CrossRef]
- S. Yan and B. Yao, “Description of a radially polarized Laguerre–Gaussian beam beyond the paraxial approximation,” Opt. Lett. 32, 3367–3369 (2007). [CrossRef] [PubMed]
- G. Zhou, “Analytically vectorial structure of an apertured Laguerre–Gaussian beam in the far-field,” Opt. Lett. 31, 2616–2618 (2006). [CrossRef] [PubMed]
- I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th ed. (Academic Press, 2007).
- F.W. J.Olver, D.W.Lozier, R.F.Boisvert, and C.W.Clark (eds.), in NIST Handbook of Mathematical Functions(Cambridge University, 2010), p. 260.
- A. Cerjan and C. Cerjan, “Analytic solution of flat-top Gaussian and Laguerre–Gaussian laser field components,” Opt. Lett. 35, 3465–3467 (2010). [CrossRef] [PubMed]
- S. M. Barnett and L. Allen, “Orbital angular momentum and nonparaxial light beams,” Opt. Commun. 110, 670–678 (1994). [CrossRef]
- C. F. Li, T. T. Wang, and S. Y. Yang, “Comment on ‘Orbital angular momentum and nonparaxial light beams’,” Opt. Commun. 283, 2787–2788 (2010). [CrossRef]
- E. D. Rainville, “Laguerre polynomials,” in Special Functions (Chelsea, 1960), p. 209.
- L. Allen and M. J. Padgett, “The Poynting vector in Laguerre–Gaussian beams and the interpretation of their angular momentum density,” Opt. Commun. 184, 67–71 (2000). [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.