## Helmholtz Hodge decomposition of scalar optical fields |

JOSA A, Vol. 29, Issue 11, pp. 2421-2427 (2012)

http://dx.doi.org/10.1364/JOSAA.29.002421

Enhanced HTML Acrobat PDF (1278 KB)

### Abstract

It is shown that the vector field decomposition method, namely, the Helmholtz Hodge decomposition, can also be applied to analyze scalar optical fields that are ubiquitously present in interference and diffraction optics. A phase gradient field that depicts the propagation and Poynting vector directions can hence be separated into solenoidal and irrotational components.

© 2012 Optical Society of America

**OCIS Codes**

(260.0260) Physical optics : Physical optics

(260.2110) Physical optics : Electromagnetic optics

(350.0350) Other areas of optics : Other areas of optics

(350.4855) Other areas of optics : Optical tweezers or optical manipulation

(260.6042) Physical optics : Singular optics

**ToC Category:**

Optical Tweezers or Optical Manipulation

**History**

Original Manuscript: July 27, 2012

Manuscript Accepted: September 13, 2012

Published: October 22, 2012

**Virtual Issues**

Vol. 7, Iss. 12 *Virtual Journal for Biomedical Optics*

**Citation**

Monika Bahl and P. Senthilkumaran, "Helmholtz Hodge decomposition of scalar optical fields," J. Opt. Soc. Am. A **29**, 2421-2427 (2012)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-29-11-2421

Sort: Year | Journal | Reset

### References

- A. Globus, C. Levit, and T. Lasinki, “A tool for visualizing the topology of three-dimensional vector fields,” in Proceedings of IEEE on Visualization (IEEE, 1991), pp. 33–40.
- K. Polthier and E. Preuss, “Identifying vector field singularities using a discrete Hodge decomposition,” in Visualization and Mathematics III, H. C. Hege and K. Polthier, eds. (Springer Verlag, 2002), pp. 113–134.
- Y. Tong, S. Lombeyda, A. N. Hirani, and M. Desbrun, “Discrete multiscale vector field decomposition,” ACM Trans. Graph. 22, 445–452 (2003). [CrossRef]
- F. Petronetto, A. Paiva, M. Lage, G. Tavares, H. Lopes, and T. Lewiner, “Meshless Helmholtz-Hodge decomposition,” IEEE Trans. Vis. Comput. Graphics 16, 338–342 (2010). [CrossRef]
- F. M. Denaro, “On the application of the Helmholtz–Hodge decomposition in projection methods for incompressible flows with general boundary conditions,” Int. J. Numer. Methods Fluids 43, 43–69 (2003). [CrossRef]
- I. Kaya, A. P. Santhanam, C. Imielinska, and J. Rolland, “Modeling air-flow in the tracheobronchial tree using computational fluid dynamics,” in Proceedings of 2007 MICCAI Workshop on Computational Biomechanics (2007), pp. 142–151.
- R. Fedkiw, J. Stam, and H. W. Jensen, “Visual simulation of smoke,” in Proceedings of ACM SIGGRAPH 2001, Proceedings of the 28th Annual Conference on Computer Graphics and Interactive Techniques, Eugene Fiume, ed. (Association for Computing Machinery, 2001), pp. 15–22.
- A. M. Stewart, “Angular momentum of light,” J. Mod. Opt. 52, 1145–1154 (2005). [CrossRef]
- M. Hattori and S. Komatsu, “An exact formulation of a filter for rotation in phase gradients and its applications to wavefront reconstruction problems,” J. Mod. Opt. 50, 1705–1723(2003). [CrossRef]
- G. Molina-Terriza, J. P. Torres, and L. Torner, “Twisted photons,” Nat. Phys. 3, 305–310 (2007). [CrossRef]
- M. Berry, “Optical currents,” J. Opt. A 11, 1464–1475 (2009). [CrossRef]
- M. Born and E. Wolf, Principles of Optics (Cambridge University, 2002).
- 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]
- 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]
- S. F. Arnold, L. Allen, and M. Padgett, “Advances in optical angular momentum,” Laser Photon. Rev. 2, 299–315(2008). [CrossRef]
- M. Padgett and L. Allen, “Optical tweezers and spanners,” Phys. World 10, 35–38 (1997).
- M. S. Soskin and M. V. Vasnetsov, “Singular optics,” Prog. Opt. 42, 219–276 (2001). [CrossRef]
- A. M. Yao and M. J. Padgett, “Orbital angular momentum: origins, behavior and applications,” Adv. Opt. Photon. 3, 161–204 (2011). [CrossRef]
- I. V. Basistiy, M. S. Soskin, and M. V. Vasnetsov, “Optical wavefront dislocations and their properties,” Opt. Commun. 119, 604–612 (1995). [CrossRef]
- I. V. Basistiy, V. Y. Bazhenov, M. S. Soskin, and M. V. Vasnetsov, “Optics of light beams with screw dislocations,” Opt. Commun. 103, 422–428 (1993). [CrossRef]
- P. Senthilkumaran, F. Wyrowski, and H. Schimmel, “Vortex stagnation problem in iterative Fourier transform algorithms,” Opt. Lasers Eng. 43, 43–56 (2005). [CrossRef]
- S. Vyas and P. Senthilkumaran, “Interferometric optical vortex array generator,” Appl. Opt. 46, 2893–2898 (2007). [CrossRef]
- J. Xavier, S. Vyas, P. Senthilkumaran, and J. Joseph, “Tailored complex 3D vortex lattice structures by perturbed multiples of three-plane waves,” Appl. Opt. 51, 1872–1878 (2012). [CrossRef]
- D. P. Ghai, S. Vyas, P. Senthilkumaran, and R. S. Sirohi, “Vortex lattice generation using interferometric techniques based on lateral shearing,” Opt. Commun. 282, 2692–2698 (2009). [CrossRef]
- J. P. Prenel and D. Ambrosini, “Flow visualization and beyond,” Opt. Lasers Eng. 50, 1–7 (2012). [CrossRef]
- G. B. Arfken and H. J. Weber, Mathematical Methods for Physicists (Elsevier, 2005).
- T. McGraw, T. Kawai, I. Yassine, and L. Zhu, “Visualizing high-order symmetric tensor field structure with differential operators,” J. Appl. Math. 2011, 1–27 (2011). [CrossRef]
- Finite difference method, http://en.wikipedia.org/wiki/Finite_difference_method .

## 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.