Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-745bb68f8f-l4dxg Total loading time: 0 Render date: 2025-02-07T17:49:46.808Z Has data issue: false hasContentIssue false

2 - Vortex transformations and vortex dynamics in optical fields

Published online by Cambridge University Press:  05 December 2012

By
G. Molina-Terriza
Edited by
David L. Andrews  and
Mohamed Babiker
G. Molina-Terriza
Affiliation:
Macquarie University
David L. Andrews
Affiliation:
University of East Anglia
Mohamed Babiker
Affiliation:
University of York
Get access

Summary

Introduction

Vortices and vorticity are common objects of study in the field of fluid dynamics [1]. In a fluid, vortices appear as spinning, often turbulent, flows, giving rise to common phenomena such as tornadoes and whirlpools. In their more discreet manifestations, fluid vortices are thought to be responsible for the destruction of bridges due to the formation of vortex streets and structural resonance [2] and for the flight of insects [3], ending a long debate in the community about the reversibility of the movement of insect wings. Because of the importance of all those natural phenomena, the study of vortex dynamics and the creation and annihilation of hydrodynamical vortices is a matter of intense study.

When the first properties of superfluids were found, the question of whether vortices could appear in such irrotational fluids was addressed by prominent scientists [4, 5]. It was found that vortices could also appear in such systems, but they could only appear as point vortices, i.e. singular locations where the vorticity of the fluid was infinite, whereas everywhere else the vorticity was strictly zero. This property was also found later on in Bose-Einstein condensates (BECs), where the quest for exciting and controlling the point vortices of quantum systems is still a hot topic. The dynamics of and processes related to the birth and destruction of vortex-antivortex pairs play an important role in the physics of these exotic systems.

Type
Chapter
Information
The Angular Momentum of Light , pp. 31 - 50
Publisher: Cambridge University Press
Print publication year: 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] H. J., Lugt. Vortex Flow in Nature and Technology. New York: J. Wiley and Sons, 1983.
[2] T., von Kármán. Aerodynamics: Selected Topics in the Light of Their Historical Development. New York; Dover Publications, 2004.
[3] C. P., Ellington, C., van der Berg, A. P., Willmott, and A. L. R., Thomas. Leading edge vortices in insect flight. Nature, 384: 626–30, 1996.Google Scholar
[4] Richard P., Feynmann. Application of quantum mechanics to liquid helium. In C. J., Gorter (ed.), Progress in Low Temperature Physics, chapter 2. New York: Interscience Publishers Inc., 1991.
[5] L., Onsager. Statistical hydrodinamics. Il Nuovo Cimento, 6 (Suppl. 2):249, 1949.Google Scholar
[6] J. F., Nye and M. V., Berry. Dislocations in wave trains. Proc. R. Soc. Lond.A, 336:165–90, 1974.Google Scholar
[7] P., Coullet, L., Gil, and F., Rocca. Optical vortices. Opt. Commun., 73:403–8, 1989.Google Scholar
[8] N. B., Baranova, B. Ya., Zel'dovich, A. V., Mamaev, N. F., Pilipetskii, and V. V., Schkunov. Dislocations of the wave-front of a speckle-inhomogeneous field (theory and experiment). Sov. Phys. JETP Lett., 33:195–9, 1981.Google Scholar
[9] H., He, M. E. J., Friese, N. R., Heckenberg, and H., Rubinsztein-Dunlop. Direct obervation of transfer of angular momentum to absorptive particles from a laser beam with a phases ingularity. Phys. Rev. Lett., 75:826–9, 1995.Google Scholar
[10] L., Paterson, M. P., MacDonald, W., Sibbert, P. E., Bryant, and K., Dholakia. Controlled rotation of optically microscopic particles. Science, 292:912–4, 2001.Google Scholar
[11] M. D., Levenson, T. J., Ebihara, G., Dai, Y., Morikawa, N., Hayashi, and S. M., Tan. Optical vortex masks for vial evels. J. Microlith. Microfa. Microsyst, 3:293–304, 2004.Google Scholar
[12] A. S., Desyatnikov, Y. S., Kivshar, and L., Torner. Optical vortices and vortex solitons. In E., Wolf (ed.), Progress in Optics, vol. XLVII, pp. 291–391. Amsterdam: Elsevier Science, 2005.
[13] Y. Y., Schechner and J., Shamir. Parameterization and orbital angular momentum of anisotropic vortices. J. Opt. Soc. Am.A, 13:967–73, 1996.Google Scholar
[14] I., Freund. Optical vortices in Gaussian random wave fields: statistical probability densities. J. Opt. Soc. Am.A, 11:1644–52, 1994.Google Scholar
[15] I., Freund and V., Freilikher. Parameterization of anisotropic vortices. J. Opt. Soc. Am.A, 14:1902–10, 1997.Google Scholar
[16] G., Molina-Terriza, E. M., Wright, and L., Torner. Propagation and control of noncanonical optical vortices. Opt. Lett., 26:163–5, 2001.Google Scholar
[17] A. E., Siegman. Lasers. Mill Valley, CA: University Science Books, 1986.
[18] G., Indebetouw. Optical vortices and their propagation. J. Mod. Opt., 40:73–87, 1993.Google Scholar
[19] D., Rozasand, C. T., Law, and G. A., Swartzlander. Propagation dynamics of optical vortices. J. Opt. Soc. Am.B, 14:3054–65, 1997.Google Scholar
[20] G., Molina-Terriza, J., Recolons, J. P., Torres, L., Torner, and E. M., Wright. Observation of the dynamical inversion of the topological charge of an optical vortex. Phys. Rev. Lett., 87:023902, 2001.Google Scholar
[21] J. J., Garcia-Ripoll, G., Molina-Terriza, V. M., Perez-Garcia, and L., Torner. Structural instability of vortices in bose-einstein condensates. Phys. Rev. Lett., 87:140403, 2001.Google Scholar
[22] R., Marchiano and J.-L., Thomas. Doing arithmetic with nonlinear acoustic vortices. Phys. Rev. Lett., 101:064301, 2008.Google Scholar
[23] L., Allen, M. W., Beijersbergen, R. J. C., Spreeuw, and J. P., Woerdman. Orbital angular momentum of light and the t ransformation of Laguerre–Gaussian laser modes. Phys. Rev.A, 45:8185–9, 1992.Google Scholar
[24] M. W., Beijersbergen, L., Allen, H. E. L. O., van der Veen, and J. P., Woerdman. Astigmatic laser mode converters and transfer of orbital angular momentum. Opt. Commun., 96:123–32, 1993.Google Scholar
[25] Michael, Berry. Much ado about nothing: optical dislocation lines (phase singularities, zeros, vortices…). In M. S., Soskin (ed.), Singular Optics, Proceedings of the SPIE, vol. 3487, pp. 1–5, 1998.
[26] S. J., van Enk and G., Nienhuis. Eigenfunction description of laser beams and orbital angular momentum of light. Opt. Commun., 94:147–58, 1992.Google Scholar
[27] G., Molina-Terriza, L., Torner, E. M., Wright, J. J., Garcia-Ripoll, and V. M., Perez-Garcia. Vortex revivals with trapped light. Opt. Lett., 26:1601–3, 2001.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×