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-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-19T21:19:59.904Z Has data issue: false hasContentIssue false

3 - Vector beams in free space

Published online by Cambridge University Press:  05 December 2012

By
E. J. Galvez
Edited by
David L. Andrews  and
Mohamed Babiker
E. J. Galvez
Affiliation:
Colgate University
David L. Andrews
Affiliation:
University of East Anglia
Mohamed Babiker
Affiliation:
University of York
Get access

Summary

Introduction

Higher-order modes of optical beams have been the subject of many studies over the past 20 years [1, 2]. Because laser resonators deliver in principle quite complex spatial patterns, spatial modes of beams were studied intensively when lasers were first developed [3]. Beams in higher-order spatial modes are solutions of the paraxial wave equation, with Hermite-Gauss and Laguerre-Gauss beams being the most important families of beams. These are solutions of the wave equation in Cartesian and cylindrical coordinates, respectively. The latter beams have been at the heart of a revival of research on higher-order modes due to the orbital angular momentum that they carry [4]. They have also received much attention due to the phase singularities present in their transverse amplitude [5]. Higher-order modes have stimulated much research in the application of forces and torques to objects in optical tweezers [1, 2]. Their usefulness has carried higher-order spatial modes further into new paths, in studies with non-classical sources of light and applications in quantum information [6].

The beams mentioned above are scalar solutions of the wave equation and thus independent of the polarization of the light. Vector beams are formed by the non-separable combinations of spatial and polarization modes. This enhanced modal space produces an interesting set of beams that offer new effects and applications. The origin of these beams is not recent either, as the possibility of combining higher-order spatial modes and polarization started with those early studies of modes as well.

Type
Chapter
Information
The Angular Momentum of Light , pp. 51 - 70
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] Allen, L., Barnett, S. M., and Padgett, M. J. (eds.), 2003, Optical Angular Momentum. Bristol: Institute of Physics.
[2] Andrews, D. L. (ed.), 2008, Structured Light and Its Applications. Burlington, VT: Academic Press.
[3] Siegman, A. E., 1986. Lasers. Mill Valley, CA: University Science Books.
[4] Allen, L., Beijersbergen, M. W., Spreeuw, R. J. C., and Woerdman, J. P., 1992. Orbital angular momentum of light and the transformation of Laguerre–Gaussian laser modes. Phys. Rev.A, 45, 8185–9.Google Scholar
[5] Soskin, M. and Vasnetsov, M. V., 2001. Singular optics. Progress in Optics 42, 219–76.Google Scholar
[6] Molina-Terriza, G., Torres, J.P., and Torner, L., 2007, Twisted photons. Nature Phys., 3, 305–10.Google Scholar
[7] Fontana, J. R. and Pantell, R. H. 1983. A high-energy, laser accelerator for using the inverse Cherenkov effect. J. Appl. Phys., 54, 4285–8.Google Scholar
[8] Quabis, S., Dorn., R., Eberler, M., Glöckl, O., and Leuchs, G., 2000, Focusing light to a tighter spot. Opt. Commun., 179, 1–7.Google Scholar
[9] Dorn, R., Quabis, S., and Leuchs, G., 2003, Sharper focus for a radially polarized light beam. Phys. Rev. Lett., 91, 233901-1–4.Google Scholar
[10] Maurer, C., Jesacher, A., Fürhapter, S., Bernet, S., and Ritsch-Marte, M., 2007., Tailoring of arbitrary optical vector beams. New J. Phys., 9, 78-1–20.Google Scholar
[11] Freund, I., 2002, Polarization singularity indices in Gaussian laser beams. Opt. Commun., 201, 251–70.Google Scholar
[12] Beijersbergen, M. W., Allen, L., van der Veen, H. E. L. O., and Woerdman, J. P., 1993, Astigmatic laser mode converters and transfer of orbital angular momentum. Opt. Commun., 96, 123–32.Google Scholar
[13] Padgett, M. J. and Courtial, J., 1999, Poincaré-sphere equivalent for light beams containing orbital angular momentumOpt. Lett., 24, 430–2.Google Scholar
[14] Agarwal, J., 1999, SU(2) structure of the Poincaré sphere for light beams with orbital angular momentumOpt. Soc. Am.A, 16, 2914–6.Google Scholar
[15] Mushiake, Y., Matsumura, K., and Nakajima, N., 1972, Generation of radially polarized optical beam mode by laser oscillation. Proc. IEEE, 60, 1107–9.Google Scholar
[16] Youngsworth, K. S. and Brown, T. G., 2000, Focusing of high numerical aperture cylindrical vector beams. Opt. Express, 7, 77–87.Google Scholar
[17] Baumann, S. M., Kalb, D. M., MacMillan, L. H., and Galvez, E. J., 2009, Propagation dynamics of optical vortices due to Gouy phase. Opt. Express, 17, 9818–27Google Scholar
[18] Beckley, A. M., Brown, T. G. Brown, and Alonso, M. A., 2010, Full Poincaré beams. Opt. Express, 18, 10777–85.Google Scholar
[19] Zhan, Q., 2009, Cylindrical vector beams: from mathematical concepts to applications. Adv. Opt. Photon., 1, 1–57.Google Scholar
[20] Tidwell, S. C., Ford, D. H., and Kimura, W. D., 1990, Generating r adially polarized beams interferometrically. Appl. Opt., 29, 2234–9.Google Scholar
[21] Quabis, S., Dorn, R., and Leuchs, G., 2005, Generation of a radially polarized doughnut mode of high quality. Appl. Phys.B, 81, 597–600.Google Scholar
[22] Stalder, M. and Schadt, M., 1996, Linearly polarized light with axial symmetry generated by liquid-crystal polarization converters. Opt. Lett., 21, 1948–1950.Google Scholar
[23] Bomzon, Z., Biener, G., Kleiner, V. and Hasman, E., 2002, Radially and azimuthally polarized beams generated by space variant dielectric subwavelength gratings. Opt. Lett., 27, 285–7.Google Scholar
[24] Oron, R., Blit, S., Davidson, N., Friesem, A. A., Bomzon, Z., and Hasman, E., 2000, The formation of laser beams with pure azimuthal and radial polarization. Appl. Phys. Lett., 77, 3322–4.Google Scholar
[25] Kozawa, Y. and Sato., S., 2005, Generation of radially polarized laser beam by use of a conical Brewster prism. Opt. Lett., 30, 3063–5.Google Scholar
[26] Volpe, G. and Petrov, D., 2004, Generation of cylindrical vector beams with few-mode fibers excited by Laguerre–Gaussian beams. Opt. Commun., 237, 89–95.Google Scholar
[27] Ramachandran, S., Kristensen, P., and Yan, M.F., 2009, Generation and propagation of radially polarized beams in optical fibers. Opt. Lett., 34, 2525–7.Google Scholar
[28] Milione, H. I. Sztul, Alfano, R. R., and Nolan, D. A., 2009. Stokes polarimetry of a hybrid vector beam from a spun elliptical core optical fiber. Proc. SPIE, 7613, 761305–10.
[29] Fadeyeva, T. A., Shvedov, V. G., Izdebskaya, Y. V. et al., 2010, Spatially engineered polarization states and optical vortices in uniaxial crystal. Opt. Express, 18, 10848–63.Google Scholar
[30] Buinyi, I. O., Denisenko, V. G., and Soskin, M. S., 2010, Topological structure in polarization resolved conoscopic patterns for nematic liquid crystal cells. Opt. Commun., 282, 143–55.Google Scholar
[31] Walter, P., Aspelmeyer, M., Resch, K. J., and Zeilinger, A., 2005, Experimental violation of a cluster state Bell inequality. Phys. Rev. Lett., 95, 020403-1–4.Google Scholar
[32] Walter, P., Resch, K.J., Rudolph, T. et al., 2005, Experimental one-way quantum computing. Nature, 434 169–76.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org 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
×