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-848d4c4894-tn8tq Total loading time: 0 Render date: 2024-07-04T15:01:50.375Z Has data issue: false hasContentIssue false

4 - Optical beams with orbital angular momentum in nonlinear media

Published online by Cambridge University Press:  05 December 2012

By
A. S. Desyatnikov  and
Y. S. Kivshar
Edited by
David L. Andrews  and
Mohamed Babiker
A. S. Desyatnikov
Affiliation:
The Australian National University
Y. S. Kivshar
Affiliation:
The Australian National University
David L. Andrews
Affiliation:
University of East Anglia
Mohamed Babiker
Affiliation:
University of York
Get access

Summary

A summary is not available for this content so a preview has been provided. Please use the Get access link above for information on how to access this content.
Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
The Angular Momentum of Light , pp. 71 - 97
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] Kivshar, Yu. S. and Agrawal, G. P. 2003. Optical Solitons: From Fibers to Photonic Crystals. San Diego, CA: Academic Press.
[2] Malomed, B. A. 2002. Variational methods in nonlinear fiber optics and related fields. In Wolf, E. (ed), Progress in Optics, vol. 43. Amsterdam: Elsevier, pp. 71–193.
[3] Kruglov, V. I. and Vlasov, R. A. 1985. Spiral self-trapping propagation of optical beams in media with cubic nonlinearity. Phys. Lett.A, 111(8–9), 401–4.Google Scholar
[4] Nye, J. F. and Berry, M. V. 1974. Dislocations in wave trains. Proc. Royal Soc. London Series A Math. Phy. Sci., 336(1605), 165–90.Google Scholar
[5] Allen, L., Barnett, S. M., and Padgett, M. J. 2003. Optical Angular Momentum. Institute of Physics Pub.
[6] Soskin, M. S. and Vasnetsov, M. V. 2001. Singular optics. In Wolf, E. (ed), Progress in Optics, vol. 42. Amsterdam: Elsevier, pp. 219–70.
[7] Dennis, M. R., O'Holleran, K., and Padgett, M. J. 2009. Singular optics: optical vortices and polarization s ingularities. In Wolf, E. (ed), Progress in Optics, vol. 53. Amsterdam: Elsevier, pp. 293–363.
[8] Desyatnikov, A. S., Kivshar, Yu. S., and Torner, L. 2005. Optical vortices and vortex solitons. In Wolf, E. (ed), Progress in Optics, vol. 47. Amsterdam: Elsevier, pp. 291–391.
[9] Kivshar, Yu. S. and Pelinovsky, D. E. 2000. Self-focusing and transverse instabilities of solitary waves. Phys. Rep., 331(4), 118–95.Google Scholar
[10] Tikhonenko, V., Christou, J., and Luther-Davies, B. 1995. Spiraling bright spatial solitons formed by the breakup of an optical vortex in a saturable self-focusing medium. J. Opt. Soc. Am.B, 12(11), 2046–52.Google Scholar
[11] Tikhonenko, V., Christou, J., and Luther-Davies, B. 1996. Three dimensional bright spatial soliton collision and fusion in a saturable nonlinear medium. Phys. Rev. Lett., 76(15), 2698–701.Google Scholar
[12] Bigelow, M. S., Zerom, P., and Boyd, R. W. 2004. Breakup of ring beams carrying orbital angular momentum in sodium vapor. Phys. Rev. Lett., 92(8), 083902–4.Google Scholar
[13] Chen, Z., Shih, M.-F., Segev, M., Wilson, D. W., Muller, R. E., and Maker, P. D. 1997. Steady-state vortex-screening solitons formed in biased photorefractive media. Opt. Lett., 22(23), 1751–3.Google Scholar
[14] Petrov, D. V., Torner, L., Martorell, J., Vilaseca, R., Torres, J. P., and Cojocaru, C. 1998. Observation of azimuthal modulational instability and formation of patterns of optical solitons in a quadratic nonlinear crystal. Opt. Lett., 23(18), 1444–16.Google Scholar
[15] Soto-Crespo, J. M., Wright, E. M., and Akhmediev, N. N. 1992. Recurrence and azimuthal-symmetry breaking of a cylindrical Gaussian beam in a saturable self-focusing medium. Phys. Rev.A, 45(5), 3168–75.Google Scholar
[16] Firth, W. J. and Skryabin, D. V. 1997. Optical solitons carrying orbital angular momentum. Phys. Rev. Lett., 79(13), 2450–3.Google Scholar
[17] Torres, J. P., Soto-Crespo, J. M., Torner, L., and Petrov, D. V. 1998. Solitary-wave vortices in quadratic nonlinear media. J. Opt. Soc. Am.B, 15(2), 625–7.Google Scholar
[18] Skryabin, D. V. and Firth, W. J. 1998. Dynamics of self-trapped beams with phase dislocation in saturable Kerr and quadratic nonlinear media. Phys. Rev.E, 58(3), 3916–30.Google Scholar
[19] Stegeman, G. I. and Segev, M. 1999. Optical spatial solitons and their interactions: universality and diversity. Science, 286(5444), 1518–23.Google Scholar
[20] Poladian, L., Snyder, A. W., and Mitchell, D. J. 1991. Spiraling s patial solitons. Opt. Commun., 85(1), 59–62.Google Scholar
[21] Nikolov, N. N., Neshev, D., Krolikowski, W., Bang, O., Rasmussen, J. J., and Christiansen, P. L. 2004. Attraction of nonlocal dark optical solitons. Opt. Lett., 29, 286–8.Google Scholar
[22] Fratalocchi, A., Peccianti, M., Conti, C., and Assanto, G. 2004. Spiraling and cyclic dynamics of nematicons. Mol. Cryst. Liq. Cryst., 421, 197–207.Google Scholar
[23] Fratalocchi, A., Piccardi, A., Peccianti, M., and Assanto, G. 2007. Nonlinearly controlled angular momentum of soliton clusters. Opt. Lett., 32, 1447–9.Google Scholar
[24] Fratalocchi, A., Piccardi, A., Peccianti, M., and Assanto, G. 2007. Nonlinear management of the angular momentum of soliton clusters: theory and experiment. Phys. Rev.A, 75(6), 063835.Google Scholar
[25] Steblina, V. V., Kivshar, Yu. S., and Buryak, A. V. 1998. Scattering and spiraling of solitons in a bulk quadratic medium. Opt. Lett., 23(3), 156–8.Google Scholar
[26] Buryak, A. V. and Steblina, V. V. 1999. Soliton collisions in bulk quadratic media: comprehensive analytical and numerical study. J. Opt. Soc. Am.B, 16(2), 245–55.Google Scholar
[27] Malomed, B. A. 1998. Potential of i nteraction between two- and three-dimensional solitons. Phys. Rev.E, 58(6), 7928–33.Google Scholar
[28] Simos, C., Coudrec, V., and Barthelemy, A. 2002. Experiences sur les interactions de type particulaire de solitons multicolores: fusion, répulsion, enroulement en spirale. J. Phys. IV, 12(5), 211–12.Google Scholar
[29] Shih, M.-F., Segev, M., and Salamo, G. 1997. Three-dimensional spiraling of interacting s patial solitons. Phys. Rev. Lett., 78(13), 2551–24.Google Scholar
[30] Desyatnikov, A. S. and Maimistov, A. I. 1998. Interaction of two spatially separated light beams in a nonlinear Kerr medium. JETP, 86(6), 1101–16.Google Scholar
[31] Schjodt-Eriksen, J., Schmidt, M. R., Rasmussen, J. J., Christiansen, P. L., Gaididei, Y. B., and Berge, L. 1998. Two-beam interaction in saturable media. Phys. Lett.A, 246(5), 423–8.Google Scholar
[32] Garcia-Ripoll, J. J., Perez-Garcia, V. M., Ostrovskaya, E. A., and Kivshar, Yu. S. 2000. Dipole-mode vector solitons. Phys. Rev. Lett., 85(1), 82–5.Google Scholar
[33] Carmon, T., Uzdin, R., Pigier, C., Musslimani, Z. H., Segev, M., and Nepomnyashchy, A. 2001. Rotating propeller solitons. Phys. Rev. Lett., 87(14), 143901–4.Google Scholar
[34] Skryabin, D. V., McSloy, J. M., and Firth, W. J. 2002. Stability of spiralling solitary waves in Hamiltonian systems. Phys. Rev.E, 66(5), 055602–4.Google Scholar
[35] Stepken, A., Belic, M. R., Kaiser, F., Krolikowski, W., and Luther-Davies, B. 1999. Three dimensional trajectories of interacting incoherent photorefractive solitons. Phys. Rev. Lett., 82(3), 540–3.Google Scholar
[36] Belic, M. R., Stepken, A., and Kaiser, F. 1999. Spiraling behavior of photorefractive s creening solitons. Phys. Rev. Lett., 82(3), 544–7.Google Scholar
[37] Krolikowski, W., Luther-Davies, B., Denz, C. et al. 1999. Interaction of two-dimensional spatial incoherent solitons in photorefractive medium. Appl. Phys.B, 68(5), 975–82.Google Scholar
[38] Denz, C., Krolikowski, W., Petter, J. et al. 1999. Dynamics of formation and interaction of photorefractive screening solitons. Phys. Rev.E, 60(5), 6222–65.Google Scholar
[39] Desyatnikov, A. S., and Kivshar, Yu. S. 2002. Rotating optical soliton clusters. Phys. Rev. Lett., 88(5), 053901.Google Scholar
[40] Desyatnikov, A., Denz, C., and Kivshar, Y. 2004. Nonlinear optical beams carrying phase dislocations. J. Opt. A-Pure Appl. Opt., 6(5), S209–12.Google Scholar
[41] Kartashov, Y. V., Molina-Terriza, G., and Torner, L. 2002. Multicolor soliton clusters. J. Opt. Soc. Am.B, 19(11), 2682–91.Google Scholar
[42] Kartashov, Y. V., Crasovan, L. C., Mihalache, D., and Torner, L. 2002. Robust propagation of two-color soliton clusters supported by competing nonlinearities. Phys. Rev. Lett., 89(27), 273902–4.Google Scholar
[43] Mihalache, D., Mazilu, D., Crasovan, L. C., Malomed, B. A., Lederer, F., and Torner, L. 2003. Robust soliton clusters in media with competing cubic and quintic nonlinearities. Phys. Rev.E, 68(4), 046612–8.Google Scholar
[44] Crasovan, L. C., Kartashov, Y. V., Mihalache, D., Torner, L., Kivshar, Yu. S., and Perez-Garcia, V. M. 2003. Soliton “molecules”: robust clusters of spatiotemporal optical solitons. Phys. Rev.E, 67(4), 046610–5.Google Scholar
[45] Mihalache, D., Mazilu, D., Crasovan, L. C., Malomed, A., Lederer, F., and Torner, L. 2004. Soliton clusters in three-dimensional media with competing cubic and quintic nonlinearities. J. Opt. B: Quantum Semicl. Opt., 6(5), S333–40.Google Scholar
[46] Berge, L. 1998. Wave collapse in physics: principles and applications to light and plasma waves. Phys. Rep., 303(5–6), 260–370.Google Scholar
[47] Barthelemy, A., Froehly, C., Shalaby, M., Donnat, P., Paye, J., and Migus, A. 1993. In Martin, J.J. et al. (ed), Ultrafast Phenomena VIII. Berlin: Springer, pp. 299–305.
[48] Barthelemy, A., Froehly, C., and Shalaby, M. 1994. Proc. SPIE Int. Soc. Opt. Eng., 2041, 104.
[49] Soljacic, M., Sears, S., and Segev, M. 1998. Self-trapping of “necklace” beams in self-focusing Kerr media. Phys. Rev. Lett., 81(22), 4851–4.Google Scholar
[50] Soljacic, M. and Segev, M. 2000. Self-trapping of “necklace-ring” beams in self-focusing Kerr media. Phys. Rev.E, 62(2), 2810–20.Google Scholar
[51] Soljacic, M. and Segev, M. 2001. Integer and fractional angular momentum borne on self-trapped necklace-ring beams. Phys. Rev. Lett., 86(3), 420–3.Google Scholar
[52] Desyatnikov, A. S. and Kivshar, Yu. S. 2002. Spatial optical solitons and soliton clusters carrying an angular momentum. J. Opt. B: Quantum Semicl. Opt., 4(2), S58–65.Google Scholar
[53] Abramochkin, E. G. and Volostnikov, V. G. 2004. Spiral light beams. Phys. Usp., 74, 1177–203.Google Scholar
[54] Daria, V. R., Palima, D. Z., and Glückstad, J. 2011. Optical twists in phase and amplitude. Opt. Express, 19, 476–81.Google Scholar
[55] Desyatnikov, A. S., Sukhorukov, A. A., and Kivshar, Yu. S. 2005. Azimuthons: spatially modulated vortex solitons. Phys. Rev. Lett., 95(20), 203904.Google Scholar
[56] Carr, L. D., Clark, C. W., and Reinhardt, W. P. 2000. Stationary solutions of the one-dimensional nonlinear Schrödinger equation. II. Case of attractive nonlinearity. Phys. Rev.A, 62(6), 063611.Google Scholar
[57] Berry, M. V. 2009. Optical currents. J. O. A: Pure Appl. Opt. 11(9), 094001.Google Scholar
[58] Bekshaev, A. and Soskin, M. 2006. Rotational transformations and transverse energy flow in paraxial light beams: linear azimuthons. Opt. Lett., 31(14), 2199–201.Google Scholar
[59] Maucher, F., Buccoliero, D., Skupin, S., Grech, M., Desyatnikov, A., and Krolikowski, W. 2009. Tracking azimuthons in nonlocal nonlinear media. Opt. Quantum Electr, 41, 337–48. doi: 10.1007/s11082-009-9351-9.Google Scholar
[60] Vuong, L. T., Grow, T. D., Ishaaya, A. et al. 2006. Collapse of optical vortices. Phys. Rev. Lett., 96(13), 133901.Google Scholar
[61] Krolikowski, W., Ostrovskaya, E. A., Weilnau, C. et al. 2000. Observation of dipole-mode vector solitons. Phys. Rev. Lett., 85(7), 1424–17.Google Scholar
[62] Zhang, P., Huang, S., Hu, Y., Hernandez, D., and Chen, Z. 2010. Generation and nonlinear self-trapping of optical propelling beams. Opt. Lett., 35(18), 3129–31.Google Scholar
[63] Minovich, A., Neshev, D. N., Desyatnikov, A. S., Krolikowski, W., and Kivshar, Yu. S. 2009. Observation of optical azimuthons. Opt. Express, 17(26), 23610–16.Google Scholar
[64] Rochester, S. M., Hsiung, D. S., Budker, D., Chiao, R. Y., Kimball, D. F., and Yashchuk, V. V. 2001. Self-rotation of resonant elliptically polarized light in collision-free rubidium vapor. Phys. Rev.A, 63(4), 043814.Google Scholar
[65] Briedis, D., Petersen, D., Edmundson, D., Krolikowski, W., and Bang, O. 2005. Ring vortex solitons in nonlocal nonlinear media. Opt. Express, 13, 435–43.Google Scholar
[66] Yakimenko, A. I., Zaliznyak, Yu. A., and Kivshar, Yu. 2005. Stable vortex solitons in nonlocal self-focusing nonlinear media. Phys. Rev.E, 71(6), 065603.Google Scholar
[67] Rotschild, C., Cohen, O., Manela, O., Segev, M., and Carmon, T. 2005. Solitons in nonlinear media with an infinite range of nonlocality: first observation of coherent elliptic solitons and of vortex-ring solitons. Phys. Rev. Lett., 95(21), 213904.Google Scholar
[68] Rotschild, C., Segev, M., Xu, Z., Kartashov, Y. V., Torner, L., and Cohen, O. 2006. Two-dimensional multipole solitons in nonlocal nonlinear media. Opt. Lett., 31(22), 3312–14.Google Scholar
[69] Conti, C., Peccianti, M., and Assanto, G. 2003. Route to nonlocality and observation of accessible solitons. PRL, 91(7).Google Scholar
[70] Conti, C., Peccianti, M., and Assanto, G. 2004. Observation of optical spatial solitons in a highly nonlocal medium. Phys. Rev. Lett., 92(11), 113902.Google Scholar
[71] Krolikowski, W., Bang, O., Nikolov, N. I. et al. 2004. Modulational instability, solitons and beam propagation in spatially nonlocal nonlinear media. J. Opt.B, 6(5), S288–94.Google Scholar
[72] Snyder, A. W. and Mitchell, D. J. 1997. Accessible solitons. Science, 276(5318), 1538–41.Google Scholar
[73] Buccoliero, D., Desyatnikov, A. S., Krolikowski, W., and Kivshar, Yu. S. 2007. Laguerre and Hermite soliton clusters in nonlocal nonlinear media. Phys. Rev. Lett., 98(5), 053901.Google Scholar
[74] Lopez-Aguayo, S., Desyatnikov, A. S., Kivshar, Yu. S., Skupin, S., Krolikowski, W., and Bang, O. 2006. Stable rotating dipole solitons in nonlocal optical media. Opt. Lett., 31(8), 1100–2.Google Scholar
[75] Skupin, S., Bang, O., Edmundson, D., and Krolikowski, W. 2006. Stability of two-dimensional spatial solitons in nonlocal nonlinear media. Phys. Rev.E, 73(6), 066603.Google Scholar
[76] Skupin, S., Saffman, M., and Królikowski, W. 2007. Nonlocal stabilization of nonlinear beams in a self-focusing atomic vapor. Phys. Rev. Lett., 98(26), 263902.Google Scholar
[77] Ye, F., Kartashov, Y. V., and Torner, L. 2008. Stabilization of dipole solitons in nonlocal nonlinear media. Phys. Rev.A, 77(4), 043821.Google Scholar
[78] Lopez-Aguayo, S., Desyatnikov, A. S., and Kivshar, Yu. S. 2006a. Azimuthons in nonlocal nonlinear media. Opt. Express, 14(17), 7903–78.Google Scholar
[79] Skupin, S., Grech, M., and Królikowski, W. 2008. Rotating s oliton solutions in nonlocal nonlinear media. Opt. Express, 16(12), 9118–31.Google Scholar
[80] Zhang, Y., Skupin, S., Maucher, F., Pour, A. G., Lu, K., and Królikowski, W. 2010. Azimuthons in weakly nonlinear waveguides of different symmetries. Opt. Express, 18(26), 27846–57.Google Scholar
[81] Buccoliero, D., Desyatnikov, A. S., Krolikowski, W., and Kivshar, Yu. S. 2008. Spiraling multivortex solitons in nonlocal nonlinear media. Opt. Lett., 33(2), 198–200.Google Scholar
[82] Abramochkin, E. G. and Volostnikov, V. G. 2004. Generalized Gaussian beams. J. Opt. A: Pure Appl. Opt., 6(5), S157.Google Scholar
[83] Rozanov, N. 2004. On the translational and rotational motion of nonlinear optical structures as a whole. Opt. Spectroscopy, 96, 405–8. doi: 10.1134/1.1690033.Google Scholar
[84] Buccoliero, D. and Desyatnikov, A. S. 2009. Quasi-periodic t ransformations of nonlocal spatial solitons. Opt. Express, 17(12), 9608–13.Google Scholar
[85] Kaminer, I., Rotschild, C., Manela, O., and Segev, M. 2007. Periodic solitons in nonlocal nonlinear media. Opt. Lett., 32(21), 3209–11.Google Scholar
[86] Yakimenko, A. I., Lashkin, V. M., and Prikhodko, O. O. 2006. Dynamics of two-dimensional coherent structures in nonlocal nonlinear media. Phys. Rev.E, 73(6), 066605.Google Scholar
[87] Kartashov, Y. V., Torner, L., Vysloukh, V. A., and Mihalache, D. 2006. Multipole vector solitons in nonlocal nonlinear media. Opt. Lett., 31(10), 1483–15.Google Scholar
[88] Buccoliero, D., Desyatnikov, A. S., Krolikowski, W., and Kivshar, Yu. S. 2009. Boundary effects on the dynamics of higher-order optical spatial solitons in nonlocal thermal media. J. Opt.A, 11(9), 094014.Google Scholar
[89] Flach, S. and Gorbach, A. V. 2008. Discrete breathers – advances in theory and applications. Phys. Rep., 467(1–3), 1–116.Google Scholar
[90] Buccoliero, D. 2009. PhD thesis. The Australian National University.
[91] Desyatnikov, A. S., Buccoliero, D., Dennis, M. R., and Kivshar, Yu. S. 2010. Suppression of collapse for spiraling elliptic solitons. Phys. Rev. Lett., 104(5), 053902.Google Scholar
[92] Chiao, R. Y., Garmire, E., and Townes, C. H. 1964. Self-trapping of optical beams. Phys. Rev. Lett., 13, 479–80.Google Scholar
[93] Moll, K. D., Gaeta, A. L., and Fibich, G. 2003. Self-similar optical wave collapse: observation of the townes profile. Phys. Rev. Lett., 90(20), 203902.Google Scholar
[94] Boyd, R. W., Lukishova, S. G., and Shen, Y. R. 2009. Self-focusing, Past and Present: Fundamentals and Prospects. Berlin: Springer.
[95] Fibich, G. and Ilan, B. 2003. Self-focusing of circularly polarized beams. Phys. Rev.E, 67(3), 036622.Google Scholar
[96] Courtial, J., Dholakia, K., Allen, L., and Padgett, M. J. 1997. Gaussian beams with very high orbital angular momentum. Opt. Commun., 144, 210–13.Google Scholar
[97] Crosignani, B. and Porto, P. Di. 1993. Nonlinear propagation in Kerr media of beams with unequal transverse widths. Opt. Lett., 18(17), 1394–16.Google Scholar
[98] Goncharenko, A. M., Logvin, Yu. A., Samson, A. M., Shapovalov, P. S., and Turovets, S. I. 1991. Ermakov Hamiltonian systems in nonlinear optics of elliptic Gaussian beams. Phys. Lett.A, 160(2), 138–42.Google Scholar
[99] Goncharenko, A. M, Logvin, Yu. A., Samson, A. M, and Shapovalov, P. S. 1991. Rotating elliptical gaussian beams in nonlinear media. Opt. Commun., 81(3–4), 225–30.Google Scholar
[100] Abdullaev, J., Desyatnikov, A. S., and Ostrovskaya, E. A. 2011. Suppression of collapse for matter waves with orbital angular momentum. J. Opt.: Special issue on orbital angular momentum, 13(6), 064023.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
×