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-pftt2 Total loading time: 0 Render date: 2024-05-20T23:32:56.566Z Has data issue: false hasContentIssue false

8 - Nonlinear effects and gap–soliton formation in periodic media

Published online by Cambridge University Press:  01 July 2009

Maksim Skorobogatiy  and
Jianke Yang
Maksim Skorobogatiy
Affiliation:
Ecole Polytechnique, Montréal
Jianke Yang
Affiliation:
University of Vermont
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
Fundamentals of Photonic Crystal Guiding , pp. 210 - 229
Publisher: Cambridge University Press
Print publication year: 2008

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

Fleischer, J. W., Segev, M., Efremidis, N. K., and Christodoulides, D. N.. Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices, Nature 422 (2003), 147–150.CrossRefGoogle ScholarPubMed
Argyros, A., Birks, T. A., Leon-Saval, S. G.et al. Photonic bandgap with an index step of one percent, Opt. Express 13 (2005), 309.CrossRefGoogle ScholarPubMed
Szameit, A., Burghoff, J., Pertsch, T.et al. Two-dimensional soliton in cubic fs laser written waveguide arrays in fused silica, Opt. Express 14 (2006), 6055–6062.CrossRefGoogle ScholarPubMed
Eisenberg, H., Silberberg, Y., Morandotti, R., Boyd, A., and Aitchison, J.. Discrete spatial optical solitons in waveguide arrays, Phys. Rev. Lett. 81 (1998), 3383–3386.CrossRefGoogle Scholar
Iwanow, R., Schieck, R., Stegeman, G.et al. Observation of discrete quadratic solitons, Phys. Rev. Lett. 93 (2004), 113902.CrossRefGoogle ScholarPubMed
Dalfovo, F., Giorgini, S., Pitaevskii, L. P., and Stringari, S.. Theory of Bose–Einstein condensation in trapped gases, Rev. Mod. Phys. 71 (1999), 463–512.CrossRefGoogle Scholar
Xu, K., Liu, Y., Abo-Shaeer, J. R.et al. Sodium Bose–Einstein condensates in an optical lattice, Phys. Rev. A 72 (2005), 043604.CrossRefGoogle Scholar
Pelinovsky, D. E., Sukhorukov, A. A., and Kivshar, Y. S.. Bifurcations and stability of gap solitons in periodic potentials, Phys. Rev. E 70 (2004), 036618.CrossRefGoogle ScholarPubMed
Yang, J. and Lakoba, T. I.. Universally-convergent squared-operator iteration methods for solitary waves in general nonlinear wave equations, Stud. Appl. Math. 118 (2007), 153–197.CrossRefGoogle Scholar
Shi, Z. and Yang, J.. Solitary waves bifurcated from Bloch-band edges in two-dimensional periodic media, Phys. Rev. E 75 (2007), 056602.CrossRefGoogle ScholarPubMed
Martin, H., Eugenieva, E. D., Chen, Z., and Christodoulides, D. N.. Discrete solitons and soliton-induced dislocations in partially coherent photonic lattices, Phys. Rev. Lett. 92 (2004), 123902.CrossRefGoogle ScholarPubMed
Yang, J. and Musslimani, Z.. Fundamental and vortex solitons in a two-dimensional optical lattice, Opt. Lett. 28 (2003), 2094–2096.CrossRefGoogle Scholar
Vakhitov, N. G. and Kolokolov, A. A.Stationary solutions of the wave equation in the medium with nonlinearity saturation, Izv Vyssh. Uchebn. Zaved. Radiofiz. 16 (1973), 1020–1028.Google Scholar
Lou, C., Wang, X., Xu, J., Chen, Z., and Yang, J.. Nonlinear spectrum reshaping and gap-soliton-train trapping in optically induced photonic structures, Phys. Rev. Lett. 98 (2007), 213903.CrossRefGoogle ScholarPubMed
Fischer, R., Trager, D., Neshev, D. N.et al. Reduced-symmetry two-dimensional solitons in photonic lattices, Phys. Rev. Lett. 96 (2006), 023905.CrossRefGoogle ScholarPubMed
Bartal, G., Manela, O., Cohen, O., Fleischer, J. W., and Segev, M.. Observation of second-band vortex solitons in 2D photonic lattices, Phys. Rev. Lett. 95 (2005), 053904.CrossRefGoogle ScholarPubMed
Yang, J., Makasyuk, I., Bezryadina, A., and Chen, Z.. Dipole and quadrupole solitons in optically-induced two-dimensional photonic lattices: theory and experiment, Stud. Appl. Math. 113 (2004), 389–412.CrossRefGoogle Scholar
Neshev, D. N., Alexander, T. J., Ostrovskaya, E. A.et al. Observation of discrete vortex solitons in optically induced photonic lattices, Phys. Rev. Lett. 92 (2004), 123903.CrossRefGoogle ScholarPubMed
Fleischer, J. W., Bartal, G., Cohen, O.et al. Observation of vortex-ring discrete solitons in 2D photonic lattices, Phys. Rev. Lett. 92 (2004), 123904.CrossRefGoogle ScholarPubMed
Ostrovskaya, E. A. and Kivshar, Y. S.. Matter-wave gap vortices in optical lattices, Phys. Rev. Lett. 93 (2004), 160405.CrossRefGoogle ScholarPubMed

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
×