We gratefully acknowledge support from
the Simons Foundation and member institutions.
Full-text links:

Download:

Current browse context:

math.AP

Change to browse by:

References & Citations

Bookmark

(what is this?)

Mathematics > Analysis of PDEs

Title: Bifurcation and Asymptotics of Cubically Nonlinear Transverse Magnetic Surface Plasmon Polaritons

Abstract: Linear Maxwell equations for transverse magnetic (TM) polarized fields support single frequency surface plasmon polaritons (SPPs) localized at the interface of a metal and a dielectric. Metals are typically dispersive, i.e. the dielectric function depends on the frequency. We prove the bifurcation of localized SPPs in dispersive media in the presence of a cubic nonlinearity and provide an asymptotic expansion of the solution and the frequency. The problem is reduced to a system of nonlinear differential equations in one spatial dimension by assuming a plane wave dependence in the direction tangential to the (flat) interfaces. The number of interfaces is arbitrary and the nonlinear system is solved in a subspace of functions with the $H^1$-Sobolev regularity in each material layer. The corresponding linear system is an operator pencil in the frequency parameter due to the material dispersion. Because of the TM-polarization the problem cannot be reduced to a scalar equation.
The studied bifurcation occurs at a simple isolated eigenvalue of the pencil. For geometries consisting of two or three homogeneous layers we provide explicit conditions on the existence of eigenvalues and on their simpleness and isolatedness. Real frequencies are shown to exist in the nonlinear setting in the case of PT-symmetric materials. We also apply a finite difference numerical method to the nonlinear system and compute bifurcating curves.
Comments:
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph); Pattern Formation and Solitons (nlin.PS)
MSC classes: 35Q61, 35B32
Cite as: arXiv:2311.17838 [math.AP]
  (or arXiv:2311.17838v1 [math.AP] for this version)

Submission history

From: Tomas Dohnal [view email]
[v1] Wed, 29 Nov 2023 17:41:35 GMT (672kb,D)

Link back to: arXiv, form interface, contact.
{"cc_re__cc_re__cc_by_4_0": ["1.17838\"\n        dc:title=\"Bifurcation and Asymptotics of Cubically Nonlinear Transverse Magnetic\n  Surface Plasmon Polaritons\"\n        trackback:ping=\"http://arxiv.org/trackback/2311.17838\" />\n    </rdf:RDF>\n-->\n\n<div id=\"abs\">\n<div class=\"extra-services\">\n\n<div class=\"full-text\">\n<span class=\"descriptor\">Full-text links:</span>\n<h2>Download:</h2>\n<ul>\n<li><a href=\"/pdf/2311.17838\" accesskey=\"f\">PDF</a></li>\n<li><a href=\"/format/2311.17838\">Other formats</a></li>\n</ul>\n<div class=\"abs-license\"><a href=\"http://creativecommons.org/licenses/by/4.0/\" title=\"Rights to this article\"><img src=\"/icons/licenses/by-4.0.png\"/></a></div>\n</div><!--end full-text-->\n\n<div class=\"browse\">\n<h3>Current browse context:</h3>\n<div class=\"current\">math.AP</div>\n<div class=\"prevnext\"><span class=\"arrow\"><a href=\"http://arxiv.org/prevnext?site=export.arxiv.org&amp;id=2311.17838&amp;context=math.AP&amp;function=prev\" accesskey=\"p\" title=\"previous in math.AP (accesskey p)\">&lt;&nbsp;prev</a></span>&nbsp;|&nbsp;<span class=\"arrow\"><a href=\"http://arxiv.org/prevnext?site=export.arxiv.org&amp;id"], "copyright__copyright__copyright": ["c materials. We also apply a finite difference numerical method to the nonlinear system and compute bifurcating curves.\nComments:\nSubjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph); Pattern Formation and Solitons (nlin.PS)\nMSC\u00a0classes: 35Q61, 35B32\nCite\u00a0as: arXiv:2311.17838 [math.AP]\n\u00a0 (or arXiv:2311.17838v1 [math.AP] for this version)\n\nSubmission history\n\nFrom: Tomas Dohnal [view email]\n[v1] Wed, 29 Nov 2023 17:41:35 GMT (672kb,D)\n\nLink back to: arXiv, form interface, contact."]}