Codimension 2 and 3 situations in a ring cavity with elliptically polarized electromagnetic waves

PHYSICA D-NONLINEAR PHENOMENA

卷:259

Article

Martin, D. A.¹ 

[1] Univ Nacl Mar del Plata, Fac Ciencias Exactas & Nat, Dept Fis, Buenos Aires, DF, Argentina

关键词: Nonlinear optics;    Lugiato-Lefever equation;    Elliptical polarization;    Transverse pattern formation;    Turing-Turing codimension 2;    Turing-Hopf codimension 2;   

DOI  :  10.1016/j.physd.2013.05.008

来源: Elsevier

【 摘 要 】

We study pattern formation on the plane transverse to propagation direction, in a ring cavity Filled with a Kerr-like medium, subject to an elliptically polarized incoming field, by means of two coupled Lugiato-Lefever equations. We consider a wide range of possible values for the coupling parameter between different polarizations, (B) over bar, as may happen in composite materials. Positive and also negative refraction index materials are considered. Examples of marginal instability diagrams are shown. It is shown that, within the model, instabilities cannot be of codimension higher than 3. A method for finding parameters for which codimension 2 or 3 takes place is given. The method allows us to choose parameters for which unstable wavenumbers fulfill different relations. Numerical integration results where different instabilities coexist and compete are shown. (c) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free