PHYSICAL REVIE% E VOLUME 50, NUMBER 2 AUGUST 1994 Optical domain walls Boris A. Malomed* Department of Applied Mathematics, School of Mathematical Sciences, Raymond and Beverly Sackler Facalty of Exact Sciences, Tel Aviv University, Ramat Amv M978, Israel (Received 21 April 1994) Dynamical properties of the domain walls (DW's) in the light beams propagating in nonlinear optical fibers are considered. In the bimodal fiber, the DW, as it was recently demonstrated nu- merically, separates two domains with diferent circular polarizations. This DW is found here in an approximate analytical form. Next, it is demonstrated that the fiber s twist gives rise to an effective force driving the DW. The corresponding equation of motion is derived by means of the momentum- balance analysis, which is a technically nontrivial problem in this context (in particular, an effective mass of the DW proves to be negative). Since the sign of the twist-induced driving force depends on the DW's polarity, the DW's with opposite polarities can collide, which leads to the formation of their stable bound state. This is a domain of a certain circular polarization squeezed between semi-infinite domains of another polarization. In the absence of the twist, the DW can be driven by the Raman eHect, but in this case the sign of the force does not depend on the DW's polarity and the bound state is not possible. Finally, a similar problem is considered for the dual-core fiber (coupler). In this case, the DW is a dark soliton in one core in the presence of the homogeneous field in the mate core. The dark soliton is driven by a force induced by the coupling with the mate core. The bound state of two dark solitons also exists in this system. The effects considered may find applications, e.g. , for the optical storage of information. PACS number(s): 42.81.Gs, 42. 81. gb, 47.54.+r, 03.40.Kf I. INTRODUCTION The domain walls (DW's) furnish the simplest type of a stable defect in nonlinear patterns. Alongside the classi- cal static DW's in ferromagnets and aniferromagnets, the study of the DW-like defects in dynamical nonlinear pat- terns has recently attracted a great deal of attention [I- 7]. The dynamical DW's which seem most similar to the classical static ones in the magnetic systems are the walls between rolls with different orientations in the Rayleigh- Benard convection [1, 3], or between rolls and hexagons [2, 3], or, at last, between the hexagons and the trivial state below onset [3]. These DW's may be regarded as linear defects in two-dimensional nonlinear systems, al- though they are actually given by solutions of effectively one-dimensional coupled Ginzburg-Landau (GL) equa- tions [2, 3]. Similar solutions describe the DW s which are kinks (phase jumps) in purely one-dimensional systems, e.g. , in the GL equation with the parametric pumping [5]. Finally, quiescent and moving kinks which separate domains occupied by difFerent stable phases (described, e.g. , by the quintic GL equation [4]) can also be regarded as one-dimensional DW's. Recently, study of the DW's was started in systems of coupled nonlinear Schrodinger (NLS) equations govern- ing propagation of light in nonlinear optical fibers [6] and nonlinear planar lightguides [7]. In these nonlinear op- tical systems, the walls separate domains with different circular polarization of light. While in the analysis devel- oped in Ref. [6] the dispersion was neglected, it was taken into account in Ref. [7]. In the latter work, two types of 'Electronic address: malomedmath. tau. ac.il solutions of the coupled NLS equations were considered: periodic arrays of the DW's and solitary walls. Although the full dynamics described by coupled GL equations and by coupled NLS equations are very difFerent (dissipative in the former case and conservative in the latter case), their static solutions coincide. The same pertains to the stability properties of those solutions. In particular, the solitary DW considered in the context of the nonlinear lightguides in Ref. [7] exactly coincides with a partic- ular case of the solution found in Ref. [3] for the do- main boundary between rolls with different orientations in the convection patterns (periodic solutions, however, were not considered in Ref. [3]). As another example of a DW in nonlinear optical fibers, it is relevant to mention the exact solution describing a full transformation of a pomp wave into the Stokes wave, obtained in the &ame- work of a system of NLS equations for the two waves coupled by the Raman interaction [20]. The main objective of this work is to consider some important properties of the polarization DW s in non- linear optical fibers. The analysis will be based on the coupled NLS equations for the linear polarizations (while in Ref. [7] the basic polarizations were circular). Two additional important physical factors will be taken into account, viz. , the linear coupling which accounts for the twist of the fiber and the Raman effect. In Sec. II it will be demonstrated that, in the presence of the twist, which will be treated as a small perturbation, usual static DW solutions are not possible; instead, a stable bound state of two DW's with opposite polarities appears. It repre- sents a finite domain with a certain circular polarization sandwiched between semi-infinite domains of the oppo- site circular polarization, which may be regarded as a prediction of a dynamical state in the nonlinear optical 1063-651X/94/50(2)/1565(7)/$06. 00 50 1565 1994 The American Physical Society