Malomed, Boris AMayteevarunyoo, ThawatchaiOstrovskaya, ElenaKivshar, Yuri2009-08-122010-12-202009-08-122010-12-20Physical Review, E, Statistical, Nonlinear and Soft Matter Physics 71.5 (2005): 056616/1-91539-3755http://hdl.handle.net/10440/685http://digitalcollections.anu.edu.au/handle/10440/685We derive two systems of coupled-mode equations for spatial gap solitons in one-dimensional (1D) and quasi-one-dimensional (Q1D) photonic lattices induced by two interfering optical beams in a nonlinear photorefractive crystal. The models differ from the ordinary coupled-mode system (e.g., for the fiber Bragg grating) by saturable nonlinearity and, if expanded to cubic terms, by the presence of four-wave-mixing terms. In the 1D system, solutions for stationary gap solitons are obtained in an implicit analytical form. For the Q1D model and for tilted (“moving”) solitons in both models, solutions are found in a numerical form. The existence of stable tilted solitons in the full underlying model of the photonic lattice in the photorefractive medium is also shown. The stability of gap solitons is systematically investigated in direct simulations, revealing a nontrivial border of instability against oscillatory perturbations. In the Q1D model, two disjointed stability regions are found. The stability border of tilted solitons does not depend on the tilt. Interactions between stable tilted solitons are investigated too. The collisions are, chiefly, elastic, but they may be inelastic close to the instability border.9 pageshttp://www.sherpa.ac.uk/romeo/index.php "Author can archive pre-print (ie pre-refereeing) … post-print (ie final draft post-refereeing) … [and] publisher's version/PDF. Link to publisher version … [and] Copyright notice required. Publisher's version/PDF can be used on … employers web site." - from SHERPA/RoMEO site (as at 25/02/10). ©2005 The American Physical SocietyKeywords: Optical beams; Oscillatory perturbations; Photonic lattices; Four wave mixing; Lattice constants; Mathematical models; Optical properties; Perturbation techniques; Photons; Solitons2005-05-2610.1103/PhysRevE.71.0566162015-12-11