We develop the theory of nonlinear localised modes (intrinsic localised modes or discrete breathers) in two-dimensional (2D) photonic crystal waveguides. We consider different geometries of the waveguides created by an array of nonlinear dielectric rods in an otherwise perfect linear 2D photonic crystal, and demonstrate that the effective interaction in such waveguides is nonlocal, being described by a new type of nonlinear lattice models with long-range coupling and nonlocal nonlinearity. We reveal the existence of different types of nonlinear guided modes which are also localised in the waveguide direction, and describe their unique properties including bistability. 42.70.Qs, 42.79.Gn, 42.65.Wi, 42.65.Tg

We investigate stability of (2+1)-dimensional ring solitons of the nonlinear Schrödinger equation with focusing cubic and defocusing quintic nonlinearities. Computing eigenvalues of the linearised equation, we show that rings with spin (topological charge) s = 1 and s = 2 are linearly stable, provided that they are very broad. The stability regions occupy, respectively, 9% and 8% of the corresponding existence regions. These results finally resolve a controversial stability issue for this class of models.

We review our recent work toward designing large mode area fibers for high power applications. We show that appropriately designed doped multimode fibers can be used to provide robust single-mode output when used in Ž . fiber laser cavities. Single-mode SM fiber mode field diameters of ; 35 m are demonstrated with record SM pulse energies of 0.5 mJ at 1550 nm with a repetition rate of 200 Hz. Energies approaching 1 mJ are obtained with a slight compromise in mode quality. A modification in the laser cavity results in a passively modelocked laser giving femtosecond pulses with nanojoule energies. ᮊ

We demonstrate that parametric interaction of a fundamental beam with its second harmonic in bulk media, in the presence of self-defocusing third-order nonlinearity, gives rise to the first ever examples of completely stable localized ring-shaped solitons with intrinsic vorticity n=1 and n=2. The stability is demonstrated both in direct simulations and by computing eigenvalues of the corresponding linearized equations. A potential application of the (2+1)-dimensional ring solitons in optics is a possibility to design a reconfigurable multichannel system guiding signal beams.