Time dispersion plays an important role in the propagation of femtosecond pulses through water. The combined e ects of time dispersion, radial di raction and the Kerr nonlinearity on the pulse propagation are analyzed and it is shown that normal time dispersion leads to signi cant temporal broadening of ultrashort pulses and that it increases the threshold power for catastrophic self-focusing.

We study discrete vector solitons and vortices in two-dimensional photonic lattices with Kerr nonlinearity and demonstrate novel types of stable, incoherently coupled dipoles and vortex-soliton complexes that can be excited by Gaussian beams. We also discuss what we believe to be novel scenarios of the charge-flipping instability of incoherently coupled discrete vortices.

We predict the existence of stable nonlinear localized modes near the band edge of a two-dimensional reduced-symmetry photonic crystal with a Kerr nonlinearity. Employing the technique based on the Green function, we reveal a physical mechanism of the mode stabilization associated with the effective nonlinear dispersion and long-range interaction in the photonic crystals.

We numerically investigate counter-propagating beams in a one-dimensionally, periodic structure with non-instantaneous Kerr nonlinearity for the design of efficient optical limiters. The performance of the Photonic Band Gap optical limiter with different response times is compared with the instantaneous case. Dynamic range and the cutoff intensity can be improved over a range of relaxation times.

We study nonlinear modes of dual-core photonic crystal fiber couplers made of a material with the focusing Kerr nonlinearity. We find numerically the profiles of symmetric, antisymmetric, and asymmetric nonlinear modes and analyze all-optical switching generated by the instability of the symmetric mode. We also describe elliptic spatial solitons controlled by the waveguide boundaries.

We report experimental and numerical results on the dynamics of gain-guided solitons in a passively mode-locked erbium-doped fiber laser made of purely normal dispersion fibers. We show that formation of the soliton in the laser is a result of mutual interaction and balance among the cavity transmission, fiber Kerr nonlinearity, gain saturation, and filtering over one cavity round trip.

We address soliton reflection/transmission at interface between a uniform medium and an optical lattice with focusing Kerr nonlinearity. We reveal that such interfaces afford rich new opportunities for controlling the reflection and transmission coefficients and the nonlinear Snell law, the key control parameters being the spatial frequency and depth of refractive index modulation in the lattice.