Modulation Instability of Ultrashort Pulses in Quadratic Nonlinear Media beyond the Slowly Varying Envelope Approximation

We report a modulational instability (MI) analysis of a mathematical model appropriate for ultrashort pulses in cascaded quadratic-cubic nonlinear media beyond the so-called slowly varying envelope approximation. Theoretically predicted MI properties are found to be in good agreement with numerical simulation. The study shows the possibility of controlling the generation of MI and formation of solitons in a cascaded quadratic-cubic media in the few cycle regimes. We also find that stable propagation of soliton-like few-cycle pulses in the medium is subject to the fulfilment of the modulation instability criteria

Observation of two-dimensional superlattice solitons

We observe experimentally two-dimensional solitons in superlattices comprising alternating deep and shallow waveguides fabricated via the femtosecond-laser direct writing technique. We find that the symmetry of linear diffraction patterns as well as soliton shapes and threshold powers largely differ for excitations centered on deep and shallow sites. Thus, bulk and surface solitons centered on deep waveguides require much lower powers than their counterparts on shallow sites

Observation of two-dimensional defect surface solitons

We report on the experimental observation of two-dimensional solitons located in defect channels at the surface of a hexagonal waveguide array. The threshold power for the excitation of solitons existing owing to total internal reflection grows with decrease of the refractive index in negative defects and vanishes for sufficiently strong positive defects. Negative defects can also support linear surface modes existing owing to Bragg-type reflections