Localization of optical pulses in guided wave structures with only fourth order dispersion

Inspired by the recent realization of pure-quartic solitons (Blanco-Redondo et al. (2016) 1]), in the present work we study the localization of optical pulses in a similar system, i.e., a silicon photonic crystal air-suspended structure with a hexagonal lattice. The propagation of ultrashort pulses in such a system is well described by a generalized nonlinear Schrödinger (NLS) equation, which in certain conditions works with near-zero group-velocity dispersion and third order dispersion. In this case, the NLS equation has only the fourth order dispersion term. In the present model, we introduce a quasiperiodic linear coefficient that is responsible to induce the localization. The existence of Anderson localization has been confirmed by numerical simulations even when the system presents a small defocusing nonlinearity.