We predict the existence of gap solitons in the nonlinear fractional Schrödinger equation (NLFSE) with an imprinted optically harmonic lattice. Symmetric/antisymmetric nonlinear localized modes bifurcate from the lower/upper edge of the first/second band in defocusing/focusing Kerr media. A unique feature we revealed is that, in focusing Kerr media, stable solitons appear in the finite bandgaps with the decrease of the Lévy index, which is in sharp contrast to the standard NLSE with a focusing nonlinearity. Nonlinear bound states composed by in-phase and out-of-phase soliton units supported by the NLFSE are also uncovered. Our work may pave the way for the study of spatial lattice solitons in fractional dimensions.

We report the existence and stability properties of multipeaked solitons in a defocusing Kerr medium with an imprinted complex optical lattice featuring a parity-time (PT) symmetry. Various families of soliton solutions with a different number of peaks are found in the first finite gap of the lattice. Linear stability analysis corroborated by direct propagation simulations reveals that multipeaked gap solitons can propagate stably in a wide range, provided that their propagation constant exceeds a critical value. Our findings demonstrate, for the first time, the existence of stable multipeaked gap solitons in a PT-symmetric lattice.

Generalization of Fractional Schrödinger equation (FSE) into optics is fundamentally important, since optics usually provides a fertile ground where FSE-related phenomena can be effectively observed. Beam propagation management is a topic of considerable interest in the field of optics. Here, we put forward a simple scheme for the realization of propagation management of light beams by introducing a double-barrier potential into the FSE. Transmission, partial transmission/reflection, and total reflection of light fields can be controlled by varying the potential depth. Oblique input beams with arbitrary distributions obey the same propagation dynamics. Some unique properties, including strong self-healing ability, high capacity of resisting disturbance, beam reshaping, and Goos-Hänchen-like shift are revealed. Theoretical analysis results are qualitatively in agreements with the numerical findings. This work opens up new possibilities for beam management and can be generalized into other fields involving fractional effects.

We study the stability of multipole-mode solitons in one-dimensional thermal nonlinear media. We show how the sample geometry impacts the stability of multipole-mode solitons and reveals that the tripole and quadrupole can be made stable in their whole domain of existence, provided that the sample width exceeds a critical value. In spite of such geometry-dependent soliton stability, we find that the maximal number of peaks in stable multipole-mode solitons in thermal media is the same as that in nonlinear materials with finite-range nonlocality.

No abstract