[en] We report on the dynamics of vortex solitons in circular waveguide arrays featuring modulation of both the linear and nonlinear refractive indices. Out-of-phase competition between both effects supports multipeaked vortex solitons with higher topological charges. A vortex solution can be found only when its charge is less than half of the number of waveguides. It may expand or shrink radially with the propagation constant, depending on the ratio between the topological charge and the number of waveguides. Surprisingly, vortex solitons with higher charges are more stable than those with lower charges, which is very rare and contrary to the stability of vortices in uniform or lattice-modulated media. Our findings suggest an alternative way for the realization of stable vortex solitons with higher charges.

[en] We address the nonlinear dynamics of binary Bose-Einstein condensates with mutually symmetric spinor components trapped in an optical lattice. The interaction between the repulsive Lee–Huang–Yang nonlinearity and the intercomponent attraction as well as Bragg scattering of an optical lattice results in formation of multi-peaked quantum droplets. Even- and odd-symmetric droplets can bifurcate from Bloch modes of the corresponding periodic systems. Linear stability analysis corroborated by direct evolution simulations reveals that even-symmetric droplets with different norms and different number of peaks can evolve stably at the same chemical potential, i.e., multi-stable droplets are possible in the present scheme. Besides the droplets in the semi-infinite gap, the properties of droplets in the first finite bandgap are also discussed. Both even- and odd-symmetric droplets are stable in almost their whole existence domains. We reveal that optical lattice plays an important role for the stabilization of droplets, in sharp contrast to the nonlinear system without a lattice modulation. We, thus, furnish a paradigmatic example of multi-stable quantum droplets held in optical lattices.

[en] A distant-neighbor quantum-mechanical method is used to study the nonlinear optical wave mixing in graphene nanoflakes (GNFs), including sum- and difference-frequency generation, as well as four-wave mixing. Our analysis shows that molecular-scale GNFs support quantum plasmons in the visible spectrum region, and significant enhancement of nonlinear optical wave mixing is achieved. Specifically, the second- and third-order wave-mixing polarizabilities of GNFs are dramatically enhanced, provided that one (or more) of the input or output frequencies coincide with a quantum plasmon resonance. Moreover, by embedding a cavity into hexagonal GNFs, we show that one can break the structural inversion symmetry and enable otherwise forbidden second-order wave mixing, which is found to be enhanced by the quantum plasmon resonance too. This study reveals that the molecular-sized graphene could be used in the quantum regime for nanoscale nonlinear optical devices and ultrasensitive molecular sensors. (special topic)