Topologically enhanced nonlinear optical response of graphene nanoribbon heterojunctions.

We study the nonlinear optical properties of heterojunctions made of graphene nanoribbons (GNRs) consisting of two segments with either the same or different topological properties. By utilizing a quantum mechanical approach that incorporates distant-neighbor interactions, we demonstrate that the presence of topological interface states significantly enhances the second- and third-order nonlinear optical response of GNR heterojunctions that are created by merging two topologically inequivalent GNRs. Specifically, GNR heterojunctions with topological interface states display third-order harmonic hyperpolarizabilities that are more than two orders of magnitude larger than those of their similarly sized counterparts without topological interface states, whereas the second-order harmonic hyperpolarizabilities exhibit a more than ten-fold contrast between heterojunctions with and without topological interface states. Additionally, we find that the topological state at the interface between two topologically distinct GNRs can induce a noticeable red-shift of the quantum plasmon frequency of the heterojunctions. Our results reveal a general and profound connection between the existence of topological states and an enhanced nonlinear optical response of graphene nanostructures and possible other photonic systems.

Fundamental and vortex gap solitons in quasiperiodic photonic lattices.

We address the existence and stability of fundamental, single-charged vortex, and double-charged vortex gap solitons in two-dimensional quasiperiodic photonic lattices imprinted in a Kerr-type medium. Fundamental and vortex gap solitons can bifurcate from linear localized states or their combination supported by quasiperiodic lattices for both defocusing and focusing nonlinearities. We find that the three types of solitons mentioned above are stable in the entire existence domain for defocusing nonlinearities, and that they can also be stable at a lower power level for focusing nonlinearities. At higher power, unstable solitons are characterized by a ring-shaped symmetry-breaking distribution, and the unique spot profile formed is repeatedly observed with changes in propagation distance.

Surface modes in plasmonic Bragg fibers with negative average permittivity.

We investigate surface modes in plasmonic Bragg fibers composed of nanostructured coaxial cylindrical metal-dielectric multilayers. We demonstrate that the existence of surface modes is determined by the sign of the spatially averaged permittivity of the plasmonic Bragg fiber, ε¯. Specifically, localized surface modes occur at the interface between the cylindrical core with ε¯<0 and the outermost uniform dielectric medium, which is similar to the topologically protected plasmonic surface modes at the interface between two different one-dimensional planar metal-dielectric lattices with opposite signs of the averaged permittivity. Moreover, when increasing the number of dielectric-metal rings, the propagation constant of surface modes with different azimuthal mode numbers is approaching that of surface plasmon polaritons formed at the corresponding planar metal/dielectric interface. Robustness of such surface modes of plasmonic Bragg fibers is demonstrated as well.

Topological surface plasmons in superlattices with changing sign of the average permittivity.

We address the topological properties of one-dimensional plasmonic superlattices composed of alternating metallic and dielectric layers. We reveal that the Zak phase of such plasmonic lattices is determined by the sign of the spatial average of their permittivity, ε¯, and as such the topology and their associated interfacial (edge) states are extremely robust against structural disorder. Our study shows that the topologically protected interfacial modes occurring at the interface between two plasmonic lattices with opposite signs of ε¯ can be viewed as the generalization of the conventional surface plasmon polaritons existing at metallic-dielectric interfaces.

Transverse Anderson localization of light near Dirac points of photonic nanostructures.

We perform a comparative study of the Anderson localization of light beams in disordered layered photonic nanostructures that, in the limit of periodic layer distribution, possess either a Dirac point or a Bragg gap in the spectrum of the wavevectors. In particular, we demonstrate that the localization length of the Anderson modes increases when the width of the Bragg gap decreases, such that in the vanishingly small bandgap limit, namely when a Dirac point is formed, even extremely high levels of disorder are unable to localize the optical modes residing near the Dirac point. A comparative analysis of the key features of the propagation of Anderson modes formed in the Bragg gap or near the Dirac point is also presented. Our findings could provide valuable guidelines in assessing the influence of structural disorder on the functionality of a broad array of optical nanodevices.