We demonstrate that graphene-based photonic superlattices provide a versatile platform for electrical and all-optical control of photonic beams with deep-subwavelength accuracy. Specifically, by inserting graphene sheets into periodic metallodielectric structures, one can design optical superlattices that possess photonic Dirac points (DPs) at frequencies at which the spatial average of the permittivity of the superlatticeε vanishes. Similar to the well-known zero-n band gaps, we show that these zero-ε DPs are highly robust against structural disorder. We also show that, by tuning the graphene permittivity via the optical Kerr effect or electrical doping, one can induce a spectral variation of the DP exceeding 30 nm, at mid-IR and THz frequencies. The implications of this wide tunability for the photonic Zitterbewegung effect in a vicinity of the DP are also explored.

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We address the topological properties of onedimensional 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 sign ofε can be viewed as the generalization of the conventional surface plasmon polaritons existing at metallic-dielectric interfaces. The nontrivial topological properties of matter have been attracting increasing interest in condensed matter physics, as the theory of band topology explains a series of striking phenomena like quantum Hall effect [1][2][3] and topological insulators [4][5][6][7][8]. Starting from the duality between their mathematical description, similar concepts and ideas have been introduced into the realm of optics and nontrivial topological effects have been demonstrated across a variety of optical systems [9]. Perhaps the simplest optically topological structure is analogous to the celebrated Su-Schrieffer-Heeger (SSH) model for polyacetylene [10], in which a chain of sites with alternating sign of the coupling constant exhibits two topologically distinct phases and topologically protected interfacial modes exist at the interface between two topologically distinct chains. Realization of the SSH model in photonic systems includes dimerized dielectric waveguides [11] and dielectric nanoparticles [12], as well as metallic nanodisks [13]. Furthermore, edge states between coupled plasmonic waveguides described by the SSH model have been investigated in graphene [14] and plasmonic waveguide arrays [15]. These structures are optically discrete thus they closely mimic the original SSH model. On the other hand, topological properties and associated edge states of one-dimensional (1D) photonic structures have also been investigated in continuous periodic systems, i.e., beyond the tight-binding approximation and other discrete models [16, 17].All the topological properties of 1D structures mentioned above can be characterized by a single physical quantity, the so-called Zak phase [18]. This is a special kind of Berry phase, associated to 1D bulk bands. The characterization of the Zak phase of matter is of fundamental importance to the understanding of topology related physical properties of condensed matter systems. Optics is emerging as an alternative platform to study such topology induced phenomena, as in many cases it provides more suitable theoretical and experimental tools to explore them. In particular, specific ways to measure the Zak phase in optical systems have been proposed theoretically [19] and implemented experimentally by employing optical waveguide systems [20][21][22][23].In this Letter, we focus on topological properties of 1D plasmonic superlattices composed o...

We propose a distant-neighbor quantum-mechanical (DNQM) approach to study the linear and nonlinear optical properties of graphene nanoflakes (GNFs). In contrast to the widely used tight-binding description of the electronic states that considers only the nearest-neighbor coupling between the atoms, our approach is more accurate and general, as it captures the electron-core interactions between all atoms in the structure.Therefore, as we demonstrate, the DNQM approach enables the investigation of the optical coupling between two closely separated, but chemically unbound GNFs. We also find that the optical response of GNFs depends crucially on their shape, size, and symmetry properties.Specifically, increasing the size of nanoflakes is found to shift their accommodated quantum plasmon oscillations to lower frequency. Importantly, we show that by embedding a cavity into GNFs, one can change their symmetry properties, tune their optical properties, or enable otherwise forbidden second-harmonic generation processes.