Theoretical and computational analysis of second- and third-harmonic generation in periodically patterned graphene and transition-metal dichalcogenide monolayers

Remarkable optical and electrical properties of two-dimensional (2D) materials, such as graphene and transition-metal dichalcogenide (TMDC) monolayers, offer vast technological potential for novel and improved optoelectronic nanodevices, many of which relying on nonlinear optical effects in these 2D materials. This article introduces a highly effective numerical method for efficient and accurate description of linear and nonlinear optical effects in nanostructured 2D materials embedded in periodic photonic structures containing regular three-dimensional (3D) optical materials, such as diffraction gratings and periodic metamaterials. The proposed method builds upon the rigorous coupled-wave analysis and incorporates the nonlinear optical response of 2D materials by means of modified electromagnetic boundary conditions. This allows one to reduce the mathematical framework of the numerical method to an inhomogeneous scattering matrix formalism, which makes it more accurate and efficient than previously used approaches. An overview of linear and nonlinear optical properties of graphene and TMDC monolayers is given and the various features of the corresponding optical spectra are explored numerically and discussed. To illustrate the versatility of our numerical method, we use it to investigate the linear and nonlinear multiresonant optical response of 2D-3D heteromaterials for enhanced and tunable second- and third-harmonic generation. In particular, by employing a structured 2D material optically coupled to a patterned slab waveguide, we study the interplay between geometric resonances associated to guiding modes of periodically patterned slab waveguides and plasmon or exciton resonances of 2D materials.Comment: 28 pages, 21 figure

Optically controllable coupling between edge and topological interface modes of graphene metasurfaces

Nonlinear topological photonics has been attracting increasing research interest, as it provides an exciting photonic platform that combines the advantages of active all-opticall control offered by nonlinear optics with the unique features of topological photonic systems, such as topologically-protected defect-immune light propagation. In this paper, we demonstrate that topological interface modes and trivial edge modes of a specially designed graphene metasurface can be coupled in a tunable and optically controllable manner, thus providing an efficient approach to transfer optical power to topologically protected states. This is achieved in a pump-signal configuration, in which an optical pump propagating in a bulk mode of the metasurface is employed to tune the band structure of the photonic system and, consequently, the coupling coefficient and wave-vector mismatch between edge and topological interface modes. This tunable coupling mechanism is particularly efficient due to the large Kerr coefficient of graphene. Importantly, we demonstrate that the required pump power can be significantly reduced if the optical device is operated in the slow-light regime. We performed our analysis using both \textit{ab initio} full-wave simulations and a coupled-mode theory that captures the main physics of this active coupler and observe a good agreement between the two approaches. This work may lead to the design of active topological photonic devices with new or improved functionality

Accurate near-field calculation in the rigorous coupled-wave analysis method

The rigorous coupled-wave analysis (RCWA) is one of the most successful and widely used methods for modeling periodic optical structures. It yields fast convergence of the electromagnetic far-field and has been adapted to model various optical devices and wave configurations. In this article, we investigate the accuracy with which the electromagnetic near-field can be calculated by using RCWA and explain the observed slow convergence and numerical artifacts from which it suffers, namely unphysical oscillations at material boundaries due to the Gibb's phenomenon. In order to alleviate these shortcomings, we also introduce a mathematical formulation for accurate near-field calculation in RCWA, for one- and two-dimensional straight and slanted diffraction gratings. This accurate near-field computational approach is tested and evaluated for several representative test-structures and configurations in order to illustrate the advantages provided by the proposed modified formulation of the RCWA.Comment: 13 pages, 12 figure

Nonlinear optics in diamond-fin photonic nanowires: soliton formation and frequency comb generation

We present a detailed study of the nonlinear optical properties of newly developed subwavelength diamond-fin waveguides, along with an analysis of soliton generation and pulse spectral broadening in these structures. Our rigorous mathematical model includes all the key linear and nonlinear optical effects that govern the pulse dynamics in these diamond waveguides. As a relevant application of our investigations, we demonstrate how these waveguides can be employed to efficiently generate frequency combs in the visible spectral domain

Optically and Electrically Tunable Dirac Points and Zitterbewegung in Graphene-Based Photonic Superlattices

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 metallo-dielectric structures one can design optical superlattices that posses photonic Dirac points (DPs) at frequencies at which the spatial average of the permittivity of the superlattice, $\bar{ \varepsilon}$, vanishes. Similar to the well-known zero-$\bar{n}$ bandgaps, we show that these zero-$\bar{\varepsilon}$ 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 \SI{30}{\nano\meter}, at mid-IR and THz frequencies. The implications of this wide tunability for the photonic Zitterbewegung effect in a vicinity of the DP are explored too.Comment: 5 pages, 5 figures, to appear in Phys. Rev. B as a Rapid Communicatio

Giant second-harmonic generation in photonic crystal slabs possessing double-resonance bound states in the continuum

The ability to confine and guide light makes photonic crystals (PhCs) a promising platform for large local field enhancement, which enables efficient nonlinear processes at the nanoscale. Here, we utilize optical bound states in the continuum (BICs) to engineer sharp resonances with high quality factors. By investigating the angleresolved reflection spectra, we demonstrate that two PhC slabs with different configuration but the same lattice constant support a pair of at-Γ and a pair of off-Γ resonances, respectively. In both cases, BIC-type resonances are observed at the fundamental frequency while BIC-like resonances are found at the second harmonic. This double-resonance phenomenon is subsequently used to significantly enhance the second-harmonic generation from PhC slabs. The maximum values of the SHG are several orders of magnitude larger than those corresponding to the reference slabs. We consider that our approach based on double-resonance BICs provides a novel way to realize enhanced harmonic generation in photonic nanodevices