Theory of pulsed four-wave mixing in one-dimensional silicon photonic crystal slab waveguides

We present a comprehensive theoretical analysis and computational study of four-wave mixing (FWM) of optical pulses co-propagating in one-dimensional silicon photonic crystal waveguides (Si-PhCWGs). Our theoretical analysis describes a very general setup of the interacting optical pulses, namely we consider nondegenerate FWM in a configuration in which at each frequency there exists a superposition of guiding modes. We incorporate in our theoretical model all relevant linear optical effects, including waveguide loss, free-carrier (FC) dispersion and FC absorption, nonlinear optical effects such as self- and cross-phase modulation (SPM, XPM), two-photon absorption (TPA), and cross-absorption modulation (XAM), as well as the coupled dynamics of free-carriers FCs and optical field. In particular, our theoretical analysis based on the coupled-mode theory provides rigorously derived formulas for linear dispersion coefficients of the guiding modes, linear coupling coefficients between these modes, as well as the nonlinear waveguide coefficients describing SPM, XPM, TPA, XAM, and FWM. In addition, our theoretical analysis and numerical simulations reveal key differences between the characteristics of FWM in the slow- and fast-light regimes, which could potentially have important implications to the design of ultracompact active photonic devices

Computational Study of Second- and Third-Harmonic Generation in Periodically Patterned 2D-3D Heteromaterials

Remarkable optical and electrical properties of graphene and other two-dimensional (2D) materials provide significant potential for novel optoelectronic applications and devices, many of which depend on nonlinear optical effects in these 2D materials. In this paper we use a theoretical and computational formalism we have recently introduced to efficiently and accurately compute the linear and nonlinear optical response of nanostructured 2D materials embedded in periodic structures containing regular three-dimensional (3D) materials, such as diffraction gratings or periodic metamaterials. Thus, we use the proposed method to demonstrate enhanced nonlinear optical interactions in periodically patterned photonic nanostructures via resonant excitation of phase-matched nonlinear waveguide modes, enhanced nonlinearity of nanostructures containing graphene and other 2D nanomaterials, such as WS2, and multi-continua Fano resonances for increasing the nonlinear efficiency of hybrid 2D-3D photonic heteromaterials

Polarization control using passive and active crossed graphene gratings

Graphene gratings provide a promising route towards the miniaturization of THz metasurfaces and other photonic devices, chiefly due to remarkable optical properties of graphene. In this paper, we propose novel graphene nanostructures for passive and active control of the polarization state of THz waves. The proposed devices are composed of two crossed graphene gratings separated by an insulator spacer. Because of specific linear and nonlinear properties of graphene, these optical metasurfaces can be utilized as ultrathin polarization converters operating in the THz frequency domain. In particular, our study shows that properly designed graphene polarizers can effectively select specific polarization states, their thickness being about a tenth of the operating wavelength and size more than 80× smaller than that of similar metallic devices. Equally important, we demonstrate that the nonlinear optical properties of graphene can be utilized to actively control the polarization state of generated higher harmonics

Tunable and dual-broadband giant enhancement of second-harmonic and third-harmonic generation in an optimized graphene-insulator-graphene metasurface

We demonstrate a scheme to dramatically enhance both the second- and third-harmonic generation (SHG, THG) in a graphene-insulator-graphene metasurface. The key underlying feature of our approach is the existence of a double-resonance phenomenon, namely, the metasurface is designed to possess fundamental plasmon resonances at both the fundamental frequency and the higher harmonic. This dual resonant field enhancement, combined with a favorable spatial overlap of the optical near fields, lead to the increase of the THG and SHG by ∼ 10 9 and ∼ 10 6 , respectively. We also demonstrate that by tuning the Fermi energy of the graphene gratings the dual-resonance property can be locked in over a remarkably broad spectral range of ∼ 20 THz , which is more than three orders of magnitude larger than the spectral tunability achievable in metal-based plasmonic systems. Importantly, the enhanced nonlinear frequency generation process can be readily switched in the same system between the second and third harmonic. This type of graphene metasurface could open up new avenues towards the development of novel ultracompact and multifrequency active photonic nanodevices

Optically controllable coupling between edge and topological waveguide modes of certain graphene metasurfaces

In this paper, optically controllable and topologically protected plasmon transport is implemented via a topological nanohole plasmonic waveguide coupled to a standard edge mode of a graphene metasurface. By introducing nanoholes with different sizes in the unit cell, one breaks the spatial-inversion symmetry of a graphene metasurface in which the topological waveguide is constructed, leading to the emergence of topologically protected modes located in a nontrivial band-gap. Based on the strong Kerr effect and tunable optical properties of graphene, the coupling between the edge and topological interface modes can be efficiently controlled by optical means provided by an optical pump beam injected in a bulk mode. In particular, by tuning the power inserted in the bulk mode, one can control the difference between the wave-vectors of the topological and edge modes and consequently the optical power coupled in the topological mode. Our results show that when the pump power approaches a specific value, the edge and topological modes become phase-matched and the topological waveguide mode can be efficiently excited. Finally, we demonstrated that the optical coupling is strongly dependent on the group-velocity of the pump mode, a device feature that can be important in practical applications

Enhanced optical nonlinearities in 2D-3D heteromaterials

Summary form only given. Remarkable optical and electrical properties of graphene [1] and other two-dimensional (2D) materials provide significant potential for novel optoelectronic applications and devices, many of which depend on nonlinear optical effects in these 2D materials [2, 3]. In this paper, we will review some recent results [4, 5] pertaining to nonlinear optical effects in nanostructured bulk optical media containing homogeneous or nanopatterned 2D materials

Ab initio Computational Study of Quantum Plasmons in Graphene Nanoflakes

We investigate the potential merit in using nanometer-sized graphene flakes as building blocks of twodimensional (2D) quantum metamaterials. The choice of the building blocks is crucial to the design of quantum metamaterials with desired properties, graphene nano-structures being promising candidates towards this end. Thus, they can be grown either by bottom-up chemical synthesis or top-down electronbeam patterning in various shapes, densities, topology, and size, down to the molecular scale. We show that this versatility provides a wide range of parameters to tune the optical properties of graphene-based 2D quantum metamaterials

Efficient Numerical Computation of Second-Harmonic Scattering by Clusters of Nanoparticles

In this paper, we introduce a transfer matrix method (TMM) for efficient calculation of second-harmonic generation (SHG) from clusters of nanospheres made of centrosymmetric materials. Different from current TMM formulations, our approach goes beyond the single particle configuration, thus greatly expanding its practical relevance. In addition, we incorporate in our method the contributions of both the surface and bulk nonlinear polarizations. This is especially valuable for the accurate analysis of purely dielectric systems, such as clusters of silicon or silica nanospheres, which are widely used in nanophotonics

BER in Slow-Light and Fast-Light Regimes of Silicon Photonic Crystal Waveguides: A Comparative Study

In this letter, we present an in-depth comparison between the bit-error ratio (BER) of optical systems containing silicon photonic crystal (Si-PhC) waveguides (Si-PhCWs) operating in the slow- and fast-light regimes. Our analysis of these optical interconnects employs the time domain Karhunen-Loève expansion method for the statistical analysis of the optical signal and relies on a full theoretical model and its linearized form to describe the propagation of noisy optical signals in Si-PhCWs. These models incorporate all key linear and nonlinear optical effects and the mutual interaction between free-carriers and the optical field, as well as the influence of slow-light effects on the optical field and carriers dynamics. Using these tools and employing a 512-b pseudorandom bit sequence, we have studied the dependence of BER on the key system parameters, including group-velocity, input power, and signal-to-noise ratio