Martin Weismann

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 rely on nonlinear optical effects in these 2D materials. This paper 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.

Giant Nonlinear Optical Activity of Achiral Origin in Planar Metasurfaces with Quadratic and Cubic Nonlinearities.

3D chirality is shown to be unnecessary for introducing strong circular dichroism for harmonic generations. Specifically, near-unity circular dichroism for both second-harmonic generation and third-harmonic generations is demonstrated on suitably designed ultrathin plasmonic metasurfaces with only 2D planar chirality. The study opens up new routes for designing chip-type biosensing platform, which may allow for highly sensitive detection of bio- and chemical molecules with weak chirality.

Nonlinear generalized source method for modeling second-harmonic generation in diffraction gratings

We introduce a versatile numerical method for modeling light diffraction in periodically patterned photonic structures containing quadratically nonlinear non-centrosymmetric optical materials. Our approach extends the generalized source method to nonlinear optical interactions by incorporating the contribution of nonlinear polarization sources to the diffracted field in the algorithm. We derive the mathematical formalism underlying the numerical method and introduce the Fourier-factorization suitable for nonlinear calculations. The numerical efficiency and runtime characteristics of the method are investigated in a set of benchmark calculations. The results corresponding to the fundamental frequency are compared to those obtained from a reference method and the beneficial effects of the modified Fourier-factorization rule on the accuracy of the nonlinear computations is demonstrated. To illustrate the capabilities of our method, we employ it to demonstrate strong enhancement of second-harmonic generationon one- and two-dimensional optical gratings resonantly coupled to a slab waveguide. Our method can be easily extended to other types of nonlinear optical interactions by simply incorporating the corresponding nonlinear polarization sources in the algorithm.

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 Gibbs 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.

Double-resonant enhancement of third-harmonic generation in graphene nanostructures

Intriguing and unusual physical properties of graphene offer remarkable potential for advanced, photonics-related technological applications, particularly in the area of nonlinear optics at the deep-subwavelength scale. In this study, we use a recently developed numerical method to illustrate an efficient mechanism that can lead to orders of magnitude enhancement of the third-harmonic generation in graphene diffraction gratings. In particular, we demonstrate that by taking advantage of the geometry dependence of the resonance wavelength of localized surface-plasmon polaritons of graphene ribbons and discs one can engineer the spectral response of graphene gratings so that strong plasmonic resonances exist at both the fundamental frequency and third-harmonic (TH). As a result of this double-resonant mechanism for optical near-field enhancement, the intensity of the TH can be increased by more than six orders of magnitude. This article is part of the themed issue ‘New horizons for nanophotonics’.

Generalized source method for modeling nonlinear diffraction in planar periodic structures

We present a new numerical method for the analysis of second-harmonic generation (SHG) in one- and twodimensional (1D, 2D) diffraction gratings with arbitrary profile made of non-centrosymmetric optical materials. Our method extends the generalized source method (GSM), which is a highly efficient alternative to the conventional Fourier modal method, to quadratically nonlinear diffraction gratings. The proposed method consists of a two-stage algorithm. Initially, the electromagnetic field at the fundamental frequency is computed in order to obtain the second-harmonic polarization using the known second-order nonlinear susceptibility. Then the optical field at the second-harmonic frequency is computed using this polarization as an additional source term in the GSM. We show how to integrate this source term into the GSM framework without changing the structure of the basic algorithm. We use the proposed algorithm to investigate a doubly resonant mechanism that leads to strong enhancement of SHG in a nonlinear 2D circular GaAs grating mounted on top of a GaAs slab waveguide. We design this optical device such that slab waveguide modes at the fundamental and second-harmonic are simultaneously excited and phase matched by the grating. The numerically obtained resonance frequencies show good agreement with analytically computed resonance frequencies of the unperturbed slab waveguide.

Enhanced magnetic second-harmonic generation from resonant metasurfaces

We demonstrate enhancement of second-harmonic generation efficiency in sub-wavelength resonant nanostructures supporting optically induced magnetic response. This is achieved through simultaneous excitation of electric and magnetic multipoles at the second-harmonic wavelength and their constructive interference.

Computational modeling of higher-harmonic generation in periodic 2D-3D heteromaterials

We present a rigorous numerical method to analyze optical higher harmonic generation in one- and two-dimensional (1D, 2D) periodically patterned structures containing 2D materials, such as graphene, MoS2, and WSe2, and investigate resonantly enhanced nonlinear interactions in such 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.

Computational modeling of nonlinear optical response of 2D-3D heteromaterials

Remarkable physical properties of two-dimensional (2D) materials provide significant potential for novel photonic devices, many of which rely on nonlinear optical effects in these 2D materials. Here we use a theoretical and computational approach we have recently introduced to describe the linear and nonlinear optical physics of nanostructured 2D materials embedded in periodic structures containing regular three-dimensional (3D) optical media, such as diffraction gratings and metamaterials. Thus, we use the proposed method to demonstrate enhanced nonlinear optical interactions in periodic photonic nanostructures via resonant excitation of phase-matched waveguide modes, enhanced nonlinearity of nanostructures containing graphene and other 2D nanomaterials, and Fano resonances for increasing the efficiency of 2D-3D heteromaterials.