Discontinuous Galerkin Time-domain Solver Research Articles

Broadband spectral analysis of chiral nanophotonic structures at circularly polarized incidence using DGTD solver

Abstract A transient circularly polarized excitation and its implementation in a generalized dispersive material model based discontinuous Galerkin time-domain solver are proposed for spectral analysis of chiral nanophotonic structures. The expression of a circularly polarized pulse with a certain bandwidth, which is real-valued and enables multi-physics and nonlinearity, is derived comprehensively. Numerical examples of nanophotonic structures are given in this paper. Such as reflection from metallic mirrors, transmission from S-shaped dielectric metasurfaces, and the spin response of C4 symmetrically arranged right-handed enantiomers. These examples demonstrate the accuracy and capability of the proposed method.

The application of a high-order discontinuous Galerkin time-domain method for the computation of electromagnetic resonant modes

• A high-order discontinuous time-domain method is presented for computing resonant frequencies and modes. • The method incorporates the exact boundary representation of the computational domain given by a CAD model. • The results demonstrates that the rate of convergence can be affected by an inaccurate geometric description. • The method is able to provide a broad band of resonant frequencies for two and three dimensional cavities. This work presents a highly accurate and efficient methodology for the computation of electromagnetic resonant frequencies and their associated modes in cavities. The proposed technique consists of a high–order discontinuous Galerkin time-domain solver combined with a signal processing algorithm for extracting the frequency content. The methodology is capable of incorporating the CAD boundary representation of the domain. The numerical results demonstrate that incorporating the exact boundary representation results in a improved convergence rate, a phenomenon that has not been previously reported. Several numerical examples in two and three dimensions show the potential of the proposed technique for cavities filled with non-dispersive or dispersive media.

A 3D curvilinear discontinuous Galerkin time-domain solver for nanoscale light–matter interactions

Classical finite element methods rely on tessellations composed of straight-edged elements mapped linearly from a reference element, on domains which physical boundaries and interfaces are indifferently straight or curved. This approximation represents a serious hindrance for high-order methods, since they limit the accuracy of the spatial discretization to second order. Thus, exploiting an enhanced representation of physical geometries is in agreement with the natural procedure of high-order methods, such as the discontinuous Galerkin method. In this framework, we propose and validate an implementation of a high-order mapping for tetrahedra, and then focus on specific photonics and plasmonics setups to assess the gains of the method in terms of memory and performances.

Analysis of light propagation in slotted resonator based systems via coupled-mode theory

Optical devices with a slot configuration offer the distinct feature of strong electric field confinement in a low refractive index region and are, therefore, of considerable interest in many applications. In this work we investigate light propagation in a waveguide-resonator system where the resonators consist of slotted ring cavities. Owing to the presence of curved material interfaces and the vastly different length scales associated with the sub-wavelength sized slots and the waveguide-resonator coupling regions on the one hand, and the spatial extent of the ring on the other hand, this prototypical system provides significant challenges to both direct numerical solvers and semi-analytical approaches. We address these difficulties by modeling the slot resonators via a frequency-domain spatial Coupled-Mode Theory (CMT) approach, and compare its results with a Discontinuous Galerkin Time-Domain (DGTD) solver that is equipped with curvilinear finite elements. In particular, the CMT model is built on the underlying physical properties of the slotted resonators, and turns out to be quite efficient for analyzing the device characteristics. We also discuss the advantages and limitations of the CMT approach by comparing the results with the numerically exact solutions obtained by the DGTD solver. Besides providing considerable physical insight, the CMT model thus forms a convenient basis for the efficient analysis of more complex systems with slotted resonators such as entire arrays of waveguide-coupled resonators and systems with strongly nonlinear optical properties.