In this letter, a 3-D subgridding finite-difference time-domain (FDTD) approach is proposed. The calculation domain is divided into regions with dense meshes and regions with coarse meshes. By applying the proposed subgridding technique to dense grid regions, memory and computation resources can be significantly reduced. Furthermore, the Courant–Friedrich–Levy (CFL) limitation of dense mesh regions is broken by the one-step leapfrog alternately direction-implicit (ADI)-FDTD. Coarse and dense regions can adopt a uniform time step, which is limited only by the standard FDTD CFL condition for coarse meshes. In comparison with the standard FDTD approach and the subgridding FDTD approach, numerical results demonstrate the efficiency and accuracy of the proposed method.

Contrary to the local response approximation (LRA), the electromagnetic response of sub-nanometer particles and antennas is influenced by the nonlocal response arising from the free-electron spill-out effect. A generalized nonlocal optical response (GNOR) has been successful in explaining the unusual frequency shifts and spectral bandwidth broadening mechanisms, which cannot be captured by LRA models. This paper presents a comprehensive FDTD implementation of Maxwell-hydrodynamic model with the GNOR term to model the interaction between electromagnetic wave and plasmonic nanoantennas of critical size. Due to the necessity of resolving nonlocal effects with deep subnanometer grid sizes, a subgridding technique becomes crucial for achieving convergence. To this end, a novel heterogeneous CPU-GPU technique is developed to further enhance simulation efficiency. The algorithms are validated on small spherical metallic particles, revealing that the nonlocality effectively eliminates staircasing artifacts at curved interfaces, leading to a higher degree of accuracy compared to local models. Additionally, numerical results demonstrate the extended capability of the FDTD method to accurately and efficiently model the blueshift and resonant mode broadening observed in both single nanoantennas and nano-dimers. This work contributes significantly to understanding various sophisticated phenomena observed in experiments.

This letter proposes a novel parallelized three-dimensional finite-difference time domain (FDTD) method for solving Maxwell's equations in the time domain. Our approach leverages efficient domain decomposition methods on a face-centered cubic (FCC) grid, resulting in a significant efficiency improvement in comparison to the sequential face-centered cubic finite-difference time-domain (FCC-FDTD) method. To quantify this enhancement, we evaluate performance metrics such as speedup factor and parallel efficiency by comparing computation times against the serial FCC-FDTD implementation. A detailed description of the data communication strategy for electric and magnetic fields in the FCC grid is also provided. Finally, the letter concludes by validating the accuracy and efficiency of our proposed method through two illustrative numerical examples.

Difference frequency generation (DFG) is an essential phenomenon for generating far-infrared (FIR) and broadband terahertz (THz) waves, which cannot be generated by either alternating current flow-driven antennas for microwave source or pumped materials for higher frequency lights. Metallic nonlinear metasurfaces (NLMSs) as a new platform for generating THz sources were intensively developed. In this work, a nondepleted time-domain model derived from the Maxwell-hydrodynamic model is proposed where linear and nonlinear responses in metallic structures under an intense excitation are separated. By using the proposed model, only linear and low-frequency DFG signals will be considered, which makes this model suitable for unconditionally stable time-domain algorithms. A finite-difference time-domain (FDTD) method is employed to solve a set of multiphysics equations based on the proposed model. The stability of the algorithm is apparent. We validate our method by simulating THz generations from metallic NLMSs and benchmark the approach with previous numerical studies as well as our recent experimental results. In addition, the implementation of solving the DFG response can be remarkably accelerated by using the unconditionally stable algorithm.

In the study of electromagnetic (EM) applications, solving Maxwell’s equations to obtain spatial-temporal field evolution is a critical step. The deep learning (DL) is a new promising way to solve partial differential equations (PDEs), by training various neural networks to identify the mapping between inputs and solutions. These approaches are much faster than traditional computational electromagnetic methods after the networks are trained. Previous works focuses on predicting low dimensional results, while the spatial-temporal field evolution of a realistic EM simulation using four-dimensional (4D) datasets is rarely studied. In this work, we employ an innovative deep learning framework, the Fourier neural operator (FNO), to solve Maxwell's equations. FNO leverages the Fourier transform to learn mappings between high-dimensional function spaces, efficiently capturing global information and significantly improving computational efficiency and accuracy. Compared to traditional numerical algorithms, FNO achieves a two-order-of-magnitude speedup and supports super-resolution capabilities, greatly enhancing simulation efficiency. Furthermore, FNO successfully addresses the challenges of three-dimensional (3D) EM simulations, providing a new framework for solving complex EM problems.

Plasmonic metamaterials can exhibit a variety of physical optical properties that offer extraordinary nonlinear conversion efficiency for ultra-compact nanodevice applications. Furthermore, the optical-rectification effect from the plasmonic nonlinear metasurfaces (NLMSs) can be used as a compact source of deep-subwavelength thickness to radiate broadband terahertz (THz) signals. Meanwhile, a novel dual-mode metasurface consisting of a split-ring resonator (SRR) array and an epsilon-near-zero (ENZ) layer was presented to boost the THz conversion efficiency further. In this paper, to explore the mechanism of THz generation from plasmonic NLMSs, the Maxwell-hydrodynamic multiphysics model is adopted to investigate complex linear and intrinsic nonlinear dynamics in plasmonics. We solve the multiphysics model using the finite-difference time-domain (FDTD) method, and the numerical results demonstrate the physical mechanism of the THz generation processes which cannot be observed in our previous experiments directly. The proposed method reveals a new approach for developing new types of high-conversion-efficiency nonlinear nanodevices.