January 23, 2024
The finite-difference time-domain (FDTD) method is the industry’s gold-standard computational electromagnetic solver for modeling nanophotonic devices, processes, and materials.
First introduced in 1966 by Kane S. Yee, FDTD is an algorithmic approach to solving James Clerk Maxwell’s transformative equations, officially known as Maxwell’s equations. Conceived in the 19th century, these equations not only unified electricity and magnetism, but also laid the groundwork for technologies such as radio, television, and wireless communication. Yee’s numerical method was not widely referred to as FDTD until the 1980s.
Maxwell’s equations and the laws associated with them include:
In FDTD, the simulation domain is the space truncated by the simulation region and discretized by the mesh. When an FDTD simulation runs, the electromagnetic (EM) fields are calculated from Maxwell’s equations in every mesh cell and the solutions are repeatedly time-stepped. Spatial discretization allows for the representation of complex geometries and structures, while temporal discretization captures the evolution of EM fields over time.
The FDTD method is generally suitable for design cases in which some or all dimensions of the object are comparable to the size of the wavelength of light. Its accuracy and versatility make FDTD the go-to solver for a wide range of photonic designs, including:
Although FDTD presents the most general solution to Maxwell’s equations, more efficient approaches are applied to specific applications such as for maximizing design flexibility for multi-layered and diffractive optical components. Similarly, a solver combination strategy for photonic integrated components can be employed to address different structures more efficiently, such as the eigenmode expansion (EME) method for light guiding structures. Building a strategic methodology for choosing the right solver for the right problem can impact both the design process speed and efficiency, as well as the accuracy of results.
Using FDTD, designers can thoroughly study polarization and wavelength-dependent interactions of light with different materials and structures. They can receive insight into optical phenomena such as reflectance, transmission, diffraction, interference, and absorption.
The high accuracy and versatility of the FDTD method introduce some challenges, including:
Ansys Lumerical leverages multiple advanced approaches to accelerate FDTD simulations.
The FDTD algorithm in Lumerical has been fine-tuned at a fundamental level over decades to minimize computational overhead while delivering the highest accuracy. There are several patented and advanced features and functionalities to help streamline the simulation setup, including the mesh, monitors, sources, structures, materials, analysis groups, and more. Built-in advanced optimization frameworks can additionally accelerate the generation of optimized nanophotonic devices.
Ansys Lumerical FDTD has a highly optimized computational engine able to exploit multicore CPU computing systems and harness the parallel architecture of graphics processing units (GPUs) in high-performance computing (HPC) clusters. Both CPU and GPU architectures excel in parallel processing, addressing the need for simultaneous computation in FDTD simulations. HPC systems leverage this parallelism to distribute the workload, significantly enhancing simulation performance. Large simulation jobs can be partitioned into several independent computational threads to be executed in parallel enabling large simulations of 50-100 billion grid cells in less than a few hours.
As the complexity of simulations grows, so does the need for efficient and scalable computational resources. This is where the dynamic duo of Cloud Computing and HPC steps in, revolutionizing FDTD simulations. The Lumerical solution offers CPU and GPU-compatible simulation software that users can deploy on-premises or on the cloud.
For more information on FDTD simulation software on HPC and cloud, watch our webinar “Accelerating Photonic Design with HPC and Cloud.”