FDTD 101
2 hours 48 minsThis course is an introduction to the Finite-Difference Time-Domain (FDTD) Method for electromagnetics. You will learn the fundamental concepts behind electromagnetic simulation, the common sources of errors in FDTD simulations, and many advanced topics worth considering when you set up your simulations. The course includes video lectures and tutorials, and we will walk you through the basics of setting up and running electromagnetic simulations. We will use Flexcompute's Tidy3D solver for its examples, and the scripts used in the slides are publicly accessible from this website. Basic knowledge of electromagnetics and programming is recommended to get the most use out of this course.
What skills you will develop
After completing this course you will be able to:
Understand the fundamentals of the FDTD method.
Set up FDTD simulations using advanced concepts.
Compute the transmission spectrum of photonic devices using FDTD.
Perform mode analysis and inject a selected mode into a waveguide.
Model dispersive materials.
Identify common sources of errors in FDTD simulations and how to fix them.
What you will learn
Lectures
1Introduction to FDTD Simulation 11 minsStart
In this lecture, we will describe the basic concepts of EM simulation using FDTD.
2Using FDTD to Compute a Transmission Spectrum 11 minsStart
In this lecture, we show how to use FDTD to solve a basic EM problem involving the transmission of light though a slab of material.
3Applying FDTD to Photonic Crystal Slab Simulation 16 minsStart
In this lecture, we show how to apply FDTD to solve a slightly more complicated EM problem involving a photonic crystal slab that supports guided resonance.
4Prelude to Integrated Photonics Simulation: Mode Injection 10 minsStart
In this lecture, we show how to perfectly inject a specific mode into a straight waveguide. This is helpful in decreasing computational cost, and having a clean simulation without unwanted electromagnetic interference in the computational domain.
5Modeling dispersive material in FDTD 14 minsStart
6Introduction to perfectly matched layer (PML) 17 minsStart
Perfectly matched layer (PML) is commonly used to truncate unbounded computational region, since an ideal PML can completely absorb the incoming waves from all angles of the incidence without any reflection. In this lecture, we explain the basic idea behind PML, and show how to characterize the performance of PML in FDTD simulations.
7Time step size and CFL condition in FDTD 14 minsStart
The choice of time step size can have a strong impact on the behavior of FDTD algorithms. In this lecture, we provide a simple and intuitive argument on deriving an important condition on choosing time step size, known as the Courant–Friedrichs–Lewy (CFL) condition.
8Numerical dispersion in FDTD 21 minsStart
A key source of error in FDTD simulations lies in the spatial and temporal discretization. The behavior of the wave propagating in such a discrete numerical lattice can deviate from that of the physical wave. This phenomenon is known as numerical dispersion. In this lecture, we derive and visualize the effect of numerical dispersion, as well as provide a rule of thumb to suppress the error.
9Dielectric constant assignment on Yee grids 13 minsStart
In this lecture, we discuss another important source of error that arises from the imperfect description of the dielectric constant distribution of a photonic device on discrete Yee grids. We highlight some subtleties in the dielectric constant assignment on the grids that can lead to significant error. This motivates us to consider more advanced FDTD techniques such as subpixel averaging and nonuniform grid sizes.
10Introduction to subpixel averaging 13 minsStart
In this lecture, we discuss a powerful method known as subpixel averaging that enables the FDTD algorithm to capture geometric features below the discretization level. We discuss the basic ideas as well as some subtleties associated with subpixel averaging.
