Lecture 1: Introduction to FDTD Simulation
In this lecture, we will describe the basic concepts of EM simulation using FDTD.
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Lecture 2: Using FDTD to Compute a Transmission Spectrum
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.
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Lecture 3: Applying FDTD to Photonic Crystal Slab Simulation
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.
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Lecture 4: Prelude to Integrated Photonics Simulation: Mode Injection
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.
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Lecture 5: Modeling dispersive material in FDTD
Material dispersion is a very common phenomenon in which the material responds differently to light of different color. In this lecture, we show how to include material dispersion in FDTD simulations.
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Lecture 6: Introduction to perfectly matched layer (PML)
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.
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Lecture 7: Time step size and CFL condition in FDTD
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.
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Lecture 8: Numerical dispersion in FDTD
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 deviatefrom that of the physical wave. This phenomenon is known as numerical dispersion. Inthis lecture, we derive and visualize the effect of numerical dispersion, as well asprovide a rule of thumb to suppress the error.
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Lecture 9: Dielectric constant assignment on Yee grids
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.
Start
Lecture 1: Introduction to FDTD Simulation
In this lecture, we will describe the basic concepts of EM simulation using FDTD.
Start
Lecture 2: Using FDTD to Compute a Transmission Spectrum
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.
Start
Lecture 3: Applying FDTD to Photonic Crystal Slab Simulation
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.
Start
Lecture 4: Prelude to Integrated Photonics Simulation: Mode Injection
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.
Start
Lecture 5: Modeling dispersive material in FDTD
Material dispersion is a very common phenomenon in which the material responds differently to light of different color. In this lecture, we show how to include material dispersion in FDTD simulations.
Start
Lecture 6: Introduction to perfectly matched layer (PML)
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.
Start
Lecture 7: Time step size and CFL condition in FDTD
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.
Start
Lecture 8: Numerical dispersion in FDTD
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 deviatefrom that of the physical wave. This phenomenon is known as numerical dispersion. Inthis lecture, we derive and visualize the effect of numerical dispersion, as well asprovide a rule of thumb to suppress the error.
Start
Lecture 9: Dielectric constant assignment on Yee grids
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.
Start