Academics
Dop Course Outline
OS7201 Electromagnet Optics Analysis Using Finite-Difference Time-Domain Method
Last Revised: 2024-03-08
Course Objectives
After taking this course, students will develop solid understanding of basic and some advanced knowledge of the finite-difference time-domain method and hands-on coding experiences in applying this numerical method to electromagnetic optics analysis.
Prerequisite
Textbook A. Taflove, S. C. Hagness, Computational Electrodynamics, the Finite-Difference Time-Domain Method, 3rd ed, Artech House, 2005.
Topical Outline 1. Introduction
2. Electromagnetics and FDTD
Review of Maxwell’s Equations, Physical Boundary Conditions, Constitutive Relations, Flow of Maxwell’s Equations, Finite-Difference Approximation, The First FDTD Algorithm
3. Formulation and Implementation of 1D FDTD (I)
Yee grid scheme, Finite-Difference Approximation of Maxwell’s Curl Equations, Governing Equations for 1D FDTD, Derivation of Basic Update Equations, Implementation of Basic Update Equation
4. Formulation and Implementation of 1D FDTD (II)
Numerical Boundary Conditions, Grid Resolution, Courant Stability Condition, Perfect 1D Boundary Condition, Sources, Total-Field/Scattered-Field Soft Source, Fourier Transform, Reflectance and Transmittance, Sequence for Code Development, Convergence, Grid Dispersion, Incorporating Loss
5. Formulation and Implementation of 2D FDTD
From 3D to 2D Maxwell’s Equations, Update Equations, Boundary Conditions, FDTD Algorithm for 2D Simulations, Minimizing Simulation Time, 2Grid Technique, Fitting Structures to a Cartesian Grid
6. The Perfectly Matched Layer
Uniaxial Perfectly Matched Layer (UPML), Conventional PML, PML Parameters, Implementation of UPML in 2D FDTD, Ez Mode, TF/SF Source
7. Grating Diffraction and Plane-Wave spectrum
Wave Vectors, Phase Matching at An Interface, Waves in Periodic Media, Plane Wave Spectrum
Prerequisite
Textbook A. Taflove, S. C. Hagness, Computational Electrodynamics, the Finite-Difference Time-Domain Method, 3rd ed, Artech House, 2005.
Topical Outline 1. Introduction
2. Electromagnetics and FDTD
Review of Maxwell’s Equations, Physical Boundary Conditions, Constitutive Relations, Flow of Maxwell’s Equations, Finite-Difference Approximation, The First FDTD Algorithm
3. Formulation and Implementation of 1D FDTD (I)
Yee grid scheme, Finite-Difference Approximation of Maxwell’s Curl Equations, Governing Equations for 1D FDTD, Derivation of Basic Update Equations, Implementation of Basic Update Equation
4. Formulation and Implementation of 1D FDTD (II)
Numerical Boundary Conditions, Grid Resolution, Courant Stability Condition, Perfect 1D Boundary Condition, Sources, Total-Field/Scattered-Field Soft Source, Fourier Transform, Reflectance and Transmittance, Sequence for Code Development, Convergence, Grid Dispersion, Incorporating Loss
5. Formulation and Implementation of 2D FDTD
From 3D to 2D Maxwell’s Equations, Update Equations, Boundary Conditions, FDTD Algorithm for 2D Simulations, Minimizing Simulation Time, 2Grid Technique, Fitting Structures to a Cartesian Grid
6. The Perfectly Matched Layer
Uniaxial Perfectly Matched Layer (UPML), Conventional PML, PML Parameters, Implementation of UPML in 2D FDTD, Ez Mode, TF/SF Source
7. Grating Diffraction and Plane-Wave spectrum
Wave Vectors, Phase Matching at An Interface, Waves in Periodic Media, Plane Wave Spectrum
