EMP-6306
21st Century Electromagnetics
Learn the theory and the skills to design electromagnetic devices in the 21st century where digital manufacturing and exploiting the third dimension becomes dominant. A course covering the most advanced topics in electromagnetics. Topics include engineered materials, metamaterials, solid state electromagnetics, spatial transforms, spatially variant lattices, and devices.
Course Paperwork
Course Assignments
Homework
- (PDF) Homework 1 — fdder()
Final Project
- (PDF) Final Project
Course Material
Topic 1 — Preliminary Topics
Topic 2 — Electromagnetic Properties of Materials
Electromagnetic Properties of Materials
- (PDF) (Video) Lecture 2a – Introduction to EM Properties of Materials
- (PDF) (Video) Lecture 2b – The Lorentz Oscillator Model
- (PDF) (Video) Lecture 2c – Lorentz Model for Dielectrics
- (PDF) (Video) Lecture 2d – Kramers-Kronig Relations
- (PDF) (Video) Lecture 2e – Drude Model for Metals
- (PDF) (Video) Lecture 2f – Special Cases of Drude Model
- (PDF) (Video) Lecture 2g – Generalizations & Alternative Models
- (PDF) (Video) Lecture 2h – Nonlinear Materials
- (PDF) (Video) Lecture 2i – Anisotropic Materials
- (PDF) (Video) Lecture 2j – Dispersion Relation & Index Ellipsoids
- (PDF) (Video) Lecture 2k – Tensor Math
Analysis of Transmission Lines Embedded in Anisotropic Media
Topic 3 — Coupled-Mode Theory
Topic 4 — Periodic Structures
Solid State Electromagnetics
- (PDF) (Video) Lecture 4a – Introduction to Periodic Structures in Electromagnetics
- (PDF) (Video) Lecture 4b – Lattice Vectors
- (PDF) (Video) Lecture 4c – Unit Cells & Brillouin Zones
- (PDF) (Video) Lecture 4d – Electromagnetic Waves in Periodic Structures
- (PDF) (Video) Lecture 4e – Calculation Examples Of Periodic Structures
- (PDF) Appendix – Solid State Electromagnetics
Diffraction Gratings
- (PDF) (Video) Lecture 4f – Concept of Diffraction From Gratings
- (PDF) (Video) Lecture 4g – The Grating Equation
- (PDF) (Video) Lecture 4h – The Plane Wave Spectrum
- (PDF) (Video) Lecture 4i – Diffraction from Oblique Gratings
- (PDF) (Video) Lecture 4j – Applications of Diffraction Gratings
Other Types of Gratings
Animations from the Notes
- Diffraction Orders from Ruled Gratings – Normal Incidence
- Diffraction Orders from Ruled Gratings – Oblique Incidence
- Diffraction Orders from Ruled Gratings – Angle Sweep
- Diffraction Orders from Crossed Gratings – Normal Incidence
- Diffraction Orders from Crossed Gratings – Oblique Incidence
- Diffraction Orders from Crossed Gratings – Angle Sweep
Internet Resources
- Brillouin Zones – interactive summary of Brillouin zones
Topic 5 — Engineered Materials
- (PDF) (Video) Lecture 5a – Introduction To Engineered Materials
- (PDF) (Video) Lecture 5b – Metamaterials
- (PDF) (Video) Lecture 5c – Photonic Crystals
- (PDF) (Video) Lecture 5d – Homogenization And Parameter Retrieval
Calculating Photonic Bands in MATLAB
- Implementation of 2D PWEM for band calculation in MATLAB
This series of videos types and explains every line of code in MATLAB to implement the 2D plane wave expansion method as described above. The bands for a hexagonal lattice are calculated and then displayed in a professional plot from MATLAB. - Implementation of 3D PWEM for band calculation in MATLAB
This course contains lectures and coding sessions to implement a fully three dimensional plane wave expansion method in MATLAB. See every line of code in MATLAB typed and explained including calculation of the bands and displaying them in a professional plot.
Topic 6 — Design Techniques for 21st Century Electromagnetics
- Spatial Transforms
- (PDF) (Video) Lecture 6a – Introduction to Transformation Optics
- (PDF) (Video) Lecture 6b — Coordinate Transforms
- (PDF) (Video) Lecture 6c — Form Invariance of Maxwell’s Equations
- (PDF) (Video) Lecture 6d — Analytical Transformation Optics
- (PDF) (Video) Lecture 6e — Stretching Space with Transformation Optics
- (PDF) (Video) Lecture 6f — Cloaking with Transformation Optics
- (PDF) (Video) Lecture 6g — Other Applications of Transformation Optics
- (PDF) (Video) Lecture 6h — Conformal Mapping
- (PDF) (Video) Lecture 6i — Numerical Solution of Laplace’s Equation
- (PDF) (Video) Lecture 6j — Numerical Transformation Optics
- Holographic Lithography
- Spatially-Variant Lattices
- Interfacing MATLAB & CAD
MATLAB Implementations
- ($) Implementation of Numerical Transformation Optics in MATLAB
This complete course covers the finite-difference method and transformation optics and then steps the student through every single line of code in MATLAB to implement a numerical transformation optics code. After this course, the student will be able to design a cloak of any shape to hide an object of any shape. The course does not cover how to simulate the transformation optics design.
Supplemental Information
Topic 7 — Other Advanced Topics
Course Resources
- Electromagnetic and Photonic Simulation for the Beginner: Finite-Difference Frequency-Domain in MATLAB
Perfect book to get started in computational electromagnetics. Includes theory, derivations, and all MATLAB codes for simulating waveguides, transmission liens, diffraction gratings, guided-mode resonance filters, frequency selective surfaces, metamaterials, metasurfaces, invisibility cloaks, surface waves and others. - Animated Visualization of a Grating Vector
- Short course on Generating Spatially-Variant Lattices
- Download .zip files with MATLAB codes
- test_fdder.p — Homework #1 asks you to write the function fdder() which constructs derivative operators for collocated grid. This test_fdder.p program tests your fdder() function to ensure that all features are working properly. See Homework #1 for details.
- fdders.p — This function acts just like fdder() except that is only produces derivative matrices for small grids. It is provided here simply to help troublshoot your fdder() function.
Note: The above items are protected function files and have a “.p” extension. They work just like “.m” files, but they cannot be opened to view the code inside them.