## EECS 224 - Fundamentals of Electromagnetics and Photonics

**CATALOG DESCRIPTION:** Introduction to electromagnetic waves in electrical engineering. Topics include: concepts of transmission lines, electrostatics and magnetostatics; Maxwell's equations for time-varying fields; plane-wave propagation, reflection, and transmission; introduction to fiber optics and photonics.

**REQUIRED TEXTS:**

1. F. Ulaby, Fundamentals of Applied Electromagnetics , 6th edition (2010), Prentice Hall.

**REFERENCE TEXT:**

1. J. Edminister, Schaum's Outline of Theory and Problems of Electromagnetics , McGraw-Hill.

**COURSE COORDINATOR: Prof. Allen Taflove**

**COURSE GOALS: **Provide the electrical engineering student with the foundation required to analyze electromagnetic fields and waves, and to understand the impact of electromagnetic wave phenomena upon modern technology such as high-speed digital circuits and fiber optics.

**PREREQUISITES: **EECS 202, EECS 221, multivariable calculus + differential equations

**DETAILED COURSE TOPICS:**

- Week 1 Why study electromagnetics? Introduction to transmission lines: lumped-element model, transmission line differential equations, impulsive wave propagation and reflection, bounce diagram.

- Week 2 Transmission lines, continued: sinusoidal excitation, input impedance, standing waves, Smith Chart, impedance transformation and matching.

- Week 3 Central forces. Electrostatics: Coulomb’s Law, electric potential, electric flux, Gauss’ Law.

- Week 4 Electrostatics, continued: electric field boundary conditions, basic electric field physics of dielectrics, capacitance, electrostatic field energy.
- Week 5 Magnetostatics: right-hand rule, Lorentz force, Biot-Savart relation, torques.
- Week 6 Magnetostatics, continued: magnetic properties of materials, magnetic field boundary conditions, Ampere’s Law, inductance, magnetostatic field energy.
- Week 7 Motional electromotive force, motors and generators, Lenz’s Law. Faraday’s Law, voltage-current relation for an inductor, transformers. Displacement current and the generalized Ampere’s Law. Time-dependent Maxwell’s equations. Electric and magnetic field boundary conditions.
- Week 8 Application of the time-dependent Maxwell’s curl equations to plane-wave propagation in free space. Power flow in the electromagnetic field. Sinusoidal steady-state specialization, Helmholtz equation.
- Week 9 Linear, circular, and elliptical polarization of plane electromagnetic waves. Sinusoidal electromagnetic wave propagation in lossy materials, skin effect. Time-averaged Poynting vector and power flow. Plane electromagnetic wave reflection and transmission at a material interface for normal incidence.
- Week 10 Plane electromagnetic wave reflection and transmission at a material interface for oblique incidence, parallel and perpendicular polarization cases. Snell’s Law. Critical angle and total internal reflection. Brewster angle. Conservation of the time-averaged power flow at a dielectric interface.

**GRADES: **Homework 10%, take-home Midterm Exam 30%, take-home Final Exam 60%.

**COURSE OBJECTIVES:** When a student completes this course, s/he should understand:

1) Theoretical foundations of static electric and magnetic fields: Coulomb's Law, charge conservation, Biot-Savart Law, Faraday's Law, Ampere's Law, and Gauss' Laws. Key concepts include field boundary conditions, potential functions, and energy storage.

2) Basic electrical properties of conductors, semiconductors, dielectrics, and magnetic materials.

3) Fundamental concepts of resistance, capacitance, and inductance.

4) Lenz's Law and the operation of simple motors and generators.

5) Fundamentals of transmission lines.

6) Propagation of plane electromagnetic waves in unbounded media, including power flow.

7) Fundamental concepts of plane-wave reflection and transmission at material interfaces, leading to geometrical optics.

8) Why the study of electromagnetics is important in the modern world and what is exciting about current research activities in electromagnetics and photonics.

A**BET CONTENT CATEGORY: **25% Math and Basic Science, 75% Engineering.