D. J. Griffiths, Introduction to Electrodynamics, 4th ed., Ch. 9
Electromagnetic waves in vacuum, transverse plane-wave solutions and polarization foundations.
EM-04
Course overview
Electromagnetic waves, polarization & interfaces
Starting from the full Maxwell system, establish how electromagnetic disturbances propagate. This course builds the wave equation before plane waves, polarization, interface conditions and energy flow.
5/5available
Prerequisites
- EM-01 — electrostatics and Gauss's law
- EM-02 — magnetic fields
- EM-03 — Faraday, Ampère–Maxwell and energy
By the end of this course
- Derive the wave equations from Maxwell's laws.
- Establish transversality and polarization.
- Analyze interface conditions and reflected/transmitted fields.
- Connect propagation, power and wave impedance.
Syllabus
Electromagnetic waves, polarization & interfaces
Starting from the full Maxwell system, establish how electromagnetic disturbances propagate. This course builds the wave equation before plane waves, polarization, interface conditions and energy flow.
- 01→
Derive the wave equation from Maxwell
From the four source-free vacuum Maxwell equations to propagating transverse E and B fields: derive both vector wave equations, identify c from SI constants, check the missing constraints and state exactly where the argument fails in matter.
120–150 min · Intermediate → advanced · available - 02→
Monochromatic plane waves
Fix AoN's harmonic convention, read propagation from constant-phase planes, derive k=ω/c and the transverse Maxwell amplitude constraints, recover the signed E–B–k triad and vacuum wave impedance, then express the most general transverse complex amplitude as the bridge to polarization.
155–200 min · Intermediate → advanced · available - 03→
Polarization: ellipse, Jones & Stokes
From the two complex transverse field components, derive the polarization ellipse, classify linear/circular/elliptical states, make rotation sense convention-explicit, build normalized Jones vectors and basis transforms, and define Stokes parameters with an explicit S₃ sign before extracting ellipse azimuth and ellipticity.
190–250 min · Intermediate → advanced · available - 04→
Interfaces & Fresnel amplitudes
Derive Maxwell boundary conditions, tangential phase matching, reflection law and Snell refraction, then obtain TE/s and TM/p Fresnel FIELD-amplitude coefficients in an explicitly signed basis. Resolve the p-basis sign trap at normal incidence, derive Brewster and critical angles, and delimit lossy, anisotropic and sheet-conductive cases.
210–275 min · Intermediate → advanced · available - 05→
Power flow, R/T & wave impedance
Close the wave sequence by deriving the cycle-averaged Poynting flux for AoN peak phasors, converting Fresnel FIELD amplitudes into power coefficients, auditing R+T energy conservation, and extending intrinsic impedance and dissipation to conducting media and 2D conductive sheets.
190–245 min · Intermediate → advanced · available
Reference backbone
References
Cited by derivation, with explicit source-free and constitutive assumptions.
J. D. Jackson, Classical Electrodynamics, 3rd ed., Ch. 7
Plane-wave propagation, the electromagnetic wave equation and extension to media.
E. Collett, Field Guide to Polarization, SPIE
Polarization ellipse, Jones vectors, basis changes and Stokes parameters with explicit convention tracking.
IEEE Std 145-2013
Antenna polarization terminology and handedness/viewing-convention discipline.