An electromagnetic wave is a self-propagating oscillation of electric and magnetic fields, perpendicular to each other and to the direction of travel. No medium is required — EM waves propagate in vacuum at the speed of light.

Wave Properties

A plane wave travelling in the z-direction has:

The wavenumber \(k = 2\pi/\lambda = \omega/c\), angular frequency \(\omega = 2\pi f\), wavelength \(\lambda = c/f\).

The EM Spectrum

• ELF / VLF < 30 kHz — submarine communications, power lines
• MF / HF 300 kHz–30 MHz — AM radio, shortwave
• VHF / UHF 30 MHz–3 GHz — FM radio, TV, WiFi, cellular
• Microwave 3–300 GHz — radar, satellite, 5G, microwave ovens, MRI
• Infrared / Visible / UV above 300 GHz
• X-ray / Gamma very high frequencies — ionising radiation

Polarisation

The polarisation of an EM wave describes the orientation of the electric field vector. Linear polarisation: E oscillates in one plane. Circular polarisation: E rotates, tracing a helix. In MRI, circular (quadrature) polarisation of the B1 field is used to improve SNR by 40%.

Poynting Vector

Power flow per unit area is given by the Poynting vector: \(\mathbf{S} = \mathbf{E} \times \mathbf{H}\) (W/m²). Time-averaged power: \(\langle S \rangle = E_0^2 / (2\eta)\) where \(\eta = \sqrt{\mu/\varepsilon}\) is the wave impedance (377 Ω in free space).