Transverse electromagnetic wave
An EM plane wave in which both E and B oscillate perpendicular to the propagation direction k, and perpendicular to each other. The Gauss-law constraints ∇·E = 0 and ∇·B = 0 force the transverse structure in vacuum.
Definition
An electromagnetic wave in vacuum is transverse: both the electric field E and the magnetic field B oscillate in directions perpendicular to the direction of propagation k. Further, E and B are perpendicular to each other, and the triad (E, B, k) forms a right-handed coordinate system with |B| = |E|/c. This structure is forced by Maxwell's equations: ∇·E = 0 in source-free vacuum rules out any longitudinal component of E along k, and the curl equations tie E and B together in the perpendicular orthogonality.
The transverse structure is what allows polarisation to be a meaningful concept. Because E has two independent degrees of freedom perpendicular to k (rather than a single longitudinal direction), a wave can be linearly polarised along one axis, linearly polarised along the orthogonal axis, or a phased superposition (circular, elliptical). Longitudinal waves — like sound in a gas — have no polarisation, because there is only one direction available for oscillation. Fresnel's 1822 realisation that light must be a transverse wave was the key to explaining polarisation phenomena, which had baffled earlier wave theorists who assumed light oscillated along k like sound.