Linear polarization
An EM wave in which E oscillates along a single fixed line perpendicular to k. Equivalent to a superposition of two circularly polarised waves of equal amplitude with opposite handedness.
Definition
A linearly polarised electromagnetic wave has its electric field oscillating along a single fixed line perpendicular to the propagation direction k. In complex notation, E(r,t) = Re[ê E₀ e^{i(k·r − ωt)}] with ê a real unit vector perpendicular to k — the polarisation direction. The field goes from +E₀ê to −E₀ê and back each period, with the magnetic field locked at 90° in the perpendicular direction.
Most light sources produce unpolarised light (a rapid random mixture of all polarisation directions), but linear polarisers — sheets of dichroic material like Polaroid film, wire-grid polarisers at long wavelengths, or crystal polarisers for precision work — select a single direction. Once linearly polarised, light obeys Malus's law on passing through a second polariser: I = I₀ cos²θ, where θ is the angle between the two polariser axes. Linear polarisation also emerges naturally from Brewster-angle reflection (the reflected wave is purely s-polarised at θ_B) and from dipole antennas (the emitted wave is linearly polarised along the antenna axis). Equivalently, linear polarisation is a coherent superposition of left- and right-circular polarisations of equal amplitude.