Circular polarization
An EM wave whose E-vector rotates in a circle at frequency ω as the wave propagates, tracing a helix in space. Left- and right-handed variants are the two independent polarisation states.
Definition
A circularly polarised electromagnetic wave has its electric field vector rotating in a circle at the angular frequency ω as the wave propagates, without changing magnitude. In a fixed plane perpendicular to k, the tip of E traces a circle once per period. In the frame of the wave, the field pattern is a helix — right-handed for right-circular (RCP) polarisation, left-handed for left-circular (LCP).
Mathematically, circular polarisation is a coherent superposition of two linear polarisations oscillating 90° out of phase with equal amplitude: E = E₀(ê₁ cos(ωt − kz) ± ê₂ sin(ωt − kz)) for RCP/LCP. Each circular polarisation carries definite angular momentum ±ħ per photon along the propagation axis, so transferring circularly polarised light to matter exerts a torque — the basis of optical-manipulation experiments with suspended absorbing particles. Circular polarisation is produced by passing linearly polarised light through a quarter-wave plate, by reflection off certain chiral media, and naturally by cyclotron radiation from relativistic electrons spiralling in magnetic fields. Radio engineers use circular polarisation for satellite communication because it is insensitive to the relative orientation between transmitting and receiving antennas.