polarizationvector

Polarization vector is a concept used in optics and electromagnetism to describe the orientation and phase of the electric field in a monochromatic plane wave. For a wave propagating in a specific direction, the electric field is transverse to the propagation direction, so the polarization vector lies in the plane perpendicular to the wavevector. In a complex representation, the electric field can be written as E(r,t) = Re{E0 e^{i(k·r − ωt)} ε̂}, where E0 is a complex amplitude and ε̂, often denoted as the polarization vector, encodes the relative amplitudes and phase between transverse components. If ε̂ is real, the polarization is linear; if ε̂ has a relative phase of ±π/2 between components, the polarization is circular or elliptical.

In practical terms, the polarization state is commonly described by the Jones vector J = [E_x; E_y], a two-component complex vector in a chosen transverse basis. The physical polarization is obtained from J by normalizing to a unit vector ε̂ = J/|J| for a pure (fully polarized) beam. Partially polarized light is described more fully by Stokes parameters, which relate to the Jones description but do not require a specific basis.

Common polarization states include linear polarization along a coordinate axis, and circular polarization with ε̂ ∝ (x̂ ± i ŷ)/√2. The polarization vector is central to applications in optical communications, imaging, and polarization-sensitive instrumentation, as well as to the design of polarizers, waveplates, and antenna systems. In related fields, a polarization vector can also refer to the polarization four-vector used to describe spin-1 particles in quantum field theory.