
Polarization is the orientation of the electric field vector of a light wave or other electromagnetic radiation.Light is a wave, and it can be imagined as a rope being shaken. Usually the rope oscillates in all directions, but if passed through a narrow fence, only oscillations along the slits remain. Polarized light is like that: it 'vibrates' strictly in one plane. Polarizing glasses work like such a fence: they block glare from water or asphalt—those horizontal oscillations that interfere with vision.
Étienne-Louis Malus discovered polarization by reflection in 1808, while observing light through a calcite crystal from the window of his home in Paris. In the 1810s, Augustin Fresnel and François Arago supplemented the wave theory of light with transverse oscillations and investigated the interference of polarized rays. James Clerk Maxwell in 1865 derived equations that explained polarization as the directionality of the electromagnetic field vectors. Quantum electrodynamics later linked polarization to photon spin, and Alain Aspect in 1982 conducted the famous experiment with polarization-entangled photons, violating Bell's inequalities.
According to Maxwell's equations, an electromagnetic wave consists of mutually perpendicular electric and magnetic fields oscillating in phase. The type of polarization is determined by the trajectory of the end of the E vector: if it oscillates along a line—linear polarization; if it rotates with constant amplitude—circular; the general case is elliptical. The intensity of light transmitted through a polarizer is described by Malus's law: I = I₀ cos²θ. Wave plates introduce a phase shift between orthogonal components, changing the polarization type. In quantum optics, a single photon exists in a superposition of two basis states, and measurement is projective and described by density matrices.
Bees and many insects see the polarization of the sky even in cloudy weather and use it for navigation. And mantis shrimp distinguish far more polarization shades than humans, helping them hunt and communicate.
| V_dep | variable | Depolarizing field voltage — voltage volt |
| P | variable | Polarization of the dielectric — polarization coulomb per metre squared |
| d | variable | Thickness of the dielectric film — thickness metre |
| ε₀ | constant | Permittivity of free space, a fundamental constant — vacuum permittivity = 8.8541878128e-12 farad per metre |
| εᵣ | constant | Dimensionless ratio of the material's permittivity to vacuum permittivity — relative permittivity |
| A | variable | Polarization vector — polarization vector |
| Δ | variable | Amplitude of the field — amplitude volt per metre |
| e_x | variable | Unit vector along x-axis — unit vector |
| e_y | variable | Unit vector along y-axis — unit vector |
| i | operator | Complex number with square -1 — imaginary unit |
| \theta | variable | Rotation angle of photon polarization — angle radian |
| g_{a\gamma} | variable | Axion-photon coupling constant — coupling constant reciprocal gev |
| \Delta a | variable | Difference in axion field value — axion field gev |
| P | variable | Degree of linear polarization — polarization degree |
| Q | variable | Stokes parameter Q (linear polarization) — stokes parameter watt per square metre |
| U | variable | Stokes parameter U (linear polarization) — stokes parameter watt per square metre |
| I | variable | Total intensity (Stokes I) — intensity watt per square metre |
| √ | operator | Takes the square root of the sum of squares — square root |
| / | operator | Divides the polarized magnitude by total intensity — division |
| z | variable | Input vector to be projected — vector |
| p | variable | Projected vector on the simplex — vector |
| proj | operator | Finds the closest point in the simplex to the input vector — projection operator |
| argmin | operator | Returns the value that minimizes the expression — argmin operator |
| ‖·‖ | operator | Computes the square root of the sum of squares — euclidean norm |
| Δθ | variable | Rotation angle of polarization plane — polarization rotation angle radian |
| λ | variable | Wavelength of light — wavelength metre |
| RM | constant | Rotation measure, proportional to integrated electron density times magnetic field along the line of sight — rotation measure = varies (e.g., 0.812 rad m^-2 for typical radian per metre squared |




















