Methods to manipulate and measure the polarization state of light or waves.Polarization control techniques are methods for generating, manipulating, and measuring the polarization state of light or other waves. Polarization describes the orientation of the electric field oscillation in a wave, and controlling it is essential for many technologies, from LCD displays to quantum communication. These techniques range from simple polarizers and waveplates to advanced adaptive optics that correct polarization distortions in real time.
The first polarizing devices were invented by Étienne-Louis Malus in 1808, who discovered polarization by reflection; the mathematical framework was developed by George Stokes in 1852.
Polarization is manipulated using birefringent materials (which have different refractive indices for different polarizations), chiral structures, or metamaterials that rotate or convert polarization states. Measurement typically involves splitting the beam into orthogonal components and comparing their intensities. Modern techniques use spatial light modulators or machine learning algorithms to reconstruct the full polarization state from a few intensity measurements, even when the signal is extremely weak — as in the case of detecting a handful of photons.
Used in optical communication to increase data capacity, in remote sensing to study atmospheric aerosols, in astronomy to map magnetic fields, and in quantum key distribution where polarization encodes secure information.
Some species of mantis shrimp can see circularly polarized light — a capability humans can only achieve with specialized optical instruments — and they use it to communicate with each other.
| \theta | variable | Polar angle on the Bloch sphere — polar angle radian |
| \phi | variable | Azimuthal angle on the Bloch sphere — azimuthal angle radian |
| |\theta,\phi\rangle | variable | Quantum state on the Bloch sphere — quantum state |
| |0\rangle | variable | Computational basis state 0 — basis state |
| |1\rangle | variable | Computational basis state 1 — basis state |
| DM | variable | Dispersion measure — dispersion measure parsec per cubic centimetre |
| n_e | variable | Electron number density — electron number density per cubic metre |
| l | variable | Path length along line of sight — length metre |
| ∫ | operator | Integration along the line of sight — integral |
| \tilde{\mu} | variable | Corrected distance modulus or magnitude — distance modulus |
| \mu | variable | Original distance modulus or magnitude — distance modulus |
| A_D | variable | Amplitude of dipole anisotropy — dimensionless |
| \hat{n} | variable | Unit vector in the direction of observation — direction |
| \hat{p} | variable | Unit vector pointing toward the dipole axis — direction |
| \cdot | operator | Scalar product of two vectors — dot product |
| 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 |
| 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 |









