concept

polarization

Polarization is the orientation of the electric field vector of a light wave or other electromagnetic radiation.
38 related articles · 6 formulas · 1 who worked here

Description

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.

History

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.

How it works

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.

Fun fact

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.

Concept graph →

Formulas

$$V_{\text{dep}} = \frac{P d}{\varepsilon_0 \varepsilon_r}$$
Voltage opposing polarization in a dielectric film of thickness d.
What is in the formula
V_depvariableDepolarizing field voltage — voltage volt
PvariablePolarization of the dielectric — polarization coulomb per metre squared
dvariableThickness of the dielectric film — thickness metre
ε₀constantPermittivity of free space, a fundamental constant — vacuum permittivity = 8.8541878128e-12 farad per metre
εᵣconstantDimensionless ratio of the material's permittivity to vacuum permittivity — relative permittivity
v_{{dep}}=\frac{pd}{\varepsilon_0\varepsilon_r} · 2606.23508
$$\mathbf{A} = \frac{\Delta}{\sqrt{2}} (\mathbf{e}_x + i \mathbf{e}_y)$$
Normalized vector representing right-hand circular polarization.
What is in the formula
AvariablePolarization vector — polarization vector
ΔvariableAmplitude of the field — amplitude volt per metre
e_xvariableUnit vector along x-axis — unit vector
e_yvariableUnit vector along y-axis — unit vector
ioperatorComplex number with square -1 — imaginary unit
a=\frac{δ}{\sqrt{2}}(e_x+ie_y) · 2606.28306
$$\theta = \frac{g_{a\gamma}}{2} \Delta a$$
Axion field difference rotates photon polarization.
What is in the formula
\thetavariableRotation angle of photon polarization — angle radian
g_{a\gamma}variableAxion-photon coupling constant — coupling constant reciprocal gev
\Delta avariableDifference in axion field value — axion field gev
θ_a(t_{\rmobs})=\frac{g_{aγ}}{2}[a(t_{\rmobs},{x}_{\rmobs})-a(t_{\rmem},{x}_{\rmem})] · 2607.04550
$$P = \frac{\sqrt{Q^2 + U^2}}{I}$$
Measure of linearly polarized intensity relative to total intensity.
What is in the formula
PvariableDegree of linear polarization — polarization degree
QvariableStokes parameter Q (linear polarization) — stokes parameter watt per square metre
UvariableStokes parameter U (linear polarization) — stokes parameter watt per square metre
IvariableTotal intensity (Stokes I) — intensity watt per square metre
√operatorTakes the square root of the sum of squares — square root
/operatorDivides the polarized magnitude by total intensity — division
p=\frac{\sqrt{q^2+u^2}}{f} · 2607.16557v1
$$\operatorname{proj}_{\Delta^{K-1}}(\mathbf{z}) = \arg\min_{\mathbf{p} \in \Delta^{K-1}} \|\mathbf{p} - \mathbf{z}\|^2$$
Projects a vector onto the probability simplex with sparsity.
What is in the formula
zvariableInput vector to be projected — vector
pvariableProjected vector on the simplex — vector
projoperatorFinds the closest point in the simplex to the input vector — projection operator
argminoperatorReturns the value that minimizes the expression — argmin operator
‖·‖operatorComputes the square root of the sum of squares — euclidean norm
\operatorname{sparsemax}({z})=\arg\min_{{p}\inδ^{k-1}}\|{p}-{z}\|^2 · 2607.00004
$$\Delta\theta = \mathrm{RM} \cdot \lambda^2$$
Rotation of polarization angle proportional to wavelength squared.
What is in the formula
ΔθvariableRotation angle of polarization plane — polarization rotation angle radian
λvariableWavelength of light — wavelength metre
RMconstantRotation 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
δθ={rm}*λ^2 · 2604.27480

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