Glossary entry

Polarization states

The ways the electric field of a light wave can move in the plane across the beam: along a fixed line (linear, or plane, polarization), around a circle (circular) or around an ellipse (elliptical), or at random (unpolarized). Every fully polarized state is two orthogonal components with a particular amplitude ratio and phase difference.

Optics fundamentalsUpdated October 2026

A light wave's polarization state describes how its electric field moves in the plane transverse to the beam. There are three fully polarized states. In linear polarization, also called plane polarization, the field oscillates back and forth along one fixed line. In circular polarization the field keeps a constant length and rotates through a full turn once per optical cycle, every 2.1 fs for 633 nm light. In elliptical polarization, the general case, the tip of the field traces an ellipse. Light whose field direction changes randomly faster than it can be measured, such as sunlight, is unpolarized, and most real light is partially polarized, a mixture of a polarized part and an unpolarized one. The polarization entry covers the physics and the optics that control it; this entry sets out the states themselves.

Two components and a phase

Any fully polarized wave traveling along $z$ can be split into two orthogonal components:

\begin{aligned} E_{x} & = E_{0 x} \cos (k z - ω t), \\ E_{y} & = E_{0 y} \cos (k z - ω t + δ) . \end{aligned}

The amplitude ratio $E_{0 y} / E_{0 x}$ and the phase difference $δ$ fix the state:

$δ = 0$ or $180 °$ : linear, at the angle $\arctan (E_{0 y} / E_{0 x})$ , or its mirror image, from the $x$ axis.
$E_{0 x} = E_{0 y}$ and $δ = \pm 90 °$ : circular.
anything else: elliptical.

The ellipse traced by the field has its major axis at an azimuth $ψ$ and an ellipticity angle $χ$ , with $\tan χ$ equal to the ratio of the minor to the major axis:

\begin{aligned} \tan 2 ψ & = \frac{2 E_{0 x} E_{0 y} \cos δ}{E_{0 x}^{2} - E_{0 y}^{2}}, \\ \sin 2 χ & = - \frac{2 E_{0 x} E_{0 y} \sin δ}{E_{0 x}^{2} + E_{0 y}^{2}} . \end{aligned}

Handedness needs a convention, and two opposite ones are in use. This site follows the optics convention of Hecht and of Born and Wolf, as the Jones vectors and Stokes parameters entries do: light is right-handed when its field rotates clockwise as seen by an observer looking toward the source. With the phase written as $k z - ω t$ as above, right-handed light has $δ$ between 0 and $- 180 °$ and $χ > 0$ ; the minus sign in the formula for $χ$ comes from that way of writing the phase, and it disappears in texts that write $ω t - k z$ .

The standard states

State	Jones vector	Normalized Stokes $(s_{1}, s_{2}, s_{3})$
Horizontal linear	$(1, 0)$	$(1, 0, 0)$
Vertical linear	$(0, 1)$	$(- 1, 0, 0)$
Linear at +45°	$(1, 1) / \sqrt{2}$	$(0, 1, 0)$
Linear at −45°	$(1, - 1) / \sqrt{2}$	$(0, - 1, 0)$
Right circular	$(1, - i) / \sqrt{2}$	$(0, 0, 1)$
Left circular	$(1, i) / \sqrt{2}$	$(0, 0, - 1)$
Right elliptical, axes along $x$ and $y$	$(\cos χ, - i \sin χ)$	$(\cos 2 χ, 0, \sin 2 χ)$

The Jones vectors use the same $e^{i (k z - ω t)}$ convention as the Jones vectors entry. For an ellipse with its major axis at azimuth $ψ$ , the normalized Stokes vector is $(\cos 2 χ \cos 2 ψ, \cos 2 χ \sin 2 ψ, \sin 2 χ)$ . On the Poincaré sphere of the Stokes parameters, linear states lie on the equator, the circular states at the poles, and elliptical states everywhere else; orthogonal states sit at opposite points.

Linear (plane) polarization

The field oscillates along one line, and together with the beam direction it defines a fixed plane, which is the origin of the older name plane polarization. Most lasers emit linearly polarized light, a sheet or wire-grid polarizer produces it from any source, and reflection produces it too: at Brewster's angle, 56.3° for glass of index 1.5, the reflected light is entirely s-polarized, which is why polarizing sunglasses, whose axis is vertical, cut glare from water and roads. A linear polarizer at angle $θ$ to linearly polarized light transmits $\cos^{2} θ$ of it (Malus's law).

Circular polarization

Equal components 90° out of phase give a field of constant length that rotates at the optical frequency, tracing a helix along the beam. A quarter-wave plate with its fast axis at 45° to linearly polarized light produces it, and the sign of that angle sets the handedness. Reflection from a mirror at normal incidence reverses the handedness, which is how a linear polarizer followed by a quarter-wave plate blocks light returning from a mirror: the returning light passes the plate again and arrives at the polarizer linearly polarized at 90° to it. Circular polarization separates the two images in polarized 3D cinema, and each circularly polarized photon carries an angular momentum of $\pm ℏ$ .

Elliptical polarization

The general state, and the one light usually takes after passing through anything birefringent. Linearly polarized light entering a quarter-wave plate at an angle $θ$ to its fast axis, with $θ$ between 0 and 45°, leaves elliptically polarized, with the ellipse's axes along the plate's axes and an axis ratio of $\tan θ$ , so that $∣ χ ∣ = θ$ ; it is right-handed when the input polarization lies clockwise of the fast axis as seen looking toward the source. Oblique reflection from a metal turns linear light elliptical unless it is purely s- or p-polarized, and ellipsometry measures surfaces and thin films by such changes. In an ordinary single-mode fiber, random birefringence turns a launched linear state into an elliptical one that changes along the fiber and with temperature and bending; polarization-maintaining fiber holds a linear state by building in strong birefringence.

Unpolarized and partially polarized light

In unpolarized light the field direction changes randomly on a time scale shorter than the measurement, so no polarizer orientation passes more than any other: an ideal polarizer passes half of it at every angle. Sunlight, incandescent lamps and most LEDs are unpolarized or nearly so. Partially polarized light is the sum of an unpolarized part and a fully polarized part, and its degree of polarization, the fraction of the power that is polarized, runs from 0 to 1. The Stokes parameters describe it; a Jones vector cannot.

A polarizer alone cannot tell circularly polarized light from unpolarized light, since both pass half their power at every angle. A quarter-wave plate in front of the polarizer can: it turns circular light into linear light, which the polarizer then extinguishes at one angle, while unpolarized light stays unpolarized. A polarimeter makes this measurement in full and reports the Stokes parameters, the degree of polarization, and the azimuth and ellipticity of the polarized part.

Polarization at interfaces and in fibers

Reflection and refraction at an interface treat the two linear states differently: the s component (field perpendicular to the plane of incidence) and the p component (field in it) have different Fresnel coefficients, and p-polarized light is not reflected at all at Brewster's angle. In waveguides the corresponding states are the TE and TM modes. In fiber communication, coherent transmission carries two independent signals on two orthogonal states of the same wavelength (polarization-division multiplexing) and separates them in the receiver's digital signal processing, while polarization-mode dispersion and polarization-dependent loss are the impairments that the differences between states cause.

Common questions

What are the types of polarization of light?

Linear (plane), circular and elliptical for fully polarized light, with circular split into right- and left-handed; light can also be unpolarized or partially polarized. Linear and circular are both special cases of elliptical polarization.

What is plane-polarized light?

Another name for linearly polarized light: the field oscillates along one fixed direction, so the field and the direction of travel lie in one plane.

What is the difference between circular and elliptical polarization?

In circular polarization the two orthogonal components have equal amplitudes and differ in phase by exactly 90°, so the field keeps a constant length as it rotates. If the amplitudes differ, or the phase differs from 90°, the field's length varies as it turns and its tip traces an ellipse, except at a phase of 0° or 180°, where the ellipse collapses to a line.

Can polarized light become unpolarized?

Not through a uniform optic acting on a single-frequency beam: a waveplate or rotator changes one polarized state into another. Light is depolarized when different parts of it are given different states and then averaged: over time by a polarization scrambler, over wavelength for broadband light by a thick birefringent plate, or over position and direction by multiple scattering.

References: M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge University Press, 1999), ch. 1. E. Hecht, Optics, 5th ed. (Pearson, 2017), ch. 8. D. H. Goldstein, Polarized Light, 3rd ed. (CRC Press, 2011).