Linear polarization and polarizers

Light as a transverse wave

Electromagnetic waves are transverse. In a plane light wave, the electric field, magnetic field, and direction of propagation are mutually perpendicular. Polarization describes the direction in which the electric field oscillates.

For a wave traveling in the x-direction, a linearly polarized electric field might be

ec{E}(x,t)=E_0cos(kx-omega t)hat{y}

In this case, the electric field always points along the y-direction, though its magnitude and sign oscillate.

Linear polarization

Light is linearly polarized when its electric field oscillates along a fixed line in the plane perpendicular to propagation. Vertical polarization, horizontal polarization, and any diagonal direction are possible.

Two perpendicular polarization directions can be treated like vector components. A linearly polarized wave at angle $heta$ to a chosen axis has component

$E_{parallel}=E_0cos heta$

along that axis.

Unpolarized light

Many ordinary light sources are unpolarized or randomly polarized. The electric field direction changes rapidly and randomly because light is emitted by many independent atoms or molecules.

Sunlight, incandescent light, and many LEDs are approximately unpolarized unless modified by scattering, reflection, or filters.

Unpolarized light can be thought of as containing equal average intensities in all transverse polarization directions.

Polarizers

A linear polarizer transmits the component of electric field along its transmission axis and absorbs or blocks the perpendicular component. If unpolarized light of intensity $I_0$ passes through an ideal polarizer, the transmitted intensity is

I=rac{1}{2}I_0

The transmitted light is linearly polarized along the polarizer's axis.

Crossed polarizers

If linearly polarized light passes through a second polarizer whose axis is perpendicular to the first, ideally no light is transmitted. The polarizers are crossed.

In practice, real polarizers are imperfect and may transmit a tiny amount. Still, crossed polarizers can produce very strong extinction.

Polarization by scattering

Scattering can polarize light. Sunlight scattered by molecules in the atmosphere becomes partially polarized. This is why polarized sunglasses can darken parts of the sky depending on viewing direction.

The degree and direction of polarization depend on the scattering geometry.

Polarization by reflection

Reflected light can be partially polarized. Glare from horizontal surfaces such as water, roads, or glass often has strong horizontal polarization. Polarized sunglasses reduce glare by blocking much of this horizontally polarized light.

This effect is described more precisely by Brewster's angle.

Applications

Polarization is used in sunglasses, photography, LCD screens, stress analysis in transparent materials, 3D movies, optical communication, microscopy, and quantum optics. Because polarization is a controllable property of light, it can carry information and reveal material structure.

The big idea

Polarization describes the orientation of light's electric field. Linear polarizers select one field component, turning unpolarized or mixed light into linearly polarized light. Since light is transverse, polarization is a fundamental wave property with many practical and scientific uses.