Polarization of Light

Tilt your head while wearing polarizing sunglasses and the glare from a wet road brightens and fades. Light has a hidden property that our eyes can’t sense directly: the direction in which its electric field points.

Linearly polarized light#

Light travelling along x has its electric field somewhere in the y–z plane, perpendicular to the motion. If the field at a point always stays along one fixed direction, say y, the light is linearly polarized (also called plane polarized) along y.

Unpolarized light#

One atom in one burst emits light with a fixed field direction. But in a lamp, a candle or the sun, countless atoms emit independently with random field directions, so the resulting field changes direction randomly and rapidly. This is unpolarized light, and it is what ordinary sources give.

Describing every case with two components

Split the field into y and z components with some phase difference δ:

• δ changes randomly: the direction of E wanders randomly. Unpolarized.
• δ = 0 or π: E_z/E_y is constant, so E stays along one line. Linearly polarized.
• δ = π/2 and E₁ = E₂: the field has constant size and its tip turns in a circle at angular speed ω. Circularly polarized.
• δ = π/2 and E₁ ≠ E₂: the tip traces an ellipse. Elliptically polarized.

Polaroids#

A device that produces polarized light from unpolarized light is a polarizer. A common one is the polaroid, a plastic sheet containing long, aligned chains of hydrocarbon molecules. At optical frequencies these chains conduct: the field component along them drives currents and is absorbed, while the component perpendicular to them passes. That perpendicular direction is the sheet’s transmission axis. Light leaving a polaroid is linearly polarized along its axis.

Malus’ law

Send linearly polarized light into a polaroid. Along the axis, it all passes; perpendicular to it, none does. At an angle θ, only the component E cos θ gets through, so the intensity (∝ E²) is

Unpolarized light averages cos²θ over all directions, so a single polaroid passes exactly half of it.

Polarization by reflection#

Light from air strikes a transparent surface. The incident, reflected and refracted rays lie in one plane, the plane of incidence. Split the field of unpolarized incident light into a part in this plane and a part perpendicular to it. The perpendicular part is reflected more strongly, so reflected light is partly polarized, and the refracted light is correspondingly richer in the in-plane part.

At one special angle the in-plane part is not reflected at all:

The refracted light is never completely polarized.

Polarization by scattering#

Light scattered by small particles is partially polarized, so the blue light of the sky is partially polarized. Our eyes can’t tell, but bees can: Karl von Frisch showed over years of experiments that bees sense both whether light is polarized and its direction of polarization, and use the sky’s pattern to navigate.