Polarization (waves)

In circular or elliptical polarization, the fields rotate at a constant rate in a plane as the wave travels, either in the right-hand or in the left-hand direction.

[8] Polarization is an important parameter in areas of science dealing with transverse waves, such as optics, seismology, radio, and microwaves.

Incoherent states can be modeled stochastically as a weighted combination of such uncorrelated waves with some distribution of frequencies (its spectrum), phases, and polarizations.

In a more general formulation with propagation not restricted to the +z direction, then the spatial dependence kz is replaced by k→ ∙ r→ where k→ is called the wave vector, the magnitude of which is the wavenumber.

Knowing the propagation direction (+z in this case) and η, one can just as well specify the wave in terms of just ex and ey describing the electric field.

Even in isotropic media, so-called inhomogeneous waves can be launched into a medium whose refractive index has a significant imaginary part (or "extinction coefficient") such as metals;[clarification needed] these fields are also not strictly transverse.

Even in free space, longitudinal field components can be generated in focal regions, where the plane wave approximation breaks down.

An extreme example is radially or tangentially polarized light, at the focus of which the electric or magnetic field respectively is entirely longitudinal (along the direction of propagation).

Note that circular or elliptical polarization can involve either a clockwise or counterclockwise rotation of the field, depending on the relative phases of the components.

The special cases of linear and circular polarization correspond to an ellipticity ε of infinity and unity (or χ of zero and 45°) respectively.

The physical electric field, as the real part of the Jones vector, would be altered but the polarization state itself is independent of absolute phase.

When considering light that is propagating parallel to the surface of the Earth, the terms "horizontal" and "vertical" polarization are often used, with the former being associated with the first component of the Jones vector, or zero azimuth angle.

[17] Conversely, the two constituent linearly polarized states of unpolarized light cannot form an interference pattern, even if rotated into alignment (Fresnel–Arago 3rd law).

In a vacuum, the components of the electric field propagate at the speed of light, so that the phase of the wave varies in space and time while the polarization state does not.

As noted above, the instantaneous electric field is the real part of the product of the Jones vector times the phase factor

where g1 and g2 are complex numbers describing the phase delay and possibly the amplitude attenuation due to propagation in each of the two polarization eigenmodes.

Circular birefringence is also termed optical activity, especially in chiral fluids, or Faraday rotation, when due to the presence of a magnetic field along the direction of propagation.

In addition to birefringence and dichroism in extended media, polarization effects describable using Jones matrices can also occur at (reflective) interface between two materials of different refractive index.

Apart from providing information on sources of radiation and scattering, polarization also probes the interstellar magnetic field via Faraday rotation.

Polarizing sunglasses exploit this effect to reduce glare from reflections by horizontal surfaces, notably the road ahead viewed at a grazing angle.

The Pfund sky compass was used in the 1950s when navigating near the poles of the Earth's magnetic field when neither the sun nor stars were visible (e.g., under daytime cloud or twilight).

[38]: 67–69 The principle of liquid-crystal display (LCD) technology relies on the rotation of the axis of linear polarization by the liquid crystal array.

That polarized light passes through the actual liquid crystal layer which may be organized in pixels (for a TV or computer monitor) or in another format such as a seven-segment display or one with custom symbols for a particular product.

Displays based on this principle are widespread, and now are used in the vast majority of televisions, computer monitors and video projectors, rendering the previous CRT technology essentially obsolete.

In a totally different sense, polarization encoding has become the leading (but not sole) method for delivering separate images to the left and right eye in stereoscopic displays used for 3D movies.

However, circular polarization makes separation of the two images insensitive to tilting of the head, and is widely used in 3-D movie exhibition today, such as the system from RealD.

Although now obsolete, CRT computer displays suffered from reflection by the glass envelope, causing glare from room lights and consequently poor contrast.

Especially due to the presence of the ground, there are some differences in propagation (and also in reflections responsible for TV ghosting) between horizontal and vertical polarizations.

The effect of free electrons in the ionosphere, in conjunction with the earth's magnetic field, causes Faraday rotation, a sort of circular birefringence.

Sky polarization was thought to be perceived by pigeons, which was assumed to be one of their aids in homing, but research indicates this is a popular myth.

Circular polarization on rubber thread, converted to linear polarization
cross linear polarized
A "vertically polarized" electromagnetic wave of wavelength λ has its electric field vector E (red) oscillating in the vertical direction. The magnetic field B (or H ) is always at right angles to it (blue), and both are perpendicular to the direction of propagation ( z ).
Electric field oscillation
Animation showing four different polarization states and three orthogonal projections.
A circularly polarized wave as a sum of two linearly polarized components 90° out of phase
Electromagnetic vectors for E , B , and k with E = E ( x , y ) along with 3 planar projections and a deformation surface of total electric field. The light is always s -polarized in the xy -plane. θ is the polar angle of k and φ E is the azimuthal angle of E .
Color pattern of a plastic box showing stress-induced birefringence when placed in between two crossed polarizers .
Paths taken by vectors in the Poincaré sphere under birefringence. The propagation modes (rotation axes) are shown with red, blue, and yellow lines, the initial vectors by thick black lines, and the paths they take by colored ellipses (which represent circles in three dimensions).
A stack of plates at Brewster's angle to a beam reflects off a fraction of the s -polarized light at each surface, leaving (after many such plates) a mainly p -polarized beam.
Stress in plastic glasses
Photomicrograph of a volcanic sand grain ; upper picture is plane-polarized light, bottom picture is cross-polarized light, scale box at left-center is 0.25 millimeter.
Effect of a polarizer on reflection from mud flats. In the picture on the left, the horizontally oriented polarizer preferentially transmits those reflections; rotating the polarizer by 90° (right) as one would view using polarized sunglasses blocks almost all specularly reflected sunlight.
One can test whether sunglasses are polarized by looking through two pairs, with one perpendicular to the other. If both are polarized, all light will be blocked.
The effects of a polarizing filter (right image) on the sky in a photograph
Colored fringes in the Embassy Gardens Sky Pool when viewed through a polarizer, due to stress-induced birefringence in the skylight
Circular polarization through an airplane plastic window, 1989