Polarization of Electromagnetic Waves |

**In General**
> see light; optics / electromagnetism.

* __Remark__: Unpolarized light must be polychromatic!

* __Malus' law__: The intensity of polarized light passing
through a linear polarizer decreases by a factor cos^{2}*α*;
> s.a. hidden variables.

* __Of sky light__: The scattering that causes the
blue sky (mostly single scattering) also polarizes it; To first approximation there are two
0-polarization points, the Sun and the anti-Sun, but double scattering causes them to split
vertically into two closely spaced points (Brewster and Babinet points, each of index 1/2).

* __Demonstration__: Black light sandwich –
a transparency foil between two polarizers, allows to see two index-1/2 singularities in
direction space.

@ __General references__:
Pye 00 [I];
Gamel & James PRA(12)-a1303
[degree of polarization, and degree of purity for two-level quantum systems];
Trippe JKAS(14)-a1401 [rev, and astronomy];
O'Shea et al a2010
[history, naked-eye visibility of polarization];
Goldberg et al a2011 [quantum theory].

@ __Stokes polarization parameters__:
Schaefer et al AJP(07)feb;
> s.a. gravitational-wave background.

@ __Polarization of skylight__: Smith AJP(07)jan [model];
Ropars et al CP(14) [and the sunstone as an ancient Viking navigational tool].

**Faraday Rotation** > s.a. cmb polarization.

* __Idea__: The rotation
of the plane of polarization of light going through a magnetic field (or
other medium); > s.a. electromagnetism
in curved spacetime.

* __Gravitational__: The rotation
of the plane of polarization of polarized electromagnetic radiation traveling
through a gravitational field; In the case of a gravitational wave, the effect
vanishes for localized (astrophysically generated) waves and is non-zero but
negligible for cosmological ones.

@ __General references__: Ganguly et al PRD(99) [degenerate relativistic];
Zavattini PRL(06)
+ pw(06)mar [observation, and axions];
Cornean & Nenciu JFA(09)-a0807 [thermodynamic limit];
Melrose ApJ(10)-a1010 [effect of magnetic-field reversals];
Oppermann et al A&A(15)-a1404 [extragalactic].

@ __Gravitational__: Perlick & Hasse CQG(93);
Sereno PRD(04);
Halilsoy & Gurtug PRD(07),
Faraoni NA(07)-a0709 [due to gravitational waves];
Schneiter et al a1812 [in the gravitational field of a laser beam].

**Other Effects**
> s.a. Coherence; earth [auroras].

* __Birefringence__: A polarization-dependent
doubling in photon propagation speed, or anisotropic index of refraction; It happens in material
media such as calcite, and in vacuum either as a quantum field theory effect in the presence
of strong electromagnetic fields, or in modified gravity theories such as bi-metric models and
Poincaré gauge theory; A similar effect can occur for gravitational waves; > s.a.
axions; finsler geometry;
modified electromagnetism; non-commutative
gauge theories; QCD phenomenology.

* __Dichroism__: Anisotropic absorption
of components of an electromagnetic wave; For example, by a grid of parallel conductors.

* __Optical activity__: The
rotation of the electric field of a plane wave traversing some materials (e.g., quartz).

@ __Optical activity__: Barbieri & Guadagnini NPB(04) [gravitational];
Agulló et al a1705-GRF [in a curved spacetime geometry, for quantum radiation].

@ __Birefringence, material medium__:
Ghosh & Fischer PRL(06)
+ pw(06)nov [in a chiral liquid];
De Lorenci & Ford a1903 [quantum induced, non-linear materials].

@ __Birefringence, vacuum__: Chen et al MPLA(07)he/06 [and vacuum dichroism, experimental searches];
Hattori & Itakura AP(13) [in strong magnetic fields];
Karbstein et al PRD(15)-a1507 [in strong inhomogeneous electromagnetic fields];
Mignani et al MNRAS(16)-a1610
+ news sn(16)dec [in X-rays from neutron stars];
Karbstein a1611-ln [pedagogical];
Schneider et al a1708 [and gravitational dynamics];
Wang a1712 [of gravitational waves].

@ __Birefringence, cosmological__: Exirifard PLB(11)-a1010 [theory];
di Serego Alighieri a1011-proc [methods, rev];
Yadav et al PRD(12)-a1207 [with cmb],
Gruppuso et al JCAP(16)-a1509 [constraints from Planck and Bicep2/Keck data];
Duval & Schücker PRD(17)-a1610,
a1804-conf [in Robertson-Walker cosmologies];
Whittaker et al a1702/MNRAS [using resolved radio sources];
> s.a. cmb polarization.

@ __Experiments and examples__:
Ouseph et al AJP(01)nov [polarization by reflection];
Holleczek et al OE(11)-a1012 [cylindrically polarized states of light].

@ __Related topics__: Berry & Dennis PRS(01) [polarization singularities in vector waves];
news sn(10)mar ["superchiral" light];
Shukla & Prakash MPLB(16)-a1610 [polarization squeezing].

> __In gravitation and cosmology__:
see kaluza-klein phenomenology; non-commutative physics;
Non-Symmetric Gravity; gravitational phenomenology;
observational cosmology; photon phenomenology in quantum
gravity; tests of general relativity with light;
tests of the equivalence principle.

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