Editing Optics (section)

====Polarisation <span class="anchor" id="Polarization"></span>====
{{Main|Polarisation (waves)}}

Polarisation is a general property of waves that describes the orientation of their oscillations. For [[transverse wave]]s such as many electromagnetic waves, it describes the orientation of the oscillations in the plane perpendicular to the wave's direction of travel. The oscillations may be oriented in a single direction ([[linear polarisation]]), or the oscillation direction may rotate as the wave travels ([[circular polarisation|circular]] or [[elliptical polarisation]]). Circularly polarised waves can rotate rightward or leftward in the direction of travel, and which of those two rotations is present in a wave is called the wave's [[polarimetry|chirality]].{{sfnmp |1a1=Hecht|1y=2017|1pp=333–334 |2a1=Young|2a2=Freedman|2y=2020|2pp=1083,1118}}

The typical way to consider polarisation is to keep track of the orientation of the electric field [[vector (geometry)|vector]] as the electromagnetic wave propagates. The electric field vector of a plane wave may be arbitrarily divided into two perpendicular [[vector components|components]] labeled {{mvar|x}} and {{mvar|y}} (with {{math|'''z'''}} indicating the direction of travel). The shape traced out in the x-y plane by the electric field vector is a [[Lissajous curve|Lissajous figure]] that describes the ''polarisation state''.{{sfnp|Hecht|2017|p=336}} The following figures show some examples of the evolution of the electric field vector (blue), with time (the vertical axes), at a particular point in space, along with its {{mvar|x}} and {{mvar|y}} components (red/left and green/right), and the path traced by the vector in the plane (purple): The same evolution would occur when looking at the electric field at a particular time while evolving the point in space, along the direction opposite to propagation.

<div style="float:left;width:170px">
[[File:Polarisation (Linear).svg|class=skin-invert-image|center|Linear polarisation diagram]]
{{center|''Linear''}}
</div>
<div style="float:left;width:170px">
[[File:Polarisation (Circular).svg|class=skin-invert-image|center|Circular polarisation diagram]]
{{center|''Circular''}}
</div>
<div style="float:left;width:170px">
[[File:Polarisation (Elliptical).svg|class=skin-invert-image|center|Elliptical polarisation diagram]]
{{center|''Elliptical polarisation''}}
</div>
{{Clear}}

In the leftmost figure above, the {{mvar|x}} and {{mvar|y}} components of the light wave are in phase. In this case, the ratio of their strengths is constant, so the direction of the electric vector (the vector sum of these two components) is constant. Since the tip of the vector traces out a single line in the plane, this special case is called linear polarisation. The direction of this line depends on the relative amplitudes of the two components.{{sfnmp|1a1=Hecht|1y=2017|1pp=330–332|2a1=Young|2a2=Freedman|2y=2020|2p=1123}}

In the middle figure, the two orthogonal components have the same amplitudes and are 90° out of phase. In this case, one component is zero when the other component is at maximum or minimum amplitude. There are two possible phase relationships that satisfy this requirement: the {{mvar|x}} component can be 90° ahead of the {{mvar|y}} component or it can be 90° behind the {{mvar|y}} component. In this special case, the electric vector traces out a circle in the plane, so this polarisation is called circular polarisation. The rotation direction in the circle depends on which of the two-phase relationships exists and corresponds to ''right-hand circular polarisation'' and ''left-hand circular polarisation''.{{sfnmp|1a1=Hecht|1y=2017|1pp=333–334|2a1=Young|2a2=Freedman|2y=2020|2p=1123}}

In all other cases, where the two components either do not have the same amplitudes and/or their phase difference is neither zero nor a multiple of 90°, the polarisation is called elliptical polarisation because the electric vector traces out an [[ellipse]] in the plane (the ''polarisation ellipse'').{{sfnmp|1a1=Hecht|1y=2017|1pp=334–335|2a1=Young|2a2=Freedman|2y=2020|2p=1124}} This is shown in the above figure on the right. Detailed mathematics of polarisation is done using [[Jones calculus]] and is characterised by the [[Stokes parameters]].{{sfnp|Hecht|2017|pp=379–383}}

=====Changing polarisation=====
Media that have different indexes of refraction for different polarisation modes are called ''[[birefringence|birefringent]]''.{{sfnp|Young|Freedman|2020|p=1124}} Well known manifestations of this effect appear in optical [[wave plate]]s/retarders (linear modes) and in [[Faraday rotation]]/[[optical rotation]] (circular modes).{{sfnp|Hecht|2017|pp=367,373}} If the path length in the birefringent medium is sufficient, plane waves will exit the material with a significantly different propagation direction, due to refraction. For example, this is the case with macroscopic crystals of [[calcite]], which present the viewer with two offset, orthogonally polarised images of whatever is viewed through them. It was this effect that provided the first discovery of polarisation, by [[Erasmus Bartholinus]] in 1669. In addition, the phase shift, and thus the change in polarisation state, is usually frequency dependent, which, in combination with [[dichroism]], often gives rise to bright colours and rainbow-like effects. In [[mineralogy]], such properties, known as [[pleochroism]], are frequently exploited for the purpose of identifying minerals using polarisation microscopes. Additionally, many plastics that are not normally birefringent will become so when subject to [[mechanical stress]], a phenomenon which is the basis of [[photoelasticity]].{{sfnmp |1a1=Hecht|1y=2017|1p=372 |2a1=Young|2a2=Freedman|2y=2020|2pp=1124–1125}} Non-birefringent methods, to rotate the linear polarisation of light beams, include the use of prismatic [[polarisation rotator]]s which use total internal reflection in a prism set designed for efficient collinear transmission.<ref>{{cite book |author=F.J. Duarte |author-link=F. J. Duarte |title=Tunable Laser Optics |edition=2nd |publisher=CRC |year=2015 |location=New York |pages=117–120 |isbn=978-1-4822-4529-5 |url=http://www.tunablelaseroptics.com |url-status=live |archive-url=https://web.archive.org/web/20150402145942/https://www.tunablelaseroptics.com/ |archive-date=2015-04-02 }}</ref>

[[File:Malus law.svg|class=skin-invert-image|right|thumb|upright=1.6|A polariser changing the orientation of linearly polarised light. In this picture, {{math|1= ''θ''{{sub|1}} – ''θ''{{sub|0}} = ''θ''{{sub|i}}}}.]]

Media that reduce the amplitude of certain polarisation modes are called ''dichroic'', with devices that block nearly all of the radiation in one mode known as ''polarising filters'' or simply "[[polariser]]s". Malus' law, which is named after [[Étienne-Louis Malus]], says that when a perfect polariser is placed in a linear polarised beam of light, the intensity, {{mvar|I}}, of the light that passes through is given by

<math display="block"> I = I_0 \cos^2 \theta_\mathrm{i} ,</math>
where {{math|''I''{{sub|0}}}} is the initial intensity, and {{math|''θ''{{sub|i}}}} is the angle between the light's initial polarisation direction and the axis of the polariser.{{sfnmp |1a1=Hecht|1y=2017|1p=338 |2a1=Young|2a2=Freedman|2y=2020|2pp=1119–1121}}

A beam of unpolarised light can be thought of as containing a uniform mixture of linear polarisations at all possible angles. Since the average value of {{math|cos{{sup|2}} ''θ''}} is 1/2, the transmission coefficient becomes

<math display="block"> \frac {I}{I_0} = \frac {1}{2}\,.</math>

In practice, some light is lost in the polariser and the actual transmission of unpolarised light will be somewhat lower than this, around 38% for Polaroid-type polarisers but considerably higher (>49.9%) for some birefringent prism types.{{sfnp|Hecht|2017|pp=339–342}}

In addition to birefringence and dichroism in extended media, polarisation effects can also occur at the (reflective) interface between two materials of different refractive index. These effects are treated by the [[Fresnel equations]]. Part of the wave is transmitted and part is reflected, with the ratio depending on the angle of incidence and the angle of refraction. In this way, physical optics recovers [[Brewster's angle]].{{sfnp|Hecht|2017|pp=355–358}} When light reflects from a [[Thin-film optics|thin film]] on a surface, interference between the reflections from the film's surfaces can produce polarisation in the reflected and transmitted light.

=====Natural light=====
[[File:CircularPolarizer.jpg|right|thumb|upright=1.8|The effects of a [[photographic filter#Polarizer|polarising filter]] on the sky in a photograph. Left picture is taken without polariser. For the right picture, filter was adjusted to eliminate certain polarisations of the scattered blue light from the sky.]]
Most sources of electromagnetic radiation contain a large number of atoms or molecules that emit light. The orientation of the electric fields produced by these emitters may not be [[statistical correlation|correlated]], in which case the light is said to be ''unpolarised''. If there is partial correlation between the emitters, the light is ''partially polarised''. If the polarisation is consistent across the spectrum of the source, partially polarised light can be described as a superposition of a completely unpolarised component, and a completely polarised one. One may then describe the light in terms of the [[degree of polarisation]], and the parameters of the polarisation ellipse.{{sfnp|Hecht|2017|p=336}}

Light reflected by shiny transparent materials is partly or fully polarised, except when the light is normal (perpendicular) to the surface. It was this effect that allowed the mathematician Étienne-Louis Malus to make the measurements that allowed for his development of the first mathematical models for polarised light. Polarisation occurs when light is scattered in the [[earth's atmosphere|atmosphere]]. The scattered light produces the brightness and colour in clear [[sky|skies]]. This partial polarisation of scattered light can be taken advantage of using polarising filters to darken the sky in [[science of photography|photographs]]. Optical polarisation is principally of importance in [[chemistry]] due to [[circular dichroism]] and optical rotation (''circular birefringence'') exhibited by [[optical activity|optically active]] ([[chirality (chemistry)|chiral]]) [[molecules]].{{sfnp|Hecht|2017|pp=353–356}}