The polarization of light

§ 1 The natural and polarized light

The emission of a photon of light is due to the transition of an electron from the excited state to the ground. The electromagnetic waves emitted by this transition is transverse, that is a vector
 and  are mutually perpendicular and perpendicular to the direction of propagation. Oscillations of the vector пare in the same plane. Light, in which vector  oscillates in one direction is called a plane-polarized light (or electromagnetic wave). Called polarized light, in which the direction of oscillation of the vector  

are ordered in some way.

Light is electromagnetic radiation of the total set of atoms. Atoms emit light waves independently of each other, so the light wave emitted by the body as a whole, is characterized by all sorts of vibrations of the light vector .equally. Light with all kinds of equally probable orientations vectoris natural. Light, which has a preferred direction of oscillation of the vector  and small amplitude oscillations of the vector in the other direction is a partially polarized. In plane polarized light plane that varies vector ,called the plane of polarization, plane, which varies vector ,called the plane of oscillation.

Vector  is a light vector, because the action of light on the matter of primary importance is the electric component of the wave field acting on the electrons in the atoms of the substance.
A distinction is also elliptically polarized light: the propagation of electrically polarized light vector
 describes an ellipse, and circularly polarized light (a special case of elliptically polarized light) - a vector describes a circle (compare with the addition of perpendicular oscillations are possible: straight line, an ellipse and a circle).


The degree of polarization is the quantity

where Imax and Imin - maximum and minimum components of the light intensity corresponding to two mutually perpendicular components of the vector   (ie, Ех  and Еу - components). For the plane of polarized light Еу = Е, Ех = 0, so P = 1. For natural light Еу = Ех = Е and Р = 0. For partially polarized light Еу = Е, Ех = (0...1)Еу, hence 0 < P <1.

If the vector into elliptically polarized light is rotated when the light propagates in a clockwise direction, the polarization is called right - against the left. In elliptically polarized light vibrations completely ordered. For elliptically polarized light concept of the degree of polarization is not applicable, so that P = 1 always.

§ 2 The analysis of polarized light by reflection and refraction.

Brewster's law. Malus law

Most simply polarized light can be obtained from natural light by reflection of light waves from the boundary between two dielectrics.

If natural light is incident on the boundary between two dielectrics (eg, air-to-glass), then part of it is reflected and part is refracted and propagates in the second medium.

Brewster's law:

At an angle of incidence equal to the Brewster angle іBr: 1. reflected from the boundary between two dielectric beam is completely polarized in the plane perpendicular to the plane of incidence, 2. the degree of polarization of the refracted beam reaches a maximum value less than unity, 3. refracted ray is partially polarized in the plane of incidence, 4. the angle between the reflected and refracted rays is equal to 90°; 4. Brewster angle is equal to the tangent of the relative refractive index

-Brewster's law.

n12 - the refractive index of the second medium with respect to the first. The angle of incidence (reflection) - the angle between the incident (reflected) ray and the normal to the surface. The plane of incidence - the plane through the incident ray and the normal to the surface.
The degree of polarization of the refracted light can be significantly enhanced by repeated refraction of the condition of the light on the boundary between at the Brewster angle. If the glass (n = 1,53) the degree of polarization of the refracted beam is ≈ 15%, after refraction at 8-10 overlapping glass plates, the light will be released almost completely polarized - ream Stoletov.
Polarized light can be obtained from a natural with polarizers - anisotropic crystals transmit light in only one direction (Iceland spar, quartz, tourmaline).

Polarizer, which is analyzed in the plane of polarized light, is called by the analyzer.

If on analyzer is an incident plane polarized light amplitude Е0 and intensity I0 (), the plane of polarization is at an angle φ with the plane of the analyzer, the incident electromagnetic oscillation can be decomposed into two vibrations, with amplitudes and ,

parallel and perpendicular to the plane of the analyzer.

Pass through the analyzer component parallel to the plane of the analyzer, it is a constituent

,and the perpendicular component will be delayed by the analyzer. Then the intensity of the light transmitted through the analyzer is ():


The law of Malus

Malus law: The intensity of the light transmitted through the polarizer, is directly proportional to the product of the intensity of the incident plane polarized light I0 and to the square of the cosine of the angle between the plane of the incident light and the plane of the polarizer.

If on polarizer falls natural light, the intensity of light emerging from the polarizer is half Inat I0, and then from the analyzer exit

§3 Birefringence

All crystals, except for cubic crystals -isotropic crystals, are anisotropic, that is, the properties of crystals depend on the direction. The phenomenon of double refraction was first discovered in 1667 Bartalinom a crystal of Iceland spar (a form of
СаСО3). The phenomenon of of birefringence is: a beam of light falling on an anisotropic crystal, it is split into two beams: ordinary and extraordinary, propagating at different speeds  в различных направлениях.

Anisotropic crystals are divided into uniaxial and biaxial.

In uniaxial crystals in the same direction, called the optical axis, along which the distribution is no distinction between ordinary and extraordinary rays. Any line parallel to the direction of the optical axis will also be the optical axis. Any plane passing through the optical axis and the incident beam, called the principal or main section of the crystal planes.

Distinction between ordinary and extraordinary rays:
  1. ordinary ray obeys the laws of refraction extraordinary - no;
  2. ordinary beam is polarized perpendicular to the principal plane, the plane of polarization of the extraordinary ray is perpendicular to the plane polarized ordinary ray;

  3. Besides the optical axis of the ordinary and extraordinary rays are distributed in different directions. The refractive index n0 ordinary ray is constant in all directions, therefore, the phase velocity of the ordinary ray is constant in all directions. The refractive index of the extraordinary ray ne (vph.e.) depends on the direction.

    Speed ??difference between v0 and ve for all directions except the direction of the optical axis, causes the phenomenon of double refraction in uniaxial crystals. In biaxial crystals, there are two directions along which there is no double refraction.

    The concept of the ordinary and extraordinary rays takes place until the rays propagate in the crystal, when the output of the crystal these concepts have no meaning, that is, the rays differ only in the plane of polarization.

The nature of the birefringence due to the fact that the ordinary and extraordinary rays have different speeds, as well as   ,for the ordinary and extraordinary rays will have different refractive indices n0 and nе, and since  then we can say that the root cause of birefringence is the anisotropy of the dielectric constant of the crystal. Crystals in which vе  < v0 ( nе > n0)) called positive and who vе  > v0 (nе < n0) are called negative.

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