Chapter XIX Polarization of light

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Interference and diffraction of light are arguments for wave charactiristics of light. We know that there are two types of wave processes: transverse & longitutional waves →to what are light waves belong ? Study of polarization of light makes clear that This conclusion is in according to the concept that light waves are electromagnetic waves with a definte band of frequencies. Recall that electromagnetic waves are transervse waves in which e-vectors & m-vectors oscillate in such follwing directions...

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Nội dung Text: Chapter XIX Polarization of light

GENERAL PHYSICS III Optics & Quantum Physics
Chapter XIX Polarization of light §1. Natural and polarized light. Malus’s law §2. Polarization in reflection and refraction §3. Polarization by birefringent §4. Rotation of polarizing plane
Interference and diffraction of light are arguments for wave charactiristics of light. We know that there are two types of wave processes: transverse & longitutional waves → to what are light waves belong ? Study of polarization of light makes clear that light waves is transverse waves This conclusion is in according to the concept that light waves are electromagnetic waves with a definte band of frequencies. Recall that electromagnetic waves are transervse waves in which e-vectors & m-vectors oscillate in such follwing directions x z y
§1. Natural and polarized light: 1.1 Definitions: • Light waves emmitted from natural sources are from excited molecules or atoms. • The light waves emitted by any individual molecule can be linearly Natural (unpolarized) light ray polarized (definite in direction), but any natural light source consists of a very large number of molecules with random orientation → natural light is a random mixture of linearly polarized waves with all possible transvere directions. • Definitons: Polarized light → light waves that have oscillation direction oriented in any definite way Linearly (or planely) polarized light → oscillation of light vector ( E ) is in one plane only
Oscillation Light ray Oscillation plane → the plane in which plane the light vector E oscillates Polarization Polarization plane → the plane that plane is perpendicular to osc. plane (it is used rarely) 1.2 Polarizer: How can make a polarized light beam from natural light ? → using a polarizer There are some crystal materials that have dichroism, that is, a selective absorption: one of components of the light vector is absorbed much more strongly than the other Polarizing axis Polarizing axis a) b)
Therefore if a polarizer (polaroid) is illuminated by natural light → after polarizer there will be a linearly polarized light. The direction of E vector of transmitted light is parallel to the direction called polarizing axis of polarizer. A||=A.cos 1.3 Malus’s law: A Now we are interested in the light intensity after a polarizer, Polarizer if the incident light is natural: • Before P → I ~ A2 • After P → I’ = < I cos2> = I/2 (the average over all equi-probability direction) ( : the angle between the incident and transmitted light vectors) If we rotate the polarizer around the propagation direction → we don’t observe any variation in light intensity.
What happens when the I linearly polarized light I0 emerging from a polarizer passes through a second polaroid ? Analyzer Then I = I0 cos2 Polarizer This is Malus’s law Intensity of the  the angle between : transmitted light two polarizing axises Intensity of the incident linearly polarized light of polarizer and analyzer • Rotate the second polaroid → varies → variation of light intensity I is observed. • The second polaroid helps us know about is the incident light either natural or polarized → it is called analyzer.
1.4 Partially polarized light: We have known about linearly polarized light in which the light vector E oscillates in one definite direction. There is the case of polarized light in which the light vector E oscillates in different directions (that are all, of course, perpendicular to the propagation direction), but one direction predominates over all other → it is called partially polarized light. It can be considered as a mixing of natural and linearly polarized light. When a partially polarozed lighi transmits through an analyzer → the light intensity varies from Imax to Imin . One cycle of analyzer rotation the intensity has twice got maximum anf twice got minimum. It is useful to introduce the degree of polarization P : Imax - Imin P= Imax + Imin The limit cases: Natural light → Imax = Imin → P = 0; Linear polarized light → Imin = 0 → P = 1
1.5 Cicular and elliptical polarization: Consider two coherent linearly polarized waves, and their oscillation directions are perpendicular each to other: the first is along x-axis, the second – y-axis (xOy plane  the ray) We have The composition of two such waves is the vector E whose arrowhead draws an ellipse. → then we have a polarized light wave in which the oscilation plane rotates around the propagation direction, and the head end of the light vector moves describes an ellipse. This light is called elliptically polarized. Some limit cases: • When phase difference equals m.→ the ellipse collapses to a straight line, we have a linearly polarized light • When = (2m + 1) ( and the amplitudes of two waves are equal /2) → the ellipse becomes a circle, the light is circularly polarized
§2. Polarization in reflection and refraction: Unpolarized light can be polarized, either partially or totally, by reflection. 2.1 Polarization by reflection: Plane of incidence Suppose that unpolarized natural light is incident on a reflecting surface between two transparent materials. Then by experiment one discovered that: • Waves for which E  the plane of incidence are reflected more strongly than waves for which E lies in this plane • As a result, the reflected light is partially polarized in the direction to the plane of incidence. • The level of polarization depends on the angle of incidence. • Application: sunglasses that are made from polaroids can defend from the light reflected from water or road surfaces.
2.2 Polarizing angle of incident (Brewster angle): • For every reflecting surface there exists one definite angle of incidence, at which a critical case takes place: the light waves E lies in the plane of incidence is not reflected at all and the incident beam is completely refracted. This special angle is called the polarizing angle  . p • At the polarizing angle of incident  : p The reflected light is linearly polarized p and E  the plane of incidence na The refracted light is partially polarized nb and E lies in the plane of incidence David Brewster discovered experimentally ’ that the reflected ray refraction ray (this property can also be derived by Maxwell’s theory of electromagnetic waves) • This property gives us the way to determine  : p na sin = nb sin(90o - ) = nb cos → tg = nb/na p p p p Brewster’s law
§3. Polarization by birefringence: 3.1 Ordinary and extraordinary rays: In some crystals there exists the birefringent property, that is, when a light ray transmits through crystal, it is separated into two parts: One part satisfies the ordinary refraction law (“o” ray), and the other does not (“e” ray). Properties of the “e” ray: • It does not lie in the plane of incidence • For it the expression n1sini1/n2sini2 doesn’t remain constant with variation of the angle of incidence • Even for the case of the incident angle 90 o → the “e” ray deviates from the incident direction (see picture). The birefringent phenomenon appears in allmost any tranferent crystal, besides of the crystals that are belong to the cubic system. In some crystals there exists one direction the “o” and “e” rays are not separated and have the same propagation velocity. This direction is called optical axis of the crystal, and this type of crystals is called uniaxial crystals. Any line parallel to this direction is also a optical axis.
Any plane passes the optical axis is called the principal section of crystal. Usually, one is interested in the principal section that passes the light ray. 3.2 Polarization of “o” and “e” rays: Optical axis Both the “o” and “e” rays are linearly polarized The oscillation direction of E in the “o” ray is perpendicular to the principal section, and oscillation of E in the “e” ray is in this section. These properties of polarization are applied to make polarizers: • Turmalin plate: The turmalin crystal has the dichroism property, that is, the different absorption for the “o” ray and “e” ray. The “o” ray is completely absorbed in a path length ~ 1mm, and the “e” ray remains only after turmalin plate → a turmalin plate is used as a polarizer.
• Nicol prism: William Nicol (1768-18570) discovered a way to make a polarizer, based on the birefringence. Optical axis • Two prisms are cut from a calcite crystal and polished to the form as shown in picture. The two prisms then are glued together with a cement called Canada balsam. • The specific values of angles and the choice of the cement (the choice of the index of refraction) are determined by the difference between critical angle (for the complet reflection) of the “o” and the “e” rays. As shown in the picture, after Nicol prism one has a liearly polarized light, it is the remained extraodinary ray.
§4.Birefringence in electric field – Kerr effect: 4.1 Birefringer in electric field: The birefringence expresses the optically anisotropic property of crystals. But the befringence appears also in isotropic materials in e-field. John Kerr (1824-19070) observed that optically isotropic materials exhibited uniaxial birefringent behavior when placed in an electric field. • The central part, called Kerr cell, is a cuvette with liquid and a capacitor • In the absence of electric field, the liquid is optically isotropic. If the optical axis of the analyzer is cross with respect to that of the polarizer → the light does not transmit through the system
• When an uniform electric field is applied between the capacitor plates, the liquid behaves like an uniaxial crystal with the optical axis directed along the electric field → the birefringence appears • After the capacitor the light is elliptically polarized: It is the composition of o and e rays - two waves that have perpendicular oscillation directions. By experimental measurement one obtains the following equations: • The difference in the index of refraction of o & e rays: • The path difference of the two rays: and the corresponding phase difference: • The last equation can be written in the form: Kerr constant The Kerr constant B is characterictic of a material, B depends also on temperature and the wave length  
4.2 Rotation of polarizing plane: When a linear polarized light transmits through some materials, one observed the rotation of the oscillation plane of E . Materials that have such ability are called optically active. Examples of such materials: some solid crystals (quartz), liquid (turpentine, nicotin), solutions (sugar, wine acid),… This effect is popular in sugar industry to measure the cyrup concentration (sugar-meter). • When the optical axis of the analyzer P’ is cross with respect to that of the polarizer P → it is dark after P’. • If the cylindrical vessel is filled with sugar solution → it becomes bright after the analyzer • Rotate the analyzer by an angle one makes dark again.
• By experiment one obtains the following law: where l is the path length of light in the solution, c – the concentration [ – coefficient that is called specific rotation constant. It is ] characteristic of material, and depends on wavelength   • With this formula, one can determine the concentration of the solution by measuring the angle by that the polarization plane was rotated.
Resume  Light is a transverse electromagnetic wave, and the oscillation direction of the vector E determines polarization property of light: • E oscillates in a plane (passing through the ray) → light is called linearly (or planely, or completely) polarized • E oscillates in many different directions, but one direction predominates over all other → light is called partially polarized • The arrowhead of E rotates and draws an ellipse (circular) → light is called elliptically (circularly) polarized  Light reflected from a surface is mostly partially polarized. The critical case when the angle of incidence is the polarizing angle , light is p completely linearly polarized. The polarizing angle is determined by the formula tg = n /n p b a
 In birefrengent crystals, both the “o” and the “e” rays are linearly polarized, for the “o” ray E the principal plane and for the “e” ray E lies in this plane.  The birefringence expresses the optically anisotropic property of material. In isotropic materials, the birefringence can appear when an electric field is applied.  In some materials that are called optically active, the polarizing plane rotates. For solutions, the rotation angle depends on the concentration and this effect can be applied as a way to determine the concentration of solutions.