Chapter 44 Polarization

Content of this Chapter About polarization Polarizing sheets Polarization by reflection Double refraction Circular polarization Polarization by scattering

Interference Diffraction Polarization

Electromagnetic Waves Polarization E and B are in phase E ⊥ B, and E ⊥ k, B ⊥ k, k is the direction of the wave. The speed of electromagnetic wave is c

Nature light

Unpolarized light is called nature light.

Unpolarized Unpolarized light is called nature light. Partially polarized unpolarized Partially polarized unpolarized polarized

F The plane determined by the E and the direction of propagation of the wave is called the plane of polarization of the wave. (plane polarized). E Polarization Linear Polarization Circular polarization

Polarizing sheets F Polarizing sheet absorb all electric fields perpendicular to their polarizing direction. Polarizing sheet or polarizer

Linearly Polarized Light on Linear Polarizer (Law of Malus) E tranmitted = E incident cosθ θ is the angle between the incoming light’s polarization, and the transmission axis. TA  E tranmitted = E incident cosθ I transmitted = I incident cos 2 θ Law of Malus

I=?

Example un-polarized light polarized light partially polarized light

Example

Polarization by reflection The light can be partially or completely polarized by diflection. Unpolarized light Partially polarized θpθp θrθr When the incident angle is θ p, the reflected light is completely linearly polarized (perpendicular to the plane). The refracted light is partially polarized. Brewster’s lawBrewster’s angle polarized partially polarized

A stack of glass plates polarizing sheet un-polarized polarized

Example

Double refraction The speed of light in matter Optically isotropic: the speed of light is independent of the direction of propagation in medium and of state of polarization of the light. double refraction (birefringence) c v Optically anisotropic: the index of refraction and speed are dependent on the direction of propagation in medium and of state of polarization of the light.

o-ray and e-ray Ordinary ray (o-ray): obey Snell’ law of refraction at the crystal surface. Extraordinary ray (e-ray): does not obey Snell’ law of refraction at the crystal surface.

The difference between o-ray and e-ray o-ray: with the same speed v 0 in all directions, in other words a single index of refraction n 0. e-ray: with the speed that varies with direction from v 0 to v e the index of refraction varies with direction from n 0 to n e. o ray e ray o ray e rayo ray Optic axis Principal plane

Principal indices of refraction n 0 = n e. Optic axis negative crystal it is a direction in the crystal in which v 0 =v e v0>vev0>ve positive crystal v0<vev0<ve n0<nen0<ne n0>nen0>ne negative crystal o-ray e-ray Principal plane

Summary unpolarized polarized Partially polarized Polarizing sheets I= I i cos 2 θ Law of Malus θpθp θrθr Brewster’s law c v double refraction (birefringence)

Double refraction c v Optically anisotropic: the index of refraction and speed are dependent on the direction of propagation in medium and of state of polarization of the light. Ordinary ray (o-ray): obey Snell’ law of refraction at the crystal surface. Extraordinary ray (e-ray): does not obey Snell’ law of refraction at the crystal surface. o-ray e-ray Optic axis In this direction v 0 =v e n 0 = n e v0>vev0>ve positive crystal n0<nen0<ne negative crystal v0<vev0<ve n0>nen0>ne Double refraction Principal plane

Optic axis Double refraction Optic axis

Which are o ray and e ray ? Example Optic axis What is d between two ray e ray o ray d v0>vev0>ve positive crystal n0<nen0<ne

Linearly polarized light falls on a double refracting slab (n o, n e ) with its optic axis parallel to the surface. Two polarization states that were in phase before entering the slab are out of phase when they emerge from this slab. What is d Optic axis Example Half-wave plate The slab is called half-wave plate if phase difference of o- wave and e-wave is π after they passing through the slab. Optic axis

Linearly polarized light falls on a double refracting slab (n o, n e ) with its optic axis parallel to the surface. Different phase is  /2, when they emerge from this slab. What is d Optic axis Quarter-wave plate The slab is called quarter- wave plate if phase difference of o-wave and e-wave is π/2 after they passing through the slab.

Homework: P1012 5, 6, 8, 10, 13

Double refraction c v Optically anisotropic: the index of refraction and speed are dependent on the direction of propagation in medium and of state of polarization of the light. Ordinary ray (o-ray): obey Snell’ law of refraction at the crystal surface. Extraordinary ray (e-ray): does not obey Snell’ law of refraction at the crystal surface. o-ray e-ray Optic axis In this direction v 0 =v e n 0 = n e v0>vev0>ve positive crystal n0<nen0<ne negative crystal v0<vev0<ve n0>nen0>ne Double refraction Principal plane e-ray

Example A quartz (n o =1.544, n e =1.553) under a sodium light, the optic axis is shown in the figure, to sketch the light Optic axis

Double refraction Optic axis

Linearly polarized light falls on a double refracting slab (n o, n e ) with its optic axis parallel to the surface. Two polarization states that were in phase before entering the slab are out of phase when they emerge from this slab. What is d Optic axis Example Half-wave plate The slab is called half-wave plate if phase difference of o- wave and e-wave is π after they passing through the slab. Optic axis Quarter-wave plate The slab is called quarter- wave plate if phase difference of o-wave and e-wave is π/2 after they passing through the slab.

Circular polarization Quarter-wave plate Right-circular Principal plane x-y

Circular polarization Quarter-wave plate Left-circular

Circular polarization Quarter-wave plate EllipsoidLeft-circular

Circularly polarized wave polarizing sheet unpolarized polarized Quarter-wave plate Right-circular Left-circular Circularly polarized wave

Half-wave plate Linear polarized    

unpolarized and circular polarized light Quarter-wave plate unpolarized circular polarizedlinear polarized circular polarized linear polarized

o-ray e-ray summary Optic axis In this direction v 0 =v e n 0 = n e v0>vev0>ve positive crystal n0<nen0<ne negative crystal v0<vev0<ve n0>nen0>ne Optic axis unpolarized polarizing sheet polarized Quarter-wave plate Circularly polarized wave Principal plane

Example A quartz (n o =1.544, n e =1.553) plate to be used with sodium light ( =589nm), the emission light is a circularly polarized wave what is the minimum thickness of the plate? When a linear polarized light falls on the plate, what is the rotation direction of the circularly polarized light?

Example A quartz (n o =1.544, n e =1.553) plate to be used with sodium light ( =589nm), the emission light is a circularly polarized wave what is the minimum thickness of the plate? When a linear polarized light falls on the plate, what is the rotation direction of the circularly polarized light? Right-circular Left-circular (n e =1.544, n o =1.553)

Polarization by scattering Light scattered sideways from a matter can be partially polarized.

Polarization by scattering Liquid crystal Incident emerging Polarized direction un-polarized polarized

Exercises P , 12, 14, 15, 16,