Polarized direction

Part 3 Polarization of light

§17-11 Polarization state of light§17-11 Polarization state of light

Polarized statePolarized state:the oscillating:the oscillating statestate of light vector. of light vector.

Natural lightNatural light Plane polarized lightPlane polarized lightPartially polarized lightPartially polarized light

Elliptically polarized lightElliptically polarized light

Circularly polarized lightCircularly polarized light

The electric field vector in electromagnetic The electric field vector in electromagnetic wave are sensitive for most detectors.wave are sensitive for most detectors.

-- -vector is called -- -vector is called light vector.light vector.E

E

Classification Classification

Electromagnetic wave is transverse waveElectromagnetic wave is transverse wave

1. Natural light (Unpolarized light)1. Natural light (Unpolarized light) The amplitudesThe amplitudes of light vectors along all direct of light vectors along all direct

ions at the plane which is perpendicular to the ions at the plane which is perpendicular to the direction of propagation direction of propagation have same magnitudehave same magnitude..

yx II 02

1I

0I

2. Plane polarized light2. Plane polarized light (( 线偏振光 线偏振光 or or 平面偏振光平面偏振光 )) The oscillating direction of light vector is alwayThe oscillating direction of light vector is alway

s located in a fixed plane.s located in a fixed plane.

E

Oscillating plane

Light vector

3. Partially polarized light3. Partially polarized light (( 部分偏振光部分偏振光 ))

The amplitudesThe amplitudes of light vectors along all of light vectors along all directions at the plane which is perpendicular directions at the plane which is perpendicular to the direction of propagation to the direction of propagation have different have different magnitude.magnitude.

0I

The end of the light vector moves with constant The end of the light vector moves with constant speed in a circle, or in an ellipse.speed in a circle, or in an ellipse.

4. Circularly or Elliptically polarized light 4. Circularly or Elliptically polarized light (( 圆 圆 or or 椭圆偏振光椭圆偏振光 ))

0I 0I

Poleroid

§17-12 Polarization of light Law of Malus§17-12 Polarization of light Law of Malus

I. I. Polarizing and polarization analyzing Polarizing and polarization analyzing (( 起偏和检偏起偏和检偏))

Polaroid Polaroid (( 偏振片偏振片 ))

0I Polarizing direction

Polarizing directionPolarizing direction(( 偏振化方向偏振化方向 )) ：： permittinpermitting the light vector passing through.g the light vector passing through.

1P

Polarization analyzing--Polarization analyzing--to test whether the to test whether the incident light is polarized.incident light is polarized.

Polarizing--Polarizing--natural light natural light polarizer polarizer plane plane polarized lightpolarized light

polarizer analyzer

0I 2I2P1I

01 2

1II

?2 I

1P0I 2I2P

1I1A

2A

II. II. Malus lawMalus law

1P2P

1A

2Acos1Asin1A

21

22

1

2

A

A

I

I 2cos

212 cosII

----Malus law----Malus law

AA11, A, A22—amplitudes of —amplitudes of the polarized light.the polarized light.

=0 =0 or or =180=18000, , II22==II1 1 ---- maximum maximum

DiscussionDiscussion：：

=90=900 0 oror =270=27000, , II=0 --=0 -- minimum minimum

II11

II22

00 909000-90-9000 18018000 27027000-180-18000

[Example] Two polarizing sheets are put parallel[Example] Two polarizing sheets are put parallely. Their polarized directions have the angle y. Their polarized directions have the angle 303000. . Calculate when the natural light is incident on thCalculate when the natural light is incident on the polaroids normally, the intensity ratio of transe polaroids normally, the intensity ratio of transmitting and incident light. (discuss two cases: mitting and incident light. (discuss two cases: the polaroids have not absorption the polaroids have not absorption the polaroidthe polaroids have s have 10% 10% ratio of absorption.)ratio of absorption.)

1P0I 2I2P

1I

Solution Solution ：： no absorptionno absorption

01 2

1II

020 30cos

2

1I 8

3

0

2 I

I

Assume the intensity of incident natural light is I0 .

The light is fully polarized after passing P1 . The polarized direction is parallel to P1 and the intensity is

212 cosII

After I1 passes through P2 , its polarized direction is parallel to P2 and the intensity is

the absorption ratio equals to 10%the absorption ratio equals to 10%

%)101(2

101 II

%)101(cos212 II

2

0

2 9.08

3

I

I3.0

§17-13 Polarization by Reflection and Refraction§17-13 Polarization by Reflection and Refraction

II. . Partially polarization phenomenonPartially polarization phenomenon

When a natural light is When a natural light is incident on a interface of incident on a interface of two kinds of materials, its two kinds of materials, its reflected light and reflected light and refracted light are refracted light are partially polarized light.partially polarized light.

i

i

characteristiccharacteristic ：： for reflected light, the for reflected light, the perpendicular component is larger than perpendicular component is larger than parallel component. parallel component. Refracted light is Refracted light is converse.converse.

II. II. Brewster lawBrewster lawWhen When ii equals to a special equals to a special angle angle ii00 ， ， the reflected light the reflected light is fully polarized light with is fully polarized light with the polarized direction the polarized direction perpendicular to the incident perpendicular to the incident plane.plane.

2n

1n0i 0i

Brewster angleBrewster angle

In this case In this case 00 90i

sinsin 201 nin 02 cos in

1

20tg

n

ni ----Brewster Law21n

As As

909000

)90sin( 00

2 in

NotesNotes WhenWhen i= i i= i00 ，， the the

reflected light is fully reflected light is fully polarized, polarized, the refracted the refracted light is partially light is partially polarized and has the polarized and has the maximum polarized maximum polarized degree.degree. The reflected light is of low intensity (The reflected light is of low intensity (15%15%),),

Let a natural light passes through a stacking Let a natural light passes through a stacking glass plates, the transmitted light is almost glass plates, the transmitted light is almost polarized.polarized.

0i

and the refracted light is of high intensity .and the refracted light is of high intensity .

§17-14 Double refraction§17-14 Double refraction

I. I. Birefringence (Bi-refraction) phenomenonBirefringence (Bi-refraction) phenomenon

双 折 射双 折双 折

Calcite crystal

o-ray

e-ray

Ordinary light (o-ray): Ordinary light (o-ray):

follows follows Refraction Law.Refraction Law.

Extraordinary light(e-ray): Extraordinary light(e-ray): does notdoes not follow follow Refraction Law.Refraction Law.

双折射双折射

When the crystal When the crystal rotates round the rotates round the incident lightincident light ，， o-o-ray is fixed ray is fixed and e-ray and e-ray rotates round o-rayrotates round o-ray..

II. II. Characteristic of birefringence of lightCharacteristic of birefringence of light

1. 1. Some concepts of crystallographySome concepts of crystallographyOptical axisOptical axis ：： it represents a direction that therit represents a direction that ther

e ise is no birefringence phenomenon when a light tno birefringence phenomenon when a light travels along this directionravels along this direction

Uniaxial crystalUniaxial crystal---it has one optical axis only ( cal---it has one optical axis only ( cal

citecite 方解石方解石、 、 quartz 石英石英 ))

Biaxial crystalBiaxial crystal--- --- it has two optical axes (it has two optical axes (mica

云母 sapphire 蓝宝石 ))

Principal plane Principal plane （主平（主平面）面） ：： the plane formthe plane formed by some ray (ed by some ray (oo-ray -ray or or ee-ray) and optical a-ray) and optical axis.xis.

optical axis

normalnormal

o-ray

e-ray

If the optical axis is not at the incident plane, If the optical axis is not at the incident plane, the principle planes of the principle planes of e-raye-ray and and o-rayo-ray are not are not coincide. coincide.

In the crystal.In the crystal.

O-O-ray andray and e- e-ray are pray are plane polarized light.lane polarized light.

2. Characteristics2. Characteristics

The oscillating direction The oscillating direction of of o-rayo-ray its principle its principle plane. plane.

The oscillating direction The oscillating direction of of e-raye-ray its principle its principle plane. plane.

O-ray

E-ray

When the optical axis is located in the incidenWhen the optical axis is located in the incident plane, the principle planes of t plane, the principle planes of o-ray o-ray andand e-ray e-ray coincidecoincide.. The oscillating directions of The oscillating directions of o-rayo-ray an and d e-raye-ray are are perpendicularperpendicular to each other. to each other.

o.A.o.A.

III. III. Explanation of birefringence phenomenonExplanation of birefringence phenomenonReason:Reason:The travel speed of The travel speed of oo-ray in a birefringe-ray in a birefringe

nce crystal is homogeneous isotropic. The speed nce crystal is homogeneous isotropic. The speed of of ee-ray is anisotropic.-ray is anisotropic.

O-rayO-ray ：： the wavefront is spherical surface.the wavefront is spherical surface. E-rayE-ray ： ： the wavefront is ellipic surface.the wavefront is ellipic surface.

positive crystal

negative crystal

evv 0 evv 0

O.A.O.A.

A BCD E

oe O.A.O.A.

A B

o

C

e

The explanation of Huygens principleThe explanation of Huygens principle

O.A.O.A.O.A.O.A.

A B

o

A B

e

IV. IV. Application of birefringenceApplication of birefringence

Nicle polarizing Nicle polarizing prismprism

068

068calcite crystal

55.1n

A cement from A cement from Canada treeCanada tree

068

022

048

O.A.O.A.

oe

658.1on486.1en 55.1n

I. The interference principle of polarized lightI. The interference principle of polarized light

polarizer

1P

analyzer

2P natural natural lightlight e

o

Birefringence Birefringence filmfilm

O.A.O.A.

d

§§17-15 The interference of polarized light17-15 The interference of polarized light偏振光的干涉偏振光的干涉

Polarized lightTwo coherent olarized lights

The polarized light behind The polarized light behind PP1 1 is separated into is separated into

o-rayo-ray and and e-raye-ray after it passes through the after it passes through the birefringence film. The phase difference birefringence film. The phase difference between between o-rayo-ray andand e-raye-ray isis

dnn eo )(2

' --their vibration directions --their vibration directions

and and is constant.is constant.

1P

2P

1A

eA

oA

Their amplitudes areTheir amplitudes are

sin1AAo

cos1AAe

Behind analyzerBehind analyzer ：： o-ray o-ray and and e-raye-ray have their have their vibration components on the polarized direction vibration components on the polarized direction of of PP2 2 ::

1P

2P

eA

oA

1A

oA2

eA2

cos2 oo AA

sin2 ee AA sincos1A

sincos1A

----equal amplitude,equal amplitude, but but opposite vibrating opposite vibrating direction ( i.e. having direction ( i.e. having extra phase difference extra phase difference .).)

The phase difference between two coherent The phase difference between two coherent polarized lights ispolarized lights is

'

dnn eo )(2

When the thick of birefringence film is When the thick of birefringence film is different, the interference fringes appear.different, the interference fringes appear.

The interference fringes of the polarized lights produced by quartz crystal edge.

II. Optical stress analysisII. Optical stress analysis

analyzer

2P

polarizer

1P

F

F

eo

Mechanical stressMechanical stress--birefringence material--birefringence material

dnn eo )(

2

kpd2

when the internal stress of a material is not when the internal stress of a material is not uniform, the interference fringes will appear uniform, the interference fringes will appear behind behind PP22..

The experiment shows:The experiment shows:

kpnn eo

kk ：： proportion proportion factorfactor ， ， pp ：： stressstress