Polarisation

Question 1

What is a longitudinal wave?

Answer 1

motion is along the direction of propagation

Question 2

What is a transverse wave?

Answer 2

motion is transverse (perpendicular) to the direction of motion

Question 3

Light is a 3d vector field, if it propagates along the z axis what is happening in the rest of the field?

Answer 3

the electric and magnetic fields will be confined to the x-y plane forming a 2d vector field

Question 4

How are the magnetic and electric fields related

Answer 4

B(z,t) = 1/cE(z,t)

Question 5

What is the condition under which we can neglect the light’s magnetic force compared to its electric force

Answer 5

the charge’s velocity must be much less than the speed of light

Question 6

what do you call a surface over which a plane wave is constant?

Answer 6

a wavefront

Question 7

What can we say about a plane wave

Answer 7

• it is of infinite extent
• in planes perpendicular to the propagation, the phase of the wave (and the field) is constant
• all the electric field vectors in this plane are in phase

Question 8

What are the formulae for linearly polarised light

Answer 8

Ḛ𝑥 (𝑧, 𝑡) = Re{Ḛ0 cos(a) exp[ 𝑖(𝑘𝑧 − 𝜔𝑡)]}
Ḛ𝑦 (𝑧, 𝑡) = Re{Ḛ0 sin(a) exp[ 𝑖(𝑘𝑧 − 𝜔𝑡)]}

Question 9

Why are the components of linearly polarised light always in phase?

Answer 9

The complex amplitude is the same for each component

Question 10

what are the formulae for circular polarisation?

Answer 10

Ḛ𝑥 (𝑧, 𝑡) = Re{Ḛ0 exp[ 𝑖(𝑘𝑧 − 𝜔𝑡)]}
Ḛ𝑦 (𝑧, 𝑡) = Re{−(or +)𝑖Ḛ0 exp[ 𝑖(𝑘𝑧 − 𝜔𝑡)]}

Question 11

What is the phase shift between components of circularly polarised light?

Answer 11

90 degrees

Question 12

Looking along k, what direction does right circularly polarised light rotate?

Answer 12

counterclockwise

Question 13

Looking along k, what direction does left circularly polarised light rotate?

Answer 13

clockwise

Question 14

What do you get if you combine RCPL and LCPL of the same amplitude

Answer 14

linearly polarised light

Question 15

What yields elliptically polarised light?

Answer 15

unequal arbitrary relative phase components

Question 16

what are the formulae for elliptically polarised light?

Answer 16

𝐸𝑥 (𝑧, 𝑡) = Re{Ḛ0𝑥 exp[ 𝑖(𝑘𝑧 − 𝜔𝑡)]}
𝐸𝑦 (𝑧, 𝑡) = Re{Ḛ0𝑦 exp[ 𝑖(𝑘𝑧 − 𝜔𝑡 − 𝜃)]}

Question 17

When is light unpolarised?

Answer 17

When phases of x and y polarisations fluctuate
they vary on a timescale lower than 1/omega but faster than we can measure

Question 18

What is a jones vector?

Answer 18

A 2d vector containing the two complex amplitudes which defines the polarisation state of a field.

Question 19

What is the general form of a jones vector?

Answer 19

E = |Ex|
|Ey|

Question 20

What con it be useful to consider for Jones vectors?

Answer 20

the relative values
E/Ex = | 1 |
|Ey/Ex|

Question 21

For RCP what is Ey/Ex

Answer 21

-i

Question 22

For LCP what is Ey/Ex

Answer 22

+i

Question 23

Linear general jones jector

Answer 23

sin(a)
cos(a)

Question 24

Circular general jones vector

Answer 24

1
+-i

Question 25

Elliptical general jones vector

Answer 25

A
B+-iC

Question 26

How can you calculate the polarisation of a beam after it has passed through an optical component?

Answer 26

Et = A.Ei where A is a 2x2 matrix for the component

Question 27

what is the matrix for a horizontal polariser?

Answer 27

1 0
0 0

Question 28

what is the matrix for a vertical linear polariser?

Answer 28

0 0
0 1

Question 29

what is the matrix for a quarter wave plate with the fast axis horizontal and how can it be changed if the fast axis is vertical?

Answer 29

exp(ipi/4) 1 0
0 i
change to -i

Question 30

what is the matrix for a homogeneous circular polariser right and how can it be changed for left?

Answer 30

1/2 1 i
-i 1
swap the signs on the i’s

Question 31

what is the jones vector representing the polarisation state of UPL

Answer 31

1 |
|Ay/Ax exp(𝜃𝑥 (𝑡) − 𝜃𝑦 (𝑡))|

Question 32

What is Malus’ Law

Answer 32

A^2=A0^2cos^2(𝜃)

Question 33

What happens at the polarising angle 𝜃p

Answer 33

reflected light is completely polarised orthogonal to plane of incidence
it is perpendicular to the refracted ray

Question 34

What is Brewster’s Law?

Answer 34

tan𝜃p = nb/na

Question 35

what happens when the reflected and refracted beams are at 90 degrees?

Answer 35

polarisation is parallel
reflection coefficient goes to zero
because no scattering can occur due to dipole emission pattern

Question 36

How do you derive Brewster’s Law

Answer 36

• start with snell’s law
• the incident angle plus the transmitted angle = 90
• nisin(𝜃i) = ntcos(𝜃i)

Question 37

Why does the Brewster angle effect happen?

Answer 37

at 𝜃p dipole radiators in n2 emit a characteristic patter and when the refracted and reflected rays are perpendicular there can be no emission of parallel polarised light along the dipole axis (reflected ray)

Question 38

What are the Fresnel equations?

Answer 38

analysing the incidence of light at a boundary allows calculation of the reflectivity and transmission of light at the interface

Question 39

What orientation do transverse electric waves have their electric fields with respect to the plane of incidence and the media boundary?

Answer 39

• perpendicular to the plane of incidence
• parallel to the boundary

Question 40

when does the Rtm go through zero

Answer 40

at brewster angle