Control of Polarised Light

Question 1

What are the main principles used by crystal polarisers?

Answer 1

Birefringence, Brewster’s angle and Total internal reflection

Question 2

How might 2 birefringent prisms be combined

Answer 2

rotate prisms so that ordinary polarisation in first prism is extraordinary in the second.
The perpendicular polarisation goes from high to low refractive index and undergoes TIR
Parallel polarisation transmitted near brewster’s angle

Question 3

Describe the Nicol Prism

Answer 3

2 prisms combined with parallel optic axes glued with material n between no and ne.
snells law separated beams at entrance and perpendicular polarisation undergoes TIR so it can be absorbed
parallel polarisation is transmitted near Brewster’s angle

Question 4

Describe the Wollaston Prism polarising beam splitter

Answer 4

2 rotated birefringent prisms use refraction alone to generate orthogonally polarised components

Question 5

(in words) what is the extinction ratio

Answer 5

the ratio of the transmitted irradiance through polarisers oriented parallel then crossed is the extinction ratio - ideally it would be infinity

Question 6

What does a retarder do?

Answer 6

Changes the polarisation of an incident wave because one polarisation sees more phase delay than the other and this changes the relative phase.

Question 7

How is a birefringent crystal cut to make a retarder?

Answer 7

so that its optic axis is parallel to both back and front surfaces of the plate

Question 8

What is the formula for the phase difference or retardation

Answer 8

Δ𝜙 = 2𝜋/𝜆 [|𝑛𝑜 − 𝑛𝑒|] 𝑑 (radians)

Question 9

what is the jones vector for waveplate output polarisation

Answer 9

1 |
|exp 𝑖 2𝜋/𝜆 [𝑛𝑜 − 𝑛𝑒] 𝑑|

Question 10

Assuming a 45 degree input plane polarisation, what will a quarter waveplate do?

Answer 10

create circular polarisation

Question 11

Assuming a 45 degree input plane polarisation, what will a half wave plate do?

Answer 11

rotate linear polarisation by 90 degrees

Question 12

What is the effect of a 𝜆/4 plate if linearly polarised light is incident parallel to either principal axis

Answer 12

there is no effect

Question 13

what are the principal axes for a uniaxial crystal

Answer 13

the polarisation directions of the ordinary and extraordinary ray

Question 14

What happens to a beam propagating through a 𝜆/2 plate

Answer 14

one polarisation experiences half a wavelength more phase delay than the other
the handedness of the beam will be inverted

Question 15

What is the phase difference of o and e rays emerging from a quarter wave plate

Answer 15

pi/2

Question 16

Describe a system that could be used to block reflected light

Answer 16

A 𝜆/4 plate placed between a linear polariser and a reflecting surface
the 𝜆/4 place converts the LPL to RCPL which is then reflected, changing the handedness.
The linear polariser now blocks the light that passes through the 𝜆/4 plate

Question 17

Incoming light 45 degree polarised
wave plate with axes at 0 or 90 degrees
Describe the output for a 𝜆/4 and 𝜆/2 plate

Answer 17

𝜆/4 - circular
𝜆/2 linear in opposite sign to incoming

Question 18

Incoming light 0 or 90 degree polarised
wave plate with axes at +/- 45 degrees
Describe the output for a 𝜆/4 and 𝜆/2 plate

Answer 18

𝜆/4 - circular
𝜆/2 - 90 or 0 degree polarisation

Question 19

When does no polarisation rotation occur for a wave plate

Answer 19

if the input polarisation is parallel to the wave-plate principal axes

Question 20

When can a wave-plate be called a zero-order waveplate?

Answer 20

If it has less than 2pi relative phase delay

Question 21

what is the formula for the thickness of a zero order 𝜆/4 plate

Answer 21

d = 𝜆/(4|n0-ne|)
derived from |n0-ne|d2pi/𝜆=pi/2

Question 22

what are the advantages and disadvantages of a multi-order waveplate

Answer 22

it had more than 2 pi relative phase delay
for a 𝜆/4 plate |n0-ne|d2pi/𝜆=pi/2 + N(2pi)
N is the number of waves of relative phase delay
it is thicker but much more wavelength dependent

Question 23

How do you make a thick zero order wave plate?

Answer 23

combine 2 plates with fast and slow axes opposite to each other
as long as d1-d2 is equal to d for the zero order plate, it will behave like one

Question 24

What are the components of a circular polariser?

Answer 24

a linear polariser followed by a quarter waveplate

Question 25

How could a right circular polariser be made into a right circular analyser

Answer 25

by exchanging the order of the elements

Question 26

what is the matrix representing a mirror

Answer 26

|-1 0|
| 0 1|

Question 27

what is optical activity

Answer 27

the ability of materials to rotate the direction of linear polarisation as the light travels through

Question 28

what happens to linearly polarised light in an optically active material

Answer 28

the plane of vibration is continuously rotated as it propagates along the optic axis

Question 29

what is the rotation angle in an optically active material

Answer 29

𝛽 = (𝑛𝐿 − 𝑛𝑅)(𝜋𝑑/𝜆0)

Question 30

What can happen from a Fresnel reflection

Answer 30

polarisation rotation

Question 31

When will reflection cause depolarisation

Answer 31

if the interface has different parallel x and y reflection coefficients and the light is not purely parallel or perpendicularly polarised