Polarisation Flashcards

1
Q

What is a longitudinal wave?

A

motion is along the direction of propagation

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2
Q

What is a transverse wave?

A

motion is transverse (perpendicular) to the direction of motion

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3
Q

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

A

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

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4
Q

How are the magnetic and electric fields related

A

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

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5
Q

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

A

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

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6
Q

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

A

a wavefront

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7
Q

What can we say about a plane wave

A
  • 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
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8
Q

What are the formulae for linearly polarised light

A

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

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9
Q

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

A

The complex amplitude is the same for each component

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10
Q

what are the formulae for circular polarisation?

A

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

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11
Q

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

A

90 degrees

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12
Q

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

A

counterclockwise

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13
Q

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

A

clockwise

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14
Q

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

A

linearly polarised light

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15
Q

What yields elliptically polarised light?

A

unequal arbitrary relative phase components

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16
Q

what are the formulae for elliptically polarised light?

A

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

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17
Q

When is light unpolarised?

A

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

18
Q

What is a jones vector?

A

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

19
Q

What is the general form of a jones vector?

A

E = |Ex|
|Ey|

20
Q

What con it be useful to consider for Jones vectors?

A

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

21
Q

For RCP what is Ey/Ex

22
Q

For LCP what is Ey/Ex

23
Q

Linear general jones jector

A

sin(a)
cos(a)

24
Q

Circular general jones vector

25
Elliptical general jones vector
A B+-iC
26
How can you calculate the polarisation of a beam after it has passed through an optical component?
Et = A.Ei where A is a 2x2 matrix for the component
27
what is the matrix for a horizontal polariser?
1 0 0 0
28
what is the matrix for a vertical linear polariser?
0 0 0 1
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?
exp(ipi/4) 1 0 0 i change to -i
30
what is the matrix for a homogeneous circular polariser right and how can it be changed for left?
1/2 1 i -i 1 swap the signs on the i's
31
what is the jones vector representing the polarisation state of UPL
| 1 | |Ay/Ax exp(𝜃𝑥 (𝑡) − 𝜃𝑦 (𝑡))|
32
What is Malus' Law
A^2=A0^2cos^2(𝜃)
33
What happens at the polarising angle 𝜃p
reflected light is completely polarised orthogonal to plane of incidence it is perpendicular to the refracted ray
34
What is Brewster's Law?
tan𝜃p = nb/na
35
what happens when the reflected and refracted beams are at 90 degrees?
polarisation is parallel reflection coefficient goes to zero because no scattering can occur due to dipole emission pattern
36
How do you derive Brewster's Law
- start with snell's law - the incident angle plus the transmitted angle = 90 - nisin(𝜃i) = ntcos(𝜃i)
37
Why does the Brewster angle effect happen?
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)
38
What are the Fresnel equations?
analysing the incidence of light at a boundary allows calculation of the reflectivity and transmission of light at the interface
39
What orientation do transverse electric waves have their electric fields with respect to the plane of incidence and the media boundary?
- perpendicular to the plane of incidence - parallel to the boundary
40
when does the Rtm go through zero
at brewster angle