Polarisation Flashcards
What is a longitudinal wave?
motion is along the direction of propagation
What is a transverse wave?
motion is transverse (perpendicular) to the direction of motion
Light is a 3d vector field, if it propagates along the z axis what is happening in the rest of the field?
the electric and magnetic fields will be confined to the x-y plane forming a 2d vector field
How are the magnetic and electric fields related
B(z,t) = 1/cE(z,t)
What is the condition under which we can neglect the lightβs magnetic force compared to its electric force
the chargeβs velocity must be much less than the speed of light
what do you call a surface over which a plane wave is constant?
a wavefront
What can we say about a plane wave
- 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
What are the formulae for linearly polarised light
αΈπ₯ (π§, π‘) = Re{αΈ0 cos(a) exp[ π(ππ§ β ππ‘)]}
αΈπ¦ (π§, π‘) = Re{αΈ0 sin(a) exp[ π(ππ§ β ππ‘)]}
Why are the components of linearly polarised light always in phase?
The complex amplitude is the same for each component
what are the formulae for circular polarisation?
αΈπ₯ (π§, π‘) = Re{αΈ0 exp[ π(ππ§ β ππ‘)]}
αΈπ¦ (π§, π‘) = Re{β(or +)παΈ0 exp[ π(ππ§ β ππ‘)]}
What is the phase shift between components of circularly polarised light?
90 degrees
Looking along k, what direction does right circularly polarised light rotate?
counterclockwise
Looking along k, what direction does left circularly polarised light rotate?
clockwise
What do you get if you combine RCPL and LCPL of the same amplitude
linearly polarised light
What yields elliptically polarised light?
unequal arbitrary relative phase components
what are the formulae for elliptically polarised light?
πΈπ₯ (π§, π‘) = Re{αΈ0π₯ exp[ π(ππ§ β ππ‘)]}
πΈπ¦ (π§, π‘) = Re{αΈ0π¦ exp[ π(ππ§ β ππ‘ β π)]}
When is light unpolarised?
When phases of x and y polarisations fluctuate
they vary on a timescale lower than 1/omega but faster than we can measure
What is a jones vector?
A 2d vector containing the two complex amplitudes which defines the polarisation state of a field.
What is the general form of a jones vector?
E = |Ex|
|Ey|
What con it be useful to consider for Jones vectors?
the relative values
E/Ex = | 1 |
|Ey/Ex|
For RCP what is Ey/Ex
-i
For LCP what is Ey/Ex
+i
Linear general jones jector
sin(a)
cos(a)
Circular general jones vector
1
+-i
Elliptical general jones vector
A
B+-iC
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
what is the matrix for a horizontal polariser?
1 0
0 0
what is the matrix for a vertical linear polariser?
0 0
0 1
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
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 iβs
what is the jones vector representing the polarisation state of UPL
1 |
|Ay/Ax exp(ππ₯ (π‘) β ππ¦ (π‘))|
What is Malusβ Law
A^2=A0^2cos^2(π)
What happens at the polarising angle πp
reflected light is completely polarised orthogonal to plane of incidence
it is perpendicular to the refracted ray
What is Brewsterβs Law?
tanπp = nb/na
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
How do you derive Brewsterβs Law
- start with snellβs law
- the incident angle plus the transmitted angle = 90
- nisin(πi) = ntcos(πi)
Why does the Brewster angle effect happen?
at πp 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)
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
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
when does the Rtm go through zero
at brewster angle
