1. Announcements
I should have exams back to you on Fri.

2. Reading Quiz
The element that should be used to change linearly polarized light into circularly polarized light is the
quarter waveplate
half waveplate
full waveplate

3. Reading Quiz
When multiple elements are in a beam path, the Jones matrices multiplied to find the final optical polarization are written
with the first element’s matrix on the right
with the first element’s matrix on the left
in any order

4. Silicon chip birefringence

5. Jones Matrix JM for linear polarizer
Horizontal transmission (trans. axis along x)
Vertical transmission (trans. axis along y)

6. Arbitrary angles for polarizers
Rotation of coordinates
transforms a vector from the original basis to the vector in the rotated basis.
transforms a vector from the rotated basis to the vector in the original basis.

7. Linear polarizer at arbitrary angles
Polarizer looks like in “rotated” coordinates if x’ is aligned with the transmission axis. Let’s get it in the x, y system:
transforms a matrix operator from the original basis to the matrix in the rotated basis.
JM for linear polarizer
Transmission axis at q from x axos

8. Waveplates (optical retarders)
Uniaxial crystals cut so optic axis is in the plane of the plate. Light comes in perpendicular to the plate.
Light travels fastest if E is aligned with the fast axis (bold blue line).
The optic axis is the fast axis if ____
no > ne.
no < ne.
fast
To analyze, we break light into components along and perp to the fast axis. Phase difference between the fast and slow light after the WP in terms of thickness:
slow

9. Quarter-wave plates fast slow
Choose thickness so phase difference between fast and slow light is ____
If we start with linear polarization at 45o from the fast axis, we will end up with ________ polarized light
linearly
circularly
elliptically
Hint, figure out the components (Jones vector) in the “fast-slow” coordinate system, and then do the phase shift.
fast
slow

10. Quarter-wave plates
If we start with linear polarization at 90o from the fast axis, we will end up with ________ polarized light
linearly
circularly
elliptically

11. Quarter-wave plates
If we start with linear polarization at general angle q from the fast axis, we will end up with ________ polarized light
Summary: QWP’s usual purpose is to change between linear and circular pol, which means the linear light needs to be at 45 deg to the fast/slow axes. Other orientations give elliptical.

12. Half-wave plates fast slow
Choose thickness so phase difference between fast and slow light is ____
If we start with linear polarization at 45o from the fast axis, we will end up with ________ polarized light
linearly
circularly
elliptically
Hint, figure out the components (Jones vector) in the “fast-slow” coordinate system, and then do the phase shift.
fast
slow

13. Half-wave plates
If we start with linear polarization at a general angle q from the fast axis, we will end up with ________ polarized light
linearly
circularly
elliptically
Hint: figure out the components (Jones vector) in the x’, y’ coordinate system, and then do the phase shift.
Summary: HWP’s usual purpose is to rotate linear polarization to a new line, by 2q.

14. JM for Waveplates fast slow
For waveplates, q is orientation of fast axis vs the x (H) axis.
What does the l/4 plate Jones matrix look like in the x’,y’ coordinate system? It delays the slow (y’) component by p/2.
fast
What does the l/2 plate Jones matrix look like in the x’,y’ coordinate system? It delays the slow (y’) component by p.
slow

15. JM for Waveplates
JM for quarter-wave plate
JM for half-wave-plate

16. Polarization demos again
Does our transparency sheet act more like QWP or HWP?

17. Wood fibers between crossed polarizers

18. JM for Reflection (vertical mirrors)
If a circularly polarized beam in the horizontal plane strikes a vertical mirror at say 45%, what will the final state be?
JM for Reflection (vertical mirrors)

19. Why sunlight (scattered light) is partially polarized
To get the most polarization difference, look at the molecules that have to scatter light 90 degrees to get to you
Why: dipole radiation’s angular dependence!

20. Boomerang Nebula coldest known region: 1K
Color indicates angle of polarization line. This shows that the light comes from the center. (Polarization caused by scattering light off tiny dust particles)

21. Sunset carousel demo and polarization
LCD screen teardown

22. Notes Order of matrices matters!
Fraction of intensity transmitted: compare initial and final vector squared magnitudes
Choose x to stay on your right hand as you follow the beam around reflections.

23. If a R-cir beam strikes a mirror at normal incidence, what will the resulting beam be?
L-cir
linearly polarized