1. Polarization - linear - circular
Physics 2112 Topic 24
Polarization
- linear
- circular

2. So far we have considered plane waves that look like this:Ex By
From now on just draw E and remember that B is still there: Ex

3. Linear Polarization
“I was a bit confused by the introduction of the "e-hat" vector (as in its purpose/usefulness)”

4. What this looks like….

5. What this looks like….

6. Polarizer
The molecular structure of a polarizer causes the component of the E field perpendicular to the Transmission Axis to be absorbed.

7. Polarization “Half Rule” “Cosine2 Rule” Malus’s Law
Recall:
“I can't believe your teaching us the law of "Malus"(Malice). I thought malice was to be avoided?”
“Half Rule”
“Cosine2 Rule”
Malus’s Law

8. CheckPoint 1: Two Polarizers
An unpolarized EM wave is incident on two orthogonal polarizers.
Is it possible to increase this percentage by inserting another polarizer between the original two?
yes no

9. Example 24.1: Two polarizers
Unpolarized light with an intensity of 1000W/m2 is incent on two polarizing lenses.
The transmission angle of the first lens is 90o to the x axis and the transmission angle of the second lens is 10o to the x axis.
What is the intensity of the light after it passes through the second lens?

10. There is no reason that f has to be the same for Ex and Ey:
Making fx different from fy causes circular or elliptical polarization:
Example:
At t = 0
RCP

11. What this looks like….

12. What this looks like….

13. Circular Polarization

14. Light has different Speeds?
Speed of light is different in different materials (More about this later!)
Q: How can we use this to change the relative phase between Ex and Ey?
A: Birefringence
Right hand rule
Pick right thickness to change the relative phase by exactly 90o.
quarter wave plate

15. Right or Left? Right circularly polarized Do right hand rule
“Curl fingers slow to fast”
Right circularly polarized
Do right hand rule
Fingers along slow direction
Cross into fast direction
If thumb points in direction of propagation: RCP

16. CheckPoint 3(a) A B
Identical linearly polarized light at 45o from the y-axis propagates along the z-axis. In case 1 the light is incident on a linear polarizer with polarization along the y-axis. In case 2 the light is incident on a quarter wave-plate with fast axis along the y-axis
1)Compare the intensities of the light waves after transmission.
IA < IB
IA = IB
IA > IB

17. CheckPoint 3(b) A
Linearly polarized light at 45o from the y-axis propagates along the z-axis and is incident on a quarter wave-plate with fast axis along the y-axis B
What is the polarization of the light wave in case 2 after it passed through the quarter-wave plate?
linearly polarized
left circularly polarized
right circularly polarized
undefined

18. CheckPoint 3(c) A
Linearly polarized light at 45o from the y-axis propagates along the z-axis and is incident on a quarter wave-plate with fast axis along the y-axis. B
If the thickness of the quarter-wave plate in case B is doubled, what is the polarization state of the light wave after passing through the wave plate?
linearly polarized
left circularly polarized
right circularly polarized
undefined

19. Both Ex and Ey are still there, so intensity is the same
QW Plate
PHASE
CHANGE
Both Ex and Ey are still there, so intensity is the same

20. Question A
Identical linearly polarized light at 45o from the y-axis propagates along the z-axis and is incident on a linear polarizer with polarization along the y-axis. It then incident on a quarter wave-plate with fast axis along the y-axis. B
What is the polarization of the light wave in case 2 after it passed through the quarter-wave plate?
linearly polarized
left circularly polarized
right circularly polarized
undefined

21. Example 24.2
Unpolarized light is incident on two linear polarizers and a quarter wave plate (QWP) as shown.
What is the intensity I3 in terms of I0?
fast y
45o x
slow I0
60o I1 I2 I3 z
Conceptual Analysis
Linear Polarizers: absorbs E field component perpendicular to TA
Quarter Wave Plates: Shifts phase of E field components in fast-slow directions
Strategic Analysis
Determine state of polarization and intensity reduction after each object
Multiply individual intensity reductions to get final reduction.

22. What is the intensity I3 in terms of I0?
Example 24.3
Unpolarized light is incident on two linear polarizers with no quarter wave plate as shown. y
45o x
60o I0 I1 I3 z
What is the intensity I3 in terms of I0?

23. Executive Summary: Polarizers & QW Plates: Birefringence RCP
Circularly or Un-polarized Light
Polarized Light
Polarizers & QW Plates:
Birefringence
RCP