1. Lecture 23: Polarization
Physics 212
Lecture 23: Polarization

2. What makes EM waves Which of the following do not create EM waves?
Constant current
Accelerating electron.
Electron orbiting a nucleus.
Charged pith ball rotating on a string around a circle.
E) Electron moving with constant velocity.

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

4. Linear Polarization

5. The intensity of a wave does not depend on it’s polarization:
I could have also rotated the coordinate system such that x points along hat e! So
Just like before

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

8. Two Polarizers
since the second polarizer is orthogonal to the first, no light will come through. cos(90) = 0

9. Two Polarizers
you can use a polarizer at an angle so that it takes a portion of the polarized light and basically lets the light through AT THAT ANGLE. Then, when the light reaches the second polarizer, it is no longer orthogonal to it.

10. What if we put many polarizers between?
Applet polarizer
What if we put many polarizers between?

11. 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:
At t=0
Example:

12. Circular polarization
In Physics and Astronomy, we define left/right circular polarization if the light rotates cw/ccw as seen from the receiver (looking at the incoming light). In engineering we define it as seen from the emitter!
As seen by emitter

13. Q: How do we change the relative phase between Ex and Ey?
A: Birefringence:
Anisotropic material. Light incident from different
directions propagates at different speeds.
Right hand rule
By picking the right thickness we can change the relative phase by exactly 90o.
This changes linear to circular polarization
and is called a
quarter wave plate

14. This modification does not change the intensity either:
Right Handed Circular Polarization (at t = 0)
This modification does not change the intensity either: So
Just like before

15. Circular Light on Linear Polarizer
Q: What happens when circularly polarized light is put through a polarizer along the y (or x) axis ?
I = 0
I = ½ I0
I = I0 X
Half of before

16. In case A you lose your horizontal component of the wave, however in B you retain both, just at a shift of pi/2.

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

18. Ex is missing, so
intensity is lower
Polarizer

19. What is the polarization of the light in Case 2 after it passed through the quarter wave plate?
Linearly polarized
Right circularly polarized (as seen by receiver)
Left circularly polarized (as seen by receiver)

20. Right circularly polarized (CCW) as seen by emitter
Left circularly polarized (CW) as seen by receiver.

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

22. Calculation
Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown.
What is the intensity I3 in terms of I1?
fast y
45o x
slow
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.
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.

23. Calculation (A) LCP (B) RCP (C) (D) (E) unpolarized
Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown.
fast y
45o
Light incident on QWP is linearly polarized at 45o to fast axis E1 x
RCP
slow
LCP or RCP? Easiest way: Right Hand Rule:
l/4 Ex Ey
60o I1 I2 I3 z
What is the polarization of the light after the QWP as seen by emitter?
(A) LCP (B) RCP (C) (D) (E) unpolarized x y
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.
Light will be circularly polarized after QWP
Curl fingers of RH back to front
Thumb points in dir of propagation if right hand polarized.

24. Calculation (A) I2 = I1 (B) I2 = ½ I1 (C) I2 = ¼ I1
Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown.
fast y
45o x E1
RCP
slow Ex Ey
60o I1
l/4 I2 I3 z
What is the intensity I2 of the light after the QWP?
(A) I2 = I (B) I2 = ½ I (C) I2 = ¼ I1
AFTER:
BEFORE:
No absorption: Just a phase change !
Same before & after !

25. Calculation (A) LCP (B) RCP (C) (D) (E) unpolarized
Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown.
fast y
45o x E1
RCP
slow Ex Ey
60o E3 I1
l/4
I2 = I1 I3 z
What is the polarization of the light after the 60o polarizer?
(A) LCP (B) RCP (C) (D) (E) unpolarized x y
60o
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.
Absorption: only passes components of E parallel to TA (q = 60o)
60o Ex 3 Ey E3

26. Calculation (A) I3 = I1 (B) I3 = ½ I1 (C) I3 = ¼ I1
Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown.
fast y
45o x E1
RCP
slow Ex Ey
60o E3 I1
l/4
I2 = I1
I3 = ½ I1 z
What is the intensity I3 of the light after the 60o polarizer?
The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.
(A) I3 = I (B) I3 = ½ I (C) I3 = ¼ I1 Ey E3 3
NOTE: This does not depend on q !!
60o Ex