SP Lecture 24 - Polarization

Electricity&Magnetism
Lecture 24
Electricity & Magne/sm Lecture 24, Slide 1
Optics Kit
Incandenscent Light Source
Optics Bench
Ray Table Component Holder
Ray Table
Slit
Plate
Component Holders (3)
Slit
Mask
Parallel
Ray Lens
Ray Optics
Mirror
Cylindrical Lens
Viewing
Screen
Lenses: 75, 150 and
–150 mm focal lengths
Convex/Concave
Mirror (±50 mm)
Crossed
Arrow
Target
DIFFRACTION GRATING
5276 LINES/cm
Colour Filters:
red
DIFFRACTION PLATE
A
B
C
D
E
blue-green
Virtual Image
Locators
Diffraction Scale
Polarizers
Figure 1: Equipment included in the OS-8500 Introductory Optics System
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DIFFRACTION PLATE
J
I
H
G
F
green
Variable
Aperture
Diffraction
Grating
Diffraction
Plate
Base
Position Notch
Figure 4: Component holder
Variable Aperture
Polarizer
Lens or
Mirror
Figure 5: Using The Component Holder
Top View
So far we have considered plane waves that look like this:
From now on just draw E and remember that B is s/ll there:
Electricity & Magne/sm Lecture 24, Slide 3
Linear Polarization
“I was a bit confused by the introduction of the "e-hat" vector
(as in its purpose/usefulness)”
Electricity & Magne/sm Lecture 24, Slide 4
Polarizer
The molecular structure of a polarizer causes the component of the E field perpendicular to the Transmission Axis to be absorbed.
Electricity & Magne/sm Lecture 24, Slide 5
Clicker Question
The molecular structure of a polarizer causes the component of the E field perpendicular to the Transmission Axis to be absorbed.
Eo
Suppose we have a beam traveling in the + z direc/on.
At t = 0 and z = 0, the electric field is aligned along the posi/ve x axis and has a magnitude equal to Eo
y
z
What is the component of Eo along a direc/on in the x − y plane that makes an angle of θ with respect to the x − axis? C) 0
D) Eo/sinθ
E) Eo/cosθ
θ
B) Eocosθ
s
co
Eo
A) Eosinθ
Eo
θ
y
Electricity & Magne/sm Lecture 24, Slide 6
“I can't believe your
teaching us the law
of "Malus"(Malice). I
thought malice was
to be avoided?”
Electricity & Magne/sm Lecture 24, Slide 7
CheckPoint 2
Two Polarizers
60
45
30
15
0
1
The second polarizer is orthogonal to the first
No light will come through. cos(90o) = 0
Electricity & Magne/sm Lecture 24, Slide 8
CheckPoint 4
Two Polarizers
80
60
40
20
0
1
Any non-‐horizontal polarizer aZer the first polarizer will produce polarized light at that angle
Part of that light will make it through the horizontal polarizer
Electricity & Magne/sm Lecture 24, Slide 9
There is no reason that φ has to be the same for Ex and Ey:
Making φx different from φy causes circular or ellip/cal polariza/on:
Example:
At t = 0
RCP
Electricity & Magne/sm Lecture 24, Slide 10
Q: How do we change the rela/ve phase between Ex and Ey?
A: Birefringence By picking the right thickness we can change
the rela/ve phase by
exactly 90o. Right hand rule
This changes linear to circular polariza/on and is called a quarter wave plate
Electricity & Magne/sm Lecture 24, Slide 11
“talk something about intensity”
NOTE: No Intensity is lost passing through the QWP !
BEFORE QWP:
AFTER THE SAME!
Electricity & Magne/sm Lecture 24, Slide 12
Right or Left?
“red fox”
got it?
Right circularly polarized
Do right hand rule
Fingers along slow direc/on
Cross into fast direc/on
If thumb points in direc/on of propaga/on: RCP
Electricity & Magne/sm Lecture 24, Slide 13
Circular Light on Linear Polarizer
Q: What happens when circularly
polarized light is put through a
polarizer along the y (or x) axis ?
A) I = 0
B) I = ½ I0
C) I = I0
X
Half of before
1/2
Electricity & Magne/sm Lecture 24, Slide 14
CheckPoint 6
Case A
Case B
50
38
Case A: Ex is absorbed
Case B: 25
(Ex ,Ey) phase changed
13
0
1
Electricity & Magne/sm Lecture 24, Slide 15
Intensity:
h
i
I = ✏0 c hE 2x i + hEy2 i
SE
A
PH
QW Plate
CH
AN
GE
Both Ex and Ey
are s/ll there, so
intensity is the same
Electricity & Magne/sm Lecture 24, Slide 16
h
i
I = ✏0 c hE 2x i + hEy2 i
RB
O
S
AB
Polarizer
CO
M
PO
NE
NT
Ex is missing, so
intensity is lower
Electricity & Magne/sm Lecture 24, Slide 17
CheckPoint 8
Case A
A
Case BB
40
30
RCP
1/4 λ
Z
20
10
0
1
Electricity & Magne/sm Lecture 24, Slide 18
CheckPoint 10
Case A
Case B
50
38
25
½λ
13
Z
Z
0
1
Electricity & Magne/sm Lecture 24, Slide 19
Executive Summary:
Polarizers & QW Plates:
Polarized Light
Birefringence
Circularly or Un-‐polarized Light
RCP
Electricity & Magne/sm Lecture 24, Slide 20
Demo
What else can we put in there to change the polariza/on?
Electricity & Magne/sm Lecture 24, Slide 21
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
45o
y
x
w
slo
60o
I1
I2
I3
z
Conceptual Analysis Linear Polarizers: absorbs E field component perpendicular to Transmission Axis (TA)
Quarter Wave Plate: ShiZs phase of E field components in fast-‐slow direc/ons Strategic Analysis
Determine state of polariza/on and intensity reduc/on aZer each object
Mul/ply individual intensity reduc/ons to get final reduc/on. Electricity & Magne/sm Lecture 24, Slide 22
Calculation
Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown. fast
45o
y
RCP E1
x
w
slo Ex E
y
I1
60o
λ/4
I2
z
I3
What is the polariza/on of the light aZer the QWP? y
y
A) LCP B) RCP C) x D) x E) un-‐polarized
Light incident on QWP is linearly polarized at 45o to fast axis
LCP or RCP? Easiest way: Right Hand Rule:
Light will be circularly polarized aZer QWP
Curl fingers of RH back to front
Thumb points in dir of propaga/on
if right hand polarized.
RCP
Electricity & Magne/sm Lecture 24, Slide 23
Calculation
Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown. fast
45o
y
RCP E1
x
w
slo Ex E
y
I1
60o
λ/4
I2
z
I3
What is the intensity I2 of the light aZer the QWP? A) I2 = I1 B) I2 = ½ I1 C) I2 = ¼ I1
Before:
No absorp/on: Just a phase change!
AZer:
h
i
2
2
I = ✏0 c hE x i + hEy i
Same before & aZer!
Electricity & Magne/sm Lecture 24, Slide 24
Calculation
Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown. fast
45o
y
RCP E1
x
w
slo Ex E
y
I1
60o
E3
λ/4
I2 = I1
z
I3
What is the polariza/on of the light aZer the 60o polarizer? y
y
60o
60o
A) LCP B) RCP C) x D) x E) un-‐polarized
Absorp/on: only passes components of E parallel to TA (θ = 60o)
Ey
E3
3
60o
Ex
Electricity & Magne/sm Lecture 24, Slide 25
Calculation
Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown. fast
45o
y
RCP E1
x
w
slo Ex E
y
I1
60o
E3
λ/4
I2 = I1
I3 = ½ I1
z
What is the intensity I3 of the light aZer the 60o polarizer?
A) I3 = I1
Ey
E3
B) I3 = ½ I1
C) I3 = ¼ I1
3
NOTE: This does not depend on θ !
60o
Ex
Electricity & Magne/sm Lecture 24, Slide 26
Follow-Up 1
Replace the 60o polarizer with another QWP as shown. fast
45o
y
RCP E
x
w
slo E
x E
y
slow
fast
I1
λ/4
I2 = I1
E3
Ey
I3
Ex
z
What is the polariza/on of the light aZer the last QWP?
y
y
A) LCP B) RCP C) x D) x E) un-‐polarized
Easiest way: Efast is λ/4 ahead of Eslow
Brings Ex and Ey back in phase!
Electricity & Magne/sm Lecture 24, Slide 27
Follow-Up 2
Replace the 60o polarizer with another QWP as shown. fast
45o
y
E
x
RCP w
slo E
x E
y
slow
fast
I1
Ey
Ex
I3 = I1
z
λ/4
I2 = I1
E3
What is the intensity I3 of the light aZer the last QWP?
A) I1
Before:
B) ½ I1
C) ¼ I1
No absorp/on: Just a phase change!
AZer:
Intensity = 〈E2〉
Electricity & Magne/sm Lecture 24, Slide 28
Follow-Up 3
Consider light incident on two linear polarizers as shown. Suppose I2 = 1/8 I0
y
E1
x
60o
I0
E2
I1
I1 = ½ I0
I2 = 1/8 I0
z
What is the possible polariza/on of the input light?
A) LCP
AZer first polarizer: LP along y−axis with intensity I1
B)
45o
C) un-‐polarized
AZer second polarizer: LP at 60o wrt y−axis
Intensity: I2 = I1cos2(60o) = ¼ I1
I2 = 1/8 I0 ⇒ I1 = ½ I0
D) all of above
E) none of above
Electricity & Magne/sm Lecture 24, Slide 29
Real Quarter Wave Plate
•Only shiZs light exactly λ/4 for one wavelength.
•Typically calibrated for 598 nm, Na light
•Circular Polarizers only work perfectly at 598 nm.
•Other wavelengths produce ellip-cal polariza/on.
•If you look at white light, you see colour-‐changes when you rotate circular polarizers.
•Use a Green filter, to reduce this effect. (not perfect)
•Real-‐life λ/? material, birefringent material: cellophane, clear scotch tape.
ves and Polarization
eil Alberding
Page 28-15
•E rotates counterclockwise as a func/on of /me
•E spirals clockwise as a func/on of z Text
•E rotates clockwise as a func/on of /me
•E spirals counterclockwise as Figure 28.4: Left and right circular polarization.
a func/on of z Most light sources do not produce polarized light. Individual atoms in the source radiate independently. Although at
any instant in time light received from a radiating atom in
theRadio
sourcelink
has a definite
state of polarization the state of
3D glasses
polarization changes rapidly with time. You may think of
unpolarized light as having two polarization components
Circular Polarizer Puzzle
Look at a mirror covered by a circular polarizer.
Flip the polarizer.
Explain what you see.

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