Physics 2112
Topic 24
Polarization
- linear
- circular
Electricity & Magnetism Lecture 24, Slide 1
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
Electricity & Magnetism Lecture 24, Slide 2
Linear Polarization
“I was a bit confused by the introduction of the "e-hat" vector
(as in its purpose/usefulness)”
Electricity & Magnetism Lecture 24, Slide 3
What this looks like….
Slide 4
What this looks like….
Slide 5
Polarizer
The molecular structure of a polarizer causes the component of
the E field perpendicular to the Transmission Axis to be absorbed.
Electricity & Magnetism Lecture 24, Slide 6
Polarization
“I can't believe your
“Half
teachingRule”
us the law
of "Malus"(Malice).
I thought malice
was to be avoided?”
Recall:
IE
2
“Cosine2 Rule”
Malus’s Law
Electricity & Magnetism Lecture 24, Slide 7
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?
A. yes
B. no
Electricity & Magnetism Lecture 24, Slide 8
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?
Electricity & Magnetism Lecture 24, Slide 9
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:
fx  f y = 90 =


At t = 0
2
 = 45 =  / 4
E0
Ex =
coskz  t 
2
E0
Ex =
sin kz  t 
2
RCP
Electricity & Magnetism Lecture 24, Slide 10
What this looks like….
Slide 11
What this looks like….
Slide 12
Circular Polarization
Electricity & Magnetism Lecture 24, Slide 13
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
Pick right thickness to
change the relative
phase by exactly 90o.
Right
hand
rule
quarter wave plate
Electricity & Magnetism Lecture 24, Slide 14
Right or Left?
“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
Electricity & Magnetism Lecture 24, Slide 15
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.
A. IA < IB
B. IA = IB
C. IA > IB
Electricity & Magnetism Lecture 24, Slide 16
CheckPoint 3(b)
A
B
Linearly
polarized light at
45o from the y-axis
propagates along the zaxis and is incident on a
quarter wave-plate with
fast axis along the y-axis
What is the polarization of the light wave in case 2 after it
passed through the quarter-wave plate?
A.
B.
C.
D.
linearly polarized
left circularly polarized
right circularly polarized
undefined
Electricity & Magnetism Lecture 24, Slide 17
CheckPoint 3(c)
A
B
Linearly
polarized light at
45o from the y-axis
propagates along the zaxis and is incident on a
quarter wave-plate with
fast axis along the y-axis.
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?
A.
B.
C.
D.
linearly polarized
left circularly polarized
right circularly polarized
undefined
Electricity & Magnetism Lecture 24, Slide 18
Intensity:

I =  0c Ex2  E y2

QW Plate
Both Ex and Ey
are still there, so
intensity is the same
Electricity & Magnetism Lecture 24, Slide 19
Question
A
B linearly polarized light at
Identical
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.
What is the polarization of the light wave in case 2 after it
passed through the quarter-wave plate?
A.
B.
C.
D.
linearly polarized
left circularly polarized
right circularly polarized
undefined
Electricity & Magnetism Lecture 24, Slide 20
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?
y
fast
45o
x
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.
Electricity & Magnetism Lecture 24, Slide 21
Example 24.3
Unpolarized light is incident on two linear
polarizers with no quarter wave plate as
shown.
y
45o
x
I0
60o
I1
I3
z
What is the intensity I3 in terms of I0?
Electricity & Magnetism Lecture 24, Slide 22
Executive Summary:
Polarizers & QW Plates:
Polarized Light
Birefringence
Circularly or Un-polarized Light
RCP
Ex =
E0
cos( kx)
2
Ey =
Electricity & Magnetism
E0
sin( kx)
2