Physics 2112Topic 24
Polarization - linear - circular
Electricity & Magnetism Lecture 24, Slide 1
So far we have considered plane waves that look like this:
From now on just draw E and remember that B is still there:
Electricity & Magnetism Lecture 24, Slide 2
Ex
By
Ex
“I was a bit confused by the introduction of the "e-hat" vector (as in its purpose/usefulness)”
Linear Polarization
Electricity & Magnetism Lecture 24, Slide 3
Slide 4
What this looks like….
Slide 5
What this looks like….
The molecular structure of a polarizer causes the component of the E field perpendicular to the Transmission Axis to be absorbed.
Polarizer
Electricity & Magnetism Lecture 24, Slide 6
“I can't believe your teaching us the law of "Malus"(Malice). I thought malice was to be avoided?”
Electricity & Magnetism Lecture 24, Slide 7
“Half Rule”
“Cosine2 Rule”
Polarization
Malus’s Law
Recall:
2EI
An unpolarized EM wave is incident on two orthogonal polarizers.
CheckPoint 1: Two Polarizers
Electricity & Magnetism Lecture 24, Slide 8
Is it possible to increase this percentage by inserting another polarizer between the original two?
A. yesB. no
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.
Example 24.1: Two polarizers
Electricity & Magnetism Lecture 24, Slide 9
What is the intensity of the light after it passes through the second lens?
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
RCP
Electricity & Magnetism Lecture 24, Slide 10
Example:
tkzEEx = cos20
tkzEEx = sin20
290 ff ==
yx
4/45 ==
Slide 11
What this looks like….
Slide 12
What this looks like….
Electricity & Magnetism Lecture 24, Slide 13
Circular Polarization
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.
quarter wave plateRight hand rule
Electricity & Magnetism Lecture 24, Slide 14
Light has different Speeds?Speed of light is different in different
materials (More about this later!)
Right circularly polarizedDo right hand rule
Fingers along slow directionCross into fast direction
If thumb points in direction of propagation: RCP
“Curl fingers slow to fast”
Right or Left?
Electricity & Magnetism Lecture 24, Slide 15
A B
CheckPoint 3(a)
Electricity & Magnetism Lecture 24, Slide 16
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
A B
CheckPoint 3(b)
Electricity & Magnetism Lecture 24, Slide 17
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
What is the polarization of the light wave in case 2 after it passed through the quarter-wave plate?
A. linearly polarizedB. left circularly polarizedC. right circularly polarizedD. undefined
A B
CheckPoint 3(c)
Electricity & Magnetism Lecture 24, Slide 18
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.
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. linearly polarizedB. left circularly polarizedC. right circularly polarizedD. undefined
Both Ex and Eyare still there, so
intensity is the same
QW Plate
PHASE
CHANGE
Electricity & Magnetism Lecture 24, Slide 19
Intensity:
220 yx EEcI =
A B
Question
Electricity & Magnetism Lecture 24, Slide 20
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.
What is the polarization of the light wave in case 2 after it passed through the quarter-wave plate?
A. linearly polarizedB. left circularly polarizedC. right circularly polarizedD. undefined
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.
xy
z
45ofast
slow
I1
60o
I2I3
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?
Example 24.2
Electricity & Magnetism Lecture 24, Slide 21
I0
xy
z
45o
I1
60o
I3
Unpolarized light is incident on two linear polarizers with no quarter wave plate as shown.
Example 24.3
Electricity & Magnetism Lecture 24, Slide 22
I0
What is the intensity I3 in terms of I0?
Circularly or Un-polarized LightPolarized Light
Polarizers & QW Plates:
Birefringence
0 cos( )2
=xE
E kx
0 sin( )2yE
E kx=
RCP
Executive Summary:
Electricity & Magnetism Lecture 24, Slide 23