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