# Lecture 23: Polarization

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Lecture 23: Polarization
Physics 212 Lecture 23: Polarization

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.

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

Linear Polarization

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

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

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

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.

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

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:

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

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

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

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

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

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

Ex is missing, so intensity is lower Polarizer

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)

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

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

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.

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.

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 !

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

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