Lecture 24: Polarization Physics 212 Lecture 24: Polarization

Music Who is the Artist? Stephane Grappelli Pearl Django Mark O’Connor’s Hot Swing Trio Bob Wills Hot Club of Cowtown Physics 212 Lecture 24

Lots of questions about circular polarization – we will dissect it! Hour Exam 3: 2 weeks from yesterday (Wed. Apr. 25) covers L19-26 inclusive (LC circuits to lenses. Sign up for conflicts, etc. NOW (no later than Mon. Apr. 23 at 10:00 p.m.) Your Comments “The prelecture was straightforward, but the checkpoints were challenging.” “Why is it called a quarter-wave plate? Also, please go over RCP vs LCP.” “’Different speeds of light’? You all better have a really good explanation for this or I will just have to chalk quarter wave plates up as ‘magic’.” “Please go through the handedness determination; I don’t understand it.” Lots of questions about circular polarization – we will dissect it! “I once came across a tv screen in a mall that I couldn’t see if I had my polarized sunglasses on, because of the way the the glasses were oriented. Can you repeat a kind of demonstration like that? that was cool.” “Just something that came to my mind, how do we know that the fast v and the slow v in a bire-thingy have to be at right angles with one another?” They don’t have to be in principle – some materials have three separate axes (like mica and topaz) 05 When I talked to my friends about this prelecture, some of them loved it, and the others hated it. I didn't know physics could be so polarizing. 3

Quantum Communication “WHY? Why would you ever want to do this?” Communicate and know for sure if message has been looked at by someone else (quantum mechanics): P. Kwiat, et al.

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 “I was a bit confused by the introduction of the "e-hat" vector (as in its purpose/usefulness)”

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

Quick ACT The molecular structure of a polarizer causes the component of the E field perpendicular to the Transmission Axis to be absorbed. Suppose we have a beam traveling in the + z-direction. At t = 0 and z = 0, the electric field is aligned along the positive x-axis and has a magnitude equal to Eo z y Eo What is the component of Eo along a direction in the x-y plane that makes an angle of q with respect to the x-axis? B) Eocosq A) Eosinq C) 0 D) Eo/sinq E) Eo/cosq q Eo y Eocosq What is the only angle for which Eo has no (zero) projection?

Linear Polarizers “This stuff is so wicked awesome! Go over the Law of Malice though.”

Checkpoint 1a Two Polarizers An unpolarized EM wave is incident on two orthogonal polarizers. Two Polarizers Checkpoint 1a What percentage of the intensity gets through both polarizers? A. 50% B. 25% C. 0% “Orientation changes from vertical to horizontal” “halved and halved again” “There is no parallel component that passes through the second polarizer..”

Checkpoint 1a Two Polarizers An unpolarized EM wave is incident on two orthogonal polarizers. Two Polarizers Checkpoint 1a What percentage of the intensity gets through both polarizers? A. 50% B. 25% C. 0% The second polarizer is orthogonal to the first no light will come through. cos(90o) = 0

Checkpoint 1b Two Polarizers An unpolarized EM wave is incident on two orthogonal polarizers. Two Polarizers Checkpoint 1b Is it possible to increase this percentage by inserting another Polarizer between the original two? A. Yes B. No “If the middle one creates a non vertical polarization, the percent increases.” “The percentage is already 0 and polarizers cannot increase intensity.”

Checkpoint 1b Two Polarizers An unpolarized EM wave is incident on two orthogonal polarizers. Two Polarizers Checkpoint 1b Is it possible to increase this percentage by inserting another Polarizer between the original two? A. Yes B. No Any non-horizontal polarizer after the first polarizer will produce polarized light AT THAT ANGLE Part of that light will make it through the horizontal polarizer

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: RCP

Q: How do we change the relative phase between Ex and Ey? A: Birefringence 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

NOTE: No Intensity is lost passing through the QWP ! “Does Birefringent Material absorb intensity?” NOTE: No Intensity is lost passing through the QWP ! BEFORE QWP: THE SAME !! AFTER QWP:

Right or Left ??? Right circularly polarized Do right hand rule Fingers along slow direction Cross into fast direction If thumb points in direction of propagation: RCP

Circular Light on Linear Polarizer Q: What happens when circularly polarized light is put through a polarizer along the x (or y) axis ? I = 0 I = ½ I0 I = I0 X Half of before

Identical linearly polarized light at 45o from the y-axis and propagating along the z axis is incident on two different objects. In Case A the light intercepts a linear polarizer with polarization along the y-axis In Case B, the light intercepts a quarter wave plate with vast axis along the y-axis. Checkpoint 2a A B Compare the intensities of the light waves after transmission. A. IA < IB B. IA = IB C. IA > IB “intensity will decrease in case a and remain the same, just out of phase in case B” “They both reduce the intensity at the same rate because the transmission axis angles are the same” “The waves are in synch before the polarizer and out of it after, making the intensity for Ib less.”

Checkpoint 2a A B Case A: Case B: Ex is absorbed (Ex,Ey) phase changed Identical linearly polarized light at 45o from the y-axis and propagating along the z axis is incident on two different objects. In Case A the light intercepts a linear polarizer with polarization along the y-axis In Case B, the light intercepts a quarter wave plate with vast axis along the y-axis. Checkpoint 2a A B Compare the intensities of the light waves after transmission. A. IA < IB B. IA = IB C. IA > IB Case A: Ex is absorbed Case B: (Ex,Ey) phase changed

Both Ex and Ey are still there, so intensity is the same QW Plate PHASE CHANGE Both Ex and Ey are still there, so intensity is the same

Ex is missing, so intensity is lower Polarizer ABSORB COMPONENT

Checkpoint 2b Checkpoint 2b A B A B Identical linearly polarized light at 45o from the y-axis and propagating along the z axis is incident on two different objects. In Case A the light intercepts a linear polarizer with polarization along the y-axis In Case B, the light intercepts a quarter wave plate with vast axis along the y-axis. Checkpoint 2b A B Checkpoint 2b A B What is the polarization of the light wave in Case B after it passes through the quarter wave plate?. A. linearly polarized B. left circularly polarized C. right circularly polarized D. undefined “along the y axis with no x components” “cant curl fingers from Ey to Ex using right hand rule so it must be Left Circularly Polarized” “It is slow along the x-axis and fast along y-axis.” “There is no component in the slow polarization, so none occurs.”

Checkpoint 2b Checkpoint 2b RCP A B A B Identical linearly polarized light at 45o from the y-axis and propagating along the z axis is incident on two different objects. In Case A the light intercepts a linear polarizer with polarization along the y-axis In Case B, the light intercepts a quarter wave plate with vast axis along the y-axis. Checkpoint 2b A B Checkpoint 2b A B What is the polarization of the light wave in Case B after it passes through the quarter wave plate?. A. linearly polarized B. left circularly polarized C. right circularly polarized D. undefined Z 1/4 l RCP

Checkpoint 2c Checkpoint 2c A B A B Identical linearly polarized light at 45o from the y-axis and propagating along the z axis is incident on two different objects. In Case A the light intercepts a linear polarizer with polarization along the y-axis In Case B, the light intercepts a quarter wave plate with vast axis along the y-axis. Checkpoint 2c A B Checkpoint 2c A B If the thickness of the quarter-wave plate in Case B is doubled, what is the polarization of the wave after passing through the wave plate? A. linearly polarized B. circularly polarized C. undefined “If the thickness is doubled then the relative phase is 180 degrees, which means it is linearly polarized. I think.” “Thickness does not affect how it is polarized.” “Ex and Ey will be antiparallel if thickness is doubled, so the resulting light cannot be defined.”

Checkpoint 2c Checkpoint 2c ½ l A B A B Identical linearly polarized light at 45o from the y-axis and propagating along the z axis is incident on two different objects. In Case A the light intercepts a linear polarizer with polarization along the y-axis In Case B, the light intercepts a quarter wave plate with vast axis along the y-axis. Checkpoint 2c A B Checkpoint 2c A B If the thickness of the quarter-wave plate in Case B is doubled, what is the polarization of the wave after passing through the wave plate? A. linearly polarized B. circularly polarized C. undefined ½ l Z Z

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

Demos: What else can we put in there to change the polarization?

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.

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? (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 (slow crossed into fast). 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 = I1 (B) I2 = ½ I1 (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 I3 z What is the intensity I3 of the light after the 60o polarizer? (A) I3 = I1 (B) I3 = ½ I1 (C) I3 = ¼ I1 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. Ey E3 3 NOTE: This does not depend on q !! 60o Ex

Efast is l/4 ahead of Eslow Follow Up 1 Replace the 60o polarizer with another QWP as shown. fast y 45o E RCP slow x slow Ex Ey Ey Ex E3 fast I1 l/4 I2 = I1 I3 z What is the polarization of the light after the last QWP? (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. Easiest way: Efast is l/4 ahead of Eslow Brings Ex and Ey back in phase !!

Follow Up 2 (A) I1 (B) ½ I1 (C) ¼ I1 Replace the 60o polarizer with another QWP as shown. fast y 45o x E RCP slow slow Ex Ey E3 fast I1 Ey Ex l/4 I2 = I1 z I3 = I1 What is the intensity I3 of the light after the last QWP? (A) I1 (B) ½ I1 (C) ¼ I1 AFTER: BEFORE: No absorption: Just a phase change ! 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. Intensity = < E2 >

Follow Up 3 (A) LCP (B) (C) unpolarized (D) all of above Consider light incident on two linear polarizers as shown. Suppose I2 = 1/8 I0 y x After first polarizer: LP along y-axis with intensity I1 I1 E1 60o E2 After second polarizer: LP at 60o wrt y-axis Intensity: I2 = I1cos2(60o) = ¼ I1 I0 I2 = 1/8 I0  I1 = ½ I0 I1 = ½ I0 I2 = 1/8 I0 z What is the possible polarization of the INPUT light? (A) LCP x y (B) 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. 45o Question is: What kind of light loses ½ of its intensity after passing through vertical polarizer? (C) unpolarized Answer: Everything except LP at q other than 45o (D) all of above (E) none of above