Physics 212 Lecture 24 Polarization Physics 212 Lecture

Physics 212 Lecture 24: Polarization Physics 212 Lecture 24, Slide 1

Music Who is the Artist? A) B) C) D) E) Stephane Grappelli Pearl Django Mark O’Connor’s Hot Swing Trio Bob Wills Hot Club of Cowtown

Hour Exam 3: 2 weeks from yesterday (Wed. Apr. 25) covers L 19 -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. ” “Please go through the handedness determination; I don’t understand it. ” “Why is it called a quarter-wave plate? Also, please go over RCP vs LCP. ” Lots of questions about circular “’Different speeds of light’? You all better polarization – we will dissect it! have a really good explanation for this or I will just have to chalk quarter wave plates up as ‘magic’. ” “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 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 05 another? ” They don’t have to be in principle – some materials have three separate axes (like mica and topaz) Physics 212 Lecture 24, Slide 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. Physics 212 Lecture 24, Slide 4

So far we have considered plane waves that look like this: From now on just draw E and remember that B is still there: Physics 212 Lecture 24, Slide 5

Linear Polarization “I was a bit confused by the introduction of the "e-hat" vector (as in its purpose/usefulness)” Physics 212 Lecture 24, Slide 6

Polarizers The molecular structure of a polarizer causes the component of the E field perpendicular to the Transmission Axis to be absorbed. Physics 212 Lecture 24, Slide 7

Quick ACT The molecular structure of a polarizer causes the component of the E field perpendicular to the Transmission Axis to be absorbed. Eo 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 y A) Eosinq B) Eocosq C) 0 D) Eo/sinq E) Eo/cosq What is the only angle for which Eo has no (zero) projection? z sq co 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 xaxis? Eo q y Physics 212 Lecture 24, Slide 8

Linear Polarizers “This stuff is so wicked awesome! Go over the Law of Malice though. ” Physics 212 Lecture 24, Slide 9

An unpolarized EM wave is incident on two orthogonal polarizers. Checkpoint 1 a Two Polarizers 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. . ” Physics 212 Lecture 24, Slide 10

An unpolarized EM wave is incident on two orthogonal polarizers. Checkpoint 1 a Two Polarizers 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(90 o) = 0 Physics 212 Lecture 24, Slide 11

An unpolarized EM wave is incident on two orthogonal polarizers. Checkpoint 1 b Two Polarizers 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. ” Physics 212 Lecture 24, Slide 12

An unpolarized EM wave is incident on two orthogonal polarizers. Checkpoint 1 b Two Polarizers 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 Physics 212 Lecture 24, Slide 13

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: At t=0 RCP Physics 212 Lecture 24, Slide 14

Q: How do we change the relative phase between Ex and Ey? A: Birefringence By picking the right thickness we can change the relative phase by exactly 90 o. Right hand rule This changes linear to circular polarization and is called a quarter wave plate Physics 212 Lecture 24, Slide 15

“Does Birefringent Material absorb intensity? ” NOTE: No Intensity is lost passing through the QWP ! BEFORE QWP: AFTER QWP: THE SAME !! Physics 212 Lecture 24, Slide 16

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 Physics 212 Lecture 24, Slide 17

Circular Light on Linear Polarizer Q: What happens when circularly polarized light is put through a polarizer along the x (or y) axis ? A) I = 0 B) I = ½ I 0 C) I = I 0 X Half of before Physics 212 Lecture 24, Slide 18

Identical linearly polarized light at 45 o 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. A B Checkpoint 2 a 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. ” Physics 212 Lecture 24, Slide 19

Identical linearly polarized light at 45 o 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. A B Checkpoint 2 a 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 Physics 212 Lecture 24, Slide 20

Identical linearly polarized light at 45 o 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. A A Checkpoint 2 b B B Checkpoint 2 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. ” Physics 212 Lecture 24, Slide 23

Identical linearly polarized light at 45 o 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 2 b B B Checkpoint 2 b A A 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 RCP 1/4 l Z Physics 212 Lecture 24, Slide 24

Identical linearly polarized light at 45 o 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. A A Checkpoint 2 c B B Checkpoint 2 c 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. ” Physics 212 Lecture 24, Slide 25

Identical linearly polarized light at 45 o 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 2 c B B Checkpoint 2 c A A 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 ½l Z Z Physics 212 Lecture 24, Slide 26

Executive Summary: Polarizers & QW Plates: Polarized Light Birefringence Circularly or Un-polarized Light RCP Physics 212 Lecture 24, Slide 27

Calculation Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown. What is the intensity I 3 in terms of I 1? fast 45 o y x w slo 60 o I 1 I 2 I 3 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. Physics 212 Lecture 24, Slide 29

Calculation Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown. fast 45 o y E 1 x low s I 1 RCP Ex E y 60 o l/4 I 2 I 3 z • What is the polarization of the light after the QWP? (A) LCP (B) RCP (C) y x Light incident on QWP is linearly polarized at 45 o to fast axis LCP or RCP? Easiest way: Right Hand Rule: (D) y x (E) unpolarized Light will be circularly polarized after QWP Curl fingers of RH back to front (slow crossed into fast). Thumb RCP points in dir of propagation if right hand polarized. Physics 212 Lecture 24, Slide 30

Calculation Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown. fast 45 o y E 1 x I 1 low s RCP Ex E y 60 o l/4 I 2 z I 3 • What is the intensity I 2 of the light after the QWP? (A) I 2 = I 1 BEFORE: (B) I 2 = ½ I 1 (C) I 2 = ¼ I 1 No absorption: Just a phase change ! AFTER: Same before & after ! Physics 212 Lecture 24, Slide 31

Calculation Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown. fast 45 o y E 1 x low s I 1 RCP Ex E y 60 o E 3 l/4 I 2 = I 1 I 3 z • What is the polarization of the light after the 60 o polarizer? (A) LCP (B) RCP (C) y 60 o x (D) y 60 o x (E) unpolarized Absorption: only passes components of E parallel to TA (q = 60 o) Ey E 3 3 60 o Ex Physics 212 Lecture 24, Slide 32

Calculation Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown. fast 45 o y E 1 x I 1 low s RCP Ex E y 60 o E 3 l/4 I 2 = I 1 II 33 = ½ I 1 z • What is the intensity I 3 of the light after the 60 o polarizer? (A) I 3 = I 1 Ey E 3 (B) I 3 = ½ I 1 (C) I 3 = ¼ I 1 3 NOTE: This does not depend on q !! 60 o Ex Physics 212 Lecture 24, Slide 33

Follow Up 1 Replace the 60 o polarizer with another QWP as shown. fast 45 o y RCP E x w slo E x E y I 1 slow fast Ey l/4 I 2 = I 1 I 3 Ex z • What is the polarization of the light after the last QWP? (A) LCP (B) RCP Easiest way: Efast is l/4 ahead of Eslow (C) y x (D) y x (E) unpolarized Brings Ex and Ey back in phase !! Physics 212 Lecture 24, Slide 34

Follow Up 2 Replace the 60 o polarizer with another QWP as shown. fast 45 o y E x I 1 RCP w slo E x E y slow l/4 I 2 = I 1 fast Ey E 3 I 3 = I 1 Ex z • What is the intensity I 3 of the light after the last QWP? (A) I 1 BEFORE: (B) ½ I 1 (C) ¼ I 1 No absorption: Just a phase change ! AFTER: Intensity = < E 2 > Physics 212 Lecture 24, Slide 35

Follow Up 3 Consider light incident on two linear polarizers as shown. Suppose I 2 = 1/8 I 0 y x I 0 E 1 60 o E 2 I 1 = ½ I 0 I 2 = 1/8 I 0 z • What is the possible polarization of the INPUT light? (A) LCP (B) y 45 o x (C) unpolarized • After first polarizer: LP along y-axis with intensity I 1 o • After second polarizer: LP at 60 wrt y-axis 2 o • Intensity: I 2 = I 1 cos (60 ) = ¼ I 1 • I 2 = 1/8 I 0 I 1 = ½ I 0 (D) all of above Question is: What kind of light loses ½ of its intensity after passing through vertical polarizer? (E) none of above Answer: Everything except LP at q other than 45 o Physics 212 Lecture 24, Slide 36