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Physics 212 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.

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Physics 212 Lecture 24: Polarization

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  1. Physics 212 Lecture 24: Polarization

  2. 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

  3. “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) 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.” “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 polarization – we will dissect it! “’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’.” “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.” 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.

  4. 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.

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

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

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

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

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

  10. 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..”

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

  12. 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.”

  13. 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

  14. Example: There is no reason thatfhas to be the same for Exand Ey: Making fxdifferent fromfycauses circular or elliptical polarization: At t=0 RCP

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

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

  17. 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

  18. Circular Light on Linear Polarizer Half of before Q: What happens when circularlypolarized light is put through apolarizer along the x (or y) axis ? • I = 0 • I = ½ I0 • I = I0 X

  19. Identical linearly polarized light at 45o from the y-axis and propagating along the zaxis is incident on two different objects. In Case A the light intercepts a linear polarizerwith polarization along the y-axis In Case B, the light intercepts a quarter wave platewith vast axis along the y-axis. Checkpoint 2a A B Compare the intensities of the light waves after transmission.A. IA < IBB. 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.”

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

  21. Identical linearly polarized light at 45o from the y-axis and propagating along the zaxis is incident on two different objects. In Case A the light intercepts a linear polarizerwith polarization along the y-axis In Case B, the light intercepts a quarter wave platewith 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 thequarter wave plate?.A. linearly polarized B. left circularly polarizedC. 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.”

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

  23. Identical linearly polarized light at 45o from the y-axis and propagating along the zaxis is incident on two different objects. In Case A the light intercepts a linear polarizerwith polarization along the y-axis In Case B, the light intercepts a quarter wave platewith 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 polarizedC. 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.”

  24. Identical linearly polarized light at 45o from the y-axis and propagating along the zaxis is incident on two different objects. In Case A the light intercepts a linear polarizerwith polarization along the y-axis In Case B, the light intercepts a quarter wave platewith vast axis along the y-axis. ½l Z Z 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 polarizedC. undefined

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

  26. 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 45o y x slow 60o I1 I2 z I3 • 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.

  27. Calculation RCP E1 Ex Ey l/4 • What is the polarization of the light after the QWP? (A) LCP (B) RCP (C) (D) (E) unpolarized Light incident on QWP is linearly polarized at 45o to fast axis Light will be circularly polarized after QWP y y LCP or RCP? Easiest way: Right Hand Rule: x x RCP Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown. fast 45o y x slow 60o I1 I2 z I3 Curl fingers of RH back to front (slow crossed into fast). Thumb points in dir of propagationif right hand polarized.

  28. Calculation BEFORE: Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown. fast 45o y RCP E1 x slow Ex Ey 60o I1 l/4 I2 z I3 • What is the intensity I2 of the light after the QWP? (A) I2 = I1 (B) I2 = ½ I1 (C) I2 = ¼ I1 AFTER: No absorption: Just a phase change ! Same before & after !

  29. Calculation E3 • What is the polarization of the light after the 60o polarizer? y y 60o 60o (A) LCP (B) RCP (C) (D) (E) unpolarized x x Ey E3 3 60o Ex Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown. fast 45o y RCP E1 x slow Ex Ey 60o I1 l/4 I2 = I1 z I3 Absorption: only passes components of E parallel to TA (q = 60o)

  30. Calculation I3 = ½ I1 Light is incident on two linear polarizers and a quarter wave plate (QWP) as shown. fast 45o y RCP E1 x slow Ex Ey 60o E3 I1 l/4 I2 = I1 z I3 • What is the intensity I3 of the light after the 60o polarizer? (A) I3 = I1 (B) I3 = ½ I1 (C) I3 = ¼ I1 Ey E3 3 NOTE: This does not depend on q !! 60o Ex

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

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

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

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