Transcript ppt
Physics 2112 Topic 24 Polarization - linear - circular Electricity & Magnetism Lecture 24, Slide 1 So far we have considered plane waves that look like this: Ex By From now on just draw E and remember that B is still there: Ex Electricity & Magnetism Lecture 24, Slide 2 Linear Polarization “I was a bit confused by the introduction of the "e-hat" vector (as in its purpose/usefulness)” Electricity & Magnetism Lecture 24, Slide 3 What this looks like…. Slide 4 What this looks like…. Slide 5 Polarizer The molecular structure of a polarizer causes the component of the E field perpendicular to the Transmission Axis to be absorbed. Electricity & Magnetism Lecture 24, Slide 6 Polarization “I can't believe your “Half teachingRule” us the law of "Malus"(Malice). I thought malice was to be avoided?” Recall: IE 2 “Cosine2 Rule” Malus’s Law Electricity & Magnetism Lecture 24, Slide 7 CheckPoint 1: Two Polarizers An unpolarized EM wave is incident on two orthogonal polarizers. Is it possible to increase this percentage by inserting another polarizer between the original two? A. yes B. no Electricity & Magnetism Lecture 24, Slide 8 Example 24.1: Two polarizers 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. What is the intensity of the light after it passes through the second lens? Electricity & Magnetism Lecture 24, Slide 9 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: fx f y = 90 = At t = 0 2 = 45 = / 4 E0 Ex = coskz t 2 E0 Ex = sin kz t 2 RCP Electricity & Magnetism Lecture 24, Slide 10 What this looks like…. Slide 11 What this looks like…. Slide 12 Circular Polarization Electricity & Magnetism Lecture 24, Slide 13 Light has different Speeds? Speed of light is different in different materials (More about this later!) 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. Right hand rule quarter wave plate Electricity & Magnetism Lecture 24, Slide 14 Right or Left? “Curl fingers slow to fast” Right circularly polarized Do right hand rule Fingers along slow direction Cross into fast direction If thumb points in direction of propagation: RCP Electricity & Magnetism Lecture 24, Slide 15 CheckPoint 3(a) A B 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 Electricity & Magnetism Lecture 24, Slide 16 CheckPoint 3(b) A B Linearly polarized light at 45o from the y-axis propagates along the zaxis 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. B. C. D. linearly polarized left circularly polarized right circularly polarized undefined Electricity & Magnetism Lecture 24, Slide 17 CheckPoint 3(c) A B Linearly polarized light at 45o from the y-axis propagates along the zaxis 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. B. C. D. linearly polarized left circularly polarized right circularly polarized undefined Electricity & Magnetism Lecture 24, Slide 18 Intensity: I = 0c Ex2 E y2 QW Plate Both Ex and Ey are still there, so intensity is the same Electricity & Magnetism Lecture 24, Slide 19 Question A B linearly polarized light at Identical 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. B. C. D. linearly polarized left circularly polarized right circularly polarized undefined Electricity & Magnetism Lecture 24, Slide 20 Example 24.2 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? y fast 45o x I0 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. Electricity & Magnetism Lecture 24, Slide 21 Example 24.3 Unpolarized light is incident on two linear polarizers with no quarter wave plate as shown. y 45o x I0 60o I1 I3 z What is the intensity I3 in terms of I0? Electricity & Magnetism Lecture 24, Slide 22 Executive Summary: Polarizers & QW Plates: Polarized Light Birefringence Circularly or Un-polarized Light RCP Ex = E0 cos( kx) 2 Ey = Electricity & Magnetism E0 sin( kx) 2