Physics 2112 Topic 24
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1 Physics 2112 Topic 24 Polarization - linear - circular Electricity & Magnetism Lecture 24, Slide 1
2 So far we have considered plane waves that look like this: E x B y From now on just draw E and remember that B is still there: E x Electricity & Magnetism Lecture 24, Slide 2
3 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
4 What this looks like. Slide 4
5 What this looks like. Slide 5
6 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
7 Polarization Recall: I E 2 I can't believe your teaching us the law of "Malus"(Malice). I thought malice was to be avoided? Half Rule Cosine 2 Rule Malus s Law Electricity & Magnetism Lecture 24, Slide 7
8 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
9 Example 24.1: Two polarizers Unpolarized light with an intensity of 1000W/m 2 is incent on two polarizing lenses. The transmission angle of the first lens is 90 o to the x axis and the transmission angle of the second lens is 10 o to the x axis. What is the intensity of the light after it passes through the second lens? Electricity & Magnetism Lecture 24, Slide 9
10 There is no reason that f has to be the same for E x and E y : Making f x different from f y causes circular or elliptical polarization: E x E x Example: f x fy = 90 = 2 = 45 = / 4 E0 = cos kz t 2 E0 = sin kz t 2 At t = 0 RCP Electricity & Magnetism Lecture 24, Slide 10
11 What this looks like. Slide 11
12 What this looks like. Slide 12
13 Circular Polarization Electricity & Magnetism Lecture 24, Slide 13
14 Q: How can we use this to change the relative phase between E x and E y? A: Birefringence Light has different Speeds? Speed of light is different in different materials (More about this later!) Pick right thickness to change the relative phase by exactly 90 o. Right hand rule quarter wave plate Electricity & Magnetism Lecture 24, Slide 14
15 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
16 CheckPoint 3(a) A B Identical linearly polarized light at 45 o 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. I A < I B B. I A = I B C. I A > I B Electricity & Magnetism Lecture 24, Slide 16
17 CheckPoint 3(b) A Linearly B polarized light at 45 o from the y-axis propagates along the z- axis 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. linearly polarized B. left circularly polarized C. right circularly polarized D. undefined Electricity & Magnetism Lecture 24, Slide 17
18 CheckPoint 3(c) A Linearly B polarized light at 45 o from the y-axis propagates along the z- axis 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. linearly polarized B. left circularly polarized C. right circularly polarized D. undefined Electricity & Magnetism Lecture 24, Slide 18
19 I = Intensity: 2 c E x E 2 0 y QW Plate Both E x and E y are still there, so intensity is the same Electricity & Magnetism Lecture 24, Slide 19
20 Question A Identical B linearly polarized light at 45 o 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. linearly polarized B. left circularly polarized C. right circularly polarized D. undefined Electricity & Magnetism
21 Example 24.2 Unpolarized 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 0? y x 45 o fast I 0 I 1 60 o I 2 I 3 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. z Electricity & Magnetism Lecture 24, Slide 21
22 Example 24.3 Unpolarized light is incident on two linear polarizers with no quarter wave plate as shown. y x 45 o I 0 I 1 60 o I 3 z What is the intensity I 3 in terms of I 0? Electricity & Magnetism Lecture 24, Slide 22
23 Executive Summary: Polarizers & QW Plates: Polarized Light Circularly or Un-polarized Light Birefringence RCP E x = E 0 cos( kx) 2 E y = E 0 sin( kx) 2 Electricity & Magnetism
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