Polarization - linear - circular Physics 2112 Topic 24 Polarization - linear - circular

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

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

What this looks like….

What this looks like….

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

Polarization “Half Rule” “Cosine2 Rule” Malus’s Law Recall: “I can't believe your teaching us the law of "Malus"(Malice). I thought malice was to be avoided?” “Half Rule” “Cosine2 Rule” Malus’s Law

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? yes no

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?

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

What this looks like….

What this looks like….

Circular Polarization

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 Right hand rule Pick right thickness to change the relative phase by exactly 90o. quarter wave plate

Right or Left? Right circularly polarized Do right hand rule “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

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. IA < IB IA = IB IA > IB

CheckPoint 3(b) A Linearly polarized light at 45o from the y-axis propagates along the z-axis and is incident on a quarter wave-plate with fast axis along the y-axis B What is the polarization of the light wave in case 2 after it passed through the quarter-wave plate? linearly polarized left circularly polarized right circularly polarized undefined

CheckPoint 3(c) A Linearly polarized light at 45o from the y-axis propagates along the z-axis and is incident on a quarter wave-plate with fast axis along the y-axis. B 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? linearly polarized left circularly polarized right circularly polarized undefined

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

Question A Identical linearly polarized light at 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. B What is the polarization of the light wave in case 2 after it passed through the quarter-wave plate? linearly polarized left circularly polarized right circularly polarized undefined

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? fast y 45o x slow 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.

What is the intensity I3 in terms of I0? Example 24.3 Unpolarized light is incident on two linear polarizers with no quarter wave plate as shown. y 45o x 60o I0 I1 I3 z What is the intensity I3 in terms of I0?

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