I need help with Pre lab about (Waves Polarization). This pre lab requires Matlab.

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Znex56

Engineering

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The pre lab is about wave polarization ( Sheet attached)

Please solve the problems on the pre lab sheet. You can write the answers in separate sheet.

Please number each answer correspondingly and provide explanation. You need to use Matlab for some of the problems and take screen shots for the figures from Matlab.

The Matlab file needed for the Pre Lab along with the class lectures are all attached.

The professor suggests that a Matlab version prior to 2017 to be used. If you use 2017 version, the code will run slow. Also, he suggests that you don't copy and paste the code from the file into Matlab. He suggests that you directly open the file in Matlab.

Please let me know if you have any issues ..

Thank you ,,

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Plane-Wave Propagation – Part 1 Electrical Engineering Science II – Electromagnetics Video Presentation 10/22/17 EE Science II - Electromagnetics 1 Module Objectives • Mathematically describe the electric and magnetic fields as TEM waves • Electromagnetic wave equation • Describe propagation of the EM wave in lossless and lossy media • Describe the polarization properties of an EM wave • Recognize the analogies between EM wave propagation and the flow of current/voltage relationships in transmission lines 10/22/17 EE Science II - Electromagnetics 2 Outline • Bounded/Unbounded waves • Electromagnetic Wave Equation 10/22/17 EE Science II - Electromagnetics 3 Propagating EM waves 10/22/17 EE Science II - Electromagnetics 4 Electromagnetic Wave Equation Time-Varying Maxwell’s Equations Maxwell’s equations in Phasor domain Time-Harmonic Maxwell’s equations ELECTROMAGNETIC WAVE EQUATION 10/22/17 EE Science II - Electromagnetics 5 Maxwell’s equation in Phasor domain 10/22/17 EE Science II - Electromagnetics 6 Complex Permittivity 10/22/17 EE Science II - Electromagnetics 7 Time-Harmonic Maxwell’s equations ∇ " #$ = &'( /* 2=0 ∇"1 2 ∇×#$ = −./01 2 = ./*3 #$ ∇×1 For any vector field 5⃗ ∇ " ∇×5⃗ = 0 2 = ./*3 #$ ∇×1 10/22/17 EE Science II - Electromagnetics 8 Electromagnetic Wave Equation 2 ∇×#$ = −./01 For any vector field 5⃗ 7 ⃗ ⃗ ∇× ∇×5 = ∇ ∇ " 5 − ∇ 5⃗ 10/22/17 EE Science II - Electromagnetics 9 Electromagnetic Wave Equation 7 $ 8 # + / 0*3 #$ = 0 7 7$ $ 8 #−: # =0 7 10/22/17 72 72 8 1−: 1 =0 EE Science II - Electromagnetics 10 Plane-Wave Propagation – Part 2 Electrical Engineering Science II – Electromagnetics Video Presentation 10/28/17 EE Science II - Electromagnetics 1 Outline • Plane Wave propagation in lossless media 10/28/17 EE Science II - Electromagnetics 2 Electromagnetic Wave Equation " $ ! # + & '() #$ = 0 " / () = ( − . & In a non-conducting medium 10/28/17 "$ $ ! #−- # =0 " " - = " −& '() /=0 EE Science II - Electromagnetics 3 Uniform Plane Waves "$ $ ! #+0 # =0 " Let us assume that the electric field is given in Cartesian coordinates as: #$ = 12#$3 + 42#$5 + 6̂ #$8 Substitution into the wave equation gives: " $ $ $ ! 12#3 + 42#5 + 6̂ #8 + 0 12#$3 + 42#$5 + 6̂ #$8 = 0 " " " " 9 9 9 $3 + 42#$5 + 6̂ #$8 + + 1 2# " " " 91 94 96 " +0 12#$3 + 42#$5 + 6̂ #$8 = 0 " " " 9 9 9 " $ + + + 0 # = 0 3 " " " 91 94 96 10/28/17 EE Science II - Electromagnetics 4 Uniform Plane Waves "$ $ ! #+0 # =0 " This is the general equation for the 1 − component of the wave " " " 9 9 9 " $ + + + 0 # = 0 3 " " " 91 94 96 10/28/17 EE Science II - Electromagnetics 5 Uniform plane waves - properties " 9 " $ + 0 # = 0 3 " 96 " 9 " $ + 0 # = 0 5 " 96 :;$< :3 =0 :;$= :5 =0 ?< :> :3 =0 ?= :> :5 =0 Ampere’s law ? = .&(#$ !×A 10/28/17 EE Science II - Electromagnetics 6 Uniform plane waves - solutions " 9 " $ + 0 # = 0 3 " 96 10/28/17 C EFG8 E FG8 $ #3 6 = #3B D + #3B D EE Science II - Electromagnetics 7 Transverse Electromagnetic wave Summary: This is a plane wave with with 10/28/17 EE Science II - Electromagnetics 8 Transverse Electromagnetic Wave Time Domain solution # 6, I = 12 A 6, I = 42 C #3B C #3B cos &I − 06 + M R C O/Q C S/Q cos &I − 06 + M Phase velocity 1 TU = '( Q/X For any TEM wave 10/28/17 EE Science II - Electromagnetics 9 Plane-Wave Propagation – Part 3 Electrical Engineering Science II – Electromagnetics Video Presentation 10/27/17 EE Science II - Electromagnetics 1 Outline • Polarization 10/27/17 EE Science II - Electromagnetics 2 Wave Polarization 10/28/17 EE Science II - Electromagnetics 3 Wave Polarization -./0 " ! # = %&!'( + *&!+( , 10/28/17 EE Science II - Electromagnetics 4 Linear Polarization ! #, 2 = %&3' cos 72 − 9# + *&3+ cos(72 − 9# + ;) 10/28/17 EE Science II - Electromagnetics 5 Circular Polarization ! #, 2 = %&3' cos 72 − 9# + *&3+ cos(72 − 9# + ;) 10/28/17 EE Science II - Electromagnetics 6 Elliptical Polarization 10/28/17 EE Science II - Electromagnetics 7 Laboratory #9 EE Science II Laboratory #9 Wave Polarization Pre-Laboratory Assignment Your name: _________________________ 1. Polarization of a uniform plane wave describes the locus traced by the tip of the E field vector at a given point in space as a function of time. Consider a plane wave with E field defined by the following equation: E  0.5cos(t  kz ) xˆ  0.7 cos(t  kz ) yˆ This wave propagates in the z direction and the E field has components in the x and y direction. You will visualize this polarization using MATLAB. Download the MATLAB file titled “Polarization.m” from canvas and run the code (Do not copy the code from the canvas preview and paste it into MATLAB). An interactive figure like the one shown in Figure 1 will be generated. Figure 1: Screenshot of the animation that opens when you run “Polarization.m” The x component of the E field is called Ex in the animation and the y component is called Ey. ax and ay are the magnitudes of the x and y components and for this problem are equal to 0.5 and 0.7 respectively. δ, the phase difference between the components is 0 for E. In the animation, change ax to 0.4, ay to 0.7 (press enter after you type the values). a) What do you observe? ___________________ Since the tip of the E field vector (the blue dot) moves on a line, the wave is said to be linearly polarized. b) Now consider E  3 cos(t  kz ) xˆ  3 cos(t  kz  90o ) yˆ  University of South Florida 1 EE209-pre-180313.doc Laboratory #9 In the animation, change ax = ay = 1.732 (which is 3 ) and δ = 90. Does the tip of the E field move in a circle? Take a screenshot of the animation and submit it. Now place your left hand such that the thumb points towards the direction of wave propagation. Since kz is associated with a negative sign in the equation, the wave is propagating in the +z direction. Therefore, point your thumb towards you. Do your other finger curl in the same direction as the locus? Since the locus traces a circle that can be described by the left hand (when the thumb points in the direction of wave propagation), the wave is said to be left-hand circularly polarized. Now change δ to -90. Take a screenshot of the animation and submit it. Can the locus be described using the right hand? This wave is said to be right-hand circularly polarized. c) Submit screenshots for parts (b) and (c). Press “Stop” to exit the animation. (3 Points) 2. Consider the experimental setup shown in Figure 2. Light emitted by a source is passed through two linearly polarizing plates; the first one is called the polarizer and the second is called the analyzer. When the unpolarized light (consisting of randomly oriented E fields) emitted by the source falls on the polarizer, only the electric fields parallel to the transmission axis of the polarizer are transmitted through it, resulting in linearly polarized light. This linearly polarized light is then incident on the second polarizing plate called the analyzer. The transmission axis of the analyzer makes an angle ψ with that of the polarizer. a. If the electric field incident on the analyzer has a magnitude of E 0, what is the magnitude of the electric field that is transmitted through the analyzer? Hint: To calculate the component parallel to the transmission axis of the analyzer, find the projection of the incident E field on the transmission axis of the analyzer. |E| transmitted through the analyzer = E2 = _____________ (2 points) b. The detector measures the intensity of light, which is proportional to the square of the electric field incident on it. What is the intensity measured by the detector? Answer: I = |E2|2 = ___________________ (1 Point) This equation is called Malus’ Law. c. For what value of ψ is the intensity at the detector i. Maximum? (0.5 Points) ii. Minimum? (0.5 Points) Figure 2: Polarization experiment setup.  University of South Florida 2 EE209-pre-180313.doc Plane-Wave Propagation – Part 4 Electrical Engineering Science II – Electromagnetics Video Presentation 10/29/17 EE Science II - Electromagnetics 1 Outline • Plane wave propagation in lossy media • Electromagnetic power density 10/29/17 EE Science II - Electromagnetics 2 Plane Wave propagation in lossy media "$ $ ! #−& # =0 " &: Propagation Constant " " & = −) * + − , ) 10/29/17 EE Science II - Electromagnetics +. = + − , ) 3 Attenuation of Plane Waves in lossy medium & = / + ,1 2 #$3 4 "$ − & # 4 = 0 3 " 24 " 10/29/17 EE Science II - Electromagnetics 4 Low and high frequency approximations 10/29/17 EE Science II - Electromagnetics 5 Electromagnetic Energy Density Poynting vector: Total power intercepted by A: Average power transmitted by a plane wave: " 5678 #$ = 4̂ 2; " #$ 0 ?"@A 5678 (4) = 4̂ > cos EF 2 ;. EE Science II - Electromagnetics 10/29/17 ;. = ;. > GHI 6 Laboratory #9 EE Science II Laboratory #9 Wave Polarization Summary Polarization of a uniform plane wave describes the locus traced by the tip of its electric field as a function of time. Knowledge of polarization and manipulation thereof finds applications in communication and radar, photography, liquid crystal display technology, 3D movies and images, etc. Polarized light is also used to identify minerals and properties of chemicals compounds such chirality. In this lab, you will generate linearly polarized light using a laser pointer and a polarizing plate called the polarizer. You will then use a second polarizing plate called the analyzer to identify the direction of polarization of the light. You will notice that the intensity of light transmitted through the analyzer depends on its angular orientation with respect to the polarizer. This relationship between intensity and angle between polarizing plates is governed by Malus law, which you will derive and verify experimentally. In an optional section, you will study the response of the detector, a photodiode, and how its performance can be improved by applying a reverse bias. Objectives  Gain an understanding of polarization  Derive and verify Malus law Equipment and Software  Laser – 650nm, 5mW output power  Laser mount  Linear polarizer and mount (Edmund Optics #43-784, Edmund Optics #64-556)  Analyzer with rotary mount (Edmund Optics #52-574)  Photodiode with mount and lens tube (Thorlabs SM05PD1A, Thorlabs SMR05, Thorlabs SM05L05)  Optical posts (Edmund Optics #59-000)  Post holders (Edmund Optics #58-977 ) and rail  DC power supply, oscilloscope, and function generator  MATLAB for analyzing measured data  University of South Florida 1 EE209-sum-180313.doc
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Explanation & Answer

attached is my answer

Question 1:
The MATLAB output from the given code is shown below:

a) It can be observed that a polarized electromagnetic flood of wavelength λ has its electric field
vector E wavering in the horizontal direction. The magnetic field B is dependably at right edges
to it, and both are opposite to z. The general pattern of the p...


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