ENG 403 Electromagnetic Wave Polarization Pre-Laboratory Assignment electromagnetic pre lab please answer the questions in the per lab and read the careful

ENG 403 Electromagnetic Wave Polarization Pre-Laboratory Assignment electromagnetic pre lab please answer the questions in the per lab and read the carefully.see the attachments for the pre lab also I attached the matlab code you need to use . Laboratory #8
EE Science II Laboratory #8
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 = 0.5 cos(?t ? kz)x? + 0.7 cos(?t ? kz) y?
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” 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. ?, 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)x? + 3 cos(?t ? kz + 90o ) yˆ
1
Laboratory #8
In the animation, change ax = ay = 1.732 (which is 3 ) and ? = 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 ? 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 ? 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 =
b.
(2 points)
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 ? is the intensity at the detector
i. Maximum? (0.5 Points)
ii. Minimum? (0.5 Points)
Figure 2: Polarization experiment setup.
2
clc
clear all
close all
%————————————————————————%—————————-Variable Definitions————————-%V_theta_90: A array consisting of corrected voltage in mV, Vcorrc for all
values
%of theta when phi = 90deg
%–%V_theta_270: A array consisting of corrected voltage in mV, Vcorrc for all
%values of theta when phi = 270deg
%–%DC_offset: Measured offset due to ambinent light
%theta_pol=Value of theta for max intensity in degrees
%phi_pol=Value of phi for max intensity
%————————————————————————%————————————————————————%———————Measured Data————————————–%—-Enter measured data here———————————————–V_theta_90=[]; %–Enter your values here
V_theta_270=[];%–Enter your values here
DC_offset=;%–Enter your value here
theta_pol=;%–Enter your values here
phi_pol=;%–Enter your values here
%————————————————————————-%————————————————————————-%———-Plotting the data———————————————-%—-Figure 1: Measured voltage with respect to theta———————Avg_0=(V_theta_90(1)+V_theta_270(1))/2;
V_theta_90(1)=Avg_0;
V_theta_270(1)=Avg_0;
% V_theta_90=fliplr(V_theta_90);
y_scale_max=max(max(V_theta_90),max(V_theta_270));
y_scale_min=min(min(V_theta_90),min(V_theta_270));
theta=0:10:90;
figure(‘Units’,’inches’,’Position’,[2 2 8 6])
ax1=axes(‘Position’,[0.125 0.15 0.4 0.75]);%–creating axis for
%stiching the plots in phi=90
ax2=axes(‘Position’,[0.525 0.15 0.4 0.75]);%–creating axis for
%stiching the plots in phi=270
plot(ax1,theta,V_theta_90,’LineWidth’,2);
ylim(ax1,[y_scale_min,y_scale_max])
set(ax1,’Xdir’,’reverse’,’FontSize’,18,’FontWeight’,’bold’) %–plot for phi=0
has to be reversed.
grid(ax1,’on’)
plot(ax2,theta,V_theta_270,’LineWidth’,2);
ylim(ax2,[y_scale_min,y_scale_max])
set(ax2,’YAxisLocation’,’right’,’FontSize’,18,’FontWeight’,…
‘bold’)
grid(ax2,’on’)
ylab=ylabel(ax1,’V_c_o_r_r_c (mV)’);
set(ylab,’FontSize’,20,’FontWeight’,’Bold’)
str = {‘Measured voltage’};
dim = [0.4 0.99 0.3 0];
a=annotation(‘textbox’,dim,’units’,’normalized’,’String’,str,…
‘FitBoxToText’,’on’,’LineStyle’,’none’);
set(a,’FontSize’,24)
set(a,’FontWeight’,’Bold’,’FontAngle’, ‘italic’)
str = {‘theta (degrees)’};
dim = [0.45 0.09 0.3 0];
a=annotation(‘textbox’,dim,’units’,’normalized’,’String’,str,…
‘FitBoxToText’,’on’,’LineStyle’,’none’);
set(a,’FontSize’,24)
set(a,’FontWeight’,’Bold’)
str = {‘phi=90^o’};
dim = [0.2 0.4 0.3 0];
a=annotation(‘textbox’,dim,’units’,’normalized’,’String’,str,…
‘FitBoxToText’,’on’,’LineStyle’,’None’,’Color’,[1 0 0]);
set(a,’FontSize’,20)
set(a,’FontWeight’,’Bold’)
str = {‘phi=270^o’};
dim = [0.75 0.4 0.3 0];
a=annotation(‘textbox’,dim,’units’,’normalized’,’String’,str,…
‘FitBoxToText’,’on’,’LineStyle’,’None’,’Color’,[1 0 0]);
set(a,’FontSize’,20)
set(a,’FontWeight’,’Bold’)
%——-Figure 2: Comparing measured data with ideal data——–Vmeas=[fliplr(V_theta_90) V_theta_270(2:length(V_theta_270))];
Vpp=circshift(Vmeas,[0,theta_pol/10*sind(phi_pol)]);
% Avg_vpp0=(Vpp(length(Vpp)/2)+Vpp(1+length(Vpp)/2))/2;
% Vpp(length(Vpp)/2)=Avg_vpp0;
% Vpp(1+length(Vpp)/2)=Avg_vpp0;
Vnorm=(Vpp/max(Vpp));
Vnorm_90=fliplr(Vnorm(1:length(V_theta_90)));
Vnorm_270=Vnorm(length(V_theta_90):length(Vnorm));
figure(‘Units’,’inches’,’Position’,[2 2 8 6])
ax1=axes(‘Position’,[0.125 0.15 0.4 0.75]);%–creating axis for
%stiching the plots in phi=90
hold on;
plotHandle1=plot(ax1,theta,((Vnorm_90)),’–x’,’LineWidth’,2);
plotHandle2=plot(ax1,theta,cosd(theta).^2,’-g’,’LineWidth’,2);
ylim(ax1,[0,1])
set(ax1,’Xdir’,’reverse’,’FontSize’,18,’FontWeight’,’bold’) %–plot for phi=0
has to be reversed.
grid(ax1,’on’)
ax2=axes(‘Position’,[0.525 0.15 0.4 0.75]);%–creating axis for
%stiching the plots in phi=270
hold on;
plotHandle3=plot(ax2,theta,((Vnorm_270)),’–x’,’LineWidth’,2);
plotHandle4=plot(ax2,theta,cosd(theta).^2,’-g’,’LineWidth’,2);
ylim(ax2,[0,1])
set(ax2,’YAxisLocation’,’right’,’FontSize’,18,’FontWeight’,…
‘bold’)
grid(ax2,’on’)
ylab=ylabel(ax1,’Normalized Intensity’);
set(ylab,’FontSize’,20,’FontWeight’,’Bold’)
str = {‘Comparison between Measured and Theoretical’};
dim = [0.1 0.99 0.3 0];
a=annotation(‘textbox’,dim,’units’,’normalized’,’String’,str,…
‘FitBoxToText’,’on’,’LineStyle’,’none’);
set(a,’FontSize’,20)
set(a,’FontWeight’,’Bold’,’FontAngle’, ‘italic’)
str = {‘psi (degrees)’};
dim = [0.45 0.09 0.3 0];
a=annotation(‘textbox’,dim,’units’,’normalized’,’String’,str,…
‘FitBoxToText’,’on’,’LineStyle’,’none’);
set(a,’FontSize’,24)
set(a,’FontWeight’,’Bold’)
str = {‘phi=90^o’};
dim = [0.2 0.6 0.3 0];
a=annotation(‘textbox’,dim,’units’,’normalized’,’String’,str,…
‘FitBoxToText’,’on’,’LineStyle’,’None’,’Color’,[1 0 0]);
set(a,’FontSize’,20)
set(a,’FontWeight’,’Bold’)
str = {‘phi=270^o’};
dim = [0.75 0.6 0.3 0];
a=annotation(‘textbox’,dim,’units’,’normalized’,’String’,str,…
‘FitBoxToText’,’on’,’LineStyle’,’None’,’Color’,[1 0 0]);
set(a,’FontSize’,20)
set(a,’FontWeight’,’Bold’)
legend(‘Measured Intensity’,’Theoretical Intensity’)

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