PRE LAB for electromagnetic lab

Question Description

I need just answer the questions and build a graph by matlab that is related to electromagnetic course

it will be attached everything. so that is all i need and I want you to do graph by matlab

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 0.5cos(ωt − kz ) xˆ + 0.7 cos(ωt − 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
 University of South Florida
3 cos(ωt − kz ) xˆ + 3 cos(ωt − kz + 90o ) yˆ
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EE208-pre.doc
Laboratory #8
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.
c)
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.
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 E0, 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
EE208-pre.doc

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