29: Polarization
In the last simulation a polarized wave was defined to be an electromagnetic wave that has its electric field confined to change in only one direction. In this simulation we will further investigate polarized waves. In the simulation the graph on the right shows the electric field component[s] for a plane wave traveling straight towards you in the +y direction: E(y,t) = Emax sin (ky - ωt). The two graphs on the left plots the Ex and Ez components of the electric field. The magnetic component, always perpendicular to the electric component, is not shown. In all cases the components are sinusoidal (the time component of the field is show for ω = 1 and a fixed location of z = 0).
Questions:
29.1. Play the simulation. Describe what you see. The graph on the right is what was happening in red box in the initial case of the previous simulation; an electric field oscillating in the x-direction. What is the maxium field in the present case? Is this a polarized wave?
The Poynting vector is the vector cross product of the electric and magnetic field vectors: S = E × B / μo where μo is a constant called the permeability (recall from simulation three that the speed of an electromagnetic wave is given by c = (1/μoεo)1/2 where μo is the permeability and εo is the the permittivity. The magnitude of the vector gives the intensity of an electromagnetic wave in W/m2 and the vector points in the direction that the wave is traveling. Since the magnetic field amplitude is proportional to the electric field amplitude, the Poynting vector (the intensity) is proportional to electric field amplitude squared.
29.2. If the Poynting vector points out of the screen towards you, what direction does the magnetic field point that corresponds to the electric field vector shown in the simulation initially?
29.3. The x-component of the electric field is fixed at 6 N/C. Use the slider to choose a value of 6 N/C for the value for the z-component of electric field and play the simulation. Describe what you see. How is this case similar to that of question 26.7? Is this a polarized wave?
29.4. Try some other values for Ez. Describe the case for Ex = 6 N/C and Ez = 4 N/C. Which way does the electric field vector point? These are all polarized waves with different orientations.
The phase difference determines the phase between Ex and Ez. For zero phase the two vector components start out at zero at the same time. A phase of π radians means the x-component is zero when the y-component is a maximum and vice versa.
29.5. For Ey = 6 N/C choose a phase difference of 1 π radians (use the slider to set the number of radians to 1.0). What do you observe? Now try 0.5 π radians. This case is called circularly polarized light. Note that the x- and y-components are still sine waves but the total electric vector has a fixed magnitude.
If the phase angle is not a whole number or half a whole number times π the light is elliptically polarized.
29.6. Try other values for the phase with the maximum amplitudes the same. Describe what you see. What can you conclude about whole numbers of π radians for a phase difference? What about half whole numbers? What about values in between?
29.7. In your own words, describe how an elliptically polarized electromagnetic wave looks as it probagates through space. (Recall that the wave is travelling in the z-direction which is out of the screen towards you in this case.)
Cirularly and elliptically polarized waves can be right-circularly polarized or left-circularly polarized depending on the sign of the phase angle.
29.8. Try some negative values for the phase. What is the difference between negative and positive values of phase? In which case does the polarization rotate clockwise as as the wave probagates forward?
© 2015, Wolfgang Christian and Kyle Forinash.
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