Wave-Wave Interactions: Polarization
In a linearly polarized wave, the medium is displaced back and forth along a straight line. In a circularly polarized wave, medium is displaced in a circular motion about equilibrium. For example, imagine moving one end of a taut string in a circle. This motion creates spiral wave where each element of the string moves in a circle. Circularly polarized waves are characterized by their handedness or helicity. If for example, the spiral formed by the wave goes the same way as the threads on a right handed screw, the wave is said to be right handed. In an elliptically polarized wave, the medium is displaced in elliptical motion about equilibrium.
The key to understanding how to make different polarizations is to realize that one can add two orthogonally polarized components to produce any polarization. Unlike the simple interference of waves discussed in the previous pages where waves shared the same polarization, the displacements produced by a wave generally are three-dimensional vectors, so adding two polarizations can be much harder to costruct and visualize. One can either add two perpendicular linear polarizations, e.g., vertical and horizontal, or left and right circular polarizations. By adjusting the amplitudes and phases of the two components, one can create any polarization. These components form a basis, with which any polarization can be produced. One can use either a linear basis or circular basis to produce any polarization. In the simulation below, you will be able to produce arbitrary polarizations by either adding two linearly polarized component together using a linear basis or two circularly polarized components using a circular basis.
Initially, the linearly polarized wave in the simulation below is represented in the linear basis. Press Run to see how the wave moves in time. Focus your attention on fixed position on the z-axis, and notice how the element of the wave at that position is simply moving straight up and down. Now start adding a horizontal component to the wave by moving the E_H polarization slider to the right (or by typing a non-zero number in the Horizontal Polarization E_H box and hitting return). What happens to the wave? Is it still vertically polarized? Is it still linearly polarized? What happens if you shift the horizontal component with respect to the vertical component by moving the Phase angle slider (or changing the Phase angle value in the text box)? Is the wave still linearly polarized?
Now try switching to the circular basis representation. What if you make the amplitudes of the left and right circularly polarized components equal? What if you change the phase between the two circularly polarized components? What is the amplitides are not equal? Try the extreme case where one amplitude is zero and the other is not. Can you produce a linearly polarized wave that oscillates in the vertical direction by adding left and right cirularly polarized components?
Below is another way to look at a wave using the circular polarization basis. Here each displacment is represented by a line segment from the z-axis to the waveform instead of a point. Try varying the amplitudes and phases of the left and right circularly polarized components.