FWLec21 - A. F. Peterson: Notes on Electromagnetic Fields...

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A. F. Peterson: Notes on Electromagnetic Fields & Waves 11/04 Fields & Waves Note #21 Polarization of Electromagnetic Waves Objectives: Introduce linear, circular, and elliptical polarization, and provide examples of each. Define right-handed and left-handed circular and elliptical polarization. Discuss several applications of polarization. If an observer could sit and watch an electromagnetic field as it propagates along, that observer would be able to follow the behavior of the electric field vector. The vector might oscillate back and forth along a line, as depicted in Figure 1a. Or, in some situations, the tip of the vector may trace out a circle in the transverse plane, as depicted in Figure 1b. A third possibility would be that the tip traces out an ellipse, as illustrated in Figure 1c. A fourth possibility, although one that will not be considered in any detail here, is that the vector jumps around in a random fashion (Figure 1d). The behavior of the electric field vector (and similarly the magnetic field vector) is known as the polarization of the vector. Polarization is an important parameter from the standpoint of antennas, since an antenna must be designed to radiate a certain polarization or receive a certain polarization in order to perform in an optimal way. In this Note, three different types of polarization will be defined and illustrated by example for electromagnetic plane waves. In addition, a convention will be introduced to distinguish between the two possible trajectories of a vector that traces a circular or elliptical path. In the following, we restrict our consideration to plane waves that have a sinusoidal steady state dependence on time. We will employ both time-dependent and phasor representations for these fields. Linear Polarization A wave that exhibits linear polarization has a vector that is independent of the time dependence. A simple example is given by the electric field ezt xE t z (,) ˆ cos( ) =- 0 wb (21.1) Ez xE e jz () ˆ = - 0 b (21.2) The vector part ( ˆ x ) is independent of the time function cos( ) tz - , so the vector always points in the ± ˆ x direction. A more complicated example of linear polarization is given by 1 2 3 2 0 ˆˆ cos( ) xy E t z - Ï Ì Ó ¸ ˝ ˛ -+ wbq (21.3)
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A. F. Peterson: Notes on Electromagnetic Fields & Waves 11/04 Although the vector direction of (21.3) is skewed with respect to the coordinate axes, it remains in that direction (other than the sign change due to the sinusoidal variation) for all values of time. Circular Polarization In circular polarization, the tip of the vector traces out a circle in a plane transverse to the direction of propagation. For this to occur, there are three conditions that must be satisfied exactly. First, the field must contain two perpendicular components, transverse to the direction of propagation. Second, these two components must have exactly the same magnitude. Finally, these two components must be exactly 90 out of phase (a condition known as phase quadrature ).
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FWLec21 - A. F. Peterson: Notes on Electromagnetic Fields...

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