Polarization

Polarization is one of the fundamental characteristics of any antenna. First we'll need to understand polarization of plane waves, then We'll walk through the main types of polarization. Linear Polarization Let's start by understanding the polarization of a wave. A plane electromagnetic (EM) wave is characterized by travelling in a single direction (with no field variation in the two orthogonal directions). In this case, the electric field and the magnetic field are perpendicular to each other and to the direction the plane wave is propagating. As an example, consider the single frequency E-field given by equation (1), where the field is traveling in the +z-direction, the E-field is oriented in the +x-direction, and the magnetic field is in the +y-direction. In equation (1), the symbol is a unit vector (a vector with a length of one), which says that the E-field "points" in the x-direction. A plane wave is illustrated graphically in Figure 1. Figure 1. Graphical representation of E-field travelling in +z-direction. Polarization is the figure that the E-field traces out while propagating. As an example, consider the E-field observed at (x,y,z)=(0,0,0) as a function of time for the plane wave described by equation (1) above. The amplitude of this field is plotted in Figure 2 at several instances of time. The field is oscillating at frequency f.

Figure 2. Observation of E-field at (x,y,z)=(0,0,0) at different times.

Observed at the origin, the E-field oscillates back and forth in magnitude, always directed along the x-axis. Because the E-field stays along a single line, this field would be said to be linearly polarized. In addition, if the x-axis was parallel to the ground, this field could also be described as "horizontally polarized" (or sometimes h-pole in the industry). If the field was oriented along the y-axis, this wave would be said to be "vertically polarized" (or v-pole). A linearly polarized wave does not need to be along the horizontal or vertical axis. For instance, a wave with an E-field constrained to lie along the line shown in Figure 3 would also be linearly polarized. Figure 3. Locus of E-field amplitudes for a linearly polarized wave at an angle. The E-field in Figure 3 could be described by equation (2). The E-field now has an x- and y- component, equal in magnitude. One thing to notice about equation (2) is that the x- and y-components of the E-field are in phase - they both have the same magnitude and vary at the same rate. Circular Polarization Suppose now that the E-field of a plane wave was given by equation (3): In this case, the x- and y- components are 90 degrees out of phase. If the field is observed at (x,y,z)=(0,0,0) again as before, the plot of the E-field versus time would appear as shown in Figure 4. Figure 4. E-field strength at (x,y,z)=(0,0,0) for field of Eq. (3). The E-field in Figure 4 rotates in a circle. This type of field is described as a circularly polarized wave. To have circular polarization, the following criteria must be met:

If the wave in Figure 4 is travelling out of the screen, the field is rotating in the counter-clockwise direction and is said to be Right Hand Circularly Polarized (RHCP). If the fields were rotating in the clockwise direction, the field would be Left Hand Circularly Polarized (LHCP). Elliptical Polarization If the E-field has two perpendicular components that are out of phase by 90 degrees but are not equal in magnitude, the field will end up Elliptically Polarized. Consider the plane wave travelling in the +z-direction, with E-field described by equation (4): The locus of points that the tip of the E-field vector would assume is given in Figure 5. Figure 5. Tip of E-field for elliptical polarized wave of Eq. (4). The field in Figure 5, travels in the counter-clockwise direction, and if travelling out of the screen would be Right Hand Elliptically Polarized. If the E-field vector was rotating in the opposite direction, the field would be Left Hand Elliptically Polarized. In addition, elliptical polarization is defined by its eccentricity, which is the ratio of the major and minor axis amplitudes. For instance, the eccentricity of the wave given by equation (4) is 1/0.3 = 3.33. Elliptically polarized waves are further described by the direction of the major axis. The wave of equation (4) has a major axis given by the x-axis. Note that the major axis can be at any angle in the plane, it does not need to coincide with the x-, y-, or z-axis. Finally, note that circular polarization and linear polarization are both special cases of elliptical polarization. An elliptically polarized wave with an eccentricity of 1.0 is a circularly polarized wave; an elliptically polarized wave with an infinite eccentricity is a linearly polarized wave. In the next section, we will use the knowledge of plane-wave polarization to characterize and understand antennas.