As discussed in Chapter 2, the electric and magnetic field vectors of a plane electromagnetic (EM) wave lie in a plane transverse to the direction of propagation. If the electric field varies randomly with time, then the wave is said to be unpolarized, while if it varies in a predictable manner, the wave is said to be polarized. The nature of variation of the electric field with time defines the state of polarization (SOP) of the EM wave. For example, the variation may be such that the tip of the electric field vector may move on a line, on a circle, or, in general, on an ellipse. Accordingly, the SOP of the wave is said to be linear, circular, or elliptical. In the following discussion, we provide the basic characteristics of polarized waves.
3.2 Various Polarization States
3.2.1 Linear polarization
The electric field vector of a linearly polarized wave is the easiest of the three to describe mathematically. For example, if the line over which the tip of the electric field vector moves is parallel to the x axis, then the electric field can be described as
where k = (2π / λ0)n, with n being the refractive index of the medium, λ0 the freespace wavelength, z the direction of propagation, a and δ0 the amplitude and the initial phase, respectively, and ˆx the unit vector along the x axis. Such a wave is also known as plane polarized because the electric field of such a wave always lies in a longitudinal plane (the x-z plane in this case). Without any loss of generality, we may assume that a > 0 and −π ≤ δ0 ≤ π. Thus, we may write