Linear polarization

In this situation where both dipoles receive the same signal, the two components are equal $E_y = E_z$ and

$$\vec E ( x, t) = E ( \widehat j + \widehat k ) \cos ( \omega t - k x )$$ (8.2)

If we plot the time evolution of the electric field at a fixed position (Figure 19.2) we see that it oscillates up and down along a direction which is at $45^\circ$ to the $y$ and $z$ axis.

Figure 8.2: Linear Polarization

The point to note is that it is possible to change the relative amplitudes of $E_y$ and $E_z$ by changing the currents in the oscillators. The resultant electric field is

(8.3)

The resultant electric field vector has magnitude $E = \sqrt{E_y^2 + E^2_z }$ and it oscillates along a direction at an angle with respect to the $y$ axis (Figure 19.2).

Under no circumstance does the electric field have a component along the direction of the wave i.e along the $x$ axis. The electric field can be oriented along any direction in the $y-z$ plane. In the cases which we have considered until now, the electric field oscillates up and down a fixed direction in the $y-z$ plane . Such an electromagnetic wave is said to be linearly polarized.