Topic: Electromagnetics
The electric field of a plane wave propagating in a lossless non-magnetic medium is given by the following equation
$\vec{E}(z,t)=3\cos(2\pi\times10^{9}t+\beta z)\hat{a}_{x}+2\cos(2\pi\times10^{9}t+\beta z+\frac{\pi}{2})\hat{a}_{y}$
The type of wave polarization is
- A. Right hand elliptical
- B. Right hand circular
- C. Left hand elliptical
- D. Left hand circular
Answer: A. Right hand elliptical
Explanation: The amplitudes are $E_x = 3$ and $E_y = 2$. Because the amplitudes are unequal, the polarization is elliptical. The phase difference between the y-component and x-component is $\pi/2$. At $z=0, t=0$, $\vec{E} = 3\hat{a}_x$. At $\omega t = \pi/2$, $\vec{E} = -2\hat{a}_y$. The vector rotates from the +x axis to the -y axis. Considering the wave propagates in the -z direction (due to the $+\beta z$ term), pointing the thumb in the -z direction shows the fingers curl from +x to -y (clockwise). Hence, it is right-hand elliptical.