The given phasor electric field is:

$\mathbf{E} = 2 (\hat{a}_y - j \hat{a}_z) e^{-jk_0 x} \, \text{V/m}$

where:

• $\hat{a}_y$ and $\hat{a}_z$ are the unit vectors in the $y$- and $z$-directions, respectively.
• $j$ is the imaginary unit (i.e., $j^2 = -1$).
• $k_0$ is the wavenumber, related to the wavelength $\lambda$ by $k_0 = \frac{2\pi}{\lambda}$.
• The time dependence is implicit (assuming a harmonic time dependence $e^{j\omega t}$).

Step-by-step breakdown:

1. Electric Field Components: The electric field has two components:

   • $2\hat{a}_y e^{-jk_0 x}$ in the $y$-direction (real component),
   • $-j2\hat{a}_z e^{-jk_0 x}$ in the $z$-direction (imaginary component).

2. Interpretation of Components: The $y$-component is real, and the $z$-component is imaginary, implying a phase difference of $\frac{\pi}{2}$ between the two components. Since the $z$-component is multiplied by $j$, it lags the $y$-component by $90^\circ$.

3. Polarization: Since the electric field has non-zero components in both the $y$- and $z$-directions and the two components have a phase difference of $90^\circ$, the wave is circularly polarized.

   Specifically, the wave is left-hand circularly polarized (LHCP) because the $z$-component lags behind the $y$-component by $90^\circ$. For a left-hand circularly polarized wave, the electric field vector rotates counterclockwise in the plane of the wave's propagation (if viewed from the direction of propagation).

Summary:

The wave represented by the given electric field is a left-hand circularly polarized wave, propagating in the $x$-direction. The electric field vector rotates in the $y$-$z$ plane as the wave moves forward.

Do you want further details or have any questions?

Here are 5 related questions you might find useful:

1. What is the difference between left-hand and right-hand circular polarization?
2. How is circular polarization different from linear polarization?
3. What is the significance of the wavenumber $k_0$ in wave propagation?
4. How does the phase difference between components affect wave polarization?
5. What is the general form of the electric field for an elliptically polarized wave?

Tip: Circular polarization occurs when two perpendicular components of the electric field have the same magnitude and a phase difference of $\pm 90^\circ$.