Question

Assume the presence of two uniform plane waves (E₁​​ and E₂​) propagating in the same direction. The phasor electric field intensities of E₁​​ and E₂​ are described by

E₁​(x,y,z)=(−6jaₓ​+4aᵧ​+3a​)e−j(0.6y−0.8)
E₂​(x,y,z)=(Ajaₓ​+Baᵧ​+6a​)e−j(0.6y−0.8)​
Find the polarization of E1​

Answer 1

The polarization of E1 is elliptical, as indicated by its phasor components, including both real and imaginary parts with a 90-degree phase shift in the x-direction.

Step-by-step explanation:

To find the polarization of E1, we need to look at the vector components of the electric field intensity provided for E1. The phasor of E1 is given as E1(x,y,z)=(-6jᵃₓ+4ᵂₒ+3ᵃ)exp(-j(0.6y-0.8)), which can be written in the component form as E1=-6jᵃₓ+4ᵂₒ+3ᵃ. The presence of both real and imaginary parts in the components indicates that the wave is elliptically polarized. Specifically, the -6j in the x-direction represents a 90-degree phase shift relative to the y and z components, indicating that the polarization is not linear. The polarization can generally be categorized as linear, circular, or elliptical based on the relative magnitudes and phases of the x, y, and z components. In this case, elliptical polarization is suggested due to the combination of in-phase and out-of-phase components.