# Verify definition of circular polarization in Balanis.

• yungman
In summary, there is a disagreement between Balanis' definition of circular polarization with Ey having a phase of +∏/2 respect to Ex component of the E field and the derivation provided by the speaker. The speaker believes the rotation of the E field is CCW for propagation in -ve z direction and CW for propagation in +ve z direction, based on their calculations and references from "Engineering Electromagnetics" by Ulaby. They suggest that Balanis may be incorrect and ask for confirmation. This is a result of different definitions of circular polarization used by electrical engineers and physicists.
yungman
Attached is a scan of how Balanis define plane wave with circular polarization with Ey having a phase of +∏/2 respect to Ex component of the E field. I don't quite agree with the book. The second attachment is my derivation.

The definition of CW or CCW is with respect to direction of propagation come out of the paper as indicated in my notes ( point towards you!).

The book claimed for propagation in -ve z direction, if phase is +∏/2 (n=0), the rotation is CW which is Left Hand Rotation. And the book said if the propagation is in +ve z direction, the rotation reverse to CCW.

But as I proofed in my notes: For propagation in -ve z direction, the function is $\cos(\omega{t}+kz+\frac{\pi}{2})$. Which for t=0 and plot the wave along -z, maximum occur at $kz+\frac{\pi}{2}\;=\;0\;\Rightarrow\; z=-\frac{\lambda}{4}$. This is drawn in my notes. I showed the rotation of the E in CCW and is Right Hand Rotation for propagation in -ve z direction.

On the lower part of my notes for propagation in +ve z direction, the result is backed up by "Engineering Electromagnetics" by Ulaby. That it is CW and Left Hand Rotation. Based on all these, I cautiously say Balanis is wrong. Please check my work and tell me whether I am correct or not.

Thanks

Alan

#### Attachments

• CP book.png
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• CP notes L.png
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Last edited:
It's well known that electrical engineers and physicists define the sense of circular polarization oppositely. You are looking in one book from each camp.

## 1. What is circular polarization?

Circular polarization refers to the polarization state of an electromagnetic wave in which the electric field vector rotates continuously at a constant rate as the wave propagates through space.

## 2. How is circular polarization different from linear polarization?

Linear polarization refers to the polarization state of an electromagnetic wave in which the electric field vector oscillates in a single plane as the wave propagates. In contrast, circular polarization involves the rotation of the electric field vector in a circular motion.

## 3. What is the significance of circular polarization in antenna design?

Circular polarization is important in antenna design because it allows for improved signal reception in situations where the orientation of the receiving antenna may vary or when there are obstructions that may cause signal distortion with linearly polarized waves.

## 4. How is circular polarization produced?

Circular polarization can be produced by using a combination of two perpendicular linearly polarized waves with a specific phase difference. This can be achieved through the use of specialized antenna designs or by passing linearly polarized waves through a medium with specific properties, such as a quarter-wave plate or a Faraday rotator.

## 5. What is the relationship between circular polarization and handedness?

Circular polarization is often described in terms of its handedness, which refers to the direction of rotation of the electric field vector. Right-handed circular polarization (RHCP) refers to a clockwise rotation, while left-handed circular polarization (LHCP) refers to a counterclockwise rotation. This can also be visualized as the curl of the fingers of your right or left hand, respectively, when pointing in the direction of propagation.

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