Circularly polarized waves as an orthonormal state

In summary, to show that any plane wave can be written as the sum of left-circularly polarized and right-circularly polarized waves, one can split the amplitudes into x and y components and add the corresponding E-vectors. This may require the use of trig identities.
  • #1
Hammed
3
0

Homework Statement


Show that any plane wave can be written as the sum of a left-circularly polarized wave and a right-circularly polarized wave of suitable amplitudes and phase

Homework Equations

The Attempt at a Solution


If I assume the plane wave polarizes in the z direction. It is possible to split amplitudes of waves into the x-component and y-component, after which, I do not know how to proceed with the question any longer.
 
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  • #2
Can you write expressions for the E-vectors for right and left circularly polarized waves? If so, add them and see what you get. At some point you may have to look up trig identities.
 
  • #3
kuruman said:
Can you write expressions for the E-vectors for right and left circularly polarized waves? If so, add them and see what you get. At some point you may have to look up trig identities.
Thanks, I will be able to do that.
 

1. What are circularly polarized waves?

Circularly polarized waves are electromagnetic waves in which the electric field vector rotates in a circular motion as the wave propagates. This is in contrast to linearly polarized waves, where the electric field vector oscillates in a straight line.

2. How are circularly polarized waves described as an orthonormal state?

Circularly polarized waves can be described as an orthonormal state by using two orthogonal basis vectors, one for each circular polarization state (clockwise and counterclockwise). These basis vectors are perpendicular to each other and have the same magnitude, making them orthonormal.

3. What is the significance of circularly polarized waves as an orthonormal state?

The use of circularly polarized waves as an orthonormal state allows for efficient and accurate communication and measurement of electromagnetic waves. It also allows for the separation of different polarization states, which is important in many applications such as satellite communication and medical imaging.

4. How are circularly polarized waves produced?

Circularly polarized waves can be produced by passing linearly polarized waves through a device called a quarter-wave plate. This device delays one component of the wave by a quarter of a wavelength, resulting in circular polarization.

5. Can circularly polarized waves be converted into linearly polarized waves?

Yes, circularly polarized waves can be converted into linearly polarized waves by passing them through a device called a half-wave plate. This device delays one component of the wave by half a wavelength, resulting in linear polarization. Additionally, circularly polarized waves can also be converted into linearly polarized waves by using a combination of a quarter-wave plate and a linear polarizer.

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