Circularly polarized waves as an orthonormal state

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Any plane wave can be expressed as a combination of left-circularly and right-circularly polarized waves through appropriate adjustments in amplitude and phase. The discussion emphasizes starting with the z-direction polarization and breaking down the wave into its x and y components. Participants suggest writing the electric field vectors for both types of circular polarization and then combining them to analyze the resulting wave. Trigonometric identities may be necessary for simplification during this process. The conversation concludes with a commitment to explore these expressions further.
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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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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.
 
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.
 

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