Circularly polarized waves as an orthonormal state

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SUMMARY

The discussion focuses on the decomposition of plane waves into left-circularly polarized and right-circularly polarized components. Participants emphasize the need to express the electric field vectors (E-vectors) for both types of polarization. The solution involves utilizing trigonometric identities to combine these components effectively. The key takeaway is that any plane wave can indeed be represented as a sum of these two orthonormal states, provided the correct amplitudes and phases are applied.

PREREQUISITES
  • Understanding of plane wave polarization
  • Familiarity with electric field vector representations
  • Knowledge of trigonometric identities
  • Basic concepts of circular polarization
NEXT STEPS
  • Research the mathematical representation of left-circularly polarized and right-circularly polarized waves
  • Study the application of trigonometric identities in wave decomposition
  • Explore the implications of orthonormal states in quantum mechanics
  • Learn about the physical significance of polarization in electromagnetic waves
USEFUL FOR

Students and professionals in physics, particularly those studying wave mechanics, electromagnetism, or optics, will benefit from this discussion.

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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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