What is the Brewster Angle for Circularly Polarized Light?

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SUMMARY

The Brewster angle for circularly polarized light can be determined using the Fresnel equations, which describe the behavior of light when transitioning between media with different refractive indices. In this discussion, the user seeks to find the magnetic field B, electric field E, and Poynting vector S for a circularly polarized wave reflecting off a dielectric mirror characterized by parameters μ and ε. The relationship between the angle of incidence and the polarization state is crucial, as the reflected wave becomes linearly polarized at the Brewster angle. The user also contemplates the use of complex equations for a more comprehensive analysis.

PREREQUISITES
  • Understanding of circularly polarized light and its properties
  • Familiarity with Fresnel equations for reflection and transmission
  • Knowledge of electromagnetic wave equations, including B and E fields
  • Basic principles of dielectric materials and their parameters (μ and ε)
NEXT STEPS
  • Study the derivation and application of Fresnel equations for different polarization states
  • Learn how to calculate the Brewster angle using the refractive indices of materials
  • Explore the relationship between electric and magnetic fields in electromagnetic waves
  • Investigate the use of complex representation in electromagnetic wave analysis
USEFUL FOR

Students and professionals in optics, physics, and engineering fields who are dealing with polarization of light, particularly in applications involving dielectric materials and wave interactions.

Mary 006
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Homework Statement


Hello everybody. I have a big problem with this important problem that i can't solve and i have no solution ... A circularly polarized monochromatic wave is reflected from a dielectric mirror which has parameters μ and ε. Its wave vector is k = (k0, 2k0,0). Find the magnetic field B, the electric field E and the Poynting vector S as well as the angle of incidence for which the reflected wave is linearly polarized (i.e. the Brewster angle). Calculate the energy of the system.

Homework Equations


The Attempt at a Solution


I think we have to use this (very) general equations :
B = B0.sin(ωt + δ)
rot E = - ∂B/∂t
E = -ωB0.cos (ωt + δ)
where : ω=k.c = 2∏c/λ
For the circular polarization, the electric field rotates about its axis in a circle.
Then, for linear polarization: E remains in the same plane.
For the Poynting vector : S = B x E / μ (i am not sure if for this equation i have to use μ or μo (in vacuum)). Then we can calculate the energy, I guess ...
About the angle Brewster, i think we have to use the Fresnel equations (but i don't know how ...).
I wonder whether it would be better to use the equations in the complex form (instead of the actual form equations (real form)).

Can you help me, please ? Thank you in advance.
I know that what i have written is not very usefull ... And I'm sorry.
 
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Thing about how reflection works for different polarizations, and how you can resolve circular polarization into components wrt the plane of the mirror.
 

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