What is the Jones Matrix of a mirror at an angle?

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Discussion Overview

The discussion revolves around determining the Jones Matrix of a mirror at a non-zero angle of incidence in the context of optical polarization. Participants explore the implications of angle on the matrix and consider various approaches to derive it, including the use of Fresnel equations and transformation matrices.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant inquires about the Jones Matrix for a mirror at a non-zero angle of incidence, noting that the matrix for normal incidence is (1 0; 0 -1).
  • Another participant suggests that the Jones calculus may not be suitable for this situation and proposes constructing a transformation matrix to convert between |H> and |V> states and |P> and |S> states.
  • Some participants argue that using Fresnel equations for reflection is sufficient in systems involving linear and isotropic media, as there are no cross-talks between S and P polarizations.
  • One participant mentions deriving a "maltese cross" pattern for high NA objectives using the Jones formalism, indicating that the components vary with azimuthal angle.
  • A paper is referenced that provides detailed analysis relevant to the discussion.
  • A participant expresses gratitude for the information but indicates difficulty in constructing the matrix despite finding the discussion adequate for their application.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of Jones calculus and the sufficiency of Fresnel equations, indicating that multiple competing views remain and the discussion is unresolved.

Contextual Notes

There are limitations regarding assumptions about the media involved and the specific conditions under which the Jones Matrix is derived. The discussion does not resolve the mathematical steps needed to construct the matrix.

Corwin_S
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Hi,

Concerning optical polarization, what is the Jones Matrix of a mirror at a non-zero angle of incidence with respect to incoming light?

For a mirror at normal incidence the matrix is (1 0; 0 -1);
How do I incorporate the angle?
 
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Corwin_S said:
Hi,

Concerning optical polarization, what is the Jones Matrix of a mirror at a non-zero angle of incidence with respect to incoming light?

For a mirror at normal incidence the matrix is (1 0; 0 -1);
How do I incorporate the angle?

Interesting question- I'm not sure the Jones calculus can handle this. Have you tried constructing a transformation matrix to convert the |H> and |V> states into |P> and |S> states?
 
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I think using Fresnel equations for reflection is sufficient if the system only involves linear and isotropic media, as in such a system, there are no cross-talks between the S and P polarizations.
 
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blue_leaf77 said:
I think using Fresnel equations for reflection is sufficient if the system only involves linear and isotropic media, as in such a system, there are no cross-talks between the S and P polarizations.

That's what I meant, and you're right, everything needs to be well-behaved. I have derived the "maltese cross" pattern for high NA objectives using the Jones formalism by writing a Jones vector for a plane wave propagating along the optical axis using the |P> and |S> basis, the two components vary with azimuthal angle.

A good paper showing this type of analysis in detail is here: http://www.mbl.edu/cdp/files/2012/07/oe_02_943.pdf , and it should provide the OP with sufficient information.
 
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Thanks guys, I still been unable to actually construct the matrix, but this is quite adequate for the application.

Cheers
 

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