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

  1. Dec 1, 2015 #1
    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?
     
  2. jcsd
  3. Dec 1, 2015 #2

    fresh_42

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  4. Dec 1, 2015 #3

    Andy Resnick

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    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?
     
  5. Dec 2, 2015 #4

    blue_leaf77

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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.
     
  6. Dec 2, 2015 #5

    Andy Resnick

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    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 [Broken], and it should provide the OP with sufficient information.
     
    Last edited by a moderator: May 7, 2017
  7. Dec 4, 2015 #6
    Thanks guys, I still been unable to actually construct the matrix, but this is quite adequate for the application.

    Cheers
     
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