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

[Corwin_S]

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?

 

[fresh_42]

This might help: https://en.wikipedia.org/wiki/Jones_calculus

 

[Andy Resnick]

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?

 

[blue_leaf77]

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.

 

[Andy Resnick]

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.

 

[Corwin_S]

Thanks guys, I still been unable to actually construct the matrix, but this is quite adequate for the application.

Cheers