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

• Corwin_S
In summary, the Jones Matrix of a mirror at an angle is a mathematical representation used to describe the behavior of polarized light as it reflects off a mirror at a certain angle. It takes into account the polarization state of the incident light and the angle of incidence and calculates the resulting polarization state of the reflected light. This matrix can be used to analyze and manipulate polarized light in various applications, such as in optics and telecommunications.
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?

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?

Corwin_S
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.

Corwin_S
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.

Last edited by a moderator:
Corwin_S
Thanks guys, I still been unable to actually construct the matrix, but this is quite adequate for the application.

Cheers

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

The Jones Matrix of a mirror at an angle is a mathematical representation of the way in which the mirror reflects light at a certain angle. It is used to describe the polarization state of light and the transformation of its polarization state after reflection.

## 2. How is the Jones Matrix calculated for a mirror at an angle?

The Jones Matrix for a mirror at an angle is calculated using the Fresnel equations, which take into account the angle of incidence, the refractive indices of the two media, and the polarization state of the incident light. The resulting matrix is a 2x2 matrix that describes the transformation of the input polarization state to the output polarization state after reflection.

## 3. What are the possible values in a Jones Matrix for a mirror at an angle?

The values in a Jones Matrix for a mirror at an angle can range from -1 to 1. A value of 1 represents complete transmission of the incident polarization state, while a value of -1 represents complete reflection of the incident polarization state. Values in between represent a combination of reflection and transmission.

## 4. How does the angle of the mirror affect the Jones Matrix?

The angle of the mirror affects the Jones Matrix by changing the values in the matrix. As the angle of incidence changes, the amount of reflection and transmission also changes, resulting in different values in the Jones Matrix. This can also affect the polarization state of the reflected light.

## 5. Why is the Jones Matrix important in optics and photonics?

The Jones Matrix is important in optics and photonics because it allows us to understand and predict the behavior of light as it interacts with different materials, such as mirrors. It is a fundamental tool in designing and analyzing optical systems and devices, and is used extensively in fields such as telecommunications, imaging, and spectroscopy.

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