Faraday rotation and permittivity tensor

In summary, the conversation discusses the relevance of the off-diagonal imaginary components in the Hermitian permittivity tensor in understanding Faraday rotation in magneto-optic materials. The question is raised whether this knowledge is enough to solve the wave equation and calculate wave propagation, instead of using the common method of breaking linearly polarized light into left and right circularly polarized lights. The response explains that the tensor must be diagonalized and solved using matrix eigenvalue methods in order to find the two solutions representing left and right circularly polarized waves.
  • #1
Hassan2
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Dear all,

In textbooks about optics in magneto-optic materials, we often come across a Hermitian permittivity tensor with off-diagonal imaginary components. These components are relevant to the Faraday rotation of plane of polarization of light through the material.

Now my question is: Is the knowledge of the tensor enough to solve the wave equation and calculate the wave propagation ( including rotation)?

I ask this because they usually talk about breaking the incident linearly polarized light into left and right circularly polarized lights, where the refractive index is different for each. if the knowledge of permittivity tensor is enough for the calculations, why would we need such a non-easy-to-understand trick?

Your help is highly appreciated.
 
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  • #2
The point is that the wave equation with the permittivity being a tensor depending on wavenumber has two solutions (for given direction of the k vector and frequency) which turn out to correspond to left and right circularly polarized waves. Basically, you have to find a basis where the permittivity tensor is diagonal. This is a matrix eigenvalue problem which you can solve with the usual methods.
 
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Likes Hassan2
  • #3
Very clear.Thanks.
 

1. What is Faraday rotation?

Faraday rotation is a phenomenon in which the plane of polarization of light is rotated as it passes through a material in the presence of a magnetic field.

2. How does Faraday rotation occur?

Faraday rotation occurs due to the interaction between the magnetic field and the electrons in a material. The electrons experience a force from the magnetic field, causing them to rotate and change the direction of the light's polarization.

3. What is the permittivity tensor?

The permittivity tensor is a mathematical representation of the dielectric properties of a material. It describes how a material responds to an electric field, taking into account its anisotropic nature.

4. How is the permittivity tensor related to Faraday rotation?

The permittivity tensor is related to Faraday rotation because it determines the strength and direction of the rotation of the light's polarization. The permittivity tensor must be anisotropic for Faraday rotation to occur.

5. What are some applications of Faraday rotation and the permittivity tensor?

Faraday rotation and the permittivity tensor have a variety of practical applications, including in telecommunications, optical isolators, and materials characterization. They are also important in understanding the magnetic properties of materials and in the development of new technologies, such as spintronics and magneto-optical devices.

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