[Electromagnetism,optics]How to attack a problem of dielectric tensor?

[buoyant]

Hi, I am currently making an effort to solve a boundary value problem of electromagnetic field.

The problem is as follows:

The region ##y<0## is vacuum. The region ##y \geq 0## is filled with material with ##\mu=\mu_0## and dielectric tensor ## \left( \begin{array}{ccc}
\alpha & i\beta & 0 \\
-i\beta & \alpha & 0 \\
0 & 0 & \gamma \end{array} \right) ##.

If the wave ##\vec{E} = E_0 \hat{x} exp[i(\frac{\omega}{c}y-\omega t)] ## is incident from the left, what the electric field would be?

I tried to solve with boundary condition deduced from Maxwell's eqns, but I coincided essentially unsolvable determinant. I cannot find how the wave would go eventually.(I thought the polarization of the wave would be eigenvectors of the dielectric tensor, but I can get the direction of propagation so that I couldn't use boundary condition) Is there anyone who can give any advice on this?

Thanks in advance.

 

[Andy Resnick]

Hint: the dielectric tensor relates components of E with components of D. While I don't recognize that particular form of dielectric tensor, any reasonable text discussing crystal optics should help you work through the problem.

 

[buoyant]

Thanks a lot Resnick!
I'll think more. Is there any text or website you recommend? I think I have to consider birefringence but not sure how to do that

 

[buoyant]

now i solved it. i was silly. thanks

 

[sardar]

I can understand your frustration with this problem. It can be challenging to solve boundary value problems in electromagnetism, especially when dealing with a complex material like a dielectric with a tensor. However, there are some steps you can take to approach this problem.

Firstly, it is important to review the basics of electromagnetism and optics, including Maxwell's equations and the properties of dielectric materials. This will help you understand the physical principles behind the problem and guide your approach.

Next, it may be helpful to break down the problem into smaller, more manageable parts. For example, you can start by considering the behavior of the wave in vacuum, where the dielectric tensor is simply the identity matrix. Then, you can introduce the dielectric tensor and solve for the wave behavior in that material.

Additionally, you can try using different numerical or computational methods to solve the problem. This can include finite difference or finite element methods, which can handle complex material properties like a dielectric tensor.

It may also be useful to consult with colleagues or experts in the field for advice or guidance. They may have insights or approaches that you haven't considered.

Overall, solving this problem will require a combination of theoretical knowledge, problem-solving skills, and perseverance. I wish you the best of luck in finding a solution.