[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