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

  1. Dec 9, 2013 #1
    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.
  2. jcsd
  3. Dec 9, 2013 #2

    Andy Resnick

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    Science Advisor
    Education Advisor

    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.
  4. Dec 9, 2013 #3
    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
  5. Dec 21, 2013 #4
    now i solved it. i was silly. thanks
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