# Uniaxial crystal D direction

1. Oct 21, 2011

### v_pino

1. The problem statement, all variables and given/known data

Here you will calculate the direction of energy flow in a uniaxial crystal. The crystal has dielectric constant $$\varepsilon$$ in the x and y directions and $$\varepsilon_z$$ in the z direction.

(a) Assume the wavevector makes an angle $$\theta$$ relative the z-axis of the crystal. What is the angle of the D vector with respect to this axis? Now, use the inverse of the dielectric tensor to obtain the direction of E from the direction of D.

2. Relevant equations

3. The attempt at a solution

$$\varepsilon = \begin{bmatrix} \varepsilon & 0 & 0 \\ 0 & \varepsilon & 0 \\ 0 & 0 & \varepsilon_z \end{bmatrix}$$

$$\begin{bmatrix} D_x\\ D_y\\ D_z\\ \end{bmatrix} = \begin{bmatrix} \varepsilon & 0 & 0 \\ 0 & \varepsilon & 0 \\ 0 & 0 & \varepsilon_z \end{bmatrix} \begin{bmatrix} E_x\\ E_y\\ E_z \end{bmatrix}$$

And I know that birefringe causes the wave to separate such that:

$$D_e$$ is in the y-z plane perpendicular to S, the poynting vector and $$D_0$$ is parallel to x-axis.

Can you give me some hints or reading materials as to solving the problem? Thank you.
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution