# Planar Electric Field in Glass, how to express it?

The field must have properties such as planar wave and moving in glass so

$$\bar E=E \left( \hat i t + \hat j \sin(kz-wt) + \hat k \cos(kz-wt+\phi) \right)$$

that is also moving in the x-axis and right-hand-circular-polarized so the phase difference $\phi=\pm \pi/2$ (more on p.557 in Understanding Physics -book and here). I need some natural constants to express the permittivity with the electric field $\bar E$. The wave must move in glass. It has refractive indices so that $n_1 \sin(\theta_1)=n_2 \sin(\theta_2)$, more here.

I. How can I express electric field in Glass?

$$\bar D= \epsilon_0 \bar E + \bar P = \epsilon_0 (1+\chi) \bar E = \epsilon_r \epsilon_0 E$$

where the permittivity applies to the electric field. Now you have the electric field in terms of permittivity and $\bar D$ is the density of the wave in the material. $\bar E$ is the outside -field while the $\bar P$ is the inner polarization -thing.

II. How can I get planar wave?

According to this here, the planar wave can be expressed as

$$U(\bar r, t) = A_0 e^{i \left( \bar k \cdot \bar r - wt + \phi \right)}$$

but now I am confused how I can get the phase difference there.

Perhaps related

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...I am stuck to the planar wave -thing...I need somehow specify the phase difference there so that getting circular-right-hand-polarized. Having two $e$ -terms? – hhh Sep 2 '12 at 11:46
Alone discussion here, trying to understand the planar wave deeper in complex -form. – hhh Sep 2 '12 at 11:54
...my friend guided me to the wave-equation here, perhaps reading wrong material...not sure, investigating. – hhh Sep 2 '12 at 11:58