# Plasma Optics (III)

First, we need to remember that the relation between $\omega$ and f is linear, as described from $\omega=2\pi f$. We also know that f and $\lambda$ are inversely proportional, which we can see from $\lambda=\frac{c}{f}$. This means that the behaviour of wavelength and frequency is opposite to each other. When the value of wavelength is high, we will get low value of frequency and vice versa.

The implications of dielectric function, from Plasma Optics (II)

are described as follows:

• When incoming light interacting with the material has frequency lower than plasma frequency of the material, such that $\omega<\omega_p$, we will get negative value of the dielectric function. It implies the light is reflected from the surface of the material when the wavelength of the incident light is higher than the plasma wavelength of the material.
• When incoming light interacting with the material has frequency higher than plasma frequency of the material, such that $\omega>\omega_p$, we will get positive value of the dielectric function. It implies the light is propagated through the surface of the material when the wavelength of the incident light is lower than the plasma wavelength of the material.

The above statements agree with the illustration given in the Figure 1 from Plasma Optics (I).

If the value of $\omega_p=1$ and the incoming light has $\omega$ varying from 0 to 2, the response of the dielectric function is given in the figure 2.

How can negative dielectric function give rise to the reflected light? How can positive dielectric function give rise to the propagated light? We will try to find out in the next section.