EM Waves In Different Materials

Free Space

In free space, permittivity is $\epsilon_0$.

Dielectrics

In a dielectric, permittivity is $\epsilon$ which is some real value.

Conductors

In conductors, permittivity depends on frequency. In a perfect conductor, permittivity is imaginary.

A “good” conductor is defined as

\[\frac{\sigma}{\omega\epsilon} >> 1\]

Lossy Dielectrics and Bad Conductors

In a lossy dielectric, which can also be considered a bad conductor, permittivity is complex.

\[\epsilon(1-j\frac{\sigma}{\omega\epsilon})\]

$k$ is also complex

\[k = k' - jk''\] \[\tilde E(\vec r) = \hat x E_0e^{-jkz}=\hat x E_0e^{-jk'z}e^{-k''z}\]

The real part of the exponent is responsible for the wave decaying. Physically, the decay is due to bound charges “rubbing” against each other and losing energy to heat.

Plasma

In plasma, the charges are free to move around and thus we don’t have the decay that a lossy dielectric has.

Relations

Condition	Material
$\epsilon=\epsilon_0$	Free space
$\epsilon$ is real	Dielectric
$\epsilon$ is imaginary	Conductor
$\epsilon$ is complex	Lossy dielectric or bad conductor