# Is light wave also transverse in media?

1. Nov 29, 2011

### blenx

It is no doubt that light is a transverse wave in vaccum. But is it also holds true for the case when light is in a medium?

2. Nov 30, 2011

### Bill_K

Not in an anisotropic medium, such as a crystal. That is, when the dielectric constant ε depends on direction. Then you find that the two electric vectors D and E are not even parallel. D is transverse, but E is not.

3. Nov 30, 2011

### vanhees71

Also in a plasma there is a longitudinal mode, related to plasma oscillations (plasmons).

4. Nov 30, 2011

### chrisbaird

To answer the OP more directly, if the medium is linear, uniform and isotropic, then all of the electrodynamic equations look the same, except that the permeability/permittivity of free space constants get replaced with the permeability/permittivity constants of the material. As a result, transverse plane waves propagate in such a medium in the same way as in vacuum. This is the most common case in everyday life (such as light traveling in water or glass). If the medium is not linear, uniform, or isotropic, then you get extra things happening.

5. Dec 1, 2011

### blenx

But if we express the Maxwell equation with potential in Coulmb gauge,
[/tex]
\begin{gathered} {\nabla ^2}\varphi = - \rho /{\varepsilon _0}\quad ,\quad {{\boldsymbol{E}}_{\text{L}}} = - \nabla \varphi \\
\square {{\boldsymbol{A}}_{\text{T}}} = {\mu _0}{{\boldsymbol{J}}_{\text{T}}}\quad ,\quad {{\boldsymbol{E}}_{\text{T}}} = - \frac{{\partial {{\boldsymbol{A}}_{\text{T}}}}}{{\partial t}}\quad ,\quad {\boldsymbol{B}} = \nabla \times {{\boldsymbol{A}}_{\text{T}}} \\ \end{gathered}
[tex]
we can see that the scalar potential which corresponds to the longitudinal electric field does not satisfy the wave equation. So is it appropriate to treat the longitudinal electric field as one component of the light wave?

6. Dec 1, 2011

### chrisbaird

blenx, all those equations you just wrote are the free-space (vacuum) versions of Maxwell's equations. I thought from your OP you were curious about waves in matter. The Coulomb gauge is typically only useful in free space, or in linear, uniform, isotropic materials which act like free space as long as you use the right permittivity/permeability of the material in the equations. Those equations show that traveling electromagnetic waves in free space are transverse, although there is a non-traveling near-field longitudinal component.

7. Dec 1, 2011

### DrDu

You should at least add not optically active to you list of conditions or absence of spatial dispersion in more generality.

8. Dec 2, 2011

### blenx

The equations I wrote are general, as long as the charge/current density is understood as the bound charge/current density in media. Of course one can use the polarization and magnetization to replace them, but that dose not change the number of unkonwn quantities. From the equations in Coulmb gauge, one can immediately know that the origin of the longitudinal electric field in media is the existence of the bound charges. What confuses me is whether such longitudinal component should be regarded as the wave's component.