1. Dec 2, 2011

### issacnewton

Hi

I have some comments/questions about the terminology used for dielectrics in physics textbooks. Linear dielectric means that components of $\vec{P}$ are linear
combination of the components of $\vec{E}$.

Homogeneous dielectric means that dielectric constant is not the function of coordinates.

Isotropic dielectric means that at any given point inside the dielectric , the dielectric constant (and hence $\chi$ ) is same in all directions, which ,means that all off diagonal elements in the matrix $\chi$ are zero.

Physics textbooks most often talk about homogeneous isotropic linear dielectric. But some times they relax some conditions but don't specify the nature of the dielectric exactly. Lot of sloppy language there.

Now I am just trying to play with these 3 words and see what I get. for example , consider,
homogeneous nonisotropic linear dielectric. So here $\chi$ is a tensor and
off diagonal elements are non zero. Further it is not function of coordinates.
Do such dielectrics exist ?

Next, consider nonhomogeneous isotropic linear dielectric. Here $\chi$ is a scalar
which is a function of coordinates and we still have linearity. Again do such materials exist ?

Finally, nonhomogeneous nonisotropic nonlinear dielectrics. I know J.D.Jackson talks about
non linear dielectrics , but I am not sure if he talks about this particular case, which is
most general. Do such materials exist ?

thanks

2. Dec 5, 2011

### middling

Any mixture of different nonisotropic, nonlinear dielectrics would
by the definition of homogeneous (uniform in composition) be
a NONhomogeneous, nonisotropic, nonlinear dielectric. But it might be
thought misleading to call it a single dielectric.

3. Dec 5, 2011

### nasu

Even for anisotropic dielectric you can have the off-diagonal elements zero, if you choose the right axes. For the case of isotropic the diagonal elements are all the same so there is actually only one constant.

4. Dec 5, 2011

### issacnewton

but do the kind of materials exist as I asked ?

5. Dec 5, 2011

### nasu

First, linearity is an approximation that holds more or less, for fields weak enough.
So you may rather ask if the linear, isotropic, homogenous really exist or not.

Next, examples of anisotropic dielectrics are many single-crystal dielectrics with symmetry other than cubic. At low field they are linear. And homogenous, more or less.

Nonlinear is most everything at large fields.

Non-homogenous may be a composite material.

6. Dec 5, 2011

### issacnewton

thanks nasu.......makes sense