# Examples of mediums which are not linear, homogeneous and isotropic

In electromagnetics we are taught that mediums can be linear/nonlinear,isotropic/anisotropic,homogeneous/non-homogeneous...we also learn their definitions. Now we are told that if nothing is specified then take the medium to be linear,homogeneous and isotropic. I want to know examples of those mediums which do not follow these criteria as I have never encountered such.

• Every real medium is nonlinear, anisotropic and non-homogeneous. – AccidentalFourierTransform Feb 28 '16 at 17:30
• ok so we have to work with approximations then..... but how to deal with permittivity,permeabilty or conductivity of anisotropic media which will come as tensors ?.....taking eigen values through diagonalization? – Debajyoti Datta Feb 28 '16 at 17:35
• That is discussed thoroughly in any book on electromagnetism. Maybe you should wait until that is explained by your teacher, or grab a book on the subject. – AccidentalFourierTransform Feb 28 '16 at 17:37
• I am an electrical engineering student and I have seen no text on engineering electromagnetics that deals this topic heavily...could you please name a few books or maybe give me some hints on which I can think? – Debajyoti Datta Feb 28 '16 at 17:41
• Look up birefringent materials, like Iceland spar; or Land's polarizing film. Many crystaline materials are not isotropic - hence clevage planes. And yes, tensors are useful in studying these cases; usually in the upper level courses, perhaps senior level. – Peter Diehr Feb 28 '16 at 18:47

Remember that electromagnetism includes light waves.

• Any semi-transparent volumetric medium can have space-varying properties (transparency, colors) and thus be heterogeneous.
• Polarisers, and indeed many of gems, are not isotropic, because of the cristal network orientations.
• Various materials show some saturation or change of property at very high intensity (because there are not supra-conductors)

Moreover there exist 2 kinds of mediums: continuous medium, and composed medium. E.g. cloud/fog/smoke are made of very numerous and small objects floating in air. But

• These objects can have a non-symmetrical shape, and be consistantly oriented (e.g. ice cristal in some clouds, big non-spherical water droplet), causing anisotropy.

• There density (number per cubic meter) is very likely to varies (cloud/fog/smoke have borders :-) ).

• these are all general information..useful though..I wanted something mathematical – Debajyoti Datta Feb 29 '16 at 4:53
• Your question was " I want to know examples of those mediums which do not follow these criteria as I have never encountered such." What "mathematical" do you expect here, then ? – Fabrice NEYRET Feb 29 '16 at 6:33
• mathematically speaking, some constants won't be constant, and some k.laplacians(phi) are indeed div(k.grad(phi)) with k not a constant. – Fabrice NEYRET Feb 29 '16 at 6:42
• actually I wanted to know about examples of non linear,non homogeneous,anisotropic media as well as their general analysis.....as for example in anisotropic media the medium properties like permittivity,permeability,etc are all tensors...we have been told.....n practical situations how people deal with tensors....hope you would get where I am trying to go – Debajyoti Datta Feb 29 '16 at 16:49
• Well so what you actually want is a text book. It would be a bit too much to expect people here to build one just for you through these answers ;-) . Or maybe narrow the question to something more specific. – Fabrice NEYRET Feb 29 '16 at 20:11

Regarding anisotropy, the common one is quartz. For quartz you commonly see ordinary/extraordinary rays refracted according to the two refractive indices of the two axes.

Silica optical fibres have a small nonlinearity. Because of symmetry, their even order nonlinearities go to zero but the third order nonlinearity exists and is used in soliton communication (where the nonlinearity counteracts the dispersion).

Nonlinear crystals are used in lasers for sum frequency generation. E.g. an Argon laser at 488 nm (blue) can be made to emit 244 nm in the UV with a properly aligned BBO crystal.

Nonlinearity is something we commonly experience in diodes, in this case the non-homogeneity of the doping creates a nonlinear response.