# Superposition principle in arbitrary medium

1. Oct 16, 2010

### Heirot

Does the superposition principle for wave equations (say electromagnetic) hold also for non homogeneous and anisotropic media? I.e. can one always represent a wave traveling in an arbitrary direction as a sum of waves propagating along the principal axes of, e.g. dielectric tensor $$\epsilon_{ik}$$?

Thanks

2. Oct 16, 2010

### Andy Resnick

The superposition principle is violated in nonlinear materials- some basic examples are the Stark and Kerr effects.

Another effect is the spectral changes that occur as partially coherent light propagates in free space (sometimes called the Wolf effect)- but this may not count as a violation of superposition.

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2915902/

http://www.sciencedirect.com/scienc...4d4d39ef9500de32bd2e9337d46bda5b&searchtype=a
http://www.opticsinfobase.org/abstract.cfm?uri=josaa-7-9-1591

3. Oct 16, 2010

### Heirot

So, as long as the medium is linear, superposition holds as a rule?

4. Oct 16, 2010

### Andy Resnick

Yes- at least, I am unaware of any exceptions.