For several days now, I have been trying to decouple Maxwell's equations in bianisotropic media so that I end up with a form that involves only one variable (of E, D, B, H), i.e. a so-called 'wave equation'.

I am assuming the existence of magnetic monopoles, and am not taking spatial/temporal derivatives of material coefficient tensors $\epsilon, \mu$ nor coupling tensors $\xi, \zeta$. I was hoping to keep the polarizability $P$ and magnetization $M$ as well.

I use the following notating and constitutive relations:

$${D}=\epsilon{E}+ \xi{H} + {P}, $$ $${B}=\mu{H} + \zeta{E} + {M}, $$ $$ {E}=\epsilon^{-1}({D}- \xi{H}-{P} ) $$ $${H}=\mu^{-1}({B} - \zeta{E}- {M}). $$

However, no matter what tricks I pull (using vector calculus identities, taking curls, time derivatives and making substitutions), I cannot seem to write Maxwell's equations in terms of only one variable.

Almost all the literature out there describes the source-free regime with constant coefficients, but I do not want these assumptions. A few papers discuss wave equations in specific media, but they weren't general enough. Other than for these, I haven't been too lucky with my reading.

Therefore I was hoping someone could direct me at a resource that will help me decouple Maxwell's equations to get the wave equations I need, or point out a simple trick that's been keeping me from solving my problem. Also, can all this be done in the first place?



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