I am having a bit problem understanding the phase relation between current source and the generated eletromagnetic field components.
Assume a very small current element( a very small current running in direction x)(essentially an electric dipole) in a non-homogenous loss periodic medium. the only knowledge about the medium is the mu and epsilon profile plus eigenvalues of the medium. The structure is like a waveguide so most of the radiation is expected to couple one of the eigenvalues. what is the phase relation between the generated electromagnetic field(dominant eigenvalue) and the driving current?(assuming phasor fields). It must be somehow related to the tangental and normal electric and magnetic fields of the dominant eigenvalue.
could it be independent of the meduim, simply 1 or -1?