Boudary conditions, rough interface (Electrodynamics)

[sukharef]

Hello.
I'd like to know, does anybody know any information about finding boudary conditions for E, H vectors
in case of rough interface, if phi(x) function is set.

Maybe such kind of case ( 2D or 3D case) has been considered somewhere.
Thank you in anvance.

 

[Simon Bridge]

In classical physics, they are the same as for the boundary conditions for a smooth interface - but each point on the surface will have a different tangent angle. This can get arbitrarily complicated.