We're currently applying Maxwell's Equations to an optical fibre, and I don't quite understand the boundary conditions at the core-cladding interface.

I've been told that (where E and H are the electric and magnetic field vectors):

What does 'no currents' mean? Why is it the H field continuous if there are no currents? Or is it the other way around? I understand a bit about displacement current, and that sort of thing but am having trouble joining the dots.

And I understand what the other boundary conditions are, but do not understand why they are conditions. Why are the other two so?

I'd appreciate any insight/pointers to some good reference material.

Thanks in advance,

Tom.

P.S. sorry to not use the template... it didn't seem to fit.