Surface polaritons at the sharp interface between media

1 Surface polaritons at the sharp interface between media 

If the thickness of the surface layer in which a surface exciton-polariton is localized considerably exceeds the lattice constant of a crystal, the electric and magnetic field strength vectors, i.e. vectors E and H of a wave with energy hw in both media (in vacuum and in the crystal the crystal is assumed to be nonmagnetic so that the magnetic induction vector B = H), satisfy Maxwell s equations 

Let us assume that the crystal surface coincides with the plane z = 0, that the half-space z 0 is vacuum (e j = Sij), and that the half-space z 0 is a cubic crystal with a dielectric function e(w) (spatial dispersion is neglected so far). Hence, we are interested in the solutions of Maxwell s equations that vanish as z — oo we shall look for them in the following form  

In relations (12.6) ei, e2 and e3 are real unit vectors directed along the x-, y-and z-coordinate axes, respectively. From the first two equations (12.5) it follows that the vector Eg1 is collinear with the vector K( b and the vector Eg2 -1 with the vector K 2), i.e. 

The electric field vectors at a sharp interface between media must satisfy the boundary conditions 

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