Gap Plasmon’s and the van der Waals interaction consider two semi-infinite media with plane surfaces z = 0, d. The dielectric function of the identical media is ε(w). Show that for surface Plasmon’s symmetrical with respect to the gap the frequency must satisfy ε(w) = -tanh (Kd/2), where K² = k²_t + k²_y. The electric potential will have the form φ = f(z) exp (ik_xx + ik_yy – iwt) Look for non-retarded so1utio11-that is, solutions of the Laplace equation rather than of the wave equation. The sum of the zero-point energy of all gap modes is the non-retarded part of the van der Waals attraction between the two specimens-see N. G. van Kampen, B. R. A. Nijboer, and K. Schram, Physics Letters 26A, 307 (1968).