Coupling of light into meallic thin films We are interested in investigating the properties of a surface plasmon-polariton propagating at the interface of a metal with a complex dielectric constant, & = &+im, and a dielectric with a dielectric constant, a, that is real and frequency independent. The electromagnetic wave associated with the electron density wave is TM in nature and the fields are schematically shown in the Figure below. Dielectric Metal E N ++ +++ X Em H (II) The magnetic field, H, of this wave is described by the following two equations: For z 0 (in the dielectric): H = (0,Hd, 0) expi(kx+k-cot) Where ksp is the wave vector of the surface plasmon-polariton in the propagation direction, kzd and kzm are the wave vectors orthogonal to the metal dielectric interface, and co is its frequency. From Maxwell's equations and the appropriate boundary conditions at the metal/dielectric interface one can derive various useful relationships. For example, in class we derived a relation relating k and kzm- = kim_kzd Ed m (III) It is also true that in both the metal and the dielectric the magnitude of the total wave vector, kt, of the surface plasmon-polariton is related to the magnitude of its components in the x and z directions: @ k = k + k = & where i can be either m (= metal) or d(= dielectric) Questions: 1) Show that the dispersion relation for the surface plasmon polariton is given by: C 1/2 2) Show that under the conditions that