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6) (15 pt) Plasmon modes in metal films and metal nanoparticles The dispersion relation of surface plasmon polaritons (SPPs) on a metal surface is given as Emed Em + Ed (a) Find the condition for SPP resonance. (b) Find the SPP resonance frequency Wsp. (You can use the Drude model for the metal dielectric w function: Em(W) = 1 - w2+iyo (c) Compare the magnitude of SPP resonance frequencies (i) on the metal glass interface and (ii) on the metal air interface. Which one is larger? (d) The localized plasmon (LP) condition in a metal nanoparticle is given as Em + 2d = 0. Find the LP resonance frequency Wlp