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Problems 1. An example of an inhomogeneous EM plane wave is a Surface plasma polariton. Find an expression for its wave function in the literature. 2. Consider a dielectric. On the graphs like those below, indicate values of the real and imaginary parts of the permitivity for static fields. Indicate the behavior in the high frequency limit. Sketch possible frequency dependances for the two permittivity functions at intermediate frequencies and explain. What can you say about the sign of E" and why? Plot E' / VS w and 8" VS w graphs. 3. (a) Plug a plane wave into the wave equation for a non-magnetic medium to find a relation between E(W), w and k that holds regardless of the form of E(W) (b) Assume the permittivity has the form (84.5), with a = Eoo representing the permittivity due to the positive ions and N1 the concentration of free electrons, so = Eoo Where, Wp is the "dressed" plasma frequency. For this case find the dispersion relation W VS k , for transverse electromagnetic waves in a plasma. Plot it and compare it to the form of the curve for vacuum. (c) What kind of behavior does the k = 0 value of W correspond to? What about at large k ?

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