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Surface plasmon polaritons at metal / insulator interfaces

  1. Oct 21, 2016 #1
    1. The problem statement, all variables and given/known data
    Consider the metal-vacuum interface located at z = 0,the metal filling the entire half-space z ≥ 0, vacuum filling (!?) the half-space z < 0. The dielectric function in the metal in the long-wavelength limit is given by:
    fd7a516016b09d30cdfca8d7c47caf37627.png
    where ε0 is the vacuum permittivity. In the metal a solution of Laplace’s equation ∇2φ = 0 is
    29a96a81799c97e4145b6ee2d4a179db105.png
    8b51affd50a3b66259d31e5d9bdf6c72888.png
    2. Relevant equations


    3. The attempt at a solution
    Tried to solve this problem for 8 hours, still no result. Maybe some of you might help?
     
  2. jcsd
  3. Oct 21, 2016 #2

    Twigg

    User Avatar
    Gold Member

    a) How are E and the scalar potential related? Note: the tangential derivative in this case is simply ##\frac{\partial}{\partial x}##, and the normal derivative is ##\frac{\partial}{\partial z}##. Check to see if the solutions provided satisfy the boundary condition that the tangential component of the electric field is continuous at the interface (z=0).

    b) Similar to (a), but now you check the normal direction and use the macroscopic formalism (D as opposed to E). The problem tells you that the normal component of D will be continuous (means 0 free charge at the interface). Use the given formula for the dielectric function of the metal and solve for ##\omega##. What can you conclude about the optically-active oscillations at the interface?
     
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