2. Interface plasmons. We consider the plane interface \( z=0 \) between metal 1 at \( z>0 \) and metal 2 at \( z<0 \). Metal 1 has bulk plasmon frequency \( \omega_{p 1} ; \) metal 2 has \( \omega_{p 2} \). The dielectric constants in both metals are those of free-electron gases. Show that surface plasmons associated with the interface have the frequency \[ \omega=\left[\frac{1}{2}\left(\omega_{p 1}^{2}+\omega_{p 2}^{2}\right)\right]^{1 / 2} \]
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At the interface between the two metals, the total electric field must be continuous. This means that the sum of the electric fields in each metal must be zero at the interface. We can write this condition as \( E_1 + E_2 = 0 \), where \( E_1 \) and \( E_2 \) are Show more…
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