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Lorenzo Stella edited Plasmonics.tex
over 9 years ago
Commit id: 262418aa7fc249490e4b2d958fe2b95ee49aa57d
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The metal (complex) permittivity then reads
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\begin{equation}\label{eq:non-local-optics}
\epsilon_{r}\left({\bf
k},\omega\right)=\epsilon_{\infty}-\frac{\omega_{p}^{2}}{\omega\left(\omega+i\gamma\right)-\beta^{2}v_{F}^{2}{\bf k}^{2}}\;, k},\omega\right)=\epsilon_{\infty}-\frac{\omega_{p}^{2}}{\omega\left(\omega+i\gamma\right)-\beta^{2}{\bf k}^{2}}\;.
\end{equation}
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The parameter $\beta$ can be fitted to model the experimental data,
although the values $\beta=\sqrt{3/5}$, where $v_{F}$ is the Fermi
velocity and $\beta$ is, in principle,
another free parameter, although the values $\beta=\sqrt{3/5}$ velocity, is suggested by the Thomas-Fermi approximation.
(\textbf{CITE} Boardman, A. D. Electromagnetic Surface Modes)
Regardless the level of sophistication of the permittivity model,
all classical calculations assume that electrons are strictly confined