Lorenzo Stella edited Plasmonics.tex  over 9 years ago

Commit id: 262418aa7fc249490e4b2d958fe2b95ee49aa57d

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The metal (complex) permittivity then reads  %  \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}  %  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