deletions | additions       diff --git a/Plasmonics.tex b/Plasmonics.tex  index 9f178e2..8f932fc 100644  --- a/Plasmonics.tex  +++ b/Plasmonics.tex 
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structure calculations. A nanoplasmonic system --- e.g., made by metal  nanoparticles (MNPs) --- can be a few tens of nm across, while the  region of strong field enhancement --- e.g., in the gap between two  MNPs --- can be less than 1 nm across (\textbf{CITE} Baumberg). across.\cite{Savage_2012}  The field enhancement, $h\left({\bf r}\right)$, is essentially a classical  observable, defined as  % 
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Large field enhancements are the key to single molecule surface-enhanced  Raman spectroscopy (SERS) and values as large as $h\approx1000$ (the  intensity of the SERS signal scales as $h^{4}$) are predicted by  classical electromagnetic calculations. (\textbf{CITE} Katrin Kneipp  et al 2002 J. Phys.: Condens. Matter 14 R597 doi:10.1088/0953-8984/14/18/202) calculations.\cite{Kneipp_2002}  In classical calculations the electronic response is model by the  macroscopic permittivity of the material. The classical Drude model  gives the following simple and robust approximation of the metal (complex) 
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the plasma frequency, $\omega_{p}$, and the relaxation rate, $\gamma$,  are: $\epsilon_{\infty}=9.5$, $\hbar\omega=8.95$ eV and $\hbar\gamma=69.1$  meV.(\textbf{CITE} Grady CPL 2004) Non-local correction to the Drude  model can be also included by considering the plasmon dispersion.  (\textbf{CITE} Dobson, J. F.; Le, H. M. High-Frequency Hydrodynamics  and Thomas-Fermi Theory. J. Mol. Struct. (THEOCHEM) 2000, 501, 327\textminus{}338.  ) dispersion.\cite{Dobson_2000}  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}}\;,