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The quantum of plasma oscillation, arising from the quantisation of plasma oscillations

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Why can we allow the speed of light being infinite in case of Surface Plasmons?

polariton as really being solely being comprised of a surface plasmon (i.e. there is no mixing between light and the surface plasmon at these large values of $k_x$. … It averages over a large portion of the $k_x$ axis above and effectively measures only the surface plasmon. …
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