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We present a theory for determining the localized surface plasmon resonance shifts of arbitrarily shaped metal nanoparticles on a substrate. Using a pseudoparticle concept, an expression for the particle-substrate interaction is derived, providing both physical insight and formulas to estimate the shifted plasmon resonance. The theory is verified against measured scattering spectra of nanorods on substrates. Simple formulas are provided to calculate the resonance of nanorods, spheres, and ellipsoids on dielectric substrate.
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Vernon et al. (2010) studied this question.
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