Calculation of longitudinal surface plasmon frequencies in noble metal nanorods

The longitudinal surface plasmon oscillation frequencies of long enough noble metal nanorods are analyzed theoretically. An expression for frequency dependence on aspect ratio accounting for the contribution of d-electrons into the dielectric function of metal is obtained. The results of calculations for gold nanorods in aqueous solution are compared with various experiments and good agreement is demonstrated. An analytical expression for the surface plasmon resonance sensitivity with respect to changes in the refractive index of surrounding media is obtained.