Multipole plasmons in metal nanorods: Scaling properties and dependence on particle size, shape, orientation, and dielectric environment

T-matrix formalism was used to study the multipole resonances excited by electromagnetic plane waves in gold and silver nanorods whose shape was modeled by prolate spheroids and cylinders with flat or semispherical ends (s-cylinders). The particle diameters and aspect ratio were varied from 20 to 80 nm and from 2 to 20, respectively. By using extended precision T-matrix codes, we calculated the extinction, absorption, and scattering spectra for random and fixed orientations of the particle axis with respect to the incident transverse magnetic (TM) and transverse electric (TE) polarized light, where the reference plane is defined by the particle axis and the incident wave vector. We found that the parity of a given spectral resonance number n coincides with the parity of their multipole contributions l, where l is equal to or greater than n, and the total resonance magnitude is determined by the lowest multipole contribution. The random-orientation resonances are excited most effectively by the TM scattering configurations, except for the short-wavelength resonance, which equals the sum of the dominant dipole TE resonance and the other multipole contributions. The even multipole resonances are maximal at intermediate orientations, whereas the odd multipoles can effectively be excited at both perpendicular and intermediate orientations of the rod axis with respect to the TM incident wave. In particular, the quadrupole resonance can be excited only by the TM incident wave, and the resonance magnitude is maximal for orientation of the particle symmetry axis near 54 degrees with respect to the incident light. Finally, we found that the multipole resonance wavelengths obey a universal linear scaling when plotted versus the particle aspect ratio divided by the resonance number. This remarkable property of multipole resonances can be understood in terms of a simple concept based on plasmon standing waves excited in metal nanowires by an electric field of incident light (Schider et al. Phys. Rev. B 2003, 68, 155427). The refractive index sensitivity of the multipole resonance wavelength to a dielectric environment also exhibits linear scaling properties. Specifically, the relative shift of the resonance wavelength is proportional to the relative refractive index increment with a universal angular slope coefficient.