In this paper, the effects of inner core radius, shell thickness, the dielectric function of middle nanoshell and surrounding medium on localized surface plasmon resonance (LSPR) of gold-dielectric-silver nanotube are studied based on the quasi-static approximation. Theoretical calculation results show that LSPR of gold-dielectric-silver nanotube and LSPR numbers can be well optimized by tuning the geometrical parameters. The longer wavelength of |ω−⟩ mode takes place a distinct red-shift with an increase in the inner core radius and the thickness of middle dielectric layer, while a blue-shift with increasing outer shell thickness. The physical mechanisms are investigated based on induced charges, plasmon hybridization theory and phase retardation. In addition, the effect of middle dielectric function and surrounding medium on LSPR , the local electric field distribution are also reported. Our study provides a way to analyze and broaden the applications of gold-dielectric-silver nanotube.

The energy of a spring with a well-distributed mass ms is theoretically studied in this paper. The solution of the wave equation is derived in detail, and then the kinetic energy and potential energy of the spring are studied with the wave equation, as well as the kinetic energy of the oscillating mass M. The kinetic energy and potential energy of the spring, and total energy are numerically simulated for different ratios ms/M with considering the spring's mass, which makes the property of energy of the oscillating system understood easily.

We theoretically investigate a fundamental problem in the spring oscillator for a uniformly distributed mass. The wave equation and its solution method are derived in detail. The kinetic energy of the spring and oscillator, the elastic potential energy of the spring, and the oscillating period of the system are solved using a wave equation. Our results show that the total energy and each order harmonic energy of the oscillating system are constant. In addition, the oscillating period of the system is also reported, which is equal to one-third of the spring mass m added to the mass M when m ≤ M.

Due to the plasmon hybridization between nanowire and outer nanotube, the geometrical parameters of nanotube take great effect on absorption cross section and local electric field enhancement. In this paper, we study the effects of the inner nanowire radius, shell thickness, middle dielectric functions and surrounding medium functions on absorption cross section and local electric field enhancement of bimetallic three-layered nanotubes, gold-dielectric-silver (GDS) nanotube and silver-dielectric-gold (SDG) nanotube in detail based on quasi-static theory. The results show that the thickness of outer nanotube plays a more role to tune local surface plasmon resonance (LSPR) than that of inner nanowire, whereas a better LSPR could be obtained with a higher surrounding dielectric function. In addition, the local electric field enhancement is also investigated. The maximum local electric field enhancement could be obtained with smaller thickness of dielectric layer and higher surrounding dielectric function. Our study provides a way to analyze optical properties of GDS and SDG nanotube and also broaden their applications in sensor and optical data storage.