Second quantization model for surface plasmon polariton in metallic nano wires

Abstract

Abstract. A model of effective Hamiltonian is proposed in second quantization representation for system of surface plasmons and photon (polariton) in metallic nano wires. The dispersion relation curves of surface plasmon polariton was calculated by mean of the Bogoliubov diagonalization method. The surface plasmon photon vertexes are considered. The conditions for excitation surface plasmon, existence plasmon radiate modes, and a possible application of metallic nano wires were also discussed. IntroductionIn the last tens years, the new field of plasmon has been developed, which discussed the interesting features of metals with nano structure, exciting with an electromagnetic radiation: the plasmon resonance.The plasmon is a quasiparticle resulting from the quantization of plasma oscillations. Plasmons are collective oscillations of the free electron gas density. A Plasmon can couple with a photon to create another quasiparticle called a plasmon polariton. Surface plasmons are plasmons which are restricted in surfaces and interact strongly with light resulting in a polariton. They occur in the interface of a vacuum and material with a small positive imaginary and large negative real dielectric constant. It is usually a metal or doped dielectric.The result of this combination is the interesting optical properties of absorption and scatter in the Vis -IR region and can be exploited for many applications in modern technology. They also play an important role in new interesting physics phenomena such as Surface Enhanced Raman Spectroscopy (SERS), Surface Plasmon Energy Transfer (SET), and Forster Resonance Energy Transfer (FRET) and have numerous other applications in plasmonics and nanotechnology and medical treatments [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16].Since for all these surface plasmon polariton (SPP) systems the downscaling of the cross section is not limited by the light wavelength, they represent a promising alternative to dielectric optical waveguides. Thus, there is a substantial interest in the fundamental properties of SPP propagation in nanoscale structured matter, which is determined by the respective dispersion relations.Nowadays, the experimental determination of the dispersion relation in the confined metallic films with nanoscopic cross sections nanowires is a challenging task, as the methods such as total internal reflective attentuated spectroscopy cannot be applied easily because of the small size