The Resonance Frequency Of Surface Plasmon Of Smallsizes Metallic Nanoparticles

The optical properties of metallic nanoparticles are decided by thecollective oscillation of conduction electrons, i.e. the elementary excitation ofsurface plasmon. Compared to the plasmon collective oscillation behavior ofblock material, the elementary excitation of metallic nanoparticles surfaceplasmon could be irradiated by external light, so they have abnormal opticalproperties. The metallic nanoparticles have great applications prospective inoptical device, biological markers, solar battery, nonvolatile memories,nanotechnology, to name just a few. Meanwhile, they are one of theintersections of multiple disciplines such as Atomic and Molecular Physics,Quantum and Nanoscience, Statistics and Condensed matter physics, attackingtheoretical and experimental personnel of different subject.This paper mainly studies the optical properties of metallic nanoparticlesless than10nm. Theoretical and experimental show that the optical propertiesof small sizes metallic nanoparticles are determined by the free valence electron, which produce a collective electronic oscillation by the role of theexternal electric field, namely surface plasmon. It decays by means of Landaudamping, which is the way of plasmon turn to particle-hole.In jellium model, the positive ion cores of metallic nanoparticles treat asa positive charge background, on which the free valence electrons move. Forthe less than10nm metallic nanoparticles, the optical properties are studied bya theoretical model that the physical picture is very clear. The electronicHamiltonian can be divided in three parts in this model. The first partdescribes the electronic center of mass movement. The second one is themovement of freedom of valence electron, which consist of the environmentof plasmon excitation. And the third is the couple between these twosubsystems, providing the way of plasmon damping.This model is widely used to study the optical properties of the smallsizes metallic nanoparticles. One of the most important shortages is to employthe classic electronic density of states, that’s why this model is calledsemi-classical theoretical model. The free valence electrons of metallicnanoparticles that get the mean field potential is Woods-Saxon potential, andthere is no analytical expression. So the model couldn’t obtain the analyticsolution of the Schr dinger equation. In order to overcome this deficiency, thepotential is replaced by a multi-step approximate potential. We can get theaccurate energy levels and piecewise analytic wave-functions. And then thesemi-classical model extends the full quantum model. Using this model, we calculated the resonance frequency of surface plasmon of small sizes metallicnanoparticles (the Sodium atoms).The Mie theory of classic electromagnetic fields had given the resonancefrequency of surface plasmon of metallic nanoparticles. However, theresonance frequency of small sizes metallic nanoparticles observed inexperiment relative to the classic frequency appeared red-shift. This red-shiftcomes from two effects, one is the spill-out effect. The other is the coupling ofthe plasmon and electronic environment.