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Plasmons from 3D to 1D Motivation Stained glass rose window Notre Dame de Paris Drude-Lorentz-Model • Valence electrons of metals can be described as a free electron gas • Damping ɣ is explained through collisions with the nuclei which are fixed Dielectric function and plasma frequency • The angular frequency of the electron density oscillating around the average density is called plasma frequency ω𝑝 • The dielectric function depends on the angular frequency ε𝑟 ω = 1 − ω2𝑝 ω2 for most metals ω𝑝 is in the ultraviolet region Reflectivity • R= ñ−1 | |² ñ+1 with ñ = ε𝑟 ω • R is 1 for ω ≤ ω𝑝 decreasing for ω > ω𝑝 0 for ω = ∞ Maxwell‘s equations Plasma oscillations • Equation can be split up in an transverse and longitudinal part 2 ∂ 𝐸𝑡 2 2 + ω 𝐸 − 𝑐 ∆𝐸𝑡 = 0 transverse part 𝑝 𝑡 2 ∂𝑡 2 ∂ 𝐸𝑙 2 + ω 𝐸𝑙 = 0 longitudinal part 𝑝 2 ∂𝑡 • The longitudinal part corresponds to the harmonic oscillator Plasma oscillations • Transverse solution 𝑐 2 𝑘 2 = ω2 − ω2𝑝 • Longitudinal solution ω = ω𝑝 Plasmons • Light = transverse wave • Plasmon = longitudinal wave • => plasmons can not be excited directly by light but by techniques of inelastic scattering • 𝐸𝑜𝑢𝑡 = 𝐸𝑖𝑛 - nħω𝑝 Surface Plasmons • Localized at the interface between a plasma and a dielectric • Have transversal and longitudinal electric field components Thanks for your attention! Sources • Optical Properties of Solids (Oxford Master Series in Physics) Mark Fox • Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light - M. Born, E. Wolf • Plasmonics: Fundamentals and Applications –Stefan Alexander Maier • http://webstaff.itn.liu.se/~alira/hjo_coe_seminar.ppt • http://web.pdx.edu/~larosaa/Applied_Optics_464564/Lecture_Notes_Posted/2010_Lecture7_SURFACE%20PLASMON%20POLARITONS%20AT%20%20ME TALINSULATOR%20INTERFACES/Lecture_on_the_Web_SURFA CE-PLASMONS-POLARITONS.pdf