Localized surface plasmon resonance dielectric medium

The nonlinear polarization Pi(fl, r ) of Eq. (10) is a pnrely local surface polarization because it only depends on the value of the fields at location r. Because it depends on the fundamental field inside the particle, it is subjected to resonances when the quantity s(ft)) + 2e , vanishes, where e(w) is the complex dielectric function of the metal and that of the surrounding medium. On the opposite, the nonlinear polarization 2( 2, E) of the form of Eq. (11) is a non local nonlinear polarization since it depends on spatially varying fields within the particle. Similarly to the first order contribution, it is subjected to resonances when the quantity 2e(w) + 3e vanishes. These resonances are the usual surface plasmon resonances of the particle. Within the condition of non magnetic media, the magnetic dipole field does not introduce any resonances. We neglect higher order terms. 

Small metallic particles are well known to exhibit LSPRs. Surface plasmons are collective excitations of surface charge which under suitable conditions can be excited by an external optical field. Localized surface plasmons (LSPs) are oscillations of surface charge on a finite structure with fields that decay exponentially from the surface of the structure in both directions normal to the surface. The structure may be composed of a metal surrounded by a dielectric, or it may be composed of a dielectric surrounded by a metal. Examples include metallic nanoparticles and nanobubbles embedded in metals. Nanoholes in metal films also support LSPRs even though a hole is not entirely surrounded by the metal film. The surface plasmon resonance wavelength is determined by the size, shape, and material of the stmcture and the surrounding medium. 

LSPR frequency is dependent on the size, shape, material properties and the effect of the dielectric medium around the nanoparticles. They determine the position and width of the plasmon resonance. Due to the confinement of the SP to the metal nanoparticle, excitation of surface plasmons can result in selective photon absorption, scattering and a large enhancement of the local electric field in the close vicinity of the metal nanoparticles. Hence, varying these parameters offers the tunable resonance position to engineer plasmonic structures to target weakly absorbing regimes of various types of solar cells [5]. 

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