Plasmonic nanoparticles are particles whose electron density can couple with electromagnetic radiation of wavelengths that are far larger than the particle due to the nature of the dielectric-metal interface between the medium and the particles: unlike in a pure metal where there is a maximum limit on what size wavelength can be effectively coupled based on the material size. What differentiates these particles from normal surface plasmons is that plasmonic nanoparticles also exhibit interesting scattering, absorbance, and coupling properties based on their geometries and relative positions. These unique properties have made them a focus of research in many applications including solar cells, spectroscopy, signal enhancement for imaging, and cancer treatment. Their high sensitivity also identifies them as good candidates for designing mechano-optical instrumentation. Plasmons are the oscillations of free electrons that are the consequence of the formation of a dipole in the material due to electromagnetic waves. The electrons migrate in the material to restore its initial state; however, the light waves oscillate, leading to a constant shift in the dipole that forces the electrons to oscillate at the same frequency as the light. This coupling only occurs when the frequency of the light is equal to or less than the plasma frequency and is greatest at the plasma frequency that is therefore called the resonant frequency. The scattering and absorbance cross-sections describe the intensity of a given frequency to be scattered or absorbed. Many fabrication processes or chemical synthesis methods exist for preparation of such nanoparticles, depending on the desired size and geometry. The nanoparticles can form clusters (the so-called "plasmonic molecules") and interact with each other to form cluster states. The symmetry of the nanoparticles and the distribution of the electrons within them can affect a type of bonding or antibonding character between the nanoparticles similarly to molecular orbitals. Since light couples with the electrons, polarized light can be used to control the distribution of the electrons and alter the mulliken term symbol for the irreducible representation. Changing the geometry of the nanoparticles can be used to manipulate the optical activity and properties of the system, but so can the polarized light by lowering the symmetry of the conductive electrons inside the particles and changing the dipole moment of the cluster. These clusters can be used to manipulate light on the nano scale.
Theory
The quasistatic equations that describe the scattering and absorbance cross-sections for very small spherical nanoparticles are:
σ s c a t t = 8 π 3 k 4 R 6 | ε p a r t i c l e − ε m e d i u m ε p a r t i c l e + 2 ε m e d i u m | 2 {\displaystyle {{\sigma }_{\rm {scatt}}}={\frac {8\pi }{3}}{{k}^{4}}{{R}^{6}}{{\left|{\frac {{{\varepsilon }_{\rm {particle}}}-{{\varepsilon }_{\rm {medium}}}}{{{\varepsilon }_{\rm {particle}}}+2{{\varepsilon }_{\rm {medium}}}}}\right|}^{2}}}
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