Understanding photoluminescence of metal nanostructures based on an oscillator model

Abstract

Scattering and absorption properties of metal nanostructures have been well understood based on the classic oscillator theory. Here, we demonstrate that photoluminescence of metal nanostructures can also be explained based on a classic model. The model shows that inelastic radiation of an oscillator resembles its resonance band after external excitation, and is related to the photoluminescence from metallic nanostructures. The understanding based on the classic oscillator model is in agreement with that predicted by a quantum electromagnetic cavity model. Moreover, by correlating a two-temperature model and the electron distributions, we demonstrate that both one-photon and two-photon luminescence of the metal nanostructures undergo the same mechanism. Furthermore, the model explains most of the emission characteristics of the metallic nanostructures, such as quantum yield, spectral shape, excitation polarization and power dependence. The model based on an oscillator provides an intuitive description of the photoluminescence process and may enable rapid optimization and exploration of the plasmonic properties.

Unified Treatment for Scattering and Photoluminescence Properties of Strongly Coupled Metallic Nanoparticle Chains based on a Coupling Classic Harmonic Oscillator Model

“…(11) Secondly, we deal with the PL properties. As our previous work demonstrates 23 , PL term origins from the general solutions of the homogeneous linear equations:…”

“…However, the spectra shapes of these coupled systems are seldom estimated in theory. In a previous work, we investigate the spectra of metallic nanoparticles with individual mode without any coupling 23 . In another previous work, we only consider the dimer case for the coupled system.…”

“…An individual metallic nanostructure with single mode can be treated as an oscillator with its intrinsic frequency ω 0 and damping coefficient β 0 , the behavior of which has been discussed in our previous work 23 . When it comes to two coupled nanostructures (assume these two are the same), the coupling coefficients between them can be evaluated as 24 :…”

“…where D −1 is the inverse of matrix D. The total far field emission of the electric field is proportional to the accelerations of the oscillators [23][24][25] :…”

“…(13). We can rewrite the solutions as α k± = −β k ± iω k , k = 1, 2, ..., n. Due to the large difference from the excitation frequency, we omit the solutions of "α k+ " as our previous work does 23,24 . Therefore, the total solutions for Eq.…”