Integral equation method for analyzing purcell effect in plasmonic system

Integral equation method is applied to analyze the Purcell effect in plasmonic system in this paper. By applying the Fermi´s golden rule, the Purcell effect of a quantum emitter can be calculated from the local density of states (LDOS), which can be further expressed by the imaginary part of the Green´s function of the whole system. To obtain this Green´s function numerically, the layered medium Green´s function is utilized to simplify the modeling of planarly layered substrate, where the surface plasmon polaritons (SPPs) can be sustained. The metallic nano scatterers are introduced to excite the localized surface plasmons (LSP), and the effect of both is obtained by solving the corresponding integral equation. Numerical results are shown at the end of this paper.