Volume Integral Equation Method for Numerical Green's Function Calculation

This paper investigates the spontaneous emission of quantum emitters within metal nanostructures by calculating the numerical Green's function with the volume integral equation (VIE) method. Compared to differential equations, the VIE has less unknowns and can be accelerated by fast Fourier transform. Particularly, the discretization of Hertzian dipole source and the utilization of different iterative solvers are discussed in detail. The work offers a fast and accurate solution to calculate numerical Green's function, which is fundamentally important to quantum electromagnetics.