This repository contains numerical simulations for calculating the electromagnetic Green's function of a multi-layer structure and analyzing the dynamics of a quantum emitter coupled to a surface plasmon. The codes were developed as part of coursework. Check the full reports for context here and here

• Metallic slab: modeled with a simple Drude model with zero hydrodynamic parameter.
• Media: standard dielectric constants were used.
• Constants: standard constants was used for speed of light and conversions.

Green's Tensor Calculation This notebook focuses on the fundamental electromagnetic properties of the system.

• Physics Model: Implements Fresnel reflection coefficients (rij) and total reflection coefficients (rT) for a thin metallic slab sandwiched between vacuum and a substrate (e.g., silica).
• Calculations: Computes the Real and Imaginary parts of the Green's function components ($G_{xx}$ and $G_{zz}$) via numerical integration over the wavevector $k_\rho$.
• Visualization: Plots the variation of Green's function components against intervals of:
  • Frequency ($\omega$)
  • Slab Thickness ($t$)
  • Dipole-Surface Distance ($z$)

Quantum Emitter Time Evolution NOTE: This section was a numerical reproduction of the course instructor, A. González-Tudela et al's paper "Reversible dynamics of single quantum emitters near metal-dielectric interfaces"]) This notebook uses the Green's function results obtained from the first notebook to simulate the quantum dynamics.

• Spectral Density: Calculates the spectral density $J(\omega)$ based on the imaginary part of the Green's function.
• Dynamics: Solves the integro-differential equation governing the probability amplitude $c(t)$ of the emitter's excited state.
• Visualization: Plots the spectral density and the population decay $|c(t)|^2$ over intervals of:
  • Wavelength (positions normalized to wavelength)
  • Time (to study the time evolution)

• Python 3.x
• numpy
• scipy
• matplotlib