This example uses the well-known Young’s double slit experiment to demonstrate the spatial coherence of sources within an FDTD simulation.
Solvers: FDTD, VarFDTD
The script file runs the simulation for the cases where the only the top slit is open, only the bottom slit is open, and the case where both slits are open.
As the plane wave propagates through the slit, diffraction occurs, making the slit act as a point source. The resulting field profile on the screen is a roughly Gaussian shaped intensity profile from each slit when only one is open at a time.
When both of the slits are open at the same time, the resulting intensity profile recorded by the monitor is not the simple the addition of the two intensity profiles shown above. Instead, it is a coherent sum, that includes the interference terms between the two point sources.
It is important to understand that individual FDTD simulations are always coherent. Never the less, it is possible to obtain incoherent results by running multiple simulations and adding the results incoherently. The figure below shows the resulting profile for an incoherent system.
The example script runs 3 simulations, but you can get both incoherent and coherent results by running only the two simulations where only one slit is open and adding the results incoherently (\(|E_1| ^2+|E_2|^2\)) and coherently (\(|E_1+E_2|^2\))