gaussian plane wave source in fdtd
Why do you have to use FDTD? Have you considered a beam propagation method (BPM)? These are very popular for nonlinear optics simulations and they are easier to implement.
I am not sure of your exact application, but you will likely want to implement your source using the total-field/scattered-field (TF/SF) approach. I describe doing this for plane wave sources in my dissertation. You can download it here:
It is also described in Taflove's book on FDTD which has been uploaded somewhere to the EDABoard E-books forum.
You will need to modify the TF/SF technique to inject a Gaussian source, but the implementation is exactly the same as a plane wave source. Instead of a uniform amplitude and phase, your source will be Gaussian.
I will warn you that the math describing a Gaussian light beam is derived using the paraxial approximation so it does not rigorously satisfy Maxwell's equations. If you try to inject this directly in FDTD (a rigorous technique), you may get some crazy results. I have three suggestions for you:
1. Do a literature search to see if this has been done before and how they did it.
2. Pass a plane wave source through an aperture to construct your Gaussian beam. It can be a lossy dielectric aperture to vary the amplitude and phase as well.
3. You can just use (2) as your source, or you can record the amplitude and phase of this source and just incorporate that directly into your model using TF/SF. You can be sure this source will rigorously satisfy Maxwell's equations so you won't get any strange behavior.
Good luck!!
-Tip