total internal reflection gaussian

I need to create a Pulsed gaussian beam (ie. both gaussian in time and spatial domains) for Total internal reflection calculations. I would rather like to implement this using Meep (FDTD method).

Does anyone implemented or having some experience on that.

thanks a lot.

you mean something like sin(omega*t*dt) * exp( -( (t-toffset)/(width) ) **2 ) ?
or just leave the sine be and only take the gaussian.
For spatial purpose, just add the pulse the the grid wherever you want it to have, for total error calculations the center grid point might be a good choice.
Advice from Tavlof: take at least 3*offset>=width for smooth transition (if I remember correctly)

works well in FDTD of nearly any kind as far as I know.
1/2/3D and Mur, PML and CPML is what I know that works in.

Thanks for the reply.
For the time domain pulse, your formula work. That part is already available as a inbuilt function in meep.

But the problem is spatial profile. I can add the same exp( -( (x-xoffset)/(width) ) **2 ) kind of thing to the source plane to have gaussian envelope. But then the problem is, it creates the beam waist at this excitation point. (for my case like 2D, then it is a source line having this gaussian amplitude profile)

What i want is to move the beam waist to preferably to the Medium interface (say y= y0) and exciting the grid at (y= y1) kind of thing.

Can't you just add the source to the grid at a specific point?
F(xs,ys) = exp(...) ?
Then just set xs/ys the the values you want it to be.

Sorry if i'm mistaken. Since i want to do reflection coefficient calculation via TIR, then i need to place the source plane at some distance away from the media interface, (and preferably to the PML layers as well i suppose).

But when i place the sources like that, they will propagate as expanding manner. What I want is having a pulse which is like focused gaussian beam. Please find the attachments.

Oh I see.
Well in that case I'd say you should use the TF/SF method that allows the source field and the scattered field to propagate like seperatly in the domain. This method is mainly used for plane wave incidents as it's not that easy as it looks to implement a plane wave in a free FDTD (except in 1D). An entire wall emitting would be feasible for this particular problem maybe but thats just a guess. You will always get a circular (cylindrical or donut like) wave propagating due to the nature of the FDTD as one clearly can see in the two pics you supplied. The TF/SF resolves that issue.
Look into
Computational Electrodynamics The Finite-Difference Time-Domain Method 2d ed- A. Taflove.
You will find anything (and much more) you need in there, not only for TF/SF but all the rest with sources and discussion of problems that come with them.

janK