# Fluorescence Enhancement Au nanoparticle distance dependence

I am working with the FDTD Fluorescence Enhancement example here:
https://apps.lumerical.com/sp_fluorescence_enhancement.html

I am trying to reproduce the distance dependence on the radiative efficiency in the plot by the example paper above.

However, I am having trouble reproducing it. The example given in the application by lumerical has a 20nm sphere, but when I increase it to 30nm , and try to change distances between dipole and sphere, my results don’t seem to converge, as the results aren’t within the -dx, +dx theoretical range.

Even in the orignial setup, if I increase the mesh accuracy from 2.5 nm (original mesh size) to 1.25 nm while keeping everything else the same, the data does not converge.

Here is original data:

Here is same data with 1.25 nm mesh instead of 2.5 nm:

It’s already starting to get worse.

When I change the sphere to 30nm radius, and do dipole distance sweep (to coincide with the reference paper) with 1.25nm mesh , I no longer get my FDTD data in between -dx, +dx. For example 15nm distance:

60nm distance:

All I am doing is changing the parameters in fluorescence_decay_setup.lsf . I am changing dipole distance, sphere size and I am using the transmission box since it’s finer mesh and I also want to eventually take the dipole closer to the sphere to see the dip in gammarad/gamarad0 as in the paper.

Any help would be greatly appreciated!

Hello @vmenon,

Thank you for the question. Have you tried setting the use dipole box variable as 1 in your quantum efficiency analysis group? The default setting is 0, but this can be inaccurate for small mesh sizes on the order of \lambda/1000. This is discussed on the newer fluorescence enhancement example page, available here:

Let me know if this helps.

Yes I have the setting as 1. I will look into more detail at this newer example you provided and see if I can make it work. Thank you for the response!

There are some differences between the two examples, as well as some additional information on the new example’s page. Let me know if it helps improve your results!

I am using transmission box in the new example as well, but what confuses me is if I keep all settings the same, but simply improve the mesh from 2.5nm down to 1 or 0.5nm, the system starts to diverge from theoretical predictions. I would need a small mesh in order to properly assess QE at small dipole distances. So i’m not sure how to approach it if smaller mesh is giving me worse results compared to theory. Below I have data for 2.5nm mesh (as in example), 1.5nm, 1nm, 0.5nm

2.5 nm mesh

1.5nm mesh

1nm mesh

0.5 nm mesh

Is it possible that this is being caused by lightning rod effects, as discussed at the bottom of the fluorescence enhancement page? This could be especially important if the dipole is close to the nanoparticle.

Also, could you post your new simulation file so I could take a look?

I didn’t notice any lightning rod effects to my knowledge. Here are the files. At the end of the day I am simply interested in reproducing the emission enhancement plot (b) in the original post from the fluorescence reference paper. Thank you!

Thank you for posting the new files. If lightning rod effects are not the issue, there are a couple more possibilities for what may be causing the problem. There can be added difficulties when using a very fine mesh, for example:

• Scattering at interfaces between areas with different mesh densities due to a change in grid dispersion. You can try to reduce this by reducing the mesh size of the simulation outside the monitor box.