Optics Problem - Maximum Dipole Emission

[AntSC]

I am stuck with considering a problem. I don't even really know where to start so any pointers would be a great help.
I am considering a semi-analytic model for some data i have. The situation is looking at how light propogates from a point source in diamond to air. At the surface of the diamond is a diamond hemisphere and at the centre of a hemisphere is the dipole emitter. The model assumes no interface between the surface of the diamond and the diamond hemisphere, just one continuous medium.
The simulations that i ran were to find out the amount of light that was transmitted from the hemisphere to air. In the first case the dipole was simulated at the centre of the hemisphere but then it was interesting change the position of the dipole relative to the hemisphere. In this particular case i was looking at changing the vertical position of the dipole (ie. how far into the bulk or how close to the top of the hemisphere) (diagram attached). One might expect that the maximum transmission of light will occur when the dipole is centred in the hemisphere. There all light is incident normal to the diamond hemisphere:air interface. The results showed a maximum at a point below the centre of the hemisphere (graph attached).
This is what needs to be investigated and is where i am at an impasse with developing a semi-analytic model to show why the maximum is not when the dipole is centred in the hemisphere. I just don't know where to start. I know I'm going to have to use the wavevector but i just don't know in which way. Feeling stupid so any help will be greatly appreciated.
Thanks,
Ant

 

[mfb]

A bit below? That is interesting. I would have expected it a bit into the hemisphere, as more light reaches the hemisphere surface then.

I think without more details it is tricky to find the reason for that increase.

I just don't know where to start.

Analyze your simulations?
Maybe it is just a bug.

What happens if you remove the solid block around the hemisphere?
What happens at z=-5µm, z=-10µm, z=-20µm or anything far away from the hemisphere? Does it decrease with ~1/r^2?

 

[AntSC]

Thanks for the reply.
After a lot of head scratching i found a solution by considering a simple ray diagram. It matches the results i got, which is good news.
If you're interested i'll share.
Cheers, A

 

[mfb]

How does it explain the increased emission? :)