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? :)

 

[sardar]

onio

Dear Antonio,

Thank you for reaching out for help with your optics problem. It seems like you have already made some progress with your simulations and have some interesting results to work with. I completely understand feeling stuck and not knowing where to start when it comes to developing a model for your data. Here are some pointers that may help you to move forward:

1. Begin by clearly defining your problem and the parameters involved. In this case, your problem is focused on understanding the relationship between the position of the dipole emitter and the maximum transmission of light from the diamond hemisphere to air. Make sure to define the relevant variables, such as the position of the dipole and the wavevector, and their relationships to each other.

2. Review the basic principles of optics and wave propagation. This will help you to understand the behavior of light as it passes through different media and interfaces. It may also give you some insights into why the maximum transmission is not occurring when the dipole is centered in the hemisphere.

3. Consider the different factors that could affect the transmission of light in your system. Are there any other interfaces that could be affecting the propagation of light? Are there any other materials or structures that could be influencing the behavior of the dipole emitter?

4. Look for patterns or trends in your data. Are there any relationships between the position of the dipole and the maximum transmission of light? Are there any other variables that seem to be correlated with the maximum transmission?

5. Use your simulation results as a starting point for developing a semi-analytic model. Start by simplifying the problem and making assumptions that will make it easier to analyze. For example, you could assume that the diamond hemisphere is a perfect sphere, or that the dipole emitter is a point source with a specific emission pattern.

6. Use mathematical equations and principles to describe the behavior of light in your system. This could involve using wave equations, Snell's law, or other relevant equations from optics.

7. Test your model against your simulation results and make adjustments as needed. This will help you to refine your model and make sure it accurately represents your data.

I hope these pointers will help you to make progress with your optics problem. Don't feel discouraged if it takes some time and effort to develop a solid model. It's a complex problem and it takes time to understand and explain it. Don't hesitate to reach out for further help or clarification if needed.

Best of luck with your research!

S