Simulating WLS tube response with photon wave

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I am trying to simulate a cylindrical WLS tube with two PMTs at both end. The setup is shown in the following images where the WLS paint and the PMT are put inside a glass vessel. To test the response of the PMTs, I tried shooting plane waves of photon on the vessel surface with different incident angles from a few meters distance. For head on beams with 0 deg incident angle, I was expecting more photons will enter the vessel, leading to more photon getting absorbed by the WLS paint. Also, due to isotropic emission of the WLS material, I was expecting to record maximum photon with the PMTs near 0 deg incident angle. However, for some reason, I’m getting maximum photon count around 45 deg incident angle. I tried plotting the photon count as a function of zenith angle (90 deg - incident angle) and I saw a sudden bump near 45 degree, whereas this maximum count should be around 0 degree incident angle (90 deg zenith angle). Could someone please explain why should more photon enter the vessel medium near 45 degree instead of 0 degree incident angle? Also, **Could this be happening due to the shape of the photon wave I’m using?**The outside of the vessel environment has a lower refractive index than the vessel medium. Please let me know if u need more information!

The normal incident image:
image (22)
The 45 deg incident angle image:

Plot showing photon count as a function of zenith angle (90 deg zenith is 0 deg incident angle)

There are many factors involved here. Because photons are emitted isotropically, I would expect that the number of photons produced per incoming photon will be the same, regardless of angle.

Is your plot showing number of photons as a function of flux, or number of photons per absorbed photon? If it is per flux, then you have to account for the probability of transmission through the glass and WLS fiber as a function of angle/indices of refraction.

Is it possible that at 45 degrees you will have total internal reflection of the incoming photon, and it will be itself absorbed on the PMT? Where as at a more direct angle the photon will transmit through the WLS if it is not absorbed

Hi! My plot is showing the number of photons reaching the PMT as a function of Zenith angle. So, for 0 degree zenith angle, the photons travel parallel to the the tube surface and for 90 degree, it’s the head on incident with 0 degree incident angle with the surface normal of the tube. I am consistently getting a huge jump around 40 degree as shown in the figure. Would you think of it as an optimal angle where the photons that don’t get absorbed by WLS material are trapped due to internal reflection, but also the ones that get absorbed are sufficiently large in number to make that sudden increase in photon count around 40 degree?

I have some surprising updates on my results. I tracked the number of photons that gets absorbed by the WLS paint material for both 45 degree and head on incident of photons. The results are presented in the following image. Interestingly, for head on incident, a lot more photons are getting absorbed (13K) compared to 45 degree (9K), however, still for 45 degree, almost twice as much photon is reaching the PMT than head on beam. Here, # of photon absorbed includes only the photons that got absorbed and re-emitted. If WLS emission is indeed isotropic, I should expect head on beam to produce more hit instead of 45 degree.

I think you need to distinguish between your photons that you are shooting at your WLS material, and ones created in your WLS. Because the generation of photons in the WLS is isotropic, the number of these photons counted by the PMT depends only on the location of the event. The total number of events (absorbed photon in the WLS), is dependent on your incoming angle.

In your table, it looks like more photons reach the vessel at 90 degrees, which is expected due to a higher cross section at 90 degrees than 45 degrees. For both, half of those that reach the vessel are absorbed in the WLS. I would expect that a higher % of those at 90 degrees get absorbed, as they would travel through more material. Based on the large jump in your plot, what you are seeing is the angle at which total internal reflection starts. So your initial photons become trapped in the WLS, and either hit the photocathode, or produce more photons via wavelegth shifting

That makes a lot more sense and I suppose exactly what’s happening. Thank you so much for your feedback!

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