Hey I suggest you do the following,
You keep your 2D simulation but you run 3 simulations with your Dipole, in all orthogonal directions, X,Y,Z.
Then you average the results (this is similar to equal emission in all directions).
You can adjust your theta and phi values accordingly, but you should have the blue arrows point once in all 3 directions.
When using a electric dipole, there will be almost no emission in the direction of the blue arrows.
Now regarding the theoretical values of getting that efficiency, you’re forgetting something important, geometry.
It’s much harder to calculate, and you would have to use ray-tracing/shadow-casting (tricky).
A point source emits light in a sphere like shape. Now if you want to calculate 50% you need to collect half the sphere.
To do this you would need a bigger half sphere around it or and infinitely big plane with an acceptance angle of 90.
Now you can’t make an infinitely large plane, because of simulation restriction, but even large planes give the issue that I have multimode instead of single mode. Which would make this much more complex.
The other option in THEORY would be to place the dipole directly against the Waveguide/LSC. However this is not really doable in simulations.
The best options is making a straight waveguide/LCS that extends through your PML boundaries and then placing your QD in the center. That way half the ligth(sphere) is sent to the front and the other to the back. Placing a monitor at both sides, should give you what you’re looking for. If you would add up both monitors you should get your collection efficiency, note both monitors should give the same values. When using a waveguide you need to pay close attention to losses and probably use an expansion monitor.
Yes your LCS has a ~50% collection efficiency but only of the light that hits it. So if only 1/8 of thetotalemitted light hits the LCS, then it’s ~50% of 1/8, ~6%.