A couple of mode matching solutions for the north cavity that look promising have been found.
I'm thinking the following plan 2c to be implemented.
- We'll use the PMC in each path
- We also need to insert a FI in each path (to use the reflected light from the cavities)
- EOMs after the PMC will be inserted for the in-vacuum cavities PDH
These constrains the mode macthing to be done with the use of three lenses. One to focus the beam
into the BB EOM and the other two to mode match the North cavity.
Question1: Can we place the FI without changing the mode matching solution?
Answer: In Plan1 the profile caluclation is shown. As you can find there, considering that
the maximum distance from the waist of the PMC for the FI is ~ 1.32m (FI length ~ 10cm)
we have a diameter around ~2mm.
Question2: OK. We need to use some focusing lenses. How strong will they be?
Answer: In Plan2-a/b/c the profile caluclations with the sensitivity to the displacement of the lenses
are shown. As you can find there, we have at the FI a beam radius that is around ~750um at most.
However the three setups show a different sensitivity with Plan2a and 2c being lens sensitive to lens
displacement compared to 2b.
Along with the discussion above, I will use 2c. (or 2a looks applicable too)
For all the profiles the reference point is the waist at the PMCc (330um), zero point in the plots
and the cavity waist is located at 1.96m far from the PMC waist.
Plan 1: FI after the two MM lenses
In this case we have 3 lenses of focal "fi"(mm) located at "li"(m):
l1 = 0.16;
l2 = 0.762;
l3 = 1.107;
f1 = 0.1432;
f2 = 0.688;
f3 = 0.572;
If we want to "risk" a 2 mm diameter beam into the FI.
The following plans 2(a,b,...) have all the FI in the between the two MM lenses. I just report
one figure with the setup:
l1 = 0.183;
l2 = 0.773;
l3 = 1.32;
f1 = 0.229;
f2 = 0.143;
f3 = 0.229;
We can place the FI around 1.2m or further than the North cavity. The further we go and the smaller is the beam
until we reach the waist at 0.9m.
Sensitivity of lenses displacement
Dipending on which directions we move the lenses we may have 20% mismatch with a displacement of ~4cm for lens 2
while for Lens 3 only few percent.
l1 = 0.117;
l2 = 0.951;
l3 = 1.313;
f3 = 0.143;
l1 = 0.148;
l2 = 0.683;
l3 = 1.325;
f2 = 0.1719;
This shows to be less sensitive to the lens displacement, compared to the others. Furthermore we notice that the two lenses are somehow indipendent as the curve are more circular;
There is something not ok with the Gouy phase, I need to cross check what is wrong there. I should fix this doubt later, for now it is not important.
I would propose plane 2c
Data are currently stored in a shared Box Inc folder, but we may wanto create an svn folder for all our data.