This study looks at the effects of differential ITM/ETM RoC change, common ITM/ETM RoC change, and differential ITEM lenses change on the DARM sensing function as we track several quantities such as the mismatch between the ARM cavities, ARMs-SRC mismatch, and the beam spot size on TMs.
FINESSE results suggest that the mismatch between the arms through the ITMs (both RoC and lenses) has the biggest effect on the sensing function.
In all of these cases, we start with a minimized mismatch between all cavities to less than 0.01% by changing the RoC of several optics until the mismatches are minimized. All mismatches are calculated with the “model.cavity_mismatches_table()” function in FINESSE .
Steps to generate these plots:
- Changing a parameter (RoC or focal length)
- Lock the model using DC readout after each change
- Calculate and plot the sensing function
For the RoC, the 3rd line is always the minimized mismatches case. Maximum mismatch I created was ~0.9%
Case1: Differential ITMs RoC
Starting with the case of differential ITMs RoC changes by ±2%. ITMX RoC increases while ITMY RoC decreases. The mismatch between the ARMs and the SRC also changes, but that is smaller than the mismatches between the ARMs themselves.
This has a strong effect on the sensing function shape at low frequencies. It seems that there is a stronger optical spring as the mismatch between the arms increases. The label on the plots show the ITMs RoC in diopters calculated as 2/RoC.
Changing which RoC increases and which decreases results in the same sensing functions.
The plot attached shows that result. And a table (attached as .png) shows the mismatches, diopters and more.
Case2: Differential ITM lenses focal lengths
Similarly, I change ITM lenses' focal lengths. Since, as defined in FINESSE at least, ITMXlens is negative and ITMYlens is positive, a differential change means that ITMXlens diverges the beam stronger every time (becomes less negative. e.g -3*10^5 m instead of -5*10^5) , and ITMYlens converges less, meaning it becomes a bigger positive number. Diopters in this case are calculated as 1/f
This creates a differential mismatch between the ARM cavities. The result is very similar to that of differential ITMs RoC changes.
The plot and the table attached show the sensing functions.
Case3: Differential ETM RoC
This also creates a mismatch between the arms that is bigger between the ARMs and the SRC. This will only affect the carrier’s mode, but not the sidebands, like the ITMs do.
This case does not have a big effect on the sensing function, as the ITMs (RoC and lenses). The sensing function plot and table are attached.
Case4: Common ITM RoC
Now, I keep the ARMs mode matched to each other but I mismatch the ARMs to the SRC by changing the ITMs RoC. This has a bigger effect on the DARM sensing function compared to ETMs but smaller than the ITM. Interestingly, this is the only case that shows a pro-spring behavior
The sensing function plot and table are attached.
From this investigation, it seems that the mismatch between the ARM cavities has the biggest effect on the sensing function, rather than the mismatch between the ARM cavities and the SRC.
Qualitatively, this suggests that the sensing function’s shape is an indicator of how well the arms are mode-matched to each other.
