Measured Astigmatism due to ZM2
We've been investigating astigmatism in HAM 7 recently, and have found that ZM2 seems to be a prime suspect. The actuation strength of the PSAMs depends sensitively on the beam spot size, so any astigmatism in the ZM2 optic will couple strongly to the optical beam due to its large beam size (w = 2.5 mm).
In 90815 we measured the beam profile before ZM4 and found that the astigmatism at that point does depend sensitively on the strain gauge setting for ZM4. Below I compute the astigmatism in terms of the 1D overlap integral between the X and Y beam parameters. This is a useful metric, since it tells us roughly what the maximum mode overlap we can achieve with another stigmatic mode (eg the SQZ-OMC mode overlap).
| ZM2 SG (V) | X/Y 1D Overlap |
|---|---|
| 1.3 | 0.98 |
| 3.15 | 0.993 |
| 3.8 | 0.98 |
| 4.5 | 0.955 |
| 6.0 | 0.96 |
Here, we notice that the overlap depends strongly on the ZM2 settings. It can be quite bad for some strain gauge settings, but actually doesn't look too bad at the nominal operating point for O4 (3.15 V). From the characterization data at Caltech, we know that the PSAM astigmatism can vary significantly with different settings, so this isn't surprising. See this analysis from Lee: Google Slides
The value for 3.15 V is roughly consistant with the recent measurement of the mode between ZM2 and ZM3. I did a fit of the measurements in aLog 91142 and found that, at the nominal strain gauge setting, the XY overlap after ZM2 is 0.997. Since ZM2 is double passed and actuates primarily on the beam defocus at FC1, we naively expect its contribution to the XY overlap right before ZM4 to be ~0.994. This assumption doesn't alwasy hold, particularly if the beam is poorly mode matched to the FC and the retro beam at ZM2 has a very different spot size.
See the attached zip file for further analysis of the data from aLog 91142. The data from this aLog also suggests that centering the beam better on ZM2 would reduce the astigmatism after ZM2 by about 50% at the nominal strain gauge setting. This data doesnt appear to show a significant change in astigmatism for smaller offsets in the strain gauge setting, though the lack of data at the waist might be impacting the fit somewhat.
| ZM2 SG (V) | Old Pos | New Pos |
|---|---|---|
| 2.65 | .998 | .998 |
| 3.15 | .997 | .9988 |
| 3.65 | .9975 | .998 |
It seems that the severity of our astigmatism issue with ZM2 will depend on whether our mode matching to the FC has changed significantly when we replaced the VOPO in December. If we need to change the ZM2 setting significantly to fix the mode matching to the filter cavity, astigmatism will start to limit our matching to the OMC.
Sensitivity of the FC path
This raises an interesting question: Why have ZM2 be a PSAM in the first place? In principle, we are just mode matching between two static cavity modes. We should be able to do this with a ZM2 optic with a fixed RoC. In practice, the need for tunability is dictated by how sensitive the mode matching solution is and how well we know the various parameters.
In order to mode match between the OPO (waist size < 100 um) to the filter cavity (waist size ~ 1cm) over a path of < 5 m in length, we require the beam to be diverging rapidly past ZM2. See the attached Wield plots for the telescope: Tangential and Saggital
This results in the mode matching solution being quite sensitive to the following parameters: The ZM2 ROC, the ZM2 - to - FC1 distance, and the RoC of the FC1 AR surface.
I made wS plots using Finesse which show how the mode at the HR surface of FC1 depends on the following parameters. I made some assumptions about what the nominal values are for the FC AR and ZM2 RoCs which I'm sure aren't 100% accurate. I think that's fine for now: we just want to see how offsets in the parameter values impact the mode matching to help us gain intuition:
- ZM2 RoC
- FC1 AR RoC
- ZM2 to FC1 distance. In practice this can be varied by sliding ZM3 around to shorten/lengthen the total path
These plots show the 2D overlap for both the horizontal (plotted with X markers) and vertical (plotted with * markers) q parameters (this analysis includes only the astigmatism from the OPO and ZM2 AOI). We see that all three DoFs are fairly degenerate, primarily impacting the beam defocus at FC1.
The original design for the optical path was to use a variable ZM2 to compensate for the manufacturing tolerences of the ZM2 and FC1 RoC's.
However, these plots suggest that one could also compensate for this by moving the position of ZM3 instead of changing the ZM2 RoC. It looks like LLO has actually played around with this degeneracy in the past (59774). One can also translate L2 to fix these issues, but this can only compensate for small mismatches.
Upshot
In summary, I hope we find that the current PSAM setting for ZM2 gives us good SQZ-FC mode matching and we don't have any urgent reason to make significant changes to the FC path to address astigmatism issues. If this does end up being an issue, or if we decide to revisit this for A#, it looks like there might be a way to make the FC path work without a PSAM, though it would take a fair amount of effort to implement.
