Summary:

I did some more investigation of what the appropriate cavity geometry would be for the OMC. Unsurprisingly, depending on the incident mode content, the preferred operating point changes. So how do we choose what the "correct" model is? Is it accurate to model the output beam HOM content from NPROs (is this purely determined by the geometry of the lasing cavity?), which we can then propagate through the PMC, IMC, and CARM cavities? This modeling will be written up in the design document shortly.

*Colorbar label errata - instead of 1 W on BS, it should read 1 W on PRM. The heatmaps take a while to generate, so I'll fix that in a bit.

Update 230pm PDT: I realize there are some problems with these plots. The critically coupled f2 sideband getting transmitted through the T=10% SRM should have significantly more power than the transmission through a T=100ppm optic. For similar modulation depth (which we have), I think it is indeed true that there will be x1000 more f2 power than f1 power for both the IFO AS beam and the LO pickoff through the PRC. But if the LO is picked off elsewhere, we have to do the numbers again.

Details:

Attachment #1: Two candidate models. The first follows the power law assumption of G1201111, while in the second, I preserved the same scaling, but for the f1 sideband, I set the DC level by assuming a PRG of 45, modulation depth of 0.18, and 100 ppm pickoff from the PRC such that we get 50 mW of carrier light (to act as a local oscillator) for 10 W incident on the back of PRM. Is this a reasonable assumption?

Attachment #2: Heatmaps of the OMC transmission, assuming (i) 0 contrast defect light in the carrier TEM00 mode, (ii) PRG=45 and (iii) 1 W incident on the back of PRM. The color bar limits are preserved for both plots, so the "dark" areas of the plot, which indicate candidate operating points, are darker in the left-hand plot. Obviously, when there is more f1 power incident on the OMC, more of it is transmitted. But my point is that the "best operating point(s)" in both plots are different.

Why is this model refinement necessary? In the aLIGO OMC design, an assumption was made that the light level of the f1 sideband is 1/1000th that of the f2 sideband in the interferometer AS beam. This is justified as the RC lengths are chosen such that the f2 sideband is critically coupled to the AS port, but the f1 is not (it is not quite anti-resonant either). For the BHD application, this assumption is no longer true, as long as the LO beam is picked off after the RF sidebands are applied. There will be significant f1 content as well, and so the mode content of the f1 field is critical in determining the OMC filtering performance.