Differential misalignment of the OMCs
40m BHD will employ two OMCs on the BHD platform. We will have two SOSs for each of the LO and AS beams. The challenge here is that the input beam must optimally couple to the OMCs simultaneously. This is not easy as we won't have independent actuators for each OMC. e.g. The alignment of the LO beam can be optimally adjusted to the OMC1, but this, in general, does not mean the beam is optimally aligned to the OMC2.
When a beam with the matched mode to an optical cavity has a misalignment, the power coupling C can be reduced from the unity as
where is the waist radius, is the divergence angle defined as , and are the beam lateral translation and rotation at the waist position.
The waist size of the OMC is 500um. Therefore = 500um and = 0.68 mrad. If we require C to be better than 0.995 according to the design requirement document (T1900761). This corresponds to (only) to be 35um and (only) to be 48urad. These numbers are quite tough to be realized without post-installation adjustment. Moreover, the OMCs themselves have individual differences in the beam axis. So no matter how we set the mechanical precision of the OMC installation, we will introduce a maximum of 1mm and ~5mrad uncertainty of the optical axis.
Suppose we adjust the incident beam to the OMC placed at the transmission side of the BHD BS. The reflected beam at the BS can be steered by picomotors. The distance from the BS to the OMC waist is 12.7" (322mm) according to the drawing.
So we can absorb the misalignment mode of (, ) = (0.322 , ). This is a bit unfortunate. 0.322m is about 1/2 of the rayleigh range. Therefore, this actuation is still angle-dominated but a bit of translation is still coupled.
If we enable to use the third picomotor on the BHD BS mount, we can introduce the translation of the beam in the horiz direction. This is not too huge therefore we still want to prepare the method to align the OMC in the horiz direction.
The difficult problem is the vertical alignment. This requires the vertical displacement of the OMC. And we will not have the option to lower the OMC. Therefore if the OMC2 is too high, we have to raise the OMC1 so that the resulting beam is aligned to the OMC2. i.e. we need to maintain the method to raise both OMCs. (... or swap the OMCs). From the images of the OMC beam spots, we'll probably be able to analyze the intracavity axes of the OMCs. So we can always place the OMC with a higher optical axis at the transmission side of the BHD BS.