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Message ID: 16158     Entry time: Mon May 24 20:55:00 2021
 Author: Koji Type: Summary Category: BHD Subject: How to align two OMCs on the BHD platform?

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.

Requirement

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

$C = 1 - \left(\frac{a}{\omega_0}\right)^2 - \left(\frac{\alpha}{\theta_0}\right)^2$

where $\omega_0$ is the waist radius, $\theta_0$ is the divergence angle defined as $\theta_0 \equiv \lambda/ \pi \omega$, $a$ and $\alpha$ are the beam lateral translation and rotation at the waist position.

The waist size of the OMC is 500um. Therefore $\omega_0$ = 500um and $\theta_0$ = 0.68 mrad. If we require C to be better than 0.995 according to the design requirement document (T1900761). This corresponds to $a$ (only) to be 35um and $\alpha$ (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.

So we can absorb the misalignment mode of ($a$, $\alpha$) = (0.322 $\theta$, $\theta$). 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.