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Message ID: 17041     Entry time: Thu Jul 28 13:09:28 2022
Author: yehonathan 
Type: Update 
Category: BHD 
Subject: Mode matching considerations 

The LO beam was found to have a power of 60uW, 10% of the power expected. We are pretty sure about the expectation because the AS beam has a power of 300uW, roughly the expected power. Additionally, the visibility of the MICH fringes in the BHDR is 40%.

If the mode-matching is perfect then we expect the visibility to be \text{VIS}=\frac{I_\text{max}-I_\text{min}}{I_\text{max}+I_\text{min}}=\frac{2\sqrt{I_\text{LO}I_\text{AS}}}{I_\text{LO}+I_\text{AS}}=\frac{2\sqrt{300\cdot 60}}{300+600}

which is roughly 74.5%.

If there is some mode-mismatch one can show that the visibility is \text{VIS}=\frac{2\sqrt{M}\sqrt{I_\text{LO}I_\text{AS}}}{I_\text{LO}+I_\text{AS}}, where M=\left|\frac{\int \left(E_\text{LO}^\star E_\text{AS} \right)\mathrm{d}x \mathrm{d}y}{\sqrt{I_\text{LO}I_\text{AS}}}\right|^2 is the mode-mismatch.

Using Finesse model I calculated \sqrt(M)=0.93 in the MICH configuration so the expected visibility is around 70%, far away from the observed 40%. To explain the observed visibility the mode mismatch would have to be ~ 30% which is very unlikely.

So it could either be a ghost beam or that the LO beam is clipped so badly that it also degrades its phase front (and therefore the mode-matching). The fact that we see fringes on the LO beam might suggest knife edge clipping on one of the auxiliary optics in the BS chamber.

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