I did a quick calculation to see if the offset of the arm length which I tried last night was reasonable or not.

The conclusion is that the 20 nm offset that i tried could be a bit too close to a resonance of the 55 MHz sidebands.

A reasonable offset can be more like 10 nm or so where the phases of all the laser fields don't get extra phases of more than ~ 5 deg.

The attached plot shows where the resonances are for each sideband as a function of the displacement from the carrier's resonance.

The red solid line represent the carrier, the other solid lines are for the upper sidebands and the dashed lines are for the lower sidebands.

The top plot shows the cavity power and the bottom plot shows how much phase shift the fields get by being reflected by the arm cavity.

Apparently the closest resonances to the the main carrier one are that of the 55 MHz sidebands, and they are at +/- 22 nm.

So if we displace the arm length by 22 nm, either of the 55 MHz sidebands will enter in the arm cavity and screw up the sensing matrix for the 55 MHz family.