Let's see if the ripples observed in the MC ringdown can be due to tilt motion of the mirrors.
The time it takes to produce a phase shift corresponding to N multiples of 2*pi is given by:
t = sqrt(2*N*lambda/(L*omega_T^2*(alpha_1+alpha_2)))
L is the length of the MC (something like 13m), and alpha_1, alpha_2 are the DC tilt angles of the two mirrors "shooting into the long arms of the MC" produced by the MC control with respect to the mechanical equilibrium position. omega_T is the tilt eigenfrequency of the three mirrors (assumed to be identical). lambda = 1.064e-6m;
The time it takes from N=1 to N=2 (the first observable ripple) is given by: tau1 = 0.6/omega_T*sqrt(lambda/L/(alpha_1+alpha_2))
The time it takes from N=2 to N=3 is given by: tau2 = 0.77*tau1
etc
First, we also see in the measurement that later ripples are shorter than early ripples consistent with some accelerated effect. The predicted ripple durations tau seem to be a bit too high though. The measurements show something like a first 14us and a late 8us ripple. It depends somewhat on the initial tilt angles that I don't know really.
In any case, the short ripple times could also be explained if the tilt motions start a little earlier than the ringdown, or the tilt motion starts with some small initial velocity. The next step will be to program a little ringdown simulation that includes mirror tilts and see what kind of tilt motion would produce the ripples exactly as we observe them (or maybe tilt motion cannot produce ripples as observed). |