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Entry  Tue Aug 28 18:28:21 2012, janosch, Metaphysics, Ringdown, ripples  
    Reply  Tue Aug 28 19:06:32 2012, Koji, Metaphysics, Ringdown, ripples  
       Reply  Tue Aug 28 19:21:37 2012, janosch, Metaphysics, Ringdown, ripples  
          Reply  Tue Aug 28 20:23:54 2012, Koji, Metaphysics, Ringdown, ripples  
             Reply  Wed Aug 29 09:35:03 2012, janosch, Metaphysics, Ringdown, ripples 2 
                Reply  Fri Aug 31 17:44:21 2012, Manasa, Update, Ringdown, Data cum_plot.png
Message ID: 7302     Entry time: Tue Aug 28 19:06:32 2012     In reply to: 7301     Reply to this: 7303
Author: Koji 
Type: Metaphysics 
Category: Ringdown 
Subject: ripples  

Isn't it just a ringing of the intracavity power as you shifted the laser frequency abruptly?


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


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).


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