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Entry  Fri Nov 1 17:01:46 2013, Gabriele, Summary, LSC, Simulation of REFL_3f signal when the arms come in refl_3f_I_vs_cavity_tuning_noresf2.pngrefl_3f_I_vs_cavity_tuning.png
    Reply  Fri Nov 1 17:44:06 2013, Koji, Summary, LSC, Simulation of REFL_3f signal when the arms come in 
       Reply  Mon Nov 4 14:11:23 2013, Gabriele, Summary, LSC, Simulation of REFL_3f signal when the arms come in 
Message ID: 9326     Entry time: Fri Nov 1 17:01:46 2013     Reply to this: 9327
Author: Gabriele 
Type: Summary 
Category: LSC 
Subject: Simulation of REFL_3f signal when the arms come in 

 I simulated how the 3f signal is affected by the resonance condition of the arms.

To keep it simple, I only simulated a double cavity. The attached plot shows the result. In x there is the arm cavity detuning from resonance (in log scale to show what happens close to the 0 value). In the y axis there is the PRC detuning. So every vertical slice of the upper plot gives a PDH signal for a given arm detuning. The bottom plot shows the power build up inside the arm, which is dominated by the carrier.

refl_3f_I_vs_cavity_tuning_noresf2.png

The 3f signal is not perturbed in any significant way by the arm resonance condition. This is good and what we expected.

However, in this simulation I had to ensure that the 1f sidebands are not perfectly anti-resonant inside the arms. They are indeed quite far away from resonance. If the modulation frequency is chosen in order to make the 1f sidebands exactly ant-resonant, the 2f will be resonant. This screws up the signal: REFL_3f is made of two contributions of equal amplitude, one on the PRC sidebands resonance and the other on the PRC carrier resonance. When the arm tuning goes to zero, these two cancels out and there is no more PDH...

refl_3f_I_vs_cavity_tuning.png

However, this is a limit case, since the frequency show match perfectly. If the modulation frequency is few arm line widths away from perfect anti-resonance, we have no problem.

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