KAGRA Logbook

[kTanaka, Ushiba]

Abstract:

We roughly calculated theoretical transmitted unbalance due to ITM reeflectivity difference.
Our calculation result is about 7.7%, which is consistent with Finesse simulation done by Hirose-san and inconsistent with what we observed.
So, arm alignment by WFS is not good or some other reasons should exist.

Detail:

After WFS loop was closed, we observed unbalance of transmitted light power (klog24598), so we roughly calculated the theoretical values to check how much difference can be acceptable in KAGRA.
Here, we considered power recycling Michelson interferometer, whose end mirrors consis of compound mirror of XARM and YARM and define the electromagnetic fields at each places when beeing on resonance like fig1.
Then, we can obtained transmitted power difference as following equation:
$\frac{P_\mathrm{X}}{P_\mathrm{Y}}=\frac{T_\mathrm{XARM}T_\mathrm{BS}}{T_\mathrm{YARM}R_\mathrm{BS}}$ ,
where $T_\mathrm{A}$ and $R_\mathrm{A}$ represent power transmittance and refrectivity of mirror A, respectively.

Power transmittance of Compound mirror of ITM and ETM can be described as
$T=\frac{T_\mathrm{ITM}T_\mathrm{ETM}}{(1-\sqrt{R_\mathrm{ITM}R_\mathrm{ETM}})^2}$ .
Here, we used the same parameter as in the simulation done by Hirose-san (klog24612) for ITMs and ETMs.
Also, we used following parameters for BS which is summarized in the characterization documents (JGW-T1503347-v2).
$T_\mathrm{BS} = 0.4996\ \mathrm{and}\ R_\mathrm{BS} = 0.5004$ .

Then, we can obtained the power difference as
$\frac{P_\mathrm{X}}{P_\mathrm{Y}}=1.077$ ,
which is consistent with Hirose-san's simulation but inconsistent with what we observed.
So, current large power inbalance is due to misalignment, clipping, and so on...