Data and Calculation for the Xarm Current Mode Matching
Two days ago, Nick, Jenne, and I took a measurement for the Green Transmission for the Xarm. I took the data and I analyzed it. The first figure attached below is the raw data plotted. I used the function findpeaks in Matlab, and I found all the peaks. Then, by taking close look at the plot, I chose two peaks as shown in the second figure attached below. I took the ratio of the TEM00 and the High order mode, and I average them. This gave me a Mode Matching of 0.9215, which this value is pretty close to the value that I predicted by using a la Mode in http://nodus.ligo.caltech.edu:8080/40m/10191, which is 0.9343. Nick and I measured the reflected power when the cavity is unlocked and when the cavity is locked, so we measured the P_{reflUnLocked}=52+1µW and P_{reflOnLocked}=16+2µW and the backgroundNoise=0.761µW. Using this information we calculated P_{refl}/P_{in}=0.297. Now, since P_{refl}/P_{in}=E_{ref}/E_{in}^{2}, we looked at the electric fields component by using the reflectivity of the mirror we calculated 0.67. The number doesn't agree, but this is because we didn't take into account the losses when making this calculation. I'm working in the calculation that will include the losses.
Today, Nick and I ordered the lenses and the mirrors. I'm working in putting together a representation of how much improvement the new design will give us in comparison to the current setup.
