Stefan, TVo, Danny

A while back Shiela and Stefan saw a not so 00 mode at the AS camera (alog 44106) that seemed to be caused by the increased common CO2 lensing. We suspected it may be due to the higher order modes sweeping through PRC resonance with the increased common lens. To identify what modes exhibit this behavior, we did the following:

• Constructed a round trip ray transfer matrix of the Power Recycling cavity using parameters from a .mat file noted in alog 30126 which relies directly on DCC document T1200470
• Replicated the round trip gouy phase of 50.0916 degrees 
• Inserted a variable lens into the round trip matrix which relies on TVo's calibration in 43632 and I identify a round trip gouy phase for the PRC when the ITMs are cold and when the ITMs are hot.
• Identify which Higher order mode sweeps through the PRC resonance (or away from anti-resonance) when increasing the common lensing which can give us an idea about which mode we were seeing at the AS port.
• When ramping up to 1 watt of CO2 power, the model (please see attached .zip file) suggests that a higher order mode of (m+n) = 5 and (m+n) = 4  increase in gain by about 25 and 4 respectively. When ramping up .45 watts,  (m+n) = 6 increases in gain by a factor of 16. (please see figures below)