Built a second SHG with the PPKTP crystal from MIT, did a measurement on the conversion efficiency and fit for the single pass nonlinear conversion efficiency Enl = 0.0055W-1. The single pass measurement of the PPKTP crystal give a nonlinearity deff = 5.41 pm/V. Generally deff of PPKTP is quoted around 9.3pm/V (Table 5.1 of Georgia's thesis)
Measurement of the phase matching curve with input power of 60 mW shows a dip around 35 celcius. The temperature controller reads in kOhm and is converted into celcius via the Steinhart-Hart equation:
A1 = 0.003354016
B1 = 0.0002569850
C1 = 2.620131e-6
D1 = 6.383091e-8
R25 = 10000
R = R_meas / R25
T = ( 1 / (A1 + (B1 * np.log(R)) + (C1 * np.log(R)**2) + (D1 * np.log(R)**3) ) ) - 273.15
Phase matching curve is plotted by using Equation 3.14, 3.20 and Table 3.2 from Sheila's thesis. I have fitted the sinc curve with T0 = 34.9 and i_max = 11.79 , 18.00 and 32.00.
Mount Saint Helens for our currently used SHG: 76239
I found a single/double pass SHG study that was done for the Virgo squeezer by Leonardi et al. here https://iopscience.iop.org/article/10.1088/1555-6611/aad84d
Daniel pointed out that Eq.2 from this paper shows an "additional phase from the red/green dispersion in the rear mirror turn around path" in the double pass scheme. I've attached a couple plots as a function of arbituary x (this variable is related to delta T) at various phase mismatch delta phi. I think the phase mismatch between the red and the green in the double pass alone might explain most of the mountains we are seeing here (?). this might not be the answer to all the problems but it's a good place to start (Figure 7 also looks very interesting).
Maybe the mountains can be patched up if we have a capability of translating one of the mirrors.