Chienming suggested to check the bandwidth of both SHG and GRMC. To make sure the BW of SHG should be smaller than the BW of GRMC.

From Eleonora's thesis, I found the FSR of SHG is 4GHz(infrared) and finesse is 75. So

BW(green of SHG) = 4000*2/75 = 106MHz

The scale information of GRMC can be found from entry before. So

FSR = c/L = 533MHz

finesse = pi*sqrt(r1*r2)/(1-r1r2) = 391

BW(GRMC) = 533/391 = 1.36 MHz

I did the calculation of Airy function(of SHG) intergration around maximum over 1.36MHz and 106MHz. The ratio is 1.5%.

Note: the bandwidth of mephisto laser is 1kHz.