I created a finesse model a single cavity then I added all i = m + n higher order modes (HOMs). I then multiplied four of these cavities with varying length and crusher ROCs together to create a single plot of the higher mode leakage through the higher cavities. The HOMs  height was chosen to match the cavity scans that torrey did on OFC1 which roughly showed that the i=1 mode was 1/10th the power of the i=0 modes and the i=2 modes were 1/100th of the i=0 modes. With these HOM amplitudes and the four cavities multiplied together we have a good model of the HOM leakage in the output filter cavities shown in the attachment: multi_cavity_modes.pdf. The model goes up to n+m = 10 HOMs. Since HOMs contribute less and less as they go up in n+m it is not likely that higher HOMs would change these results significantly. The code for this model is stored in the gquest modeling git. The plot shows the bandpass for the signal at 17.6 MHz and the suppression at the carrier frequency of 0 Hz is a little less than 10^24 in power suppression. The only major improvement to this method is to normalize the power correctly. Currently when you add a HOM it decreases the power in the i=0 mode. so as I add more modes the bandpass section stops having a gain of 1. I have temporarily solved that by increasing the power input from 1 W to 1.3 W which seems to normalize correctly. Fixing this in the future could help reduce uncertainty in this plot. Another difference between this and the real experiment is that I have assumed that the HOM distribution and relative power exiting the IFO will match the laser that we are shining into the OFCs for testing. This should still give us a better understanding of of the performance of the cavities and will give us a comparison when we are doing our final cavity scans of all four cavities. We can also use this to change how the four filter cavities are spaced and their ROCs.