HOM frequency shift for RefCav is plotted below. The second one has clearer dots.
Y axis is the frequency shift in MHz
X axis is the (n+m)th order of the Hermite Gauss mode
The waist of the beam inside the cavity is 261 um* (symmetric cavity, R =0.5m, L = 0.2032 m.)
Thus, the frequency shift between n+m+1 and n+m mode is 219.763 MHz. (see Lasers, p 762 for details)
Blue line represents the 0th order of the carrier's frequency (thus =0) The purple and the brown lines, at y= 35.5 and -35.5 MHz, are the 0th of + and - sidebands respectively.
The color dots represent the frequency shift from Higher order mode which is specified on x-axis, blue for HOM from the carrier's frequency, purple and brown for HOM from +/- sidebands.
Choosing 35.5 sideband seems to be ok, the 27th order should be small and negligible.
*The number 237 um for waist size is the effective beam waist size of the "emerging beam," not the real waist size in the cavity. The beam passes through the mirror which acts as a negative thin lens and changes the