Quote: 
Thus, the modes should be well separated
=> spacing is 4.3 MHz while FWHM is 0.311 MHz (cavity fsr = 34.5 MHz)

Something looks fishy. I calculate a transverse mode spacing of 2.21 MHzis there a factor of two missing somewhere in your analytical calculation?
delta_f = (1/2/pi) * w01  w00 = (1/2/pi) * acos(±sqrt(0.96)) /pi *2 * pi * c /2 /L = 2.21 MHz
I guess that's still OK, but if you are using 11MHz sidebands, there is a n+m=5 mode within one linewidth of resonance. Can you use 55?

May I suggest my arbcav() tool for things like this? I think it's pretty handy for just this sort of calculations. I'm actually hoping to revamp the I/O to make it much cleaner and more intuitive.
>> T = [0.055 20e6];
>> L = [4.34 4.34];
>> RoC = [115.5 1e10];
>> theta = [0 0];
>> fmod = 11e6;
>> lambda = 1064e9;
>> num_pts = 1000;
>> loss = 50e6;
>> [fin,coefs,df] = arbcav(T,L,RoC,theta,fmod,loss,lambda,num_pts);
>> fmod = 55e6;
>> [fin,coefs,df] = arbcav(T,L,RoC,theta,fmod,loss,lambda,num_pts);
