For the 40m Upgrade, we plan to eliminate the Mach-Zehnder and replace it with a single EOM driven by all three modulation frequencies that we'll need: f1=11MHz, f2=5*f1=55MHz, fmc=29.5MHz.
A frequency generator will produce the three frequencies and with some other electronics we'll properly combine and feed them to the EOM.
The frequency generator will have two crystals to produce the f1 and fmc signals. The f2 modulation will be obtained by a frequency multiplier (5x) from the f1.
The frequency multiplier, for the way it works, will inevitably introduce some unwanted harmonics into the signals. These will show up as extra modulation frequencies in the EOM.
In order to quantify the effects of such unwanted harmonics on the interferometer and thus to let us set some limits on their amplitude, I ran some simulations with Optickle. The way the EOM is represented is by three RF modulators in series. In order to introduce the unwanted harmonics, I just added an RF modulator in series for each of them. I also made sure not to leave any space in between the modulators, so not to introduce phase shifts.
To check the effect at DC I looked at the sensing matrix and at the error signals. I considered the 3f error signals that we plan to use for the short DOFs and looked at how they depend on the CARM offset. I repeated the simulations for several possible amplitude of the unwanted harmonics. Some results are shown in the plots attached to this entry. 'ga' is the amplitude ratio of the unwanted harmonics relative to the amplitude of the 11 & 55 MHz modulations.
Comparing to the case where there are no unwanted harmonics (ga = 0), one can see that not considerable effect on the error signals for amplitudes 40dB smaller than that of the main sidebands. Above that value, the REFL31I signals, that we're going to use to control PRCL, will start to be distorted: gain and linearity range change.
So 40 dB of attenuation in the unwanted harmonics is probably the minimum requirement on the frequency multiplier, although 60dB would provide a safer margin.
I'm still thinking how to evaluate any AC effect on the IFO.
** TODO: Plot DC sweeps with a wider range (+/- 20 pm). Also plot swept sines to look for changes in TFs out to ~10 kHz.