In June, we encountered some problems regarding the transmission and error signals (see images here), looking as if the laser was switched off before the cavity was filled.

Aurélien, Ronic and I discussed this on 08/27, resulting in a list of tests to perform. We :

- checked the mirrors' thickness (maybe there was some mechanical stress if they were too thick). The mirrors' thickness is 6.35mm (1/4 inch) and is consistent with the mounts size ;

- checked the mirrors' mounts' screws' tightening (maybe the mirrors were either moving if the screws were not tight enough or some mechanical stress if they were too tight). We tightened the mirrors' mounts' upper screws.

Next thing we did with Ronic was check if the error signal depended on the modulation/demodulation relative phase, which was not the case, but it should have.

Ronic added a quarter waveplate before the half waveplate in the injection system.

Today, on 08/29, the succession of the higher-order transverse modes when scanning the seeder laser's piezoelectric actuator's voltage to scan the seeder laser's optical frequency seemed a bit strange, so we checked the resonance frequencies of several occurrences of the same transverse mode :

- (0, 0) : @ -0.4V and 6.0V ;

- (1, 0) and (0, 1) : @0.5V and 6.9V.

In both cases, several occurrences were separated by about 6.4V, which corresponds to the voltage difference to scan a full FSR. The spacing between (0, 0) and (1, 0)/(0, 1) is then about 0.14*FSR.

I checked this by writing a small piece of Python code to calculate the cavity's fundamental transverse mode and its Rayleigh length, which is displayed in Figure 1, and then by calculating the resonance frequencies wrt the (0, 0) resonance frequency for the (1, 0), (0, 1) and (1, 1) transverse modes, which is displayed in Figure 2, with the following formula: $\nu_{p, n, m}=(p+\frac{(n+\frac{1}{2})\arctan(\frac{2L_{\text{cav}}}{z_{\text{R}}})+(m+\frac{1}{2})\arctan(\frac{2L_{\text{cav}}}{z_{\text{R}}})}{2\pi})\times\text{FSR}$ for a $p$ longitudinal and ($n$, $m$) transverse mode. Here, $p=1$. The spacing betwen (0, 0) and (1, 0)/(0, 1) is about 0.11*FSR, making the previous observation consistent with the calculation. Everything seems normal.

Ronic also increased the EOM modulation voltage, increasing the modulation depth for the generation of the error signal (from 100mV RMS to 300mV RMS), making the error signal depend on the modulation/demodulation relative phase, as it should. He managed to lock the laser onto the cavity for about 1s at a time.

Next steps are to optimize the PID parameters and to add a low-pass filter/AOM to cut the higher frequencies off and improve the feedback loop.