While we were using high voltage driver, we found the monitor channel give a highly distorted signal. At the begining, we thought it is the common issue of high voltage deriver. However, I just found out on yesterday that this distortion is caused by a switch on the rear panel of high voltage driver. See attached figure 1, the function of switch is to switch the sensor signal on or off. The switch is marked with a red circle in the picture.

The phenomenon is confirmed by me and like this. When you switch it on, you will see the distortion. When you switch it off, you will see almost the same with the ramp input. This is quite easy to confirm. But the question is whether it change the real output or not?

Firstly, I did the simulation of how our high voltage driver can affect the ramp signal.

1. I generate ramp signal(80Hz) in time. I use additive synthesis to approxiamte our ramp signal. It is the summing of the odd harmonics of fundamental while every other odd harmonic multiplied by -1. Then multiply the amplitude of the harmonics by one over the square of their mode number.(more details in en.wikipedia.org/wiki/Triangle_wave#Definitions) See attached figure 4. We can see the ramp signal is quite decent. 

2. Use FFT to convert time-domain ramp into frequency-domain. See attached figure 5. It shows the spectrum of ramp signal. We can see a clear peak at 80Hz. (Actually there are some harmonic peaks of 80Hz, but they have much lower amplitude and at much higher frequency. So I didn't show them.)

3. Apply the low pass filter of our high voltage driver. The corner frequency is shown in the datasheet of high voltage driver. See attached figure 2 and 3. Since our piezo's inductor is close to the data in the sheet, so we can use the value of 600Hz as pole. See attached figure 6. It shows the lowpass filter I applied.

4. Convert frequency signal back to time domain. The result is shown in attached figure 7. You can see the distortion is not sever. And the frequency or amplitude almost remain the same. From the attached figure 8, you can see much better the frequency is exactly the same with before(80Hz). 

So the comclusion of simulation is that high voltage driver should not change the ramp. The change is very trivial.

Then I checked the situation of this ramp output by looking at the scanning of OPO cavity. Figure 9 shows the scanning while the switch is off. We can see we have three TEM00. However, after I switch it on the sensor in port. I got the result of figure 10. No matter how I change the offset of high voltage driver, I can see only two TEM00. So this means the switch really changes the output of high voltage driver.

Unfortunatly, I found the switches are on for SHG's, GRMC's and IRMC's high voltage driver. So in the future, we need to take care not switch on the 'sensor in switch'. And also, for the low frequency ramp, it doesn't change the ramp shape. So the problem of discrepancy of OPO's simulation and measurement should not come from the wrong ramp signal. The ramp signal of monitor channel reflects the truth of high voltage driver output.

Since we have a new result of modulation depth, I did the simulation again. This time I also find a way to get the simulation result of optical length, Finesse, FSR and FWHM.

The problem of error signal difference becomes less sever now.

The length of cavity is composed of crystal part and air part. The air part is the part between crystal and in-coupling mirror. In the first attached figure, we can see the lateral side of OPO housing. The red line stands for the cavity length. The way to estimate it is to seperate it to three parts as it is shown in the first attached figure. 

The blue line is shown in the second attached figure. It is roughly 14mm.

The green line is shown in the third attached figure. Since we can see in the attached  fourth figure, Matteo put the crystal roughly in the center of POM_bridge. So the second part should be half of bridge thickness. It is roughly 25/2 = 12.5mm.

The last purple line is half the length of crystal. We can know from the attached figure 5, crystal length is 9.3mm. So this purple line length is 9.3/2 = 4.65mm.

So the total length is 14+12.5+4.65 = 31.15mm. It concludes 9.3mm of KTP and 21.85mm of air. The real length should be 9.3*n(KTP)+21.85*n(air). The refraction index of KTP for infrared is 1.7379. So the real optical length is 9.3*1.7379+21.85 = 16.16+21.85 =38mm

Since we measured the electrical signal we sent to OPO's EOM(see the last attached picture of elog), we can have a precise estimation for modulation depth. According to the specification(you can find it in our wiki page), the modulation depth has a linear relationship with the peak voltage. It crosses points (0, 0) and (1, 6.5), see attached figure 1 and 2. Since the curve is straight, two points is enough to know the function. Then we use the relationship between Vp and dBm, Vp = 10^((P(dBm)-10)/20). In the end, we get the function of power(dBm) and modulation depth. Since now we are sending signal of 12.6dBm, we get the modulation depth should be 0.15.

However, in the simulation of Finesse, we assume modulation depth of 0.3. So we need to do simulation again to have a more resonable error signal estimation.

Participant: Matteo and Yuhang

Since we can do the calibration from time to frequency, I did some characterization work about OPO.

0. Fit Finesse of OPO

All the other measurement needs the value of the finesee, because there is coupling between some parameters of airy function(FSR and the finesse). So we use the measuremt which has two TEM00. It has a clear FSR, so that it can degenerate and give a better fit of the finesse.  Then we use this fit value as an initial value reference for the finesse of other fits. Besides, here we take only the data around TEM00 to avoid the influence of higher order modes to the fit.

Result is finesse = 56 +/- 0.04. Detail is shown in attached figure 1.

Note: We found the high voltage driver now behaves very well. Since all the data we took for ramp comes from the monitor chanel of high voltage driver, so we think we can trust it. The good thing is that the ramp signal is quite linear and without distortion. So we think it should be fine to just take it as the real drive we send to the piezo of OPO.

1. Find calibration factor

The method is to use airy function to fit TEM00 and sidebands. The purpose is to find the time distance between TEM00 and one of the sidebands. Then we can convert this time distance to voltage distance by using the ramp signal. This voltage distance corresponds to 87.6MHz(the resonant frequency of EOM). This new resonant frequency is because of the repair of EOM. After the repair the resonant frequency becomes from 88.1245MHz to 87.6MHz. The calibration factor of frequency/voltage is universal and can be used to all the measurement of our OPO.

See attached figure 2. The result is cal = 856.08 +/- 0.19 MHz/V.

2. Fit of bandwidth

Since we have the calibration factor. We used the only TEM00 peak did the fit of bandwidth. In the code I attached, you can find every time I calculate the slope of ramp. It is quite cumbersome, but it is not avoidable. It is crucial to have a precise result. The result is shown in attached figure 3. BW = 59.93 +/- 0.21.

3. Fit of FSR and estimate of cavity length

We use again the data with two TEM00 fit the FSR(FSR is 2785.3 +/- 0.7 MHz) and cavity length(L = 53.855 +/- 0.013 mm). The method is similar with the fit of bandwidth. According to the result of FSR, we found the estimate of cavity length is 54mm. This is quite strange since according to the assemble picture Matteo uploaded and his Phd thesis, it should be around 35mm. Our result is 20mm longer than this nominal value. I guess there maybe something wrong. I will try to figure it out.

Finally, I also upload the code I used as a pdf file.

Yesterday we first locked the OPO, and we also got the error signal. Let's first compare the transmission power and error signal in reality and simulation(for p-pol).

The simulation result is attached as figure one. The measurement result is attached as figure two.

Since the transmitted power is only roughly a factor of 2.5 lower than simulation. I guess the small error signal is because of the lower gain of PD than we expected.

After get the error signal, we used SR560 to give a low pass filter and achieved lock(can last for several tens of minutes). However, we observed some oscillation which is probably caused by the noise of SR560. I measured the noise spectrum of the error signal. It is in the attached figure 3 and 4. We can see from that the peaks are the harmonic of electrical noise. 

We also measured the opto-mechanical TF. If you are interested in that, please have a look in our wiki page.

The maximization of phase is also done. The procedure is attached in figure 2, 5, 6 and 7. The shape of error signal is quite similar with the simulation. I saved the new set-up of dds2 and the name is today's date.(name: 20181010-dds2, see attached figure 8)

We also found that the amplification factor of the board made by Pier can be increased. See attached figure 9, the magnitude now is 12dBm. However, the maximum we can give is 26dBm(according to the datasheet from Qubig). Since we don't have a large enough error signal, this is also a method we can consider to increase it.

Last week we met the problem of calibration from time to frequency, however the temperature axis has been calculated according to the manual of Thorlab TED200C(to know the formula) and thermister 103JT-025(to know the B factor). The temperature we should take is in the range 2K around the nominal temperature value. So we get the attached picture, which shows the temperature we should measure.

See attached file for more details.

Actually this work started around two months ago. At the beginging, we tried to fit the original data by using poles, zeros and q. At that time, we tried to use the virgo toolbox based on matlab and got some fine results. We also tried to use LISO to do this fit.

However, for our filter design for GRMC, it is not so necessary. So I use the data we took and change it back to imaginary number and then implent zpk filters to it. Finally, by using a first order low pass filter with a coner frequency of 500Hz. And a intergrator of 30Hz(pole) and 1000Hz(zero). And the gain of 2. I got a positive result wihch is shown as attached file. I also attach the python file as attached.

• The width at half maximum of the surface reference scan is 0.65mm, same as the SPTS company.
• I measured the phase of the pump (temporarily removing the filters from the PD). It is -22deg.
  This means that for the surface reference, the calibrated phase is -81.5-(-22)=-59.5deg. Same as the SPTS company (-60deg).
  The calibrated phase for the bulk reference is -93.5-(-22)=-71.5deg. Somewhat different but similar to the SPTS company (-66deg).
• The surface calibration factor (from entry 973) is R=19 W-1, about 10% higher than  the SPTS company (16.9 W-1).

• So I measured the transmission of the sapphire. with a power meter T_sapp = 0.86
• I already measured the transmission of the bulk reference sample in entry 990. T_bulk = 0.55
• As absorption value of the bulk reference sample, instead of the nominal value from SPTS, I should use the one I measured with the power meter (entry 990) Abs = 105%/cm  
• Using the incident power P_ref=32mW, now the correct calibration factor for bulk is R = AC/DC / ( P_ref*sqrt(T_bulk) * 1.05 ) = 0.78 cm/W

Summary:
- changing the reference absorption value from 116%/cm to 105%/cm reduced the absorption value by 10%
- correcting the power with the transmission coefficient reduced the absorption value of 20% because sqrt(T_bulk/T_sapp)=0.8

So the ratio between my measurement and LMA measurement on the Tama-size sample2 (comparison in entry 984) passed from a factor of about 2 to a factor of about 1.5-1.7

Last week, we put some beam dumpers for auxiliary paths. However there is still some parts are not dumped while the main threat has been dumped.

I tried to disconnect the cable (the signal from the PD) from the spectrum analyzer and the sr560.
The noise is still around 10'000ppm. So the noise doesn't come from some ground loops.

Then I changed the current of the laser diode and rotated the HWP to keep the DC at around 2V, but the noise didn't reduce a lot (still around 7000ppm)

Then I replaced the QWP with a PBS to clean the polarization and the noise reduced by a factor of 10

The alignment changed a bit after replacing the QWP. So the screenshot shows the new calibration scan. The AC signal went from 57mV to 45mV.

Now the noise is around 950ppm. See plot

previous crossing point pinhole position

X 327.432
Y 121.255
Z 34.9000

[Yuhang, Eleonora]

We designed and implemented a new telescope for the EOM.  The goal was to increase the allowed power of the p-pol beam and find a reasonable PDH signal. 

We followed the recomandation of the seller from Qubig which suggests to use a beam of 1 mm diameter inside the EOM (the crystal side is 3mm). 

As input, we have a collimated beam ( 2 mm diameter) and we want to recover a beam with this same size after the EOM, before it recombines with the s-pol beam. In order to do so, we have  simply put two lenses with  f = 200 mm at a distance of 40 cm from each other and place the EOM  at a distance of about 10cm from the first lens, where the beam diamater is between 1 mm and 0.7 mm (see Fig1, 2  and the updated the optical layout in the wiki)

For our laser power, that is 170 mW, the power density (considering diameter of 0.7mm) is about 1W/mm^2  which is less than the treshold of the EOM (10W/mm^2).

We have installed all the optics (except for the EOM which is not yet back) and aligned and matched the beam into the OPO. In parallel we have also recovered the alignment of the s-pol beam.

Pic 3,4,5 show respectively the OPO optical spectum with p-pole beam, s-pole beam and both beams. The heighest HOM are LG modes wich are not easy to get rid of. Anway the final aligment will be done once we have also the EOM.

We repeted the transmissivity measurement.

Some comments:

1) Since we cannot lock the OPO, in order to make the mesurement, we manually adjust the piezo offset to bring the cavity on the top of the TEM00 resonance, this can affect the precison of the measurament

2) The nominal trasmissivity shoud be 1%, while we found a value that is 5 times smaller.  Note that the matching (in particular for the p-pol) is not optimal.

Conclusion: The new design of the EOM telescope seems fine and in this new configuration we should be able to increase the power on the p-pol and get a detectable PDH error signal for the OPO.

[Yuhang, Eleonora]

While waiting for the quibig EOM to be repaired, we have tried to estimate the ampituede of the PDH signal expected both in reflection and trasmission of the OPO.

We used the following paramenters:

R1:  99.975%  (crystal)

R2:  92%         (incoupling mirror)

INPUT POWER: 6 mW

MOD. DEPTH: 0.3 

PD GAIN tot: 16e2 [V/W]  (photosensitivity at 1064:  0.1 [A/W], amplification:16e3 [V/A])

BS before OPO:  R = 4% T= 87% (p-pol)

We did a simulation with Finesse (see attached plot) and confirm it with analytical computation. (We will upload the code on the wiki ) 

Conclusions:

1) The PDH signal is larger in transmission (due to the fact that in this configuration the cavity is undercoupled) 

2) The PDH signal is anyway very small (less than 10 mV pp) with the current values. 

It is for sure convenient to lock the cavity in transmission (as done in Virgo1500 and GEO) but we should also consider how to increse the signal. Some possibilities:

1) Increase the input power (change EOM telescope to increase allowed power? How much power is used in GEO and Virgo?)

2) Increase the PD gain (the current one has low photosensitivity for IR) 

3) Increase the modulation depth (is it feasable?) 

Note that the simulation has been done considering nominal reflectivity values for OPO but we observed that the transmission is lower than expected (0.18% instead of 1%), this may result in a discrepancy between the  simulation and the real signal.

[Yuhang, Eleonora]

We have locked the infrared mode cleaner. 

Some details:

1) P_in = 10mW  P_tra = 7.5mW  => Transmissvity: 75%   less then expected (90%) but enough for the homodine detection.

2) we locked it in reflection using a TAMA PD. See attached pic 1 and 2.

3) Since we use 15 MHz sidebands (same EOM as SHG) we could use TAMA demodulation board

4) We use a SR560 as temporary servo (1st order low pass, cut of frequency at 3 Hz, gain 10 after lock is engaged and 1 to acquire it) 

5) An attenuation of 40 dB had to be put on the demodulated signal before the SR560,  in order to avoid overload and be able to acquire the lock.

6) We measured the optical-mechanical TF (cavity + piezo). See attached plot (Fig 3). It Note that the high pass filter to compensate the low pass of the piezo driver has not be used. 

We have uploaded the data and the plot on the TFs wiki section.

I did some simulation of the green reflection path from the filter cavity input mirror. The detail is in the attached file.

1. I clean up the IRMC, fortunatly, the dirty is outside so we can clean it.

2. For the RF signal, I used the TAMA PD which was used for FC reflection.

3. Since we found that we cannot see the modulation produced by OPO EOM, we decided to test this EOM. This EOM is from TAMA(length = 5.5cm, Diameter = 3mm, power density = 4W/mm2, resonant frequency = 40MHz). Since I have already had a good alignment for IRMC, I didn't want to destory it. I just want to add lenses and then put EOM. Besides, I have a lot of space to put lenses and make the beam smaller than 500um of radius with a range larger than 5.5cm. So I don't want to care a lot about mode matching. Note here, the mode matching affected by additional lenses and EOM. Besides, we can compare the 15MHz sideband's power to know how different interference affect the sideband power. Because we know the power of 15MHz sideband before puting the additional lenses as a reference. The set-up of this test is attached as Fig.1. (Note here the beam power is 10mW, even for the concentrated beam, power density is 1.8W/mm2)

For the test of EOM of collimated beam inside, the 15 MHz sideband power is around -26dBm. The 40MHz is around -49dBm. (see attached Fig.2)

For the test of EOM of concentrated beam inside, the 15MHz sideband power is around -32dBm. The 40MHz is around -56dBm. (see attached Fig.3)

Here the 15 and 40MHz sideband disappeared after I blocked the beam.

From these two results, we found although the 40MHz sideband power decreases, it seems come from the worse interference(worse interference verfied by 15MHz reference). (See attached Fig.4 for bad interference)

So the conclusion is: The TAMA EOM works well and the collimation of beam doesn't matter.

-----------------------------------------------------------

15MHz sideband comes from the TAMA EOM, which is just after the main laser and before the first BS on the bench. 

A very unfortunate possible explanation of the calibration problem could be a double mistake on the true absorption value bulk reference sample from the company. The Schott glass #12.
So I measured it again with a laser and a power meter.
Incident power         =   76.7 mW
Transmitted power  =    42.5 mW    55%
Reflected power      =   5.5 mW       7.2%

Therefore the absorbed portion is  37.8%
The absorption rate 37.8% / 0.36cm = 105%/cm

This confirms the measurement done 3 years ago by Tatsumi-san elog entry 88

According to the simulation I did, I installed the lens and align the infrared mode cleaner today. After the alignment, I did the scanning of mode cleaner and monitor the mode cleaner transmission by PD. Since I have this scanning on the oscillscope, I used the data to do the fit. The result is Finesse =  192(according to entry 566, expect value should be 300-500). I will do some power budget statics after the lock of it.

Today after I installed the first lens, I check the beam parameter. It is quite far from the simulation. Then I found the reason maybe I didn't use a correct distance before. (Also here I found 200mm lens disappears)

Then I measured the beam again and used the lens we have to design the telescope. However I cannot get any result.

So I decide to remove the first along the west edge. Then I peformed the measurement. Before do that I aligned the beams to make them flat and go through the center of the lens and mirror as well as possible. Then I measured the beam agian. The result is w0 = 850um, z0 = 3.05m(relative to the 0th hole of west edge of the bench).

Then I use the result and mode matching tool in Jammt(by using the lens we have, I just update the lens situation today). The target beam parameter is calculated last time. It is w0 = 390um, z0 = 0.8875(relative to the 0th hole of the west edge of the bench). 

The simulation result is f = 250mm @ z = 0.484m, f = 75mm @ z = 0.795m. I also check this result with the optical layout we have. It doesn't overlap with the mirror we have in the optical layout.