During the last few days, we took some data which contains more than one TEM00 and also 87.6MHz sideband. We also extrapulate some more information from the data we have already have. From the analysis we did for them, I found

1. Extrapulate more information.

For the fit of only one peak, we found the fit can give more than one result. This is reasonable, since there is couple between finesse and fsr. For example, we can have two totally different result for the same measurement we did for TEM00(as in attached figure 1, you need to zoom in to see the detail). In this picture, the finesse 75, fsr 4.54GHz can give a perfect fit while the finesse 57, fsr 3.44GHz can give as well. The difference of these two fit is only that I give two different initial range of Finesse. For the first one, I give the Finesse range around 50. However, for the second one, I give the Finesse range around 70. However, the good news is that we can have FSR we expect if we fix the finesse around 70.

For the measurement of TEM00 and sideband. I also found the fit can give more than one set of result. If I give the original Finesse around 70, means around our expected value. We can get a reasonable result of cavity length. This agrees with the fit of bandwidth. See attached figure 2. The finesse now is 72 while cavity length is 39mm. Besides, this fit result give the similar calibration factor with the former fit.

However, all the fit with a finesse value around 70 give FSR around 4GHz, while the direct measurement of FSR gives 2.8GHz. The reason can be PZT cannot response linearly with our driving HV signal.

2. Measurement with TEM00(two) and sideband together

The whole measurement and fit is attached in figure 3. You can see even visually that the distance between twoTEM00 and sidebands are totally different. That is the reason why you can see the fit cannot give a result. But anyway, I tried to fit these two peaks seperately, the result is in the attached figure 4 and 5.  This time, the calibration factor becomes ridiculously different while the fit result of FSR and cavity length becomes also quite different. You can see from the seperate fit, the time difference in the first peak is 0.000501 while 0.000340 in the second peak.

3. Measurement with TEM00(three) and sideband together

The whole measurement is shown in attached figure 6. In this figure, you can see the difference of 0.2GHz in FSR causes the displacement of the peak away from the standard position. Also this causes the fit failed. I also choosed these peaks and fit them seperately. Firstly, the calibration factor is fitted around 1200, 1300, 1100 (MHz/V) seperately.  From this point of view, we can deduce the PZT scanning velocity firstly increase and then decrease. And the fit of the finesse and FSR of the first and third peak give a similar result(first: FSR = 4.9GHz, Finesse = 75  third: FSR = 3.9GHz, Finesse = 61 ). However, the fit of the second has a very large error.

The laser current is set at 200mA.
I sent the laser output on a PBS, to check how the jumps show up in the two polarizations. 
I collected the reflection with the PM100D-S145C. This is most of the power: 58mW.
The transmission (few mW) goes on a 50mm lens and a DET10N with load resistance of 500Ohm.

I watched together the analog output of the PM100D and the DET10N signal at the oscilloscope in AC coupling.
DC of PM100D is 335mV; DC of DET10N is 900mV.
I tried a similar measurement some time ago, but ince the PM100D signal is covered by high frequency noise, I couldn't see anything.
Now I filtered the signal with a SR560 set at AC coupling and low pass first order at 3kHz, gain 5.

The result is in the attached video.
Channel1 yellow is the PM100D filtered analog output. Channel2 blue is the output of the DET10N
The signal are completely anticorrelated. Apart from high frequencies of the PM100D that are filtered out by the SR560.

This proves that the jumps are due to polarization instability.

I also attach a video of the DC of the two detectors. Channel1 is the PM100D not filtered, channel2 (blue) is the DET100D. 

I took a video of the DC signal on the oscilloscope in 2 conditions

video7.avi
HWP at minimum of transmission
range 370uW
display 35uW

video8.avi
HWP at maximum of transmission
range 370mW
display 54mW

[Yuhang, Eleonora]

The green production depends on incident power and on the crystal temperature. We need to find the best temperature to have the best phase matching and maximize the green production. The measurement was performed from 5.794 to 7.787kOm, which corresponds to 312.976K to 304.767K.

The method we used is to change the p-pol beam to s-pol. In this case, we can lock OPO with this beam and at the same time have green production, since only s-pol produces green beam. In transmission of OPO, we put a dichroic mirror which reflects infrared light and transmits green. The reflected beam is focuse with a lens on the  Qubig PD used for the locking,  while the transmitted beam is focused with a lens on a  InGas PD.

The attached picture shows the green production as a function of the temperature. We see two peaks: the largest is at 306.8437 K, the second largest is at 309.3391 K.

 The IR input power was 141 mW.   At the optimal temperature (309.3391 K), we measure a the green power of 0.277 uW  while the IR trasmitted power is 0.189 mW . (Tramsmissivity:  0.13%.  Lower than that measured few days ago #elog 999)

I set the laser current at 200mA.
I used the PM100D power meter with the S145C power meter head to check the laser power fluctuations in several conditions.
I connected the analog output of the PM100D to the oscilloscope, and took some videos
I set the bandwidth of the PM to HI. I swithed OFF the auto range and set the range to 370mW.

PM right after the fiber output
display power: 61.3mW
analog out DC: 365mW
AC: video1 oscilloscope

PM after the first PBS
display power: 58.3mW
DC 350mW
AC: video2 

Then I rotated the half-wave plate to change the  PBS-HWP-PBS system transmitted power 

after PBS-HWP-PBS max transmission
display power: 54.3mW
DC: 327mV
AC: video3 
 

after PBS-HWP-PBS min transmission
display power: 0.0mW
DC: 10mV
AC: video4 

after PBS-HWP-PBS half transmission
display power: 25mW
DC: 150mV
AC:video5 

Changed the PM range to 370uW
after PBS-HWP-PBS min transmission
display power: 27uW
DC: 160mV
AC: video6 

Conclusion: looks like the fluctuations increase when the polarization rotates toward the minimum transmission.
I can't recognize the same jumps I saw in the DET10N

I checked the linearity of the system by changing the incident power of the HeNe laser.

The PD DET10A gives a DC signal proportional to the laser power. And the AC signal obtained after the lock-in demodulation is proportional to the absorption signal and to the DC. So if there is some non-linearity (for example saturation effects) it should cause the AC/DC signal to be not constant.

I put an optical density wheel to reduce HeNe power. I rotated it a bit to change the DC level, acquired some points of AC and DC in that condition, and rotated again the wheel a bit to a different DC value and so on.

The plot shows good linearity.

Temperature change causes the change of cavity length. However, PPKTP has a different refractive index for p and s polarization. So the FSR change for s and p polarization are different. If we want to make both s and p polarization resonant inside the crystal, we need to choose a good temperature or choose a good frequency difference between s and p polarization. As pointed out as the entry about the temperature we should measure, we did the measurement. Besides, we measured the calibration factor before so we can know the s-p frequency difference change according to temperature change.

The measurement was done like this, we firstly check the rotation of HWP so that the transmission of HWP keeps s-pol. At this time(almost all the light is reflected by PBS cube), the angle is 331 degrees. Then put it just in front of OPO housing, rotate HWP to have some p-pol inside OPO. In the end, we make s-pol is higher than p-pol. So we can differentiate them by hight. Then we changed temperature and made measurement.

The measurement result is listed in the last attached figure as a sheet.(detail is in the attached figure 1-17)

Most of the case, the find of frequency different is based on finding the highest and second highest peak. And then use the calibration factor and the slope of ramp signal. However, the find of frequency difference in temperature of 307.4K is performed by fitting the scanning by the addation of two airy functions.

By using these data I plot the birefringence effect in figure 18, the birefringence constant is 397.76 +/- 0.99 MHz/K.

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.