The simulation of opto-mechanical transfer function and filter design

Participaint: Yuhang and Eleonora

It is necessary to fit the opto-mechanical transfer function and filter design, otherwise we cannot use zpk function in matlab. We did this by using proper poles and zeros in proper frequencies. 

The zeros I used (corresponding q factor): 7250,13800,500,14600,25500,42000,31000,18100,21500(25,14,0.01,4,15,40,35,12,5)

The poles I used(corresponding q factor): 7000,12000,5000,8000,14800,16500,18900,26500,30000,34000,35900,46000,44900(12,15,0.03,0.6,6,18,10,2,10,10,2,0.8,30)

The gain is 28 at 100Hz.

I tried to put a low pass filter at 200Hz(q=0) with a gain of 20. And an intergrator at 0Hz(q=0). Finally a notch filter between 6950Hz(q=6) and 7550Hz(q=10).

Then I got unity gain frequency of 376Hz with 34 degrees of phase margin. The plot is in attahced Fig. 2 and blue line is data, red line is OLTF, green line is filter.

Fit of the actuator TF and of the open loop TF

Manuel, Eleonora

We plotted the transfer function of the measured actuator (plant) and fitted it with a Matlab script based on the zpk function.
We used two simple poles at 40kHz, a gain of 0.16 in DC, and a delay of 2.3e-6. see the first plot

We plot the measured open loop TF obtained using a sr560 set with a first order low pass filter at 100Hz, a gain of 200.
We fitted it as the product of the modeled plant TF and a filter TF.
The filter that best fits the data is a first order low pass at 100Hz  with a gain of 240. see the second plot
The UGF is at 3.8kHz with a phase margin of 76deg.

We verify that the loop becomes unstable for a gain of 2000 (as observed experimentally).
Indeed, the UGF becomes 23kHz and the phase margin 7deg. See the third plot.

We will use this model to design a better filter in order to have more gain at low frequencies, compatibly with the possible configurations of the sr560.

open loop transfer function and intensity noise reduction

I set the loop to control the intensity of the 1310nm laser.
first I measured the actuator transfer function with a random noise from the spectrum analizer of amplitude 200mV

Then I set a low pass filter at 100Hz, a DC offset from the waveform generator to keep the correction signal around 0, and a gain of 200.
I closed the loop and measured the open loop transfer function.

I measured the noise in the photodiode with the loop closed and without loop.
then I divided the noise without loop by (1 + the open loop transfer function) and compared with the closed loop pd noise.

If I increase the gain above 1000 the laser stops for exceeding the current limit.

Finesse of green mode cleaner

Participant: Marc and Yuhang

Today I reveived the comment from Marc and I measured the Finesse again. This time I put the ramp signal to make sure I am looking at the correct part of signal. This is of great important to find the correct FSR(Actually here the fsr corresponding to time, so maybe not good to call it fsr)

Then I use this fsr to fit only one peak so that I can see more clearly the fit.

In the end, I got a more pleasuible result. Finesse is 381. But this result is much higher than the calculation result, which is 248.

Realignment after tidy up in July 2018

Participant: Eleonora and Yuhang

Beccause we changed many cables and arranged the control devices space, we think the green should be misaligned. Yesterday, I checked that it is totally misaligned!

I did the procedure of standard alignment of green: check target on PR chamber, check the first iris, check the second iris and match incidence with reflection, finally end mirror. After these procedures, I got the new offset of each mirror's local control offset. Then I can lock green and infrared together. See attached Fig.1

	YAW	PITCH
PR	0.3	-0.07
BS	-0.11	-0.9
IM	0	1.1
EM	2.4	-2

I also found some problems and did some change during this process.

1. I connect the image of second iris to the third part of monitor. I also checked the light you can see in this second iris camera is corridor light. Because if I go to turn off the corridor light, it disappeared. See attached Fig.2

2. If you find problem in attached Fig.3, you need to reopen the program.

3. I tried to remote control of the second iris, but the network cable seems not working. 

Realignment mode cleaner and polarization check

Because we found the unexpected peak while we are scanning mode cleaner, I tried to realign it.

The mothod is to block the beam going to mirror without PZT in Mach-Zehnder. Then use the steering mirror to align and make the peak of mode-cleaner as high as possible. Then remove the block, and adjust the mirror without PZT in Mach-Zehnder.

After alignment, the unexpected peak becoms very small. So I tried to take the data and calculate Finesse. Firstly, I tried to fit with airy function. But I found the FSR here is very strange, see attached Fig.1. It's obvious that the software cannot tell us this is a good fit. So this fit is done by my hand. I don't know why this FSR can be this unstable. But maybe this can be interesting.

But I tried to fit only one peak, then I get the fit result of F=15100. See attached Fig.2. But note here, we use PD with amplification, it is 40dB means 100 times amplification. So the measurement of Finesse is only 152. If we consider R=0.992, the Finesse should be 248. So there is this discrepancy.

Beside, I checked the polarization again. This time I put a half-wave plate infront of mode cleaner, and change s to p polarization. I saw a increase of larger than 10 times of transmission on oscillscope. I talked with Matteo. From Fresnel law, p-pol has more transmissvity for the mirror now we use to dump beam. This is the main reason for this increase.

Comment to Green mode cleaner trasmission issue (Click here to view original report: 850)

I checked the input and output mirror. From the point view of marker on the side of mirror, I am sure the mirror is installed in a correct way.

I checked also the mirror from the same box, this arrow points to the HF side of this mirror.

PM100D and DET10N noise comparison - Actuator+PM100D transfer function

after setting the PM100D badwidth to 150kHz, I repeatd the measurements reported in entry 861
The plot is normalized on the gain and on the DC value.

Then I measured the transfer function of the laser modulation actuator + the integrating sphere photodiode PM100D

Characterization of the PLL phase noise between ML (master) and AUX1 or AUX2 (slave)

Partecipants: Marco, Eleonora, Yuhang, Matteo

 

We mount in a NIM box the PLL board described in the logbook entry 847. The photo of the box are 'pllboxfrontend.png' and 'pllboxtop.png'.

 

Description of the front-end:

- 2 SMA connector for the two input beat note and RF channel from DDS board not amplified

- Lemo connector (output) label MUX is a chnnel digitally configurable from the software use for diagnostic purposes (RF monitor, Beat monitor, Lock detect, etc)

- Lemo connector (output) label Fast is the correction singnal sent to lazer PZT, it can be activated or not using a switch mounted on the front panel

- Lemo connector (output) label Slow is the correction signal sent to laser PLT, it can be activated or not using a switch mounted on the front panel

 

Test of the board using AUX2 as slave laser (fig 'aux2lasrslave.pdf')

We tested the long term stability during the night ant the day later we found the PLL still locked 

We measure the PLL phase noise in three different condition (charge pump current: 4.375mA):

- MLfree running (rampe auto swithced off) rms phase noise: 4.9mrad

- ML free running (rampe auto switched on) rms phase noise: 10.6mrad

- ML non free running (filter cavity locked) rms phase noise: 16.7mrad

 

Test of the board using AUX1 as slave laser (fig 'aux1lasrslave.pdf')

We measure the PLL phase noise in three different condition  (charge pump current: 3.75mA):

- MLfree running (rampe auto swithced off) rms phase noise: 5.5mrad

- ML free running (rampe auto switched on) rms phase noise: 14.9mrad

- ML non free running (filter cavity locked) rms phase noise: 15mrad

 

For both the servo loop we noticed that the output voltage of the rampe auto is high enough to increase the ML frequency noise.

Moreover the noise reduction due to the filter cavity locking between 100 Hz and 12-15 kHz is visible in both the servo loop. 

The rampe auto noise is predominant at frequencies above the unitary gain bandwidth of the filter cavity servo loop

HeNe and 1310nm laser intenisty noise comparison

PD100D noise characterization

I did on the PM100D integrating sphere PD  the same noise checks as I did on the InGaAs PD and reported in http://www2.nao.ac.jp/~gw-elog/osl/?r=846 elog entry
the measurements though are not reliable because after making them I found that the output bandwidth was set on 15Hz. 

The procedure to use PLL

Participant: Eleonora, Marco and Yuhang.

1. Open the loop if you want to change the object you want to lock. Because we have only one board for locking up to now.

2. Reconnect the photodiode, PZT(in the back of red laser head) and pietie(int the back of white laser box and the middle one) from the previous one to the one you will control.

3. Check the photodiode output, and try to adjust steering mirrors to see if you can improve the fiber coupling or not. Sometimes if someone touch the collimator or mirror, the coupling will be changed.

4. Then connect this beatnote between these two lasers to spectrum analyzer. Remember to choose range from 0Hz to 1.3GHz. And change the temperature from the laser box. You will see from the spectrum analyzer the beatnote moves with your changing. Move it close to 20MHz, the frequency we want to use for demodulation. Note here that sometimes if the spectrum analyzer doesn't work, press the preset button. 

5. Then look at it more closely and check the level of the peak you want to lock, it should be larger than -16dB. If not, you can check again the fiber coupling. Usually try to change the polarization.

6. Move the peak as close as 20MHz. Here is a splitter(10:90), 10 percent is used to monitor while 90 percent is used to lock the PLL. Then firstly put on the fast control and then slow.

7. If you want to measure the phase noise, check firstly the level of this signal. Change the demodulation phase to make it close to zero, means fluctuating around several hundred microV to 1mV.

8. Change the demodualtion frequency and use oscilloscope to see this frequency component to get the calibration factor.

9. Use DC couple and put the close to zero signal to the network analyzer. Then you will get noise spectrum.

Main laser PZT characterization

We used the similar manner to entry 830 characterize the main laser PZT.

Note here the resonance begin before 70kHz.

Finalize the optical layout for PLL

Participant: Eleonora, Marco, Matteo and Yuhang

After realize the 7mm collimator is more suitable, we replace the 11mm one. Then we finalize the optical layout of PLL. The main task we did is the new telescope design and fiber alignment.

The new telescope is shown in attached picture. However, the actual case is a little bit different because of the Faraday influence of optical length. But we made sure the beam is very collimated with a size of 2mm in diameter.

For the fiber coupling, we develop a procedure. We assume you have already a coupled fiber.

1. Put the output of this already coupled fiber to collimator. Now, you have both light going in and back through this collimator. Then use the steering mirror to make them overlap. Always make sure the light is a good round shape after you take off the fiber from collimator.

2. Put the multimode fiber to do pre-alignment. If you did very well the first step, you will have a very large coupling directly after you put multimode fiber. Then use steering mirror to align until get 100% coupling. If you cannot, remember to check the shape after collimator is round.

3. Put the single mode fiber. If you did step 2 as we suggest, you will have very good coupling now even for this single mode fiber. Then just use the steering mirror to do standard alignment. You will get a good coupling result.(we got 70 percent)

According to this procedure, we coupled the fiber for the second main laser pick off and AUX 2 laser(p pol). We got 70% coupling for both of them.

The final layout is attached as picture two.

Some power for reference

Participant: Yuhang and Eleonora

Green power measurement

before EOM	after EOM	before AOM	before PR	before MZ
74mW	71mW	13.7mW	8.8mW	33.6mW

Infrared power mesurement

before PR	after pick off	before pick off
9.4mW	10.6mW	17mW

After rearange the control devices, we recover the green and infrared lock.

FC green transmission	FC infrared transmission
1.3V	1.6V

Comment to Data transfer from spectrum analyzer - Noise floor of SA2400, SR560, and PD (Click here to view original report: 846)

Data transfer from spectrum analyzer - Noise floor of SA2400, SR560, and PD

To transfer data from the Yokogawa SA2400, the only way is through the GPIB port. (otherwise, there is an oldfashioned paper plotter)
So, I wrote a labview program to read the spectra and save it on a file, based on a library I found here: http://sine.ni.com/apps/utf8/niid_web_display.download_page?p_id_guid=E3B19B3E936A659CE034080020E74861   
The list of commands for the GPIB is in the  (in Japanese sory...) manual I uploaded to the wiki: http://gwpo.nao.ac.jp:8989/wiki/Documents?action=AttachFile&do=view&target=SA2400+GP-IB+manual.pdf
I did some spectrum acquisitions of the photodiode signal. Average number 64. in several conditions.

Plot 1. spectrum in dbV (not normalized per rtHz)

20180625-unplugged               (noise without anything  connected)
20180625-unplugged400khz    
20180625-50ohm                     (noise with the 50ohm terminator
20180625-50ohm400khz          
20180625-darkT50ohm            (PD dark noise with a T and 50ohm terminator)
20180625-darkdirect                (PD dark noise 
20180625-darkAC                    (PD dark noise after the high pass filter box)
20180625-darkACT50ohm       (PD dark noise after the high pass filter box with a T and 50ohm terminator) 
20180625-darkDC                    (PD dark noise after the high pass filter box)

Plot 2.  spectrum in dbV/rtHz ( normalized per rtHz)
noise floor

Plot 3.  50ohm terminator as input of the SR560. Icreased the gain of the preamplifier to check where is the noise floor of the SR560.

Plot 4. Comparison of the noise floors of SR560 and PD dark noise

Plot 5. Laser on / off

to be compared with the noise on the HeNe PD

Comment to Green mode cleaner trasmission issue (Click here to view original report: 850)

From the power transmitted behind the end mirror (0.5 mw) and behind the output mirror (8.5 mW) it seems that the end mirror transmission is about 17 time smaller than the output mirror. Assuming that the output mirror transmission is 0.8%, one would deduce that the end mirror transmission is of the order of 0.05% in good agreement with the expected value. If so, the large reflection should come from an asymmetry between the input and output mirrors (which seems difficult to imagine).
On the other hand there is a strange "large" peak in the middle of the FSR. Where is that coming from? Is there a polarization problem? In the entry it is written that the polarization is OK.
Question: did somebody already check that the input and output mirrors are mounted with the HR side facing the inside of the cavity?

Beat note signal between AUX2 and the master laser

Partecipants: Marco, Eleonora ,  Yuhang 

 

We match the light of the ML into the fiber.

Input power: 3mW

Matched power: 0.71*2mW

Fiber matching: 47%

 

After that we control the matching of the AUX2 fiber:

Input power: 3.5mW

Matched power: 1.25*2mW

Fiber matching: 71%

 

Voltage level on photodiode:

ML: 7.8V

AUX1:  5.2V

Total: 2.6V

 

We found the beat note between the two lasers and we measure the following levels:

	Beat note	Amplified signal	90% signal	10 % signal
Carrier	-21dBm	-6.33dBm	-7.67 dBm	-17.60 dBm
Sideband 1° order	-33.8dBm	-17.67dBm	-18.33dBm	-29.43 dBm
Sideband 2° order	-54dBm	-38.17dBm	-38.67dBm	-49.77 dBm
Sideband 3° order	not visible	-65.33dBm	-61.50dBm	not visible

The AUX1 laser temperature was set at 30.67 °C, at the spectrum analyzer we see both the beat note and the lateral sidebands due to EOM modulation. 

The minimum level required for the beat note to lock the PLL is -16 dBm, thus the amplitude of the carrier is enough to perform the PLL locking. Concerning the sideband to perform the lock on them their level must be incresed at least of 2-3 dBm

Green mode cleaner trasmission issue

[ Yuhang, Matteo, Eleonora]

After locking the Green mode cleaner we measured a trasmissivity below 50% which is much lower than what we expected.

An extremely rough power budget gave us: 

P_in = 22 mW

P_tra = 8.5 mW

P_ref = 10.5 mW

P_tra from end mirror = 0.5 mW 

Missing = 2.5 mW

We investigated some of the following possibilities:

 

Mirrors transmissitvity

For a triangular cavity, as our modecleaner,  the transmission is given by:

T = (t_in*t_out)/1-r_in *r_out *r_end)^2 

according to the spec for the mirrors used (see pic 1) :

R_in = R_out = 0.992  and R_end > 0.995  (measured from the producer 0.9993)

= > T = 0.92  (taking R_end  0.9993)

Considering an error of +/- 0.003 in all the three nominal transimissivity, the expected cavity trasmissivity is 0.92 +/- 0.33 

 

Matching and alignment

The optical spectrum of the cavity is shown in pic.1. The alignement seems good. The sidebandes at 78 MHz ( used for the lock of the MC) are not visible while we can see the 15.2 MHz modulation that we know to be high. 

[ Note that we are sending at the 78 MHz resonant EOM, a driving  RF signal with amplitude 1 V pp which should correspond to a modulation depth of 0.185 rad. this means that the expected power in the sidebads is 0.0086]

 

input beam polarization

Yuhang used a PBS for 532nm and verified that the light is almost all in s-pol,  as it should be.

 

Conclusions:  The origin of the low MC transmissivity is not clear but the most probable hypotesis, among those considered,  is that the effective transmission of the mirrors are a bit different from the nominal ones.