Simulation of the filter cavity with the FFT code OSCAR

In order to reproduce the "Pacman" shape seen in the reflected beam (see #entry 687), I have made a simulation of the cavity using the FFT code OSCAR.

https://fr.mathworks.com/matlabcentral/fileexchange/20607-oscar?requestedDomain=true

The shape is more or less reproduced with a mismatching of 4% and a misalignemnt of 5microrad of the end mirror.

I attach the plot of the fields and the script used (it needs the code OSCAR to be used), which can be useful also for other applications. 

 

Green and Infrared error signal

Today I finished the measurement of green and infrared error signal. The delay is because of the inappropriate use of spectrum analyzer. So notice to use the unit of V/sqrtHz next time. Now we have solved this problem. I attached the result here.

I also attach the txt file here. It has not been calibrated yet. The calibration factor I used here is 2.6e-3 V/Hz(for green), 170Hz/V(for infrared).

Spikes affecting BS error signals

Yesterday at some point the lock was disturbed by some spikes affecting the BS local control signals. The problem could be temporarily solved by switching off and on the laser.

Glitches affecting end mirror signals

In the past weeks we observed in two ocassions glitches affecting the error signals of the end mirror local controls.

When the control loops are open, the glitches look like "jumps", affecting simultaneusly both pitch and yaw.

They are quite frequent and in most of the cases they cause the unlock of the cavity. In both cases the problem was solved by switching off and on the ADC in the end room. 

IR alignment improvement

Participants: Yuhang, Yuefan, Tomura, Raffaele, Eleonora

In the past days we have worked in order to improve the IR alignment.

As a first thing we placed a camera on the optical bench to look at the IR reflected beam and we tried to maximized the trasmitted power while monitoring the shape of the reflected beam. According to our understanding, in reflection we should see the superposition of the resonant TEM 00 (dephased of 180 deg after it is reflected by the cavity) and the HOM due to misalignement/mismatching which are promplty reflected. 

The procedure to align the cavity both for green and IR is the following:

1) Adjust BS position to center the beam on the end mirror (reference on the end camera screen)

2) Align the cavity for the green beam by moving input and end mirror to maximize the transmitted power

3) Move the last two steering mirror for the IR on the bench to maximize IR trasmitted power 

4) While aligning the IR we take care that it is always centered on the resonance by looking at the error signal and adjustig the AOM frequency to null its offset.

During in this activity  we realized that the alignement improvement was limited by the position of the last IR steering mirror on the bench. So we have shifted it after carefully taking some references in order not to loose the alignment. After this change we were able to improve the IR transimitted power from about 2.5 up to more than 3.5 V 

Currently in the best alignement condition we have about 1.8 V of transmitted power for the green and 3.8 for the IR.

The attached video shows the reflected and the trasmitted IR beam when we change the alignment condition in pitch and yaw by moving the steering mirror on the bench. In the case of strong misalignement the presence of first order modes becomes evident. Anyway also in the best aligment condition (about 95 %) there is still a small black dot in reflection. 

The oscilloscope in the video shows the transmitted power (yellow line) and the IR error signal (blue line).

After this change in the alignement we have verified that the IR beam in refection was not touching a side of the viewport. (See entry #659 related to this issue ) 

Comment to IR error signal (Click here to view original report: 683)

In order to calibrate the IR error signal we have scanned the resonance by adding a modulation to the AOM around the resonance driving frequency. 

We choose a triangular wave, with period 50 mHz and amplitude of 2 kHz (which corresponds to 1 kHz for the IR). This means that the resonance is crossed with a constant speed of of 200 Hz/s. 

In the first attached picture, the IR transmission and the error signal are shown during a crossing of the resonance. The x axis has been calibrated in Hz using the computation reported before.

The FWHM of the trasmission is about 116 +/- 4 Hz, corresponding to a finesse of 4310 +/- 150, which is comparable with the design and the previous measurements.

The correspondig PDH has been used to calibrate the IR error signal, finding a value of about 170 +/- 20 Hz/V

The second plot shows the calibrated IR error signal, when the cavity is on resonance. The RMS is about 4.4 +/- 0.5 Hz.

In the third plot, I have merged and calibrated the spectra of the error signal recorded with the spectrum analyzer in two different frequency regions (from 1Hz to 100 Hz and from 100 to 51kHz) and I have computed and plotted the rms. As expected it is in agreement with that found from the time series.

According to the plot, the high frequency (above 100 Hz) seems to contribute with 3.5 Hz to the total rms. The remaing (about 1 Hz)  is accumulated below. The contribution of the suspension resonances in the region from 1 to 10 Hz is visible and seems to be about 0.5 Hz.

The origin of the peak at 12 kHz and the quite complex shape of the signal are not very clear to me. 

Next step will be to comprare this spectrum with that of the green error signal in order to investigate the role played by the IR pole.

IR error signal

Participant: Yuefan, Tomura, Yuhang, Eleonora

After changing the photodiode and the mixer box, we can get a proper error signal now. From this error signal, we can get many useful information.Including:

1. We can use this error signal to tell if our alignment or frequency setting is making the TEM00 on resonance. That means if TEM00 is on resonance, the IR error signal is properly around zero. This is a very good standard to adjust our IR beam.

2. We can also use it to evaluate the locking accuracy.

3. By measuring the noise spectrum of this error signal, we can know it is correcting which frequency mostly. I attached this measurement as picture one and two. We can see that 3Hz, 500Hz and 20000Hz are the main three peak frequency.

The data corresponding to this picture you can find here
https://drive.google.com/drive/folders/1J2PmI-GSoQ-BA4gE1VS5wI8wLsPURzoF?usp=sharing

Sample2 flipped

There was an alignment issue to be checked:
The pump and the probe laser inside a thick material are subject to the Snell's law.
Since the probe has a non-zero incidence angle, the crossing point changes position inside the material according to how much material the beams have traveled in before the crossing point.
If the beams are not perfectly horizontal and well aligned the car be an asymmetry on the absorption signal if the beams imping on one surface or on the other one.

To check this, I measured a scan at the center of the sample from one side, and I flipped the sample to do the same measurement from the other surface.

Result: the two plots overlap quite well.

The arrow in the first plot indicates where the beams come from

Comment to Noise spectra of green/IR beam (Click here to view original report: 674)

We have verified that the spikes oberved in the IR transmission,  in the region above 10 kHz are prensent even if there is no light impingin on the photodiode. They are likely be due to electronics.

The installment of camera(for IR reflection) and the attempt to acquire IR error signal

Participant: Yuefan, Yuhang, Eleonora

1. The installment of camera for IR reflection

Since we have received the filter to attenuate green beam, we tried to install the camera for IR reflection today. Since the power of IR is pretty high, we also used an OD filter(factor of 2) and a partly-reflected mirror to reduce the power. During the adjustment, we can see on the screen that there are two points. The small one is on the right and below side of the large one. Then we tried to change the angle of that partly-reflected mirror and accordingly the camera. At a certain point, we could make it a round point. We believed that that was a good angle.

Then we locked the cavity, this reflection of one point changes to two points.(See attached video 1) We thought that we were looking at the TEM10 mode. However, it should be the superposition of TEM00 and TEM01. According to our knowledge, this reflection can tell us the information of alignment. That means if it is the right reflection, we can use it to refine the cavity. Since we have already been around the best position, so we move the Input mirror around this position to check. What we could see is only these two points changed brighter and weaker one after another.(See attached video 2) Even when we tried to misalign the pitch of End mirror, we couldn't see the TEM01 mode on the screen.(See attached video 3)

Video Note: the interesting part of video are all around the end of video. You can find them by using the date 20180226. You can check them through this link. https://drive.google.com/drive/folders/1v7oSk0d6ONPN-NZTNcYjIuG0ip8XCZOn?usp=sharing

After checking all the things listed above, I felt gradually that it is not the right reflection. But we cannot figure out why we can see it. We need an expert and tomorrow Raffaele will come^_^

2. Attempt to acquire IR error signal

Due to the FWHM of IR is much more narrow than GREEN. The locking accuracy of IR needs to be evaluated by having the error signal directly. Owe to the EOM modulation for SHG, we have the modulation for infrared luckily. So we separate the output of its signal generator by using SMC-type connector(to avoid signal reflection see attached picture 1). We use the reflection from the cavity as RF signal.

After separation, we succeeded in recovering the error signal for the SHG. By the way, we made this error signal pk-pk value larger than before.(See attached picture 2 and 3) Also we took the picture of different modes we got for SHG.(See attached picture 4)

For infrared error signal, we make the AOM modulate. That means the AOM driving frequency change around the best point with a certain frequency(It's like the ramp signal while we looking for the error signal). But we cannot find the error signal for IR.

For the fail of IR error signal, we found the bandwidth of IR reflection PD is not high enough. Now it is PDA36A(350-1100nm, 10MHz BW, 13mm**2), but our modulation is 15MHz. Certainly we cannot demodulate it. Besides, we also need to check if the demodulation board can work well tomorrow.

Tama size sapphire sample2 , scan and maps

I characterized the absorption of the central part of the tama-sized sapphire substrate sample#2

Pump power 10W (after the chopper). Max laser current: 7.5A

After aligning the system with the surface reference sample, and scanning the bulk reference sample for calibration (with power=30mW), I made a scan of the sapphire substrate.
Changing from the 3.6mm thick reference sample to the 60mm thick sapphire substrate we have to move backward the imaging unit by 24.9mm. Then recenter the probe on the PD maximizing the DC.

From the scan plot we can recognize the 2 surfaces of the sample (when the absorption signal drops to 0) and associate the translation stage Z coordinate to the sample coordinates. Indeed the apparent depth of the sample is different from the real one as explained in entry  242 , Since the sample is 60mm thick, it is convenient to define the sample Z coordinate to be 0 at the first surface and 60 at the second surface. On the translation stage reference system the first surface is at 44mm and the second surface is at 77.5mm. In other words, during a scan,  the crossing point pump-probe travels in the sample about 1.8 times faster than the translation stage that mpoves the sample.

I made circular maps on the XY plane at several depths in the sample. Then 2 rectangular maps on the XZ and YZ planes. A 3d overview can summarize all the maps together in comparison with the sample size (drawn as 2 circles for the surfaces boundaries)

The circular maps resolution is 100um x 100um
The rectangular maps resolution is 100um x 1mm

the waiting time from one point to the next one is 1s, according to the average and median filters of order 10.

the color scale is up to 200ppm/cm to make the maps more readable and cover most of the color range. However, on the second surface of the sample, there are some absorption peaks up to 1400 ppm/cm which are probably due to some dirt on the surface or some polishing defects  

Correction of entry672

I made a mistake in entry672. The noise is injected in the position of CAVITY(G3). So we need to use open loop TF and G1,G2,G3 to calibrate this signal.

So I measured the open loop transfer function, it agrees with the simulation of Eleonora's thesis. For the measurement, the magnitude for 20Hz is about 10^4.(See picture 1)

Then using CH2*(open loop/(G1*G2*G3))=CH1. From this formula, we can do the calibration like entey672 again. This time, the result of calibration approximatly equals to the measurment.

By the way, I also tried to insert noise of 500Hz. It aggres with the prediction, the suspension can filter this high frequency noise. After injecting this noise, we cannot see any peak on the spectrum of PZT or error signal.(See comparation of picture 2 and 3)

Mechanical Transfer Function of Local Controls

Mechanical transfer functions of local controls as of 21 February 2018.

Noise amplitude: 500mV (white noise injected into port NOISE 2)

Noise spectra of green/IR beam

Here is attached noise spectra of the filter cavity transmission and reflection. As for transmission spectra, data measured in two different frequency span were put together afterwards to retain good resolution in lower frequency range. There are spikes on IR transmission in the range above 10kHz which do not exist in reflection nor in green. We also examined IR beam before entering the cavity and confirmed that there were not such spikes (data not shown here).

IR transmission and calibrated error signal

This is the characterization of IR transmission and the corresponding calibrated error signal. It is shown in picture 1.

This calibration factor is measured while sine wave noise frequency is 28kHz. I also did the measurement for different sine wave frequency. It is shown in picture 2. For this, I have a question. Is this frequency dependence related to the transfer function of our control servo?

revisit angular perturbation

I did this angular to length perturbation test again. This time I also took the spectrum of PZT monitor. Now I found this 20Hz peak on PZT monitor's spectrum, but still not on error signal spectrum. See attached picture 1 and 2.

From the picture 2, we can read the peak value of this noise. It is 45.7407uVrms. And according to the block flow, we can calibrate this value to error signal. The formula is Err_V = K(V/Hz) * S_Hz/(1- (f/f_0)^2).

K is 3.1e-3, S_Hz is V_RMS (V) * 100 * sqrt(2) * 2e6 Hz/V=12937Hz, f_0=1.45kHz. In this case Err_V=38.8Vrms. However we read from the spectrum, it is 1.6mVrms.

We also checked the situation if there is not noise injecting to the end mirror. It is shown in picture 4 and 5. By comparing them, I found the 20Hz disappear. But the noise level for the whole frequency band(from 1Hz to 50Hz) has decreased.

Conclusion:
1. The shaking of EM can cause precisely the same frequency noise in PZT. And also the harmonic peak.
2. In the aspect of error signal, the shaking of EM noise will be distributed from one frequency to the whole band. This distribution may come from filter.
3. By using the transfer function we created before, we cannot predict the behavior of error signal in the low-frequency band.

Next step:
To solve the problem of transfer function for low-frequency.

misalignment and angular perturbation impact

participant: Tomura, yuhang

We measured the misalignment again by changing the driving frequency of AOM. The measurement shows it is around 0.168. And the standard deviation is 0.0165.(See attached picture 5) So the residual misalignment is 17% (+/-2%) .

Besides, we injected a sine-wave noise into the local control of optical lever. We choose the frequency of 20Hz, 200Hz and 500Hz. The amplitude is 1V. The noise is injected into EM (yaw and pitch). The 20Hz is appreciable on the transmission of green.(See attached picture 1)We are sure the noise is injecting to EM.(We can see it from the local control like picture2) And the frequency of the noise we are injecting is the same with the frequency we can see in the transmission signal of green light. At the same time, we measured the noise spectrum of error signal. We found it has no difference from the case without noise injecting.(For all the test, they have no difference. See picture 3 and 4)

This perturbation test may tell us that the angular to length coupling is low, so that its affect for error signal is below the present noise level.

Characterization of transmission stability

Today I follow the procedure of simultaneous lock of IR and GREEN. After locking, I took the data from the oscilloscope.

I use the data to calculate the standard deviation of IR transmission and GREEN transmission. For green, it is 0.0286. For IR, it is 0.1235.

The result is also shown as attached figure. Next step is to figure out the reason of instability.

Preliminary measurement of filter cavity round trip losses and decay time

Participants:  Eleonora, Matteo L., Raffaele, Tomura

In the past days we kept working on the characterization of the IR lock, with the main purpose of measuring the cavity losses and the decay time.

ROUND TRIP LOSSES

We observed that in good alignement condition (IR trasmission above 1.5 V), the fluctuations of the transmitted and reflected power were much less than what observed before.

In this condition we were able to measure a change in the cavity reflectivity when the cavity is resonant and when it is not and give a preliminar estimation of the round trip losses (RTL)

In Fig.1 the trasmission and the reflection of the IR are shown when a set of lock/unlocks of the cavity was done. The reflected light has been focused on a photodiode using a lens with f = 50 mm. Et the beginning of the measurement the IR light has been blocked to measure possible offsets of the photodiodes.

The technique used to switch from resoant to not resoant state was to suddenly change the driving frequency of the AOM of 5 kHz. By using the values of the reflected power in the two states (resonant and not resonant) as explained in detail in the attached pdf we estimated the RTL to be about 80 +/-12 ppm, corresponding to 0.26 ppm/m. The error is mainly do to the residual fluctuations of the refected power when the cavity is locked. The associated squeezing degradation is reported in FIg 2.

The presence of light not coupled in the cavity (mismatching/misalignement) normaly reduces the measured losses and has to be compensated in order to have a real estimation of them. In the previous calculation I assumed a mismatching of 15%. 

[An idea of the impact of the mimastch compensation: assuming no mismatching the computed losses are 70 ppm while with 20% of mismatching they becomes 85 ppm. (Details about this can be found in my thesis at pag.101)]

According to the simulation we expected about 55 ppm of RTL  (40 ppm from flatness, 10 ppm from rougness/point defects and 5 ppm from trasmission and absorpition). Note that losses from small angles scattering (between mrad and few degrees) have not been considered in this loss budget.

DECAY TIME and FINESSE

A preliminar estimation of the decay time has also been done. To do that we used different tecniques: bringing the cavity suddenly out of resonance (by stopping the lock with the servo or changing the AOM driving frequency) or cutting the light in input. The transmission and reflection in this 3 cases are reported in the second pdf attached) 

A fit of the transmitted power for the first measurement shows a decay time of 0.0027 s, corresponding to a finesse of 4250  (Finesse = pi*FSR*decaytime ). See third figure attached.

Assuming the nominal reflectivity of the mirrors, this value is compatible with RTL of about 100 ppm.

A better analysis of the decay time, with an estimation of the error bars will be done soon.

Characterization of Aux lasers and Faraday isolators

Participants: Eleonora, Tomura

We conducted characterization of  two auxiliary lasers and faraday isolators.

For two aux. lasers, beam dimension evolution along propagation were measured. Laser power during measurements were approx. 260 mW, which corresponds to 1.2A in laser current.  Attached figures shows bean waist sizes and position. The origins of x-axes were set at aperture of laser housing. The waist positions were somewhat different from what expected.

The beam polarizaiton purity was confirmed with half/quarter waveplate. It was 96.7% and 99.9% for aux1 and aux2, respectively.

Beam transmission through FI was also measured using aux laser as a light source. Pictures of two FIs were attached.

For first FI (thorlabs), transmitted power was 213 mW out of 265 mW, which means 80.4%.

For second FI (Gsaenger), it was 79%.