Jenne, Koji and I opened up the package from Raicol and examined the crystals under the microscope. The results were mixed and are summarized below. There are quite a few scratches and there is residue on some of the polished sides. There is a large chip in one and there appear to be gaps or bands in the AR coatings on the sides.

There are two albums on Picassa

1. The package is opened ...

2. The crystals under the microscope.

 Here is Crystal 724 polished side 2 with all photos along the length stitched together

EDIT: I used an IFIT (inverse fast idiot transform) to change the x-axis of the plot from Hz to m. I think xlabel('Frequency [Hz]') is in my muscle memory now..

I have redone the beam fit, this time omitting the M², which I believe was superfluous. I have made the requested changes to the plot, save for the error analysis, which I am still trying to work out (the function I used for the least squares fit does not work out standard error in fit parameters). I will figure out a way to do this and amend the plot to have error bars.

Quote:

I have redone the beam fit, this time omitting the M2, which I believe was superfluous. I have made the requested changes to the plot, save for the error analysis, which I am still trying to work out (the function I used for the least squares fit does not work out standard error in fit parameters). I will figure out a way to do this and amend the plot to have error bars.

 Are you sure about your x-axis label? 

Beautiful fitting.

Quote:

EDIT: I used an IFIT (inverse fast idiot transform) to change the x-axis of the plot from Hz to m. I think xlabel('Frequency [Hz]') is in my muscle memory now.. I have redone the beam fit, this time omitting the M2, which I believe was superfluous. I have made the requested changes to the plot, save for the error analysis, which I am still trying to work out (the function I used for the least squares fit does not work out standard error in fit parameters). I will figure out a way to do this and amend the plot to have error bars.

Theoretically the waist position of a Gaussian beam (1064) in our PPKTP crystal differs by ~6.7 mm from that of the incident Gaussian beam.

So far I have neglected such position change of the beam waist in optical layouts because it is tiny compared with the entire optical path.

But from the point of view of practical experiments, it is better to think about it.

In fact the result suggests the rough positioning of our PPKTP crystals;

we should put our PPKTP crystal so that the center of the crystal is 6.7 mm far from the waist of a Gaussian beam in free space.

(How to)

The calculation is very very simple.

The waist position of a Gaussian beam propagating in a dielectric material should change by a factor of n, where n is the refractive index of the material.

In our case, PPKTP has  n=1.8, so that the waist position from the surface of the crystal becomes longer by n.

Now remember the fact that the maximum conversion efficiency can be achieved if the waist locates at exact center of a crystal.

Therefore the waist position in the crystal should be satisfied this relation; z*n=15 mm, where z is the waist position of the incident beam from the surface and 15 mm is half length of our crystal.

Then we can find z must be ~8.3 mm, which is 6.7 mm shorter than the position in crystal.

The attached figure shows the relation clearly. Note that the waist radius doesn't change.

Jenne, Koji and I assembled the Covesion Oven today, inserted a PPKTP crystal from Raicol, aligned the crystal to a 50mW focus and
got some green beam coming out.

Covesion Oven assembly

The oven contains a brass clip that can clamp a crystal up to 10mm wide x 0.5mm high x 40mm long (according to the instructions). According to the correspondence from Covesion the clip can accomodate a crystal up to 1.5mm high. Our crystal is 1mm x 1mm x 30mm.

1. We removed the brass springs from the clip - see Koji's photos
2. We placed the Raicol PPKTP crystal (#725) into the clamp with the long polished surfaces facing out to the sides and the roughened surfaces facing up and down.
3. We balanced the 10mm x 40mm x 1mm glass plate on top of the crystal.
4. We replaced the brass springs in the top of the clip but only tightened the screws a couple of turns so they wouldn't fall out.
5. Very carefully and slowly, I tightened the screws a few turns in a star-shaped order to distribute the pressure evenly across the glass top
6. Each time I tightened all eight screws, I jiggled each of the four springs to see if there was any compression in them
7. Once the springs started to show signs of compression I stopped tightening them and tested the stability of the glass plate - a reasonable amount of pressure was required to move the plate - about the same amount required to push a SR560 across an optical table with your index finger.
8. We loosely attached the lid and moved the oven to the table

Alignment of the crystal to the focus

The oven was mounted on a 4-axis Newport translation stage. We plonked the assembly onto the table, removed the lid and adjusted the rough position so that a focus of the 1064nm beam, from a 100mm lens, was positioned near the center of the crystal - then it was clamped down to the table. From here we adjusted the alignment of the stage, using an IR card and a viewer to guide us, until we eventually saw some green beam coming out. We were all very excited by this! We optimized the alignment as best we could using the IR card and then we replaced the lid on the oven. At this point the temperature of the PPKTP was around 26.5C and the green beam coming out look quite dim. We turned the oven up to around 36 degC and observed the beam getting much brighter and we approached the optimum phase-matching condition.

We haven't done anyway quantitative measurements yet but we were pleased with how easy this first stage was.

[Edit by Koji] More photos are on Picasa album

I scanned the temperature of the crystal oven on Friday night in order that we can find the optimal temperature of the crystal for SHG.

The optimal temperature for this crystal was found to be 36.2 deg.

The crystal is on the PSL table. The incident beam on the crystal is 27.0mW with the Newport power-meter configured for 1064nm.
The outgoing beam had 26.5mW.

The outgoing beam was filtered by Y1-45S to eliminate 1064nm. According to Mott's measurements, Y1-45S has 0.5% transmission for 1064nm, while 90% transmission for 532nm. This means I still had ~100uW after the Y1-45S. This is somewhat consistent with the offset seen in the power-meter reading.

First, I scanned the temperature from 28deg to 40deg with 1deg interval.The temperature was scaned by changing the set point on the temperature controller TC-200.The measurements were done with the temperature were running. So, the crystal may have been thermally non-equilibrium.

Later, I cut the heater output so that the temperature could be falling down slowly for the finer scan. The measurement was done from 38deg to 34deg with interval of 0.1deg with the temperature running.

I clearly see the brightness of the green increase at around 36 deg. The data also shows the peak centered at 36.2deg. We also find two lobes at 30deg and 42deg. I am not sure how significant they are.

The mode profile of Gaussian beams in our PPKTP crystals was calculated.

I confirmed that the Rayleigh range of the incoming beam (1064 nm) and that of the outgoing beam (532 nm) is the same.

And it turned out that the waist postion for the incoming beam and the outgoing beam should be different by 13.4 mm toward the direction of propagation.

These facts will help us making optical layouts precisely for our green locking.

(detail)

The result is shown in the attached figure, which is essentially the same as the previous one (see the entry).

The horizontal axis is the length of the propagation direction, the vertical axis is the waist size of Gaussian beams.

Here I put x=0 as the entering surface of the crystal, and x=30 mm as the other surface.

The red and green solid curve represent the incoming beam and the outgoing beam respectively. They are supposed to  propagate in free space.

And the dashed curve represents the beams inside the crystal.

A trick in this calculation is that: we can assume that  the waist size of 532 nm is equal to that of 1064 nm divided by sqrt(2) . 

If you want to know about this treatment in detail,  you can find some descriptions in this paper;

"Third-harmonic generation by use of focused Gaussian beams in an optical super lattice" J.Opt.Soc.Am.B 20,360 (2003)"

Kiwamu and Kevin measured the beam profile of the green laser by the south arm ETM.

The following measurements were made with 1.984A injection current and 39.65°C laser crystal temperature.

Two vertical scans (one up and one down) were taken with a razor blocking light entering a photodiode with the razor 7.2cm from the center of the lens. This data was fit to

b + a*erf(sqrt(2)*(x-x0)/w) with the following results:

scan down: w = (0.908 ± 0.030)mm  chi^2 = 3.8

scan up:      w = (0.853 ± 0.025)mm   chi^2 = 2.9

giving a weighted value of w = (0.876 ± 0.019)mm at this distance.

The beam widths for the profile fits were measured with the beam scanner. The widths are measured as the full width at 13.5% of the maximum. Each measurement was averaged over 100 samples. The distance is measured from the back of the lens mount to the front face of the beam scanner.

This data was fit to w = sqrt(w0^2+lambda^2*(x-x0)^2/(pi*w0)^2) with lambda = 532nm with the following results:

For the vertical beam profile:

reduced chi^2 = 3.29

x0 = (-87   ± 1)    mm

w0 = (16.30 ± 0.14) µm

For the horizontal beam profile:

reduced chi^2 = 2.01

x0 = (-82   ± 1)    mm

w0 = (16.12 ± 0.10) µm

Note: These fits were done with the beam diameter instead of the beam radius. The correct fits to the beam radius are here: http://nodus.ligo.caltech.edu:8080/40m/2912

Hey, what a quick work!

But, wait...

1) The radius of the beam was measured by the razor blade.

2) The diameter of the beam (13.5% full-width) at each point was measured by Beam Scan. The one at z=~7cm was consistent with 1)

3) The data 2) was fitted by a function w = sqrt(w0^2+lambda^2*(x-x0)^2/(pi*w0)^2). This is defined for the radius, isn't it?

So the fitting must be recalculated with correct radius.
Make sure that you always use radius and write with a explicit word "radius" in the record.

 Here's a photo of the set-up used. The beam profile is measured relative to the f=-100mm lens.

For the vertical beam profile:

reduced chi^2 = 3.25

x0 = (-86 ± 1)mm

w0 = (46.01 ± 0.38)µm

For the horizontal beam profile:

reduced chi^2 = 2.05

x0 = (-81 ± 1)mm

w0 = (45.50 ± 0.28)µm

We succeeded in getting the reflected green beam from both ITMY and ETMY.

After we did several things on the end table, we eventually could observe these reflections.

Now the spot size of the reflection from ITMY is still big ( more than 1 cm ), so tomorrow modematching to the 40m cavity is going to be improved by putting mode matching telescopes on right positions.

An important thing we found is that, the beam height of optics which directly guides the beam to the cavity should be 4.5 inch on the end table.

(what we did)

* Aidan, Kevin and Kiwamu set the beam to be linearly polarized by rotating a QWP in front of the Innolight. This was done by monitoring the power of the transmitted light from the polarizer attached on the input of the Faraday of 1064 nm. Note that the angle for QWP is 326.4 deg.

* We put some beam damps against the rejected beam from the Faraday

* To get a good isolation with the Faraday we at first rotated the polarization of the incident beam so to have a minimum transmission. And then we rotated the output polarizer until the transmission reaches a minimum. Eventually we got the transmission of less than 1mW, so now the Faraday should be working regardless of the polarization angle of the incident beam. As we predicted, the output polaerizer seems to be rotated 45 deg from that of the input.

* Rana, Koji and Kiwamu aligned the PPKTP crystal to maximize the power of 532 nm.  Now the incident power of 1064 nm is adjusted to 250mW and the output power for 532 nm is 0.77mW. Actually we can increase the laser power by rotating a HWP in front of the Faraday.

* We injected the green beam to the chamber and aligned the beam axis to the ETMY without the modematching lenses, while exciting the horizontal motion of the ETM with f=1Hz from awg. This excitation was very helpful because we could figure out which spot was the reflection from the ETM.

* Once we made the reflected beam going close to the path of the incident beam, we then put the modematching lenses and aligned the steering mirrors and lenses. At this time we could see the reflected beam was successfully kicked away by the Faraday of 532 nm.

* Koji went to ITMY chamber with a walkie-talkie and looked at the spot position. Then he told Rana and Kiwamu to go a right direction with the steering mirrors. At last we could see a green beam from ITM illuminating the ETM cage.

* We excited the ITMY with f=2Hz vertically and aligned the ITM from medm. Also we recovered a video monitor which was abandoned around ETMY chamber so that we could see the spot on the ETM via the monitor. Seeing that monitor we aligned the ITM and we obtained the reclection from the ITM at the end table.

* We also tried to match the mode by moving a lens with f=400mm, but we couldn't obtain a good spot size.

Strange. I thought the new result became twice of the first result. i.e. w0=32um or so.

Can you explain why the waist raidus is estimated to be three times of the last one?
Can you explain why the measured radius @~70mm is not 0.8mm, which you told us last time,
but is 0.6mm?

The measurements have been done at the outside of the Rayleigh range.
This means that the waist size is derived from the divergence angle

theta = lambda / (pi w0)

At the beginning you used diameter instead of radius. This means you used twice larger theta to determine w0.
So if that mistake is corrected, the result for w0 should be just twice of the previous wrong fit.

I could not understand this operation. Can you explain this a bit more?

It sounds different from the standard procedure to adjust the Faraday:

1) Get Max transmittion by rotating PBS_in and PBS_out.

2) Flip the Faraday 180 deg i.e. put the beam from the output port.

3) Rotate PBS_in to have the best isolation.

 Now I know why Rana was wearing his bright green pants yesterday. It is nice to see the green beam in the 40m IFO again. It calls for celebration!

I stopped AWG 1Hz drive of ITMYs (south-arm) I still see unblocked beams at the ETMYs table. We have plenty of cleaned razor beam traps to be used. Please block Faraday rejects etc

The procedure you wrote down as a standard is right.   I explain reasons why we didn't do such way. 

For our situation, we can rotate the polarization angle of the incident beam by using a HWP in front of the Faraday.  

This means we don't have to pay attention about the PBS_in because the rotation of either PBS_in or the HWP causes the same effect (i.e. variable transmission ). This is why we didn't carefully check the PBS_in, but did carefully with the HWP.

Normally we should take a maximum transmission according to a instruction paper from OFR, but we figured out it was difficult to find a maximum point. In fact looking at the change of the power with such big incident (~1W) was too hard to track, it only can change 4th significant digit ( corresponds to 1mW accuracy for high power incident ) in the monitor of the Ophir power meter. So we decided to go to a minimum point instead a maximum point, and around a minmum point we could resolve the power with accuracy of less than 1mW.

After obtaining the minimum by rotating the HWP, we adjusted the angle of PBS_out to have a minimum transmission.

And then we was going to flip the Faraday 180 deg for fine tuning, but we didn't. We found that once we remove the Faraday from the mount, the role angle of the Faraday is going to be screwed up because the mount can not control the role angle of the Faraday. This is why we didn't flip it.

??? I still don't understand. What principle are you rely on?

I could not understand why you rotated the HWP to the "minimum" transmission
and then minimized the transmission by rotating the output PBS. What is optimized by this action?

Probably there is some hidden assumption  which I still don't understand.
Something like: Better transmission gives best isolation, PBS has some leakage transmission
of the S-pol light, and so on.

Tell me what is the principle otherwise I don't accept that this adjustment is "to get a good isolation with the Faraday".

P.S. you could flip the faraday without removing it from the V-shaped mount. This does not roll the Faraday.

I stopped AWG  1 Hz drive to ITMYs. ITMXe was also driven or oscillating. ITMXe damping was off, so I turned it on. It did not effect it's oscillation

for the vertical beam profile:

reduced chi^2 = 3.28

x0 = (-87 ± 1) mm

w0 = (32.59 ± 27) µm

for the horizontal beam profile

reduced chi^2 = 2.02

x0 = (-82 ± 1) mm

w0 = (32.23 ± 20) µm

In the following plots * denotes vertical data points and + denotes horizontal data points. The blue curve is the fit to the vertical data and the purple curve is the fit to the horizontal data.

Mode matching to the cavity has been done.

Now the reflection from the cavity is successfully going into the PD.

However I could not see any obvious error signal.

I should compute and re-check the expected signal level.

(mode matching of the crystal)

On the last Wednesday, Kevin and I measured the mode profile before the PPKTP crystal,  and we found the Gaussian beam at the crystal is focused too tightly (w = 38 um).

In order to achieve the best conversion efficiency the waist size should be 50.0 um. So we moved a lens, which was located before the crystal, to 7 cm more away from the crystal. Eventually we obtained a better focus (w = 50.1 um).

Thanks, Kevin. You did a good job.

(mode matching of the cavity)

I put a lens with f=-50 mm after the crystal to diverge the green beam more quickly. Then the beam is going through the Faraday of 532 nm, two final modematching lenses and ETMY at last.

By shifting the positions of these lenses, I obtained the reflection from ITMY with almost the same spot size as that of the incident. This means modemathing is good enough.

I put two more steering mirrors before its injection to the ETM, this allows us to align the beam axis against the cavity.

I aligned the axis by using the steering mirrors and now the green beam are successfully hitting the center of both the ETM and the ITM.

Then the alignment of the ETM and the ITM was adjusted from medm, so that both reflection goes in the same path as that of the incident.

And then I put a PD (Thorlabs PDA36A) to see the reflection rejected by the Faraday.

Connecting a mixer and a local oscillator (Stanford func. generator) with f=200kHz, but I couldn't see any obvious PDH signal....

Since the PD is DC coupled, the signal is almost dominated by DC voltage. Even if I inserted a high pass filter to cut off the DC, the AC signal looks very tiny..

Don't make a short cut. The beam size at a single place does not tell you anything.
Measure the mode of of the beam at multiple points. Calculate the mode matching ratio.

Align the mirrors precisely. Try to see the DC fringe. Predict the size of the DC fringe.

Test the demodulation system with a function generator. Find the 200kHz signal using the spectrum analyzer to find the signal and the optimal alignment.

Put the DC signal and the AC signal to the oscilloscope as X&Y.

Good luck.

 I measured again the mode profile of the beam going through the PPKTP crystal by using the beam scan.

The aimed beam waist is 50 um (as described in entry 2735),

and the measured profile had pretty good waist of w_x=51.36 +/- 0.0999 um and w_y=49.5 +/- 0.146 um 

The next things I have to do are - (1). re-optimization of the temperature of the crystal (2). measurement of the conversion efficiency

The attached figure is the result of the measurement. 

The mode profile of the green beam going through 40m cavity was measured.

According to the fitting the coupling efficiency to the cavity is 98.46%, but still the beam looks loosely focused.

This measurement has been done by using the oplev legs (entry #2957) to allow the beam to go through the 40m walkway.

With a beam scan set on a movable cabinet, I measured it along the 40m chamber.

Since the plot looks not so nice,  I am going to work on this measurement a little bit more after I improve the mode matching.

Here is the parameters from the fitting

I believe the error for the travel length was within 0.5 meter. The length was always measured by a tape measure.

A thing I found was that: spatial jittering of the beam gets bigger as the beam goes further. This is the main source of the error bar for the spot size. 

We should completely turn off the air conditioner when working on green locking.

Even if green beams propagates inside of chambers, the air conditioner does affect the spatial jitter of the beam. 

The attached picture was taken when Steve and I were seeing how the green beam jittered. 

At that time the beam was injected from the end table and going through inside of the ETM, the ITM and the BS camber.

Eventually it came out from the camber and hit the wall outside of the chamber. It was obvious, we could see the jittering when the air cond. was ON.

I guess I succeeded in locking of the cavity with the green beam 

 Strictly speaking, the laser frequency of the end NPRO is locked to the 40 meter arm cavity.

Pictures, some more quantitative numbers and some plots are going to be posted later.

After the alignment of the cavity I could see DC fringes in its reflection. Also I could see the cavity flashing on the monitor of  ETMY_CCD.

I drove the pzt of the NPRO with f=200kHz, and then the spectrum analyzer showed 200kHz beat note in the reflection signal. This means it's ready to PDH technique.

And then I made a servo loop with two SR560s, one for a filter and the other for a sum amp.

After playing with the value of the gain and the sign of the feedback signal, the laser successfully got lock. 

To make sure it is really locked, I measured the open loop transfer function of the PDH servo while it stayed locked. The result is shown in the attached figure.

The measured data almost agrees with the expected curve below 1kHz, so I conclude it is really locked.

However the plot looks very noisy because I could not inject a big excitation signal into the loop. If I put a big excitation, the servo was unlocked.

The current servo is obviously too naive and it only has f^-1 shape, so the filter should be replaced by a dedicated PDH box as we planed.

Congratulation! Probably you are right, but I could not get this is a real lock or something else.

1) How much was the fringe amplitude (DC) of the reflected beam? (Vref_max=XXX [V] and Vref_min=YYY [V])
    Does this agree with the expectation?

2) Do you have the time series? (V_ref and V_error)

Andri and I mounted the Raicol Crystal #724 in one of the new Covesion Ovens. The procedure was the same as before - see elog entry here.

There was one issue - the glass plate that goes on top of the crystal is coated on one side with ITO (Indium-Tin Oxide) and it's not 100% certain that this was mounted in the correct orientation. It is virtually impossible to tell which side of the glass is coated.

The base plate of the oven was tapped for an M3 hole. We retapped it for an 8-32 and bolted it to a post and that one of the New Focus 4-axis translation stage. The assembly is currently bolted to the PSL table, awaiting use.

 Here are some more plots and pictures about the end PDH locking with the green beam. 

-- DC reflection

 I expected that the fluctuation of the DC reflection had 1% from the resonant state to the anti-resonant state due to its very low finesse.

This values are calculated from the reflectivity of ETM measured by Mott before (see the wiki).

In my measurement I obtained  DC reflection of V_max=1.42 , V_min=1.30  at just after the PD.

These numbers correspond to 7.1% fluctuation. It's bigger than the expectation.

I am not sure about the reason, but it might happen by the angular motion of test masses (?)

--- time series

Here is a time series plot. It starts from openloop state (i.e. feedback disconnected).

At t=0 sec I connected a cable which goes to the laser pzt, so now the loop is closed.

You can see the DC reflection slightly decreased and stayed lower after the connection.

The bottom plot represents the feedback signal measured before a sum amp. which directly drives the pzt.

-- length fluctuation  

One of the important quantities in the green locking scheme is the length fluctuation of the cavity.

It gives us how much the frequency of the green beam can be stabilized by the cavity. And finally it will determine the difficulty of PLL with the PSL.

I measured a spectrum of the pzt driving voltage [V/Hz^1/2] and then converted it to a frequency spectrum [Hz/Hz^1/2].

I used the actuation efficiency of 1MHz/V for the calibration, this number is based on the past measurement.

RMS which is integrated down to 1Hz  is 1.6MHz.

This number is almost what I expected assuming the cavity swings with displacement of x ~< 1um.

-- flashing

A picture below is a ETMx CCD monitor.

One of the spot red circled in the picture blinks when it's unlocked. And once we get the lock the spot stays bright.

 Its OK, but the real number comes from measuring the time series of this in the daytime (not the spectrum). What we care about is the peak-peak value of the PZT feedback signal measured on a scope for ~30 seconds. You can save the scope trace as a PNG.

 I leave notes about a plan for the green locking especially on the PSL table.

 (1) open the door  of the MC13 tank to make the PSL beam go into the MC.  Lock it and then optimize the alignment of the MC mirror so that we can later align the incident beam from the PSL by using the MC as a reference.   

 (2) Remove a steering mirror located just after the PMC on the PSL table. Don't take its mount, just take only the optic in order not to change the alignment .

 (3) Put an 80% partial reflector on that mount to pick off ~200mW for the doubling . One can find the reflector on my desk.

 (4) Put some steering mirrors to guide the transmitted beam through the reflector to the doubling crystal. Any beam path is fine if it does not disturb any other setups. The position of the oven+crystal should not be changed so much, I mean the current position looks good.

 (5) Match the mode to the crystal by putting some lenses. The optimum conversion efficiency can be achieved with beam waist of w0~50um (as explained on #2735). 

 (6) Align the oven by using the kinematic mount. It takes a while. The position of the waist should be 6.7 mm away from the center of the crystal (as explained on #2850). The temperature controller for the oven can be found in one of the plastic box for the green stuff. After the alignment, a green beam will show up.

(8) Find the optimum temperature which gives the best conversion efficiency and measure the efficiency.

(7)  Align the axis of the PSL beam to the MC by steering the two mirrors attached on the periscope.

A poor lonely SR785 was found this morning roaming around in the lab in evident violation of the fundamental rule which requires all the equipment on carts to be brought back inside the lab right after use.

The people and the professors related to the case should take immediate action to repair for their misdeed.

A progress on the end PDH locking :

by using a modified PDH box the green laser on the X-end station is locked to the arm cavity.

So far the end PDH locking had been achieved by using SR560s, but it was not sophisticated filter.

To have a sophisticated filter and make the control loop more stable, the PDH box labeled "#G1" was installed instead of the SR560s.

After the installation the loop looks more stable than the before.

Some details about the modification of the PDH box will be posted later.

Although, sometimes the loop was unlocked because the sum-amp (still SR560) which mixes the modulation and the feedback signal going to the NPRO PZT was saturated sometimes.

Thus as we expected a temperature control for the laser crystal is definitely needed in order to reduce such big low frequency drive signal to the PZT.

A thermal feedback was installed to the end PDH locking and it works well. There are no saturations 

As I said the feedback signal was sometimes saturated at the sum-amp because the drive signal going to the laser PZT was large at low frequency (below 1Hz).

So I made a passive low pass filter which filters the signal controlling the temperature of the laser crystal, and put it before the temperature drive input.

Now the amount of the feedback signal got reduced when it is locked, and there are no saturations. It's very good.

(thermal property of the crystal) 

According to the specification sheet for the 1W Innolight, the thermal properties of the crystal are:

  Response coefficient : 3GHz/K 

  Temperature control coefficient : 1K/V

  Thermal response bandwidth: 1Hz 

(filter circuit and actuator response)

In order to feedback the signal blow 1Hz, a low pass fiter is needed. 

The attachment:1 shows the filter circuit I made.

Since I found that the drive input had an input impedance of 100kOhm, so I put relatively big resistors to have a moderate gain.

The expected actuator responses are also attached.

The blue curve represents the response of the PZT, the green is the thermal response including the low pass filter and the red curve is the total response composed of both the responses.

I assume that the PZT response is 1MHz/V according to Mott's measurement.

Also I assume that the thermal response intrinsically has two poles at 1Hz according to the specification listed above.

In the total response, there is a little gain reduction around 2Hz due to the cancelation of each other, but it still looks okay.

GJ!

On the wiki I summarized about the modification of the PDH box which is currently running on the end PDH locking. 

http://lhocds.ligo-wa.caltech.edu:8000/40m/Electronics/PDH_Universal_Box

The box was newly labeled "G1" standing for "Green locking #1".

We added a channel on c1psl in order to monitor the temperature of the PPKTP sitting on the PSL table.

To take continuous data of the temperature we added the channel by editing the file: target/c1psl/c1psl.db

We named the channel "C1:PSL-PPKTP_TEMP".

To reflect this change we physically rebooted c1psl by keying the crate.

Is this a setpoint temperature that we can change by writing to the channel or is it a readout of the actual temperature of the oven?

kiwamu:

This is a readout channel just to monitor the actual temperature.

The power of the green beam generated on the PSL table should be about 650uW in terms of the shot noise.

       One of the important parameters we should know is the power of the green beam on the PSL table because it determines the SNR.

The green beam finally goes to a photo detector together with another green beam coming from the arm cavity, and they make a beat signal and also shot noise.

So in order to obtain a good SNR toward the shot noise at the photo detector, we have to optimize the powers.

If we assume the green power from the arm is about 650uW,  a reasonable SNR can be achieved when these powers are at the same level. 

To get such power on the PSL table, a 90% partial reflector is needed for picking it off from the PSL as we expected.

  power dependency of SNR

      Suppose two lasers are going to a photo detector while they are beating (interfering).

The beat signal is roughly expressed by

      [signal]  ~ E_1^* E₂ + E₁ E_2^*,

                     ~ 2 ( P₁ P₂)^½ cos (phi), 

 where  E_{1 ^and} E₂ represent the complex fileds,  P₁ and P₂ represent their powers and phi is a phase difference.

This equation tells us that the strength of the signal is proportional to  ( P₁ P₂)^½  .

At the same time we will also have the shot noise whose noise level depends on the inverse square route of the total power;

          [noise] ~ ( P₁ + P₂)^½.

 According to the equations above, SNR is expressed by

        SNR = [signal] / [noise] ~ ( P₁ P₂)^½  / ( P₁ + P₂)^½.

If we assume P₁ is fixed,  the maximum SNR can be achieved when  P₂ goes to the infinity. But this is practically impossible.

Now let's see how the SNR grows up as the power P₂  increases. There are two kinds of the growing phase.

    (1) When P₂ <  P₁ , SNR is efficiently improved with the speed of  P₂^½.

    (2) But  when P₂ >   P₁ , the speed of growing up becomes very slow. In this regime increasing of  P₂ is highly inefficient for improvement of the SNR.

Thus practically P₁ ~ P₂  is a good condition for the SNR.

At this point the SNR already reaches about 0.7 times of the maximum, it's reasonably good.

 power estimation

         According to the fact above, we just adjust the green powers to have the same power levels on the PSL table.

 The table below shows some parameters I assume when calculating the powers.

         Attached figure shows a simplified schematic of the optical layout with some numbers. 

By using those parameters we can find that the green beam from the arm cavity is reduced to 650uW when it reaches the PSL table.

To create the green beam with the same power level on the table, the power of 1064 nm going to the doubling crystal should be about 150mW.

This amount of the power will be provided by putting a 90% partial reflector after the PMC.

In order to increase the green power on the PSL table, I moved the position of the Second Harmonic Generation (SHG) crystal by ~5cm.

After this modification, the green power increased from 200 uW to 640 uW. This is sufficiently good.

     As I said in the past elog entry (# 3122), the power of the green beam generated at the PSL table should be about 650 uW.

I measured the green power by the Ophir power meter and found it was ~200 uW, which made me a little bit sad.

Then I performed the beam scan measurement to confirm if the crystal  was  located on the right place. And I found the postion was off from the optimum position by ~5cm.

So I slided the postion of the SHG oven to the right place and eventually the power got increased to 640 uW.

some notes: 

(power measurement)

        The outgoing beam from the SHG crystal is filtered by Y1-45S to eliminate 1064nm.

According to Mott's measurement Y1 mirrors are almost transparent for green beams (T~90%), but highly reflective for 1064nm (T~0.5%).

All the green power were measured after the Y1 mirror by the Ophir configured to 532nm, though, the measured power might be offseted by a leakage of 1064nm from the Y1 mirror.

I didn't take this effect into account.

(beam scanning and positioning of crystal)

          Here is the properties of the incident beam. These numbers are derived from the beam scan measurement.

w0h             = 52.6657      +/- 0.3445 um

w0v             = 52.4798      +/- 0.1289  um

z0h             = 0.574683         +/- 0.001937 m

z0v             = 0.574325         +/- 0.0007267 m

Where the suffixes "h" and "v" stand for "horizontal" and "vertical" respectively.

The distances are calibrated such that it starts from the lens postion.

Both waist size are already sufficiently good because the optimum conversion can be achieved when the waist size is about 50um ( see this entry)

The measured data and their fitting results are shown in attachement 1.

         According to my past calculation the center of the crystal should be apart from the beam waist by 6.8mm (see this entry). 

So at first I put the oven exactly on the waist postion, and then I slided it by 6.8mm.

(to be done)

        I need to find an optimum temperature for the crystal in order to maximize the green power.

Previously the optimum temperature for the crystal was 38.4 deg. But after moving the position I found the optimum temperature is shifted down to around 37deg.

The feedback signal going to the laser PZT at the X end station was measured in the daytime and the nighttime.

It's been measured while the laser frequency was locked to the arm cavity with the green light.

The red curve was measured at 3pm of 8/July Friday. And the blue curve was measured at 12am of 9/July Saturday. 

As we can see on the plot, the peak-peak values are followers

              daytime:  ~ 4Vpp

       nighttime:  ~1.8Vpp

It is obvious that the arm cavity is louder in the daytime by a factor of about 2.

Note: the feedback signal is sent to the PZT only above 1Hz because the low frequency part is stabilized mostly by the crystal temperature (see this entry)

The optimum temperature for the doubling crystal on the PSL table was found to be 36.8 deg.

I scanned the temperature of the crystal from 44 deg to 29 deg, in order to find the optimum temperature where the frequency doubled power is maximized. 

(method) 

The method I performed is essentially the same as that Koji did before (see this entry).

(1) First of all, I enabled the PID control on the temperature controller TC200 and set the temperature to 44 deg.

(2) After it got 44 deg, I disabled the PID control.

(3) Due to the passive cooling of the oven, the temperature gradually and slowly decreased. So it automatically scans the temperature down to the room temperature.

(4) I recorded the power readout of the power meter: New Port 840 together with the temperature readout of TC200. The power meter was surely configured for 532 nm.

(result)

The measured data are shown in the attachment. 

The peak was found at T=36.8 deg where the power readout of  532 nm was 605 uW.

Compared with Koji's past data (see this entry), there are no big side lobes in this data. I am not sure about the reason, but the side lobes are not critical for our operation of the green locking.

 (to be done)

 Adjustment of the PID parameters

 It seems like you might inherit an offset by using step (3) b/c of the temperature gradient between the crystal and the sensing point. Depending on how large this gradient is you could increase the linear coupling from temperature to intensity noise from zero to a significant number. Phase noise should not be effected.

SInce these things (ovens) are so low time constant, shouldn't we

1. Lock to a temperature
2. Let the oven equilibrate for however long - a few tau maybe - my oven has a time constant of 60 sec, don't know if this is fast or slow compared to that
3. Measure P_532/P_1064
4. Change the setpoint
5. Go back to step 1

What did you use to filter the 2f components from your error signal? A homemade low pass or what?

Kiwamu:

I am using a homemade low pass filter.

It's just a RC passive LPF with the input impedance of 50 Ohm.

[Koji, Jenne, Kiwamu]

This is to describe the work that went on in the Cleanroom today.  Kiwamu's entry will detail the tidbits that happened in the chamber.

We engraved the periscope mounts with the mirror info for the mirrors which were placed in the periscope.  We also engraved the barrels of the optics with their info, for posterity.  Koji carefully put the mirrors into the periscopes.  Since we have wedged optics, the goal was to have the front HR surface of the mirror parallel to the plane of the mount, and leave a bit of space behind one side of the optic (if we just pushed the optic fully in, the HR surface wouldn't be flat, and would send the beam off to the left or right somewhere).  Once the mirrors were mounted in the periscopes, we checked the vertical levelness of the outcoming beam.  For the first periscope (the one which has been installed on the BS table), the beam was deflected upward (2.5)/32 inches over 55inches.  This corresponds to a 1.4mRad vertical deflection.  The second periscope (which will eventually be installed on the OMC table) had a deflection of 1/32 over 55inches, or 0.6mRad.  We did not check the side-to-side deflection for either of the periscopes.

We also engraved one more DLC mount with mirror info, and put a mirror into the mount.  This is one of the optics that was placed onto the BS table today, which Kiwamu will describe.

We removed TT#3 from the BS chamber so that it could have rubber vertical dampers installed, and be characterized.  For future reference, the #'s of the Tip Tilts refers to the serial number of the suspension block piece, which forms the top horizontal bar of the frame. 

If I understand your elog, you are just calculating the the offset in position space that you get by having a refractive index.

Did you end up changing the mode matching so that the rayleigh range (which changes with refractive index) was confocally focused inside the crystal (e.g. Zr = 15 mm?

- As you said, I just calculated the waist position in the crystal because the speed of light changes in a medium and eventually the waist position also changes.

- Yes, I did. Once you get a beam with the right waist size, you just put your crystal at the waist position with the offset.

  In fact you don't have to think about the rayleigh range inside of the crystal because what we care is the waist size and it doesn't change.

 I thought we cared about satisfying the confocal focusing parameter, that is to say we want to set Zr = 2L_crystal. If Zr changes inside the crystal, this is the number we care about..isn't it NOT the waist size, but the rayleigh range we care about? I am not entirely sure what youre response is saying you did...

1. Calculate Zr = pi * wo^2/(lamba/n)
2. Do mode matching to get this wo in free space
3. Calculate the offset you need to move the oven by using n
4. Move hte ovens

OR

1. Calculate Zr = pi*wo^2/(lamba)
2. Do mode matching to get this in free space
3. Calculate the offset you need to move your ovens using n
4. Move your ovens

I guess the waist size would also let me know - are you using 69 um or 53 um waist size?

Okay, I guess I understand what you want to know. I did the following steps.

1. calculated the conversion efficiency as a function of the waist size. I found w~50um was the optimum waist.

  Note: the confocal relation Zr = pi * wo^2/(lamba/n) = L/2  gives us almost the same optimum waist. 

elog #2735

  2.  Did mode matching to get w=50um

elog #2959

elog #3188

  3. calculated the offset

elog #2850

 4. Moved the ovens