Matt checked it in this morning and he found it's been locked during the night.

In this afternoon, Mott and I tried to find a beat note between two NPROs which are going to be set onto each end table for green locking.

At first time we could not find any beats. However Koji found that the current of innolight NPRO was set to half of the nominal.

Then we increased the current to the nominal of 2A, finally we succeeded in finding a beat note.

Now we are trying to lock the PLL.

P.S. we also succeeded in acquiring the lock

Last Friday, Matt made a frequency discriminator circuit on a bread board in order to test the idea and study the noise level. I think it will work for phase lock acquisition of Green locking.

As a result a response of 100kHz/V and a noise level of 2uV/rtHz @ 10Hz are yielded. This corresponds to 0.2Hz/rtHz @ 10Hz.

The motivation of using frequency discriminators is that  it makes a frequency range wider and easier for lock acquisition of PLLs in green locking experiment.

For the other possibility to help phase lock acquisition, Rana suggested to use a commercial discriminator from Miteq.

(principle idea)

The diagram below shows a schematic of the circuit which Matt has built.

Basically an input signal is split into two signals right after the input, then one signal goes through directly to a NAND comparator.

On the other hand another split signal goes through a delay line which composed by some RC filters, then arrive at the NAND comparator with a certain amount of delay.

After going through the NAND comparator, the signal looks like a periodic pulses (see below).

If we put a signal of higher frequency we get more number of pulses after passing through the NAND.

Finally the pulse-signal will be integrated at the low pass filter and converted to a DC signal.

Thus the amplitude of DC signal depends on the number of the pulses per unit time, so that the output DC signal is proportional to the frequency of an input signal.

(result)

By putting a TTL high-low signal, an output of the circuit shows 100kHz/V linear response.

It means we can get DC voltage of 1 V if a signal of 100kHz is injected into the input.

And the noise measurement has been done while injecting a input signal. The noise level of 0.2Hz/rtHz @ 10 Hz was yielded.

Therefore we can lock the green PLL by using an ordinary VCO loop after we roughly guide a beat note by using this kind of discriminator.

Thanks for the great entry!

In order to make this work for higher frequencies, I would add Hartmut's suggestion of a frequency dividing input stage.  If we divide the input down by 100, the overall range will be about 200MHz, and the noise will be about 20Hz/rtHz.  That might be good enough... but we can hope that the commercial device is lower noise!

With a 30mm PPKTP crystal the conversion efficiency from 1064nm to 532nm is expected to 3.7 %/W.

Therefore we will have a green beam of more than 20mW by putting 700mW NPRO.

Last a couple of weeks I performed a numerical simulation for calculating the conversion efficiency of PPKTP crystal which we will have.

Here I try to mention about just the result. The detail will be followed later as another entry.

The attached figure is a result of the calculation.

The horizontal axis is the waist of an input Gaussian beam, and the vertical axis is the conversion efficiency.

You can see three curves in the figure, this is because I want to double check my calculation by comparing  analytical solutions.

The curve named (A) is one of the simplest solution, which assumes that the incident beam is a cylindrical plane wave.

The other curve (B) is also analytic solution, but it assumes different condition; the power profile of incident beam is a Gaussian beam but propagates as a plane wave.

The last curve (C) is the result of my numerical simulation. In this calculation a focused Gaussian beam is injected into the crystal.

The numerical result seems to be reasonable because the shape and the number doesn't much differ from those analytical solutions.

Question:

Why does the small spot size for the case (A) have small efficiency as the others? I thought the efficiency goes diverged to infinity as the radius of the cylinder gets smaller.

Rana found that we had a frequency counter SR620 which might be helpful for lock acquisition of the green phase lock.

It has a response of 100MHz/V up to 350MHz which is wide range and good for our purpose. And it has a noise level of 200Hz/rtHz @ 10Hz which is 1000 times worse than that Matt made (see the entry).

The attached figure is the noise curve measured while I injected a signal of several 100kHz. In fact I made sure that the noise level doesn't depends on the frequency of an input signal.

The black curve represents the noise of the circuit Matt has made, the red curve represents that of SR620.

Good point. There is a trick  to avoid a divergence.

Actually the radius of the cylindrical wave is set to the spot size at the surface of the crystal instead of an actual beam waist. This is the idea Dmass told me before.

So that the radius is expressed by w=w₀(1+(L/2Z_R)²)^1/2, where w₀ is beam waist, L is the length of the crystal and Z_R is the rayleigh range.

In this case the radius can't go smaller than w₀/2 and the solution can not diverge to infinity.

Its a good measurement - you should adjust the input range of the 620 using the front panel 'scale' buttons to see how the noise compares to Matt's circuit when the range is reduced to 1 MHz. In any case, we would use it in the 350 MHz range mode. What about the noise of the frequency discriminator from MITEQ?

just a few infos on Silicon PDs I looked up.

If you want to go beyond the 100MHz achievable with the device I worked on,

the one thing to improve is the opamp, where Steve is trying to find OPA657.

This is a FET with 1.6GHz BWP, minimum stable gain of 7, and 4.8nV/rt(Hz) noise.

Should be ok with 750-1000 Ohm transimpedance.

The other thing you might want to change is the PD

(although it might be the 1cm PD with high bias is as fast as smaller ones with lower bias).

There are two types of other Si diodes at the 40m right now (~3mm):

-Rana and I found a Centronic OSD 15-5T in the old equipment

-Frank gave me a Hamamatsu S1223-01 on a Thorlabs pre-amp device (could be taken out).

The Centronic OSD 15-5T has up to 80pF with 12 V bias according to the datasheet.

The Hamamatsu S1223-01 is stated with 20pF only, but stated to have a max. frequency resp. of 20MHz ('-3db point').

I dont know what this means, as the corner freq. of 10pF into 50Ohm is still 160MHz.

In any case there are faster 3mm types to start with, as for example Hamamatsu S3399 (~ 90$),

which is stated to have the corner at 100MHz with 50 Ohm load.

For this type the stated capacity (20pF) looks consistent with ~100MHz corner into 50 Ohm.

So probably you can get higher BW with this one using much smaller load, as in transimpedance stage.

I made a simple PD test circuit which may allow to test PD response up to few 100MHz.

Its not for low noise, only for characterising PD response.

Here is the circuit:

The 2 capacitor values (for bypassing) are kind of arbitrary, just what I found around

(one medium, one small capacity). Could be improved by better RF types (e.g. Mica).

The PD type has no meaning. I put in the Centronic 15-T5 for a start.

The bias can be up to 20V for this diode.

The signal appears across R1. It is small, to make a large bandwidth.

R2 is just for slightly decoupling the signal from the following RF amplifier.

The wire into the RF amplifier is short (~cm). And the amplifier is supposed to have 50 Ohm

input impedance.

I use a mini circuits ZFL 500 here.

power supply for this is 15V.

I measured a jitter modulation caused by injection of a signal into laser PZTs.

The measurement has been done by putting a razor blade in the middle way of the beam path to cut the half of the beam spot, so that a change of intensity at a photodetector represents the spatial jitter of the beam.

However the transfer function looked almost the same as that of amplitude modulation which had been taken by Mott (see the entry).

This means the data is dominated by the amplitude modulation instead of the jitter. So I gave up evaluating the data of the jitter measurement.

The beams from the Innolight and Lightwave NPROs were both incident on a 1GHZ New Focus PD. Mott and I swept the temperature of the Lightwave and tracked the change in frequency of the beatnote between the two. The Innolight temperature was set to 39.61C although the actual temperature was reported to be 39.62C.

Freq. vs temperature is plotted below in the attached PDF. The slope is 2.8GHz/K.

The data is in the attached MATLAB file.

 Same thing for the Innolight Mephisto.

Not unexpected values with dn/dT around 11E-6 K^-1 and coefficient of thermal expansion = 8E-6 K^-1 and a laser resonator length of order 10cm.

Please put those numbers onto wiki somewhere at the green page or laser characterization page.

 I redid the PZT Phase Modulation measurement out to 5 MHz for both the Innolight and the Lightwave.  The previous measurement stopped at 2MHz, and we wanted to see if there were any sweet spots above 2MHz.  I also reduced the sweep bandwidth and increased the source amplitude at high frequency to reduce the noise (the Lighwave measurement, especially, was noise dominated above 1MHz).  I also plotted the ratio of PM/AM in rad/RIN, since this is the ultimate criterion on which we want to make a determination.

It looks like there is nothing extremely useful above 2MHz for either laser.  There are several candidates for the lightwave at about 140 kHz and again at about 1.4 MHz.  The most compelling peak, however, is in the innolight at 216 kHz, where the peak is about 2.3e5 rad/RIN.

Below about 30kHz, the loop suppresses the measurement, so one should focus on the region above there.

NOTE: This measurement is wrong and only remains for documentation purposes.

Koji asked me to take a profile of the output of the 1W NPRO that will be used for green locking. I used the razor-scan method, plotting the voltage output of a PD vs the position of the razor across the beam, both vertically and horizontally. This was done at 6 points along the beam path out of the laser box.

I determined the beam spot size at each point by doing a least-squares fit on the plots above in Matlab (using w as one of the fitting parameters) to the cumulative distribution functions (error functions) they should approximate.

I then did another least-squares fit, fitting the above "measured" beam profiles to the gaussian form for w vs z. Below is a summary.

It seems reasonable, though I know that M² < 1 is fishy, as it implies less divergence than ideal for that waist size. Also, like Koji feared, the waist is inside the box and thus the scan is almost entirely in the linear regime.

There is a clearly a difference in the divergence angle of the x and y beams - maybe 10-20%. Since the measurements are outside the Rayleigh range and approximately in the linear regime, the slope of the divergence in this plot should be inversely proportional to the waists - meaning the x- and y- waist sizes should differ by about 10-20%. You should check your fitting program for the waist.

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.