TL;DR: Have successfully measured the UGF of the AUX laser on my Red Pitaya! Attached is one of my data runs (pdf + txt file). 

---------------------------------------------------------------

• Figured out how to get a rudimentary coherence (use scipy.signal.coherence to get Cxy = abs(Pxy)**2/(Pxx*Pyy), then find what point is the closest to the frequency I'm inserting on that iteration of the swept sine and get the coherence closest to that). Not precisely the coherence at the frequency I'm inserting though, so not perfect... more of a lower bound of coherence.
• Figured out how to get the UGF from the data automatically (no error propagation yet... necessary next step)
• Put my red pitaya in the X-arm AUX laser control electronics (thank you to Anchal for help figuring out where to put it and locking the x-arm.) Counts dropped from 4500 to 1900 with the x-arm locked, so 58% mode matching. I lose lock at an amplitude >0.05 or so.
• Wrote a little script to take data and return a time-stamped text file with all the parameters saved and a time-stamped pdf of the TF magnitude, UGF, phase, and coherence, so should be easy to take more data next time!

----------------------------------------------------------------

• need to take more accurate coherence data
• need to propagate uncertainty on UGF (probably high...)
• take more data with higher coherence (the file attached doesn't have great coherence and even that was one of my better runs, will probably increase averaging since increasing amplitude was a problem)

Took the backup (snapshot) of /home/export as of Aug 12, 2022

controls@nodus> cd /cvs/cds/caltech/nodus_backup
controls@nodus> rsync -ah --progress --delete /home/export ./export_220812 >rsync.log&

As the last backup was just a month ago (July 8), rsync finished quickly (~2min).

[Yehonathan, JC]

Our first step in preparing for the Shutdown was to center all the OpLevs. Next is to prepare the Vacuum System for the shutdown.

[Yuta Koji]

(Report on Aug 12, 2022)

We went around the lab for the final check. Here are the additional notes.

• 1X9: The x-end frontend machine still had the AC power. The power strip to which the machine is connected was disconnected from the AC at the side of the rack. (Attachment 1)
• 1X8: The vacuum rack still supplied the AC to c1vac. This was turned off at the UPS. (Attachment 2)
• 1X6: VMI RFM hub still had the power. This was turned off at the rear switch. (Attachment 3)
• PSL: The PSL door was open (reported above). Closed. (Attachment 4)
• 1Y2: The LSC rack still had the DC power. The supplies were turned off at the KEPCO rack (the short rack). (Attachment 5)
  Note that the top-right supply for the +15V is not used. (The one in the empty slot got busted). We may need some attention to the left-most one in the second row. It indicated a negative current. Is this just the current meter problem or is the supply broken?
• Control room: The CAD WS was turned off.

I declare that now we are ready for the power outage.

All steps taken have been recorded here:
https://wiki-40m.ligo.caltech.edu/Complete_power_shutdown_2022_08

[Anchal, Paco, Tega]

Disk full issue:

c1vac was showing /var disk to be full. We moved all gunzipped backup logs to /home/controls/logBackUp. This emptied 36% of space on /var. Ideally, we need not log so much. Some solution needs to be found for reducing these log sizes or monitoring them for smart handling.

Pressure sensor malfunctioning:

We were unable to opel the PSL shuttter, due to the interlock with C1:Vac-P1a_pressure. We found that C1:Vac-P1a_pressure is not being written by serial_MKS937a service on c1vac. The issue was the the sensor itself has become bad and needs to be replaced. We believe that "L 0E-04" in the status (C1:Vac-P1a_status) message indicates a malfunctioning sensor.

Quick fix:

We removed writing of C1:Vac-P1a_pressure and C1:Vac-P1a_status from MKS937a and mvoed them to XGS600 which is using the sensor 1 from main volume. See this commit.

Now we are able to open PSL shutter. The sensor should be replaced ASAP and this commit can be reverted then.

- Disk Full: Just use the usual /etc/logrotate thing

- Vacuum gauge

I rather feel not replacing P1a. We used to have Ps and CCs as they didn't cover the entire pressure range. However, this new FRG (=Full Range Gauge) does cover from 1atm to 4nTorr.

Why don't we have a couple of FRG spares, instead?

Questions to Tega: How many FRGs can our XGS-600 controller handle?

Juan and I built an analog setup to measure some transfer functions of the MOS suspension. The setup is blocking the lab way around the PD test bench.
Excuse us for the inconvenience. It will be removed/cleared by the end of the week.

FPMI related
- Better suspension damping HIGH
 - Investigate ITMX input matrix diagonalization (40m/16931)
 - Output matrix diagonalization
 * FPMI lock is not stable, only lasts a few minutes for so. MICH fringe is too fast; 5-10 fringes/sec in the evening.
- Noise budget HIGH
 - Calibrate error signals (actually already done with sensing matrix measurement 40m/17069)
 - Make a sensitivity curve using error and feedback signals (actuator calibration 40m/16978)
 * See if optical gain and actuation efficiency makes sense. REFL55 error signal amplitude is sensitive to cable connections.
- FPMI locking
 - Use CARM/DARM filters, not XARM/YARM filters
 - Remove FM4 belly
 - Automate lock acquisition procedure
- Initial alignment scheme
 - Investigate which suspension drifts much
 - Scheme compatible with BHD alignment
 * These days, we have to align almost from scratch every morning. Empirically, TT2 seems to recover LO alignment and PR2/3 seems to recover Yarm alignment (40m/17056). Xarm seems to be stable.
- ALS
 - Install alignment PZTs for Yarm
 - Restore ALS CARM and DARM
 * Green seems to be useful also for initial alignment of IR to see if arms drifted or not (40m/17056).
- ASS
 - Suspension output matrix diagonalization to minimize pitch-yaw coupling (current output matrix is pitch-yaw coupled 40m/16915)
 - Balance ITM and ETM actuation first so that ASS loops will be understandable (40m/17014)
- Suspension calibrations
 - Calibrate oplevs
 - Calibrate SUSPOS/PIT/YAW/SIDE signals (40m/16898)
 * We need better understanding of suspension motions. Also good for A2L noise budgeting.
- CARM servo with Common Mode Board
 - Do it with single arm first

BHD related
- Better suspension damping HIGH
 - Invesitage LO2 input matrix diagonalization (40m/16931)
 - Output matrix diagonalization (almost all new suspensions 40m/17073)
 * BHD fringe speed is too fast (~100 fringes/sec?), LO phase locking saturates (40m/17037).
- LO phase locking
 - With better suspensions
 - Measure open loop transfer function
 - Try dither lock with dithering LO or AS with MICH offset (single modulation)
 - Modify c1hpc/c1lsc so that it can modulate BS and do double demodulation, and try double demodulation
- Noise Budget HIGH
 - Calibrate MICH error signal and AS-LO fringe
 - Calibrate LO1, LO2, AS1, AS4 actuation using ITM single bounce - LO fringe
 - Check BHD DCPD signal chain (DCPD making negative output when fringes are too fast; 40m/17067)
 - Make a sensitivity curve using error and feedback signals
- AS-LO mode-matching 
 - Model what could be causing funny LO shape
 - Model if having low mode-matching is bad or not
 * Measured mode-matching of 56% sounds too low to explain with errors in mode-matching telescope (40m/16859, 40m/17067).

IMC related
- WFS loops too fast (40m/17061)
- Noise Budget
- Investigate MC3 damping (40m/17073)
- MC2 length control path

- Disk full

I updated the configuration file '/etc/logrotate.d/rsyslog' to set a file sise limit of 50M on 'syslog' and 'daemon.log' since these are the two log files that capture caget & caput terminal outputs. I also reduce the number of backup files to 2.

- Vacuum gauge

The XGS-600 can handle 6 FRGs and we currently have 5 of them connected. Yes, having a spare would be good. I'll see about placing an order for these then.

TL;DR: Got the x-arm aux laser locked again and took more data - my fit on my transfer functions need improvement and my new method for finding coherence doesn't work so I went back to the first way! See attached file for an example of data runs with poor fits. First one has the questionable coherence data, second one has more logical coherence. (ignore the dashed lines.)

------------------------------------------------------------------------------------

• The aux laser on the x-arm was still off after the power shutdown, so Paco and I turned it back on, and realigned the oplev of the ETMX - initial position was P = -0.0420, Y = -5.5391.
• Locked the x-arm and took another few runs - was calculating coherence by I/Q demodulation of the buffers and then recombining the I/Q factors and then taking scipy.signal.coherence(), but for some reason this was giving me coherence values exclusively above 0.99, which seemed suspicious. When I calculated it the way I had before, by just taking s.s.coherence() of the buffers, I got a coherence around 1 except for in noisy areas of the data where it dropped more significantly, and seemed to be more correlated to the data. So I'll go back to using that way.
• I also think my fits are not great - my standard error of the fits (calculated using the coherence as weight, see Table 9.6 of Random Data by Piersol and Bendat for the formula I'm using) are enormous. Now that I have a good idea that the UGF is between 1 - 15 kHz, I'm going to restrict my frequency band and try to fit just around where the UGF would be. 

--------------------------------------------------------------------------------

To do:

• Reduce frequency band and take more data
• Get fit with better standard error, use that error to calculate the uncertainty in the UGF!

TL;DR: When the laser has good lock, the OLTF moves up and the UGF moves over!

-----------------------------------------------------------

Figured out with Paco yesterday that when the laser is locked but kind of weakly (mirrors on the optical table sliiightly out of alignment, for example), we would get a UGF around 5 kHz, but when we had a very strong lock (adjusting the mirrors until the spot was brightest) we would get a UGF around 13-17 kHz. Attached are some plots of us going back and forth (you can kind of tell from the coherence/error that the one with the lower UGF is more weakly locked, too). Error on the plots is propagated using the coherence data (see Bendat and Piersol, Random Data, Table 9.6 for the formula). 

-------------------------------------------------------------

Want to take data next week to quantitatively compare optical gain to UGF!

In the last two days Steve and I took some optics away from the both ETM end table.

This is because we need an enough space to set up the green locking stuff into the end table, and also need to know how much space is available.

Optics we took away are : Alberto's RF stuff, fiber stuff and some optics obviously not in used.

The picture taken after the removing is attached. Attachment1:ETMX, Attachment2:ETMY

And the pictures taken before the removing are on the wiki, so you can check how they are changed.

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

The PD Kiwamu removed from the Y table was TRY, which we still need.

My bad if he took that. By mistake I told him that was the one I installed on the table for the length measurement and we didn't need it anymore.

I'm going to ask Kiwamu if he can kindly put it back.

 I am going to put the PD back to the Y end table in this afternoon.

I put the TRY_PD back to the end table and aligned it. Now it seems to be working well.

Koji and kiwamu

The existing optics on the ETMX/ETMY end table were rearranged in this morning.

The main things we have done are -

1. relocation of the optical levers for ETMs ( as mentioned in koji's entry )

This relocation can make a space so that we can setup the green locking stuffs.

The optical path of the green locking is planed to start from the right top corner on the table, therefore we had to relocate the oplevs toward the center of the table.

2. relocation of the lens just before the tube

Because we are going to shoot the green beam into the arm cavity, we don't want to have any undesired lenses before the cavity.

For this reason we changed the position of the lens, it was standing just in front of the tube, now it's standing on the left side of the big mirror standing center top.

Since we did not find a significant change in its the spot size of the transmitted light, we did not change the position of all the TRANS_MON_PDs and its mirrors. And they are now well aligned.

Attachment1: ETMX end table

Attachment2: ETMY end table

We are leaving the PLL as it is locked in order to see the long term stability. And we will check the results in early morning of tomorrow.

DO NOT disturb our PLL !!

(what we did)

After Mott left, Matt and I started to put feedback signals to the temperature control of NPRO.

During doing some trials Matt found that NPRO temperature control input has an input resistance of 10kOhm.

Then we put a flat filter ( just a voltage divider made by a resistor of ~300kOhm and the input impedance ) with a gain of 0.03 for the temperature control to inject a relatively small signal, and we could get the lock with the pzt feedback and it.

In addition, to obtain more stable lock we then also tried to put an integration filter which can have more gain below 0.5Hz.

After some iterations we finally made a right filter which is shown in the attached picture and succeeded in obtaining stable lock.

Now some pedestals, mirrors and lenses are left on the PSL table, since we are on the middle way to construct a PLL setup which employs two NPROs instead of use of PSL laser.

So Please Don't steal any of them.

Modified one of the PD assemblies carrying a large SI-Diode (~10mm diameter).

Removed elements used for resonant operation and changed PD readout to transimpedance

configuration. The opamp is a CLC409 with 240 Ohm feedback (i.e. transimpedance) resistor.

To prevent noise peaking at very high frequencies and get some decoupling of the PD,

I added a small series resistor in line with the PD and the inverting opamp input.

It was chosen as 13 Ohm, and still allows for operation up to ~100MHz.

Perhaps it could be smaller, but much more bandwith seems not possible with this opamp anyway.

Changes are marked in the schematic, and I list affected components here.

(Numbers refer to version 'PD327.SCH' from 30-April-1997):

-removed L4

-connected L3 (now open pad) via 100 Ohm to RF opamp output. This restores the DC sognal output.

-removed c17

-connected pin 3 of opamp via 25 Ohm to GND

-connected kathode of PD via 13 Ohm to pin 2 of opamp

-removed L6, C26, L5, C18, and C27

-shorted C27 pad to get signal to the RF output

Measured the optical TF with the test laser setup.

(Note that this is at 1064nm, although the PD is meant to work with green light at 532nm!)

Essentially it looks usable out to 100MHz, where the gain dropped only by about

6dB compared to 10MHz.

Beyond 100MHz the TF falls pretty steeply then, probably dominated by the opamp.

The maximal bias used is -150V.

If the bias is 'reduced' from -150V to -50V, the response goes down by 4dB at 10MHz and

by 9dB at 100MHz.

 The average output was 30mV at the RF output, corresponding to 60mV at the opamp output (50Ohm divider chain).

With 240 Ohm transimpedance this yields 250µA photo-current used for these transfer functions.

 Can I please get the network analyzer back?

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