Here the technique of the impedance matching for the triple resonant circuit are explained.

In our case, the transformer should be chosen so that the impedance of the resonance at 55MHz is matched.

We are going to use the transformer to step up the voltage applied onto the EOM.

To obtain the maximum step-up-gain, it is better to think about the behavior of the transformer.

When using the transformer there are two different cases practically. And each case requires different optimization technique. This is the key point.

By considering these two cases, we can finally select the most appropriate transformer and obtain the maximum gain.

( how to maximize the gain ?)

Let us consider about the transformer. The gain of the circuit by using the transformer is represented by

         (1)

Where ZL is the impedance of the load (i.e. impedance of the circuit without the transformer ) and n is the turn ratio.

It is apparent that G is the function of two parameters, ZL and n.  This leads to two different solutions for maximizing the gain practically. 

  - case.1 : The turn ratio n is fixed.

In this case, the tunable parameter is the impedance ZL.  The gain as a function of ZL is shown in the left figure above.

In order to maximize the gain, Z must be as high as possible.  The gain G get close to 2n when the impedance ZL goes to infinity.

There also is another important thing; If the impedance ZL is bigger than the matched impedance (i.e. ZL = 50 * n^2 ), the gain can get higher than n.

  - case.2 : The impedance ZL is fixed.

In contrast to case1, once the impedance ZL is fixed, the tunable parameter is n. The gain as a function of n is shown in the right figure above.

In this case the impedance matched condition is the best solution, where ZL=50*n^2. ( indicated as red arrow in the figure )

The gain can not go higher than n somehow. This is clearly different from case1.
 

( Application to the triple resonant circuit )

Here we can define the goal as "all three resonances have gain of more than n, while n is set to be as high as possible"

According to consideration of case1, if each resonance has an impedance of greater than 50*n^2 (matched condition) it looks fine, but not enough in fact.

For example if we choose n=2, it corresponds to the matched impedance of 50*n^2 = 200 Ohm. Typically every three resonance has several kOhm which is clearly bigger than the matched impedance successfully.

However no matter how big impedance we try to make,  the gains can not be greater than G=2n=4 for all the three resonance. This is ridiculous.

What we have to do is to choose n so that it matches the impedance of the resonance which has the smallest impedance.

In our case, usually the resonance at 55MHz tends to have the smallest impedance in those three. According to this if we choose n correctly, the other two is mismatched.

However they can still have the gain of more than n, because their impedance is bigger than the matching impedance. This can be easily understand by recalling the case1.

(expected optimum gain of designed circuit)

 By using the equation (1), the expected gain of the triple resonant circuit including the losses is calculated. The parameters can be found in last entry.

The turn ratio is set as n=11, which matches the impedance of the resonance at 55MHz. Therefore 55MHz has the gain of 11.

The gain at 11MHz is bigger than n=11, this corresponds to the case1. Thus the impedance at 11MHz can go close to gain of 22, if we can make the impedance much big.

I have made a prototype circuit of the triple resonant EOM.

The attached is the measured optical response of the system.

The measured gains at the resonances are 8.6, 0.6 and 7.7 for 11MHz, 29.5MHz and 55MHz respectively.

I successfully got nice peaks at 11MHz and 55MHz. In addition resultant optical response is well matched with the predicted curve from the measured impedance.

However there is a difference from calculated response (see past entry) (i.e. more gains were expected)

Especially for the resonance of 29.5MHz, it was calculated to have gain of 10, however it's now 0.6. Therefore there must a big loss electrically around 29.5MHz.

I am going to re-analyze the impedance and model the performance in order to see what is going on.

The commercial resonant EOM of New Focus has the modulation efficiency of 50-150mrad/Vrms. ( This number is only true for those EOM made from KTP such as model4063 and model4463 )

Our triple-resonant EOM (made from KTP as well) has a 90mrad/Vrms and 80mrad/Vrms at the reosonances of 11MHz and 55MHz respectively.

Therefore our EOM is as good as those of company-made so that we can establish a new EOM company

I have measured the linearity of our triple resonant EOM (i.e. modulation depth versus applied voltage)

The attached figure is the measured modulation depth as a function of the applied voltage.

The linear behavior is shown below 4Vrms, this is good.

Then it is  slowly saturated as the applied voltage goes up above 4Vrms.

However for the resonance of 29.5MHz, it is difficult to measure below 7Vrms because of the small modulation depth.

 - - - - result from fitting - - -

11MHz: 91mrad/Vrms+2.0mrad

29.5MHz: 4.6mrad/Vrms+6.2mrad

55MHz:82mrad/Vrms+1.0mrad

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

 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.

Jenne and kiwamu

We have glued the dumbbells to the magnets that will be used for the ITMs

We made two sets of glued pair of the dumbbell and the magnet ( one set means 6 pairs of the dumbbell and the magnet. Therefore in total we got 12 pairs. )

You can see the detailed procedure we did on the LIGO document E990196.

Actually we performed one different thing from the documented procedure;

we made scratch lines on the surface of the both dumbbells and magnets by a razor blade.

According to Steve and Bod, these scratch make the strength of the glues stronger.

Now the dumbbell-magnet pairs are on the flow bench in the clean room, and supported by a fixture Betsy sent us.

- -  notes

On the bench the left set is composed by magnets of 244 +/- 3 Gauss and the right set is 255 +/- 3 Gauss.

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

The vent has been finished.

Now the pressure inside the chamber is 760 torr, and it's getting equilibrium with the atmospheric pressure.

Therefore we are ready and can open the door of the chamber tomorrow.

In order to block stray beams, I have put some beam dumps and razor blades on the PSL  table.

There were three undesired spots in total. I found two spots on the south side door of the PSL room, close to Mach-Zehnder.

Another spots was on the middle of the north door. Now they all are blocked successfully.

In this LVC meeting I discussed about triple resonant EOMs with Volker who was a main person of development of triple resonant EOMs at University of Florida.

Actually his EOM had been already installed at the sites. But the technique to make a triple resonance is different from ours.

They applied three electrodes onto a crystal instead of one as our EOM, and put three different frequencies on each electrode.

For our EOM, we put three frequencies on one electrode. You can see the difference in the attached figure. The left figure represents our EOM and the right is Volker's.

Then the question is; which can achieve better modulation efficiency ?

Volker and I talked about it and maybe found an answer,

 We believe our EOM can be potentially better because we use full length of the EO crystal.

This is based on the fact that the modulation depth is proportional to the length where a voltage is applied onto.

The people in University of Florida just used one of three separated parts of the crystal for each frequency.

Yes, I found it.

Their advantage is that their circuit is isolated at DC because of the input capacitor.

And it is interesting that the performance of the circuit in terms of gain is supposed to be roughly the same as our transformer configuration.

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.

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.

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.

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.

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)"

[Koji, Kiwamu]

The Mach-Zehnder on the PSL table was removed.

A path for 166 MHz modulation in the Mach-Zehnder (MZ) was completely removed, the setup for another path remains the same as before.

Also the photo detector and the CCD for the PMC transmittion were moved to behind the PZT mirror of PMC. 

Before removing them, we put an aperture in front of the PD for MC REFL so that we can recover the alignment toward MC by using the aperture.

After the removal we tried to re-align the EOM which imposes the sideband of 29MHz for MC.

We eventually got good alignment of 97% transmissivity at the EOM ( the power of the incident beam is 1.193W and trans was 1.160W )

And then we aligned the beam going to MC by guiding the reflected beam to the aperture we put. This was done by using the steering mirrors on the periscope on the corner of the PSL table.

Now MC got locked and is successfully resonating with TEM00.

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.

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..

 I updated the photo of ETMY end table on the wiki.

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

Yesterday Steve and I revived two legs to mount some optical breadboards outside of the end table.

These legs had been used as oplev's mounts many years ago, but now they are served for 40m upgrading. These are really nice.

By putting them on the side of the end table, a mirror mounted on the top of the leg can reflect the beam outside of the end table.

Once we pick off the green beam from the end table to its outside, the green beam can propagate through the 40m walkway along the Y-arm.

So that we can measure the beam profile as it propagates.

These legs are also going to be used during mode matching of the vacuum optics.

 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. 

In this morning I found daqawg didn't work.

After looking for the cause, I found one of the vme racks mounted on 1Y6 doesn't work correctly.

It looks like the vme rack mounting c0daqawg could not supply any power to the frontends.

Now Steve and I are trying to look for a spare for it.

Notes on May 25th

 Don't do the following things !! This causes bad cross-talking of CPUs mounted on the crate.

I moved c0daqawg and c1pem1 from 1Y6 vme crate to 1Y7 crate due to the bad power supply.

Another problem: c0dcu1 doesn't come back to the network. 

After moving them, I tried to get back them into the RFM network. However  c0dcu1 never came back, it still indicates red in C0DAQ_DETAIL.adl screen.

Alberto and I did even "nuclear option" (as instructed), but no luck.

I found the elog got down around 7:30 am in this morning.

So I restarted it by running the script: "start-elog-nodus" as instructed on the wiki.

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

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 got a VME crate from Peter's lab. It is already installed in 1Y6 instead of the old broken one.

I checked its power supply, and it looked fine. It successfully supplies +5, +12 and -12 V. And then I put c0daqawg and c1pem1 back from 1Y7.

Now I am trying to reboot all the front end computers with Peter's VME crate. A picture of the VME crate will be updated later.

 [Alex, Joe, Kiwamu]

Eventually all the front end computers came back !! 

There were two problems.

(1): C0DCU1 didn't want to come back to the network. After we did several things it turned the ADC board for C0DCU1 didn't work correctly.

(2): C1PEM1 and C0DAQAWG were cross-talking via the back panel of the crate.

(what we did)

* installed a VME crate with single back panel to 1Y6 and mounted C1PEM1 and C0DAQAWG on it. However it turned out this configuration was bad because the two CPUs could cross-talk via the back panel.

* removed the VME crate and then installed another VME crate which has two back panels so that we can electrically separate C1PEM1 and C0DAQAWG.  After this work, C0DAQAWG started working successfully.

 * rebooted all the front ends, fb40m and c1dcuepics.

 * reset the RFM bypath. But these things didn't bring C0DCU1 back.

 * telnet to C0DCU1 and ran "./startup.cmd" manually. In fact "./startup.cmd" should automatically be called when it boots.

 * saw the error messages from "./startup.cmd" and found it failed when initialization of the ADC board. It saids "Init Failure !! could not find ICS"

*  went to 1Y7 rack and checked the ADC. We found C0DCU1 had two ADC boards, one of two was not in used.

* disconnected all two ADCs and put back one which had not been in used. At the same time we changed the switching address of this ADC to have the same address as the other ADC. 

* powered off/on 1Y7 rack. Finally C0DCU1 got back.

* burtrestored the epics to the last Friday, May 21st 6:07am

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.

 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.

 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.

I found the dataviewer didn't work only on Allegra. This thing sometimes happened as described in the past entry.

I rebooted Allegra, then the problem was fixed.

  [Alberto, Kiwamu]

The MC alignment is getting better by steering the axis of the incident beam into the MC.

We found the beam spot on MC1 and MC3 were quite off-centered in the beginning of today's work. It had the coil gain ratio of 0.6:1.4 after running the A2L script.

In order to let the beam hit the center of the MC1 and MC3, we steered the bottom mirror attached on the periscope on the PSL table to the yaw direction.

And then we got better numbers for the coil gain ratio (see the numbers listed at the bottom).

For the pitch direction, there still are some rooms to improve because we didn't do anything with the pitch. It is going to be improved tomorrow or later.

Here are the amounts of off-centering on MC1 and MC3 after steering the axis. 

 C1:SUS- MC1_ULPIT_GAIN =  0.900445

C1:SUS-MC1_ULYAW_GAIN =  0.981212

C1:SUS-MC3_ULPIT_GAIN =  0.86398

C1:SUS-MC3_ULYAW_GAIN =   1.03221

[Alberto, Kiwamu]

0. have a coffee and then dress up the clean coat.

1. level the MC table

2. lock and align MC 

3. run A2L script to see how much off-centering of the spots

4. steer the periscope mirror <--- We are here

5. move the pick off mirror which is used for monitoring of MCT CCD

6. check the leveling and move some weights if it's necessary

7. shut down

I corrected the sketch of the new IOO. 

The sketch in the last entry was also replaced by the new one. 

http://nodus.ligo.caltech.edu:8080/40m/3029 

I checked the measured data of the mode profile which was taken on the last Tuesday.

For the vertical profile,

the plot shows a good agreement between the expected radius which is computed from the past measurement, and that measured on the last Tuesday.

However for the horizontal profile,

it looks like being overestimated. This disagreement may come from the interference imposed on the Gaussian spot as we've been worried. 

So I guess we should solve this issue before restarting this mode matching work.

 - The next step we should do are;

checking the effect of MMT1 on the shape of the beam spot by using a spare of MMT1

NOTE:

The expected curve in the attached figure were computed by using the fitted parameter listed on the entry 2984 .

In the calculation the MMT1 is placed at 1911mm away from MC3 as we measured.

And the focal length of MMT1 is set to be f=-2500mm.

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.

We decided not to care about the mode after MMT1.

So far Koji, Alberto and I have measured the beam profile after MMT1,

but we are going to stop this measurement and go ahead to the next step i.e. putting MMT2

There are two reasons why we don't care about the profile after MMT1:

     (1) it is difficult to fit the measured data

     (2) The position of MMT1 is not critical for the mode matching to the IFO.

The details are below.

(1) difficulty in fitting the data

The precision of each measured point looked good enough, but the fitting result varies every measurement.

The below shows the data and their fitted curves. 

In the label, "h" and "v" stand for "horizontal" and "vertical" respectively.

The solid curves represent the fitting results, varying by each measurement.

In order to increase the reliability of the fitting, we had to take some more data at further distance.

But we couldn't do it, because the beam radius already becomes 3 mm even at 2 m away from MMT1 and at this point it starts to be clipped on the aperture of the beam scan.

Thus it is difficult to increase the reliability of the fitting. 

Once if we put MMT2 the beam should have a long Rayleigh range, it means we can measure the profile at further distance, and the fitting must be more reliable.

(2) positioning of MMTs

Actually the position of MMT1 is not so critical for the mode matching. 

The most important point is the separation distance of MMT1 and MMT2.

As written in Jenne's document, if we slide the positions of MMT1 and MMT2 while keeping their appropriate separation distance, the mode match overlap still stays above 99%

This is because the beam coming from MC3 is almost collimated (ZR~8m), so the position of MMTs doesn't so matter. 

To confirm it for the real case, I also computed the mode overlap while sliding the position of MMTs by using real data. The below is the computed result.

It is computed by using the measured profile after MC3 (see the past entry).

The overlap still stay above 99% when the distance from MC to MMT is between 1300 and 3000mm.

This result suggests to us putting MMT1 as we like.  

We obtained a good mode match overlap of 99.0% for the new IOO.

And if we move the position of MMT2 by another 10 cm away from MMT1, we will have 99.6% overlap. 

Yesterday Jenne and I put MMT2 on the OMC table. MMT2 was carefully put by measuring the distance between MMT1 and MMT2.

The position looked almost the same as that drawn on the CAD design.

After putting it we measured the profile after the MMT.

The attached figure shows the computed mode overlap according to the fitting result while changing the position of MMT2 in a program code.

The x-axis is the position of MMT2, the current position is set to be zero. The y-axis is the mode match overlap.

Right now the overlap is 99.0% successfully, but this is not an optimum point because the maximum overlap can be achieved at x=100 mm in the plot.

It means we can have 99.6% by moving the position of MMT2 by another 10 cm. This corresponds to an expansion of the MMT length.

If this expansion is difficult due to the narrow available space in the chamber, maybe staying of MMT2 at the current position is fine.

           [Joe, Kiwamu]

The better mode overlap of 99.3% was achieved by moving MMT2 by ~5 cm 

In the past measurement (elog entry #3077) we already succeeded in getting 99.0% mode overlap.

But according to the calculation there still was a room to improve it by moving MMT2 by 10 cm.

Today we moved MMT2 by ~5 cm which is a reasonable amount we could move because of the narrow space in the chamber.

Eventually it successfully got the better mode overlap.

So we eventually finished mode matching of the new IOOs 

(details)

     Actually moving of MMT2 was done by flipping the mount without moving the pedestal post as Koji suggested. 

At the same time we also flipped the mirror itself (MMT2) so that the curved surface is correctly facing toward the incident beam.

By this trick, we could move the position of MMT2 without losing precious available space for the other optics in the OMC chamber.

     The attached plot shows the result of the mode measurement after the MMT.

During the fitting I neglected the data at x=27 m and 37 m because the beam at those points were almost clipped by the aperture of the beam scan.

- - Here are the fitting results

w0_v             = 2.81183       +/- 7.793e-03  mm  (0.2772%)

w0_h             = 2.9089        +/- 1.998e-02  mm  (0.687%)

z_v             = 5.35487        +/- 0.2244     m   (4.19%)

z_h             = 1.95931        +/- 0.4151     m   (21.18%)

All the distances are calibrated from the position of MMT2 i.e. the position of MMT2 is set to be zero.

        In order to confirm our results, by using the parameters listed above I performed the same calculation of mode overlaps as that posted on the last entry (see here)

The result is shown in Attachement 2. There is an optimum point at x=62mm.

This value is consistent with what we did because we moved MMT2 by ~5 cm instead of 10 cm. 

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".

I've just stolen a GPIB controller, an yellow small box, from the spectrum analyzer HP8591E.

The controller is going to be used for driving the old spectrum analyzer HP3563A for a while.

Gopal and I will be developing and testing a GPIB program code for HP3563A via the controller.

Once after we get a new GPIB controller, it will be back to the original place, i.e. HP8591E.

--- GPIB controller ----

name: teofila

address: 131.215.113.106

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.