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ID Date Authorup Type Category Subject
  2064   Wed Oct 7 11:18:40 2009 kiwamuSummaryElectronicsracks of electronics

 

I took the pictures of all racks of electronics yesterday, and then uploaded these pictures on the wiki.

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

You can see them by clicking "pictures" in the wiki page.

 

  2111   Sun Oct 18 22:05:40 2009 kiwamuUpdateLSCLSC timing issue

Today I made a measurement to research the LSC timitng issue as mentioned on Oct.16th.

*method

I put the triangular-wave into the OMC side (OMC-LSC_DRIVER_EXT) by AWG,

then looked at the transferred same signal at the LSC side (LSC_DARM_IN1) by using tdsdata.

I have compared these two signals in time domain to check whether they are the same or not.

In the ideal case it is expected that they are exactly the same.

 

*preliminary result

The measured data are shown in attached fig.1 and 2.

In the fig.1 it looks like they are the same signal.

However in fig.2 which is just magnified plot of fig.1, it shows a time-delay apparently between them.

The delay time is roughly ~50 micro sec.

The surprising is that the LSC signal is going beyond the OMC signal, although the OMC signal drives the LSC !!

We can say it is "negative delay"...

Anyway we can guess that the time stamp or something is wrong.

 

*next plan

Tomorrow I'm going to measure the transfer-function between them to see the delay more clearly.

( And I would like to fix the delay. )

Attachment 1: rough.png
rough.png
Attachment 2: detail.png
detail.png
  2114   Mon Oct 19 10:00:52 2009 kiwamuUpdateLSCRE: LSC timing issue

Of course I know there is a downconversion in OMC signal from 32k to 16k.

But I was just wondering if the delay comes from only downconversion.

And I can not find any significant noise in both signals because I use the triangular, which cause the higer harmonics and can hide the timing noise in frequency domain.

So I'm going to make the same measurement by using sinusoidal instead of triangular, then can see the noise in frequency domain.

 

Quote:

You yourself told me that tdsdata uses some downconversion from 32k to 16k!

So, how does the downconversion appears in the measurement?
How does the difference of the sampling rate appears in the measurement?
If you like to understand the delay, you have to dig into the downconversion
issue until you get the EXACT mechanism including the filter coefficients.

AND, is the transfer function the matter now?

As far as the LSC and OMC have some firm relationship, whichever this is phase delay or advance or any kind of filering,
this will not introduce any noise. If so, this is just OK.

In my understanding, the additional noise caused by the clock jitter is the essential problem.
So, did you observe any noise from the data?

Quote:

*preliminary result

The measured data are shown in attached fig.1 and 2.

In the fig.1 it looks like they are the same signal.

However in fig.2 which is just magnified plot of fig.1, it shows a time-delay apparently between them.

The delay time is roughly ~50 micro sec.

The surprising is that the LSC signal is going beyond the OMC signal, although the OMC signal drives the LSC !!

We can say it is "negative delay"...

Anyway we can guess that the time stamp or something is wrong.

 

*next plan

Tomorrow I'm going to measure the transfer-function between them to see the delay more clearly.

( And I would like to fix the delay. )

 

 

  2122   Mon Oct 19 23:14:32 2009 kiwamuUpdateLSCLSC timing issue

I measured the noise spectrum of LSC_DARM_IN1 and OMC-LSC_DRIVE_EXC by using DTT,

while injecting the sin-wave into the OMC-LSC_DRIVE by AWG.

The attached are the results.

No significant differences appears between OMC and LSC in this measurement.

It means, in this measurement we can not figure out any timing noise which might be in LSC-clock.

In addition there are the noise floor, whose level does not change in each 3-figures. The level is about ~4*10^{-8} count/sqrt[Hz]

(The source of the noise floor is still under research.)

Attachment 1: SPE20Hz.png
SPE20Hz.png
Attachment 2: SPE200Hz.png
SPE200Hz.png
Attachment 3: SPE2kHz.png
SPE2kHz.png
  2145   Mon Oct 26 18:49:18 2009 kiwamuUpdateLSCOMC-LSC timing issue

According to my measurements I conclude that LSC-signal is retarded from OMC-signal with the constant retarded time of 92usec.
It means there are no timing jitter between them. Only a constant time-delay exists.

(Timing jitter)
Let's begin with basics.
If you measure the same signal at OMC-side and LSC-side, they can have some time delay between them. It can be described as followers.

exp1.png
where tau_0 is the time delay. If the tau_0 is not constant, it causes a noise of the timing jitter.

(method)
I have injected the sine-wave with 200.03Hz into the OMC-LSC_DRIVE_EXC. Then by using get_data, I measured the signal at 'OMC-LSC_DRIVE_OUT' and 'LSC-DARM_ERR' where the exciting signal comes out.
In the ideal case the two signals are completely identical.
In order to find the delay, I calculated the difference in these signals based on the method described by Waldman. The method uses the following expression.
exp2.png
Here the tau_s is the artificial delay, which can be adjusted in the off line data.
By shifting tau_s we can easily find the minimal point of the RMS, and at this point we can get tau_0=tau_s.
This is the principle of the method to measure the delay.  In my measurement I put T=1sec. and make the calculation every 1sec. in 1 min.


(results)
Attachment is the obtained results. The above shows the minimum RMS sampled every 1sec. and the below shows the delay in terms of number of shifts.
1 shift corresponds to Ts (=1/32kHz).  All of the data are matched with 3 times shift, and all of the minimum RMS are completely zero.
Therefore I can conclude that LSC-signal is retarded from OMC-signal with constant retarded times of 3*Ts exactly, and no timing jitter has been found.
 

Attachment 3: OMC_LSC60sec.png
OMC_LSC60sec.png
  2146   Mon Oct 26 19:12:50 2009 kiwamuUpdateLSCdiagnostic script for LSC timing

The diagnostic script I've written is available in the 'caltech/users/kiwamu/work/20091026_OMC-LSC-diag/src'.

To run the script, you can just execute 'run_OMC_LSC.sh' or just call the m-file ' OMC_LSC_timinig.m'  from matlab.

 

NOTES:

The script destructs the lock of DARM and OMC, be careful if you are working with IFO.

  2153   Tue Oct 27 19:37:03 2009 kiwamuUpdateLSCcron job to diagnose LSC-timing

I set a cron job on allegra.martian to run the diagnostic script every weekend.

I think this routine can be helpful to know how the trend of timing-shift goes

The cron runs the script on every Sunday 5:01AM and diagnostics will take about 5 min.

 

! Important:

During the running of the script, OMC and DARM can not be locked.

If you want to lock OMC and DARM in the early morning of weekend, just log in allegra and then comment out the command by using 'crontab -e'

 

 

  2167   Mon Nov 2 10:56:09 2009 kiwamuUpdateLSCcron job works succesfully & no timing jitter

As I wrote on Oct.27th, the cron job works every Sunday.

I found it worked well on the last Sunday (Nov.1st).

And I can not find any timing jitter in the data, its delay still stay 3*Ts.

  2169   Mon Nov 2 13:34:36 2009 kiwamuConfigurationPSLremoved multiply resonant EOM

I removed the multiply resonant EOM that has been set by a SURF student from PSL table.

I will use it for checking the resonant circuit.

  2179   Thu Nov 5 12:34:26 2009 kiwamuUpdateComputerselog rebooted

I found elog got crashed. I rebooted the elog daemon just 10minutes before.

  2244   Wed Nov 11 20:57:06 2009 kiwamuUpdateElectronicsMulti-resonant EOM --- LC tank circuit ---

I have been working about multi-resonant EOM since last week.

In order to characterize the behavior of the each components, I have made a simple LC tank circuit.

You can see the picture of the circuit below.

DSCN0160.JPG

Before constructing the circuit, I made an "ideal" calculation of the transfer function without any assumptions by my hand and pen.

Most difficult part in the calculation is the dealing with a transformer analytically. Eventually I found how to deal with it in the analytical calculation.

The comparison of the calculated and measured transfer function is attached.

 It shows the resonant frequency of ~50MHz as I expected. Those are nicely matched below 50MHz !!

For the next step, I will make the model of the circuit with stray capacitors, lead inductors, ... by changing the inductance or something. 

 

Attachment 2: LCtank_complete.png
LCtank_complete.png
  2262   Fri Nov 13 03:38:47 2009 kiwamuUpdateElectronicsmulti-resonant EOM --- impedance of LC tank circuit ----

I have measured the impedance of the LC tank circuit which I referred on my last entry.

The configuration of the circuit is exactly the same as that time.

In order to observe the impedance, by using Koji's technique I injected a RF signal into the output of the resonant circuit.

In addition I left the input opened, therefore the measured impedance does not include the effect of the transformer.

 

- - - - - - - - - - - - results

The measured impedance is attached below; "LCtank_impedance.png"

The peak around 50MHz is the main resonance and it has impedance of ~1500 [Ohm], which should go to infinity in the ideal case (no losses).

In fact the impedance looked from the input of the circuit gets reduced by 1/n^2, where "n" is the turn ratio of the transformer.

By putting the n=4, the input impedance of the circuit should be 93 [Ohm]. This is a moderate value we can easily perform impedance-matching by some technique.

I also fitted the data with a standard model of equivalent circuit (see attachment 2).

In the figure.2 red component and red letter represents the design. All the other black stuff are parasites.

But right now I have no idea the fitted value is reasonable or not.

For the next I should check the input impedance again by the direct way; putting the signal into the input.

 

 

 

Attachment 1: LCtank_impedance.png
LCtank_impedance.png
Attachment 2: LCtank_model.png
LCtank_model.png
  2263   Fri Nov 13 05:03:09 2009 kiwamuUpdateElectronicsmulti-resonant EOM --- input impedance of LC tank ----

I measured the input impedance of the LC tank circuit with the transformer. The result is attached.

It looks interesting because the input impedance is almost dominated

by the primary coil of the transformer with inductance of 75nH (see attachment 1).

The impedance at the resonance is ~100 [Ohm], I think this number is quite reasonable because I expected that as 93 [Ohm]

 

Note that the input impedance can be derived as follower;

(input impedance) = L1 + Z/n^2.

Where L1 is the inductance of the primary coil, Z is the load in the secondary loop and n is the turn ratio.

 

I think now I am getting ready to enter the next phase \(^o^)/

Attachment 1: input_impedance.png
input_impedance.png
Attachment 2: input_impedance2.png
input_impedance2.png
  2277   Mon Nov 16 17:35:59 2009 kiwamuUpdateLSCOMC-LSC timing get synchronized !

An interesting thing was happened in the OMC-LSC timing clock.

Right now the clock of the OMC and the LSC are completely synchronized.

 The trend data is shown below. At the first two measurements (Oct.27 and Nov.1),  LSC had constant retarded time of 3Ts (~92usec.).

The last measurement, on Nov.15, number of shifts goes to zero, this means there are no retarded time.

Also the variance between the two signal gets zero, so I conclude the OMC and the LSC are now completely synchronized.

The measurement on Nov.8 is somehow meaningless, I guess the measurement did not run correctly by an influence from megatron(?)

 

OMC-LSC.png

 

  2292   Wed Nov 18 14:55:59 2009 kiwamuUpdateElectronicsmulti-resonant EOM --- circuit design ----

The circuit design of multi-resonant EOM have proceeded.

By using numerical method, I found the some best choice of the parameters (capacitors and inductors).

In fact there are 6 parameters (Lp, L1, L2, Cp, C1, C2) in the circuit to be determined.

whole_circuit.png

In general the less parameter gives the less calculation time with performing the numerical analysis. Of course it looks 6 parameters are little bit large number.

In order to reduce the arbitrary parameters, I put 4 boundary conditions.

Each boundary conditions fixed resonant peaks and valleys; first peak=11MHz, third peak=55MHz, first valley=19MHz, second valley=44MHz.

designed.png

So now the remaining arbitrary parameters successfully get reduced to 2. Only we have to do is optimize the second peak as it to be 29.5MHz.

Then I take C1 and C2 as free parameters seeing how the second peak agree with 29.5MHz by changing the value of the C1 and C2.

mont.png

the red color represents the good agreement with 29.5MHz, in contrast blue contour represents the bad.

 You can see some best choice along the yellow belt. Now what we should do is to examine some of that and to select one of those.

  2294   Wed Nov 18 16:58:36 2009 kiwamuUpdateElectronicsmulti-resonant EOM --- EOM characterization ---

In designing the whole circuit it is better to know the characteristic of the EOM.

I made impedance measurement with the EOM (New Focus model 4064) and I found it has capacitance of 10pF.

This is good agreement with the data sheet which says "5-10pF".

The measured plot is attached below. For comparison there also plotted "open" and "10pF mica".

In the interested band( from 1MHz to 100MHz), EOM looks just a capacitor.

But indeed it has lead inductance of 12nH, resistance of 0.74[Ohm], and parasitic capacitance of 5.5pF.

In some case we have to take account of those parasites in designing.

EOM_impedance.png

 

  2340   Wed Nov 25 20:44:48 2009 kiwamuUpdateElectronicsMulti-resonant EOM --- Q-factor ----

Now I am studying about the behavior of the Q-factor in the resonant circuit because the Q-factor of the circuit directly determine the performance as the EOM driver.

Here I summarize the fundamental which explains why Q-factor is important.

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

The EOM driver circuit can be approximately described as shown in figure below

trans.png

Z represents the impedance of a resonant circuit.

In an ideal case, the transformer just raise the voltage level n-times larger.  Rin is the output impedance of the signal source and usually has 50[Ohm].

The transformer also makes the impedance Z 1/n^2 smaller. Therefore this configuration gives a following relation between Vin and Vout.

eq1.png

 Where G is the gain for the voltage. And G goes to a maximum value when Rin=Z/n2. This relation is shown clearly in the following plot.

 

impedance.png

 Note that I put Rin=50 [Ohm] for calculating the plot.

Under the condition  Rin=Z/n2( generally referred as impedance matching ), the maximum gain can be expressed as;

eq2.png

 

It means that larger Z makes more efficient gain. In our case, interested Z is considered as the impedance at a resonance.

So what we should do is making a resonant circuit which has a higher impedance at the resonance (e.g. high Q-resonant circuit).

 

 

  2363   Tue Dec 8 03:53:49 2009 kiwamuUpdateSUSFree swinging spectra of ETMX

In this night, I checked the free swinging spectra of ETMX to make sure nothing wrong with ETMX by the wiping.

Compared with the past (Aug.6 2008), the spectra of ETMX doesn't show significant change.

Successfully the wiping activity didn't change its configuration so much and didn't bring bad situations.

(bad situation means for example, the suspended components hit some others).

 

 The spectra of ETMX by DTT are attached. Also you can see the past spectra in Yoichi's entry.

Yoichi's data was taken during the air-pressure condition, so it's good for comparing.

Actually I compared those data by my eyes, because I could not get the past raw data somehow.

The resonant frequencies and their typical height changed a little bit, but I think those are not significant.

NOTE: In the figure, pitch and yaw modes (~0.57Hz and ~0.58Hz) look like having a smaller Q-factor than the past.

 

Attachment 1: ETMX_air.png
ETMX_air.png
  2368   Tue Dec 8 23:13:32 2009 kiwamuUpdateSUSfree swinging spectra of ETMY and ITMX

The free swinging spectra of ETMY and ITMX were taken after today's wiping, in order to check the test masses.

These data were taken under the atmospheric pressure condition, as well as the spectra of ETMX taken yesterday.

Compared with the past (see Yoichi's  good summary in Aug.7 2008), there are no significant difference.

There are nothing wrong with the ETMY and ITMX successfully.

 --

By the way I found a trend, which can be seen in all of the data taken today and yesterday.

The resonances of pitch and yaw around 0.5Hz look like being damped, because their height from the floor become lower than the past.

I don't know what goes on, but it is interesting because you can see the trend in all of the data.

 

 

 

 

 

Attachment 1: SUS-ETMY.png
SUS-ETMY.png
Attachment 2: SUS-ITMX.png
SUS-ITMX.png
  2372   Wed Dec 9 17:51:03 2009 kiwamuUpdateSUSwatchdogs

Please do not touch the watchdogs for all SUSs except for MCs,

because I am going to measure the free swinging spectra for ITMs, ETMs, BS, PRM, SRM tonight.

Today, it is good chance to summarize those data under atmospheric pressure.

thank you.

 

  2374   Wed Dec 9 21:09:28 2009 kiwamuUpdateSUSRe: free swinging spectra of ETMY and ITMX

Okay, now the data are attached. At that time I just wanted to say like the follower.

- - -

In the free-swinging spectra around ~0.5Hz, you can see the two resonances, which come from pitch and yaw mode of the pendulum.

Note that, the vertical and the horizontal axis are adjusted to be the same for the two plots in the figure .

And I found that

* the floor levels are almost the same (the factor of about 1.5 or something like that) compared to the past.

* however the peak heights for two resonances are several 10 times smaller than the past.

* this tendency are shown in all of the data (ITMX, ETMX, ETMY).

If such variation of the peak heights is cased by the seismic activity, it means the seismic level change by several 10 times. It sounds large to me.
 

Quote:

Where is the plot for the trend?
It can be either something very important or just a daydream of you.
We can't say anything before we see the data.

Quote:

By the way I found a trend, which can be seen in all of the data taken today and yesterday.

The resonances of pitch and yaw around 0.5Hz look like being damped, because their height from the floor become lower than the past.

I don't know what goes on, but it is interesting because you can see the trend in all of the data.

 

 

Attachment 1: Pitch-Yaw_modes.png
Pitch-Yaw_modes.png
  2391   Thu Dec 10 17:13:36 2009 kiwamuUpdateSUSFree swiging spectra under the atmospheric pressure

The free swinging spectra of ITMs, ETMs, BS, PRM and SRM were measured last night in order to make sure that nothing wrong have happened by the wiping.

I think there are nothing wrong with ITMs, ETMs, BS, PRM and SRM successfully.

For the comparison, Yoichi's figure in his elog entry of Aug.7 2008 is good, but in his figure somehow PRM spectrum doesn't look correct.

Anyway, compared with his past data, there are no significant changes in the spectra. For PRM which has no counterpart to compare with, its shape of spectra looks similar to any other spectra. So I think PRM is also OK. The measured spectra are attached below.

Indeed the current data are still showing smaller peak height for their pitch and yaw modes (roughly factor of 10 ).
 
Attachment 1: summary_freeswing.pdf
summary_freeswing.pdf summary_freeswing.pdf summary_freeswing.pdf summary_freeswing.pdf summary_freeswing.pdf summary_freeswing.pdf summary_freeswing.pdf
  2401   Fri Dec 11 17:36:37 2009 kiwamuUpdateGeneralIFO restoring plan

Alberto, Jenne, Kiwamu

 

We together will lead the IFO restoring and the following is our plan.

- - - - -|- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

#.0     |  measuring the free swinging spectra                     (weekend by kiwamu)   DONE

#.1     |  turn ON the PZTs for steering mirror and so on.         (Dec.14 Mon.) DONE

#. 1            |    lock around PSL  DONE

#.2     |  deal with mechanical shutter                            (Dec.14 Mon.)DONE

#.3     |  lock MCs                                                (Dec.14 Mon.)DONE

#.4     |  align the IFO                                           (Dec.15 Tue.)DONE

#.5     |  lock full IFO                                           (Dec.15 Tue.)DONE

- - - - -|- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

 

Thank you.

  2405   Sun Dec 13 17:43:10 2009 kiwamuUpdateSUSfree swinging spectra (vacuum)

The free swinging spectra of ITMs, ETMs, BS, PRM and SRM were measured under the vacuum-condition. The attachment are measured spectra.

It looks there are nothing wrong because no significant difference appear from the past data and the current data (under atmosperic pressure).

So everything is going well.

Attachment 1: summary_FreeSwinging_vacuum.pdf
summary_FreeSwinging_vacuum.pdf summary_FreeSwinging_vacuum.pdf summary_FreeSwinging_vacuum.pdf summary_FreeSwinging_vacuum.pdf summary_FreeSwinging_vacuum.pdf summary_FreeSwinging_vacuum.pdf summary_FreeSwinging_vacuum.pdf
  2446   Tue Dec 22 15:49:31 2009 kiwamuUpdateGenerale-log restarted

I found the e-log has been down around 3:40pm, then I restarted the e-log. Now it's working.

Thanks.

  2450   Thu Dec 24 01:25:29 2009 kiwamuUpdateElectronicsimpedance analyzing

The validation for high impedance measurement has been well done.

The impedance measurement is one of the keys for designing the EOM circuit.

So far I was very struggling to measure the high impedance ( above several 1000 Ohm) at RF because the EOM circuit has a high impedance at its resonance.

Finally I realized that the measured impedance was suppressed by a parasitic resistance, which especially reduces the impedance at the resonance.

Also I found that we can extract the TRUE impedance data by subtracting the effect of the parasitic resistance from resultant data.

In order to confirm whether this subtraction works correctly or not,  the impedance was directly re-measured with another analyzer for crosscheck.

                The followers are details about the re-measurement.
 

 

(measurement )

The measurement has been performed with help from Peter and Frank. ( Thank you !)

By using  network analyzer AG4395A with the impedance test kit AG43961A (these are at the PSL lab.), the impedance of resonant circuit with EOM was measured.

The picture of setup is attached. This impedance test kit allows to measure typically 0.1 [Ohm]-1M [Ohm] and frequency range of 100kHz-500MHz.

 

(result)
The resultant plot is attached. In the plot the blue curve represents the impedance measured by usual analyzer at 40m.

Note this curve is already subtracted the effect of the parasitic resistance.

( the parasitic resistance is in parallel to the circuit and it has ~7.8k Ohm, which is measured while the probe of the analyzer stays open. )

The red curve is the re-measured data using the impedance test kit.

The important point is that; these two peak values at the resonance around 40MHz show good agreement in 10%.

The resonant frequencies for two data differs a little bit, which might be the effect of a stray capacitance ( ~several [pF] )

The red curve has a structure around 80MHz, I think this comes from the non-coaxial cables, which connect the circuit and analyzing kit.

You can see these cables colored black and red in the picture.

 

( conclusion )

Our measurement with the subtraction of the  parasitic resistance effect is working reliably !

Attachment 1: DSCN0421.JPG
DSCN0421.JPG
Attachment 2: EOM.png
EOM.png
  2453   Sun Dec 27 20:05:28 2009 kiwamuUpdateComputerscan not communicate with front-ends

In this evening I found that fb40m has been down, then I restarted fm40m successfully.

However there still is a problem, the reflective memory can not communicate with some front-end CPUs ( such as c1iscey, c1susvme, ...etc.)

Right now I don't have any ideas about this, I am leaving them as they are now .... we can deal with them tomorrow. 


The followers are what I did.

(1) ssh to fb40m then "pkill tpman"

(2) telnet to fb40m then typed "shutdown". ( These procedure are on the 40m wiki)

(3) make sure fb40m gets recovered while watching the medm screen C0DAQ_DETAIL.adl

(4) run the backup script in fb40m

(5) in order to fix the communication problem, physically turn off c1dcuepics and c0daqctrl

(6) keying some front-end CPUs. ---> still some of front ends indicate RED on the medm screen C0DAQ_DETAIL.adl ( figure attached )

 

 

Attachment 1: C0DAQ_DETAIL.png
C0DAQ_DETAIL.png
  2470   Wed Dec 30 22:17:07 2009 kiwamuUpdateGeneralCamera input and monitor output

The input channels of the cameras and the output channels for the monitors are summarized on the wiki.

The channel table on the wiki is very helpful when you want to make a change in the video matrix.

thank you.

  2523   Mon Jan 18 23:44:19 2010 kiwamuUpdateElectronicstriple resonant circuit for EOM

The first design of the triple resonant EOM circuit has been done.

If only EOM has a loss of 4 Ohm, the gain of the circuit is expected to be 11 at 55MHz

So far I've worked on investigation of the single resonant circuit and accumulated the knowledge about resonant circuits.

Then I started the next step, designing the triple resonant circuit.

Here I report the first design of the circuit and the expected gain.

 


( What I did )

At first in order to determine the parameters, such as inductors and capacitors, I have solved some equations with numerical ways (see the past entry).

In the calculation I put 6 boundary conditions as followers;

(first peak=11MHz, second peak=29.5MHz, third peak=55MHz, first valley=22MHz, second valley=33MHz, Cp=18pF)

The valley frequencies of 22MHz and 33MHz are chosen in order to eliminate the higher harmonics of 11MHz, and Cp of 18pF represents the capacitance of the EOM.

Basically the number of parameters to be determined is 6 ( L1, L2, ...,), therefore it is completely solved under 6 boundary conditions. And in this case, only one solution exists.

The point is calculation does not include losses because the loss does not change the resonant frequency.

 

whole_circuit.png

( results )

As a result I obtained the 6 parameters for each components shown in the table below.

Cp [pF] 18.1
C1 [pF]  45.5
C2 [pF] 10.0
Lp [uH] 2.33
L1 [uH] 1.15
L2 [uH] 2.33

Then I inserted the loss into the EOM to see how the impedance looks like. The loss is 4 Ohm and inserted in series to the EOM. This number is based on the past measurement .

Let us recall that the gain of the impedance-matched circuit with a transformer is proportional to square-root of the peak impedance.

It is represented by G = sqrt(Zres/50) where Zres is the impedance at the resonance.

 As you can see in the figure, Zres = 6.4 kOhm at 55MHz, therefore the gain will be G=11 at 55MHz.

Essentially this gain is the same as that of the single resonant circuit that I've been worked with, because its performance was also limited mainly by the EOM loss.

 An interesting thing is that all three peaks are exactly on the EOM limited line (black dash line), which is represented by Zres = L/CR = 1/ (2pi f Cp)^2 R. Where R = 4 Ohm.

 designed_circuit.png

( next plan )

There are other solutions to create the same peaks and valleys because of the similar solution.

 It is easy to understand if you put Cp' = Cp x N, the solutions must be scaled like L1'=L1/N, C1'=C1 x N, ...,  Finally such scaling gives the same resonant frequencies.

So the next plan is to study the effect of losses in each components while changing the similar solution.

After the study of the loss I will select an optimum similar solution.

  2525   Tue Jan 19 02:39:57 2010 kiwamuUpdateElectronicsdesign complete --- triple resonant circuit for EOM ---

The design of the triple resonant circuit has been fixed.

I found the optimum configuration, whose gain is still 11 at 55MHz even if there are realistic losses.

As I mentioned in the last entry, there are infinite number of the similar solutions to create the same resonant frequencies.

However owing to the effect of the losses, the resultant gain varies if the similar solution changes

The aim of this study is to select the optimum solution which has a maximum gain ( = the highest impedance at the resonance ).

In order to handle the losses in the calculation, I modeled the loss for both inductors and the capacitors.

Then I put them into the circuit, and calculated the impedance while changing the solutions.

 


 

(method)

1). put the scaling parameter as k in order to create the similar solution.

2). scale the all electrical parameters (L1, L2,...) by using k, so that C1'=C1 x k, L1'=L1/k ,...

3). Insert the losses into all the electrical components

4). Draw the impedance curve in frequency domain.

5). See how the height of the impedance at the resonance change

6). Repeat many time this procedure with another k.

7). Find and select the optimum k

scaling.png

There is a trick in the calculation.

I put a capacitor named Cpp in parallel to the EOM in order to scale the capacitance of the EOM (see the schematic).

For example if we choose k=2, this means all the capacitor has to be 2-times larger.

For the EOM, we have to put Cpp with the same capacitance as Cp (EOM). As a result these two capacitors can be dealt together as 2 x Cp.

So that Cpp should be Cpp = (k-1) Cp, and Cpp vanishes when we choose k=1.

 

The important point is that the scaling parameter k must be greater than unity, that is k > 1.

This restriction directly comes from Cp, the capacitance of the EOM, because we can not go to less than Cp.

If you want to put k < 1, it means you have to reduce the capacitance of the EOM somehow (like cutting the EO crystal ??)

 

(loss model)

I've modeled the loss for both the inductors and the capacitors in order to calculate the realistic impedance.

The model is based on the past measurements I've performed and the data sheet.

   Loss for Capacitor :  R(C) = 0.5 (C / 10pF)^{-0.3} Ohm

   Loss for Inductor :    R(L) = 0.1 ( L / 1uH) Ohm

Of course this seems to be dirty and rough treatment.

But I think it's enough to express the tendency that the loss  increase / decrease monotonically as  L / C get increased.

These losses are inserted in series to every electrical components.

( Note that: this model depends on both the company and the product model. Here I assume use of Coilcraft inductors and mica capacitors scattered around 40m )

 

( results )

The optimum configuration is found when k=1, there is no scaling. This is the same configuration listed in last entry

Therefore we don't need to insert the parallel capacitor Cpp in order to achieve the optimum gain.

The figure below shows the some examples of the calculated impedance. You can see the peak height decrease by increasing the scale factor k.

realistic.png

The black dash line represents the EOM-loss limit, which only contains the loss of the EOM.

The impedance at the resonance of 55MHz is 6.2 kOhm, which decreased by 3% from the EOM-loss limit. This corresponds to gain of G = 11.

The other two peaks, 11MHz and 29.5MHz dramatically get decreased from EOM-loss limit.

I guess this is because the structure below 50MHz is mainly composed by L1, L2, C1, C2.

In fact these components have big inductance and small capacitance, so that it makes lossy.

 

( next step )

The next step is to choose the appropriate transformer and to solder the circuit.

  2529   Tue Jan 19 03:27:47 2010 kiwamuUpdateElectronicsRe: triple resonant circuit for EOM

1. You are right, the gain for the single resonant circuit was about 9.3 in my measurement.

But the reason why the triple is better than the single resonant circuit comes from the transformer.

The impedance can be degraded by a loss of the transformer, because it got worse after applying the transformer in the past measurement.

Also I definitely confirmed that the circuit had the impedance of 7.2 kOhm at the resonance of 52.9MHz without the transformer.

So it shall give the gain of 12, but did not after applying the transformer.

 

2.  Yes, I think we need some variable components just in case.

 

5.  For the impedance matching, I will select a transformer so that 55MHz is matched. In contrast I will leave two lower resonances as they are.

This is because 11MHz and 29.5MHz usually tend to have higher impedance than 55MHz. In this case, even if the impedance is mismatched, the gain for these can be kept higher than 11.

I will post the detail for this mismatched case tomorrow.

 

Quote:

The design looks very good. I have some questions.

1. As far as I remember, you've got the gain of slightly worse than 10 for a 55MHz single resonant case. Why your expectation of the gain (G=11) for the highest resonance better than this?

Supposing the loss exists only on the EOM, the other part of the LC network for the triple work as an inductor at the resonant frequency. This is just equivalent as the single resonant case. So the expected gain at 55MHz should coincides with what we already have. Probably, the resistance of 4 Ohm that is used here had too rough precision???

2. How can you adjust the resonances precisely?

Do we need any variable components for Cs and Ls, that may have worse quality than the fixed one, generally speaking.
I myself has no experience that I had to tune the commercial EOM because of a drift or whatever. I hope if you can adjust the resonance with a fixed component it should be fine.

3. Changing Cp. What does it mean?

Do you put additional cap for Cp?

4. The resonances for the lower two look very narrow. Is that fine?

This will show up in a better shape if we look at the transfer function for the gain. Is this right?

If we have BW>100kHz, it is sufficient.

5. Impedance matching for the lower two resonances.

Yep. You know this problem already.

 

 

  2533   Tue Jan 19 23:26:07 2010 kiwamuUpdateElectronicsRe:Re: triple resonant circuit for EOM

Quote:

5.  For the impedance matching, I will select a transformer so that 55MHz is matched. In contrast I will leave two lower resonances as they are.

This is because 11MHz and 29.5MHz usually tend to have higher impedance than 55MHz. In this case, even if the impedance is mismatched, the gain for these can be kept higher than 11.

I will post the detail for this mismatched case tomorrow.

 

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

eq1.png         (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. 

 

matching_edit.png

 

  - 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.

designed_response.png

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.

 

  2586   Wed Feb 10 17:28:02 2010 kiwamuUpdateElectronicstriple resonant EOM ---- preliminary result

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.

Attachment 1: mod_depth.png
mod_depth.png
  2590   Thu Feb 11 16:52:53 2010 kiwamuUpdateElectronicstriple resonant EOM ---- preliminary result

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

Quote:

Hey, this looks nice, but can you provide us the comparison of rad/V with the resonant EOM of New Focus?

Quote:

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.

 

 

  2596   Fri Feb 12 13:15:41 2010 kiwamuUpdateElectronicstriple resonant EOM --- liniaryity test

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.

Our triple resonant EOM looks healthy

 - - - - result from fitting - - -

11MHz: 91mrad/Vrms+2.0mrad

29.5MHz: 4.6mrad/Vrms+6.2mrad

55MHz:82mrad/Vrms+1.0mrad

Attachment 1: linearity_edit.png
linearity_edit.png
  2601   Fri Feb 12 18:58:46 2010 kiwamuUpdateGreen Lockingtake some optics away from the ETM end table

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

Attachment 1: DSC_1164.JPG
DSC_1164.JPG
Attachment 2: DSC_1172.JPG
DSC_1172.JPG
  2606   Tue Feb 16 11:12:51 2010 kiwamuUpdateGreen LockingRe:take some optics away from the ETM end table

Quote:

Quote:

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.

  2609   Tue Feb 16 16:24:30 2010 kiwamuUpdateGreen LockingRe:Re:take some optics away from the ETM end table

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

Quote:

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.

 

  2618   Fri Feb 19 15:29:14 2010 kiwamuUpdateCOCGluing dumbbells and magnets

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.

 

  2619   Fri Feb 19 16:40:43 2010 kiwamuUpdateGreen Lockingrearrange the optics on the end table

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

Attachment 1: DSC_1202.JPG
DSC_1202.JPG
Attachment 2: DSC_1207.JPG
DSC_1207.JPG
  2635   Tue Feb 23 19:00:45 2010 kiwamuConfigurationVACvent finished

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.

  2650   Tue Mar 2 12:20:54 2010 kiwamuUpdatePSLstray beam

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.

  2682   Thu Mar 18 15:33:17 2010 kiwamuSummaryElectronicsadvantege of our triple resonant EOM

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.

Attachment 1: electrode.png
electrode.png
  2688   Sat Mar 20 18:34:19 2010 kiwamuSummaryElectronicsRE:advantege of our triple resonant EOM

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.

  2735   Tue Mar 30 21:11:42 2010 kiwamuSummaryGreen Lockingconversion efficiency of PPKTP

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.

Attachment 1: efficiency_waist_edit.png
efficiency_waist_edit.png
  2737   Wed Mar 31 02:57:48 2010 kiwamuUpdateGreen Lockingfrequency counter for green PLL

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.

Attachment 1: FCnoise.png
FCnoise.png
  2740   Wed Mar 31 11:52:32 2010 kiwamuSummaryGreen LockingRe:conversion efficiency of PPKTP

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/2ZR)2)1/2, where w0 is beam waist, L is the length of the crystal and ZR is the rayleigh range.

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

Quote:

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.

 

 

 

  2788   Mon Apr 12 14:20:10 2010 kiwamuUpdateGreen LockingPZT response for the innolight

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.

  2823   Wed Apr 21 10:09:23 2010 kiwamuUpdateGreen Lockingwaist positon of Gaussian beam in PPKTP crystals

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.

Attachment 1: focal_positin_edit.png
focal_positin_edit.png
  2850   Tue Apr 27 14:18:53 2010 kiwamuUpdateGreen Lockingwaist positon of Gaussian beam in PPKTP crystals

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)"

Attachment 1: mode_in_PPKTP.png
mode_in_PPKTP.png
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