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ID Date Author Type Categoryup Subject
  379   Wed Nov 3 01:22:57 2010 taraNotesPMCTF from PMC servo

I determined the OLG TF of the whole PMC loop, and TFs from servo paths and optical path.

 

We want to modify the PMC servo to optimize the PMC loop, so we have to know what are the TFs from part where we can modify,

and where we can't (optical path).

 

The whole TF is measured before, but I remeasured again just to make sure that there won't be any problem from the laser.

How I measure the whole TF is [here].

 

 I measured the OLG TF from the PMC servo.

The results agree well with the LISO model, see fig 1.

The pole (in LISO model)around 100kHz comes from non ideal behavior of PA85.

When I switch to ideal opamp model, the response is flat.

 

Then,

 Optical TF = Whole TF - Servo TF.

The Optical TF won't be modified. It will be used to compute the whole TF after the PMC servo modification. 

The measurement at low frequency does not look nice because the signal was suppressed by the gain.

But the TF around UGF still looks fine to work with.

  380   Wed Nov 3 02:08:06 2010 KojiNotesPMCTF from PMC servo

Incomprehensible.

Why is the optical TF not (kinda) flat?

Why does the PZT actuator completely ignored?

You need to talk to me tomorrow afternoon when I am in ATF.

Quote:

I determined the OLG TF of the whole PMC loop, and TFs from servo paths and optical path.

 

We want to modify the PMC servo to optimize the PMC loop, so we have to know what are the TFs from part where we can modify,

and where we can't (optical path).

 

The whole TF is measured before, but I remeasured again just to make sure that there won't be any problem from the laser.

How I measure the whole TF is [here].

 

 I measured the OLG TF from the PMC servo. The results agree well with the LISO model, see fig 1.

Then,

 Optical TF = Whole TF - Servo TF.

The Optical TF won't be modified. It will be used to compute the whole TF after the PMC servo modification. 

The measurement at low frequency does not look nice because the signal was suppressed by the gain.

But the TF around UGF still looks fine to work with.

 

  381   Wed Nov 3 15:38:05 2010 taraNotesPMCTF from PMC servo

Sorry for the confusion, PZT actuator is included in the optical TF. 

The plot on fig2 below shows the TF of PZT part, offset by 1 dB to match the misnomer optical path TF.

Thus, the real optical TF is rather flat with magnitude~ 1 dB, the phase shift is 180 degree,

 and the modifiable TF (LISO model) is plot on fig1. This plot has not taken the gain from the slider into account yet.

Quote:

Incomprehensible.

Why is the optical TF not (kinda) flat?

Why does the PZT actuator completely ignored?

You need to talk to me tomorrow afternoon when I am in ATF.

Quote:

I determined the OLG TF of the whole PMC loop, and TFs from servo paths and optical path.

 

We want to modify the PMC servo to optimize the PMC loop, so we have to know what are the TFs from part where we can modify,

and where we can't (optical path).

 

The whole TF is measured before, but I remeasured again just to make sure that there won't be any problem from the laser.

How I measure the whole TF is [here].

 

 I measured the OLG TF from the PMC servo. The results agree well with the LISO model, see fig 1.

Then,

 Optical TF = Whole TF - Servo TF.

The Optical TF won't be modified. It will be used to compute the whole TF after the PMC servo modification. 

The measurement at low frequency does not look nice because the signal was suppressed by the gain.

But the TF around UGF still looks fine to work with.

 

 

  382   Thu Nov 4 04:13:59 2010 KojiNotesPMCTF from PMC servo

What are the units of the vert axes?

Separate the open loop gain into three part:

- Optical Gain, Unit [V/m] or [V/Hz], usually flat or simple low path shape

- Servo Filter Gain, Unit [V/V], various shape

- Actuator Gain, Unit [m/V] or [Hz/V], flat or low path filter like up to kHz~100kHz (depending on the time constant of the RC filter),
mechanical resonances above that freq region, which usually determin the highest UGF.

You can change the servo gain by modifying the circuit.

You can change the optical gain by changing the amount of the light in the cavity / on the PD as well as changing the cavity finesse etc.

You can change the actuator gain by replacing the actuator.

Quote:

Sorry for the confusion, PZT actuator is included in the optical TF. 

The plot on fig2 below shows the TF of PZT part, offset by 1 dB to match the misnomer optical path TF.

Thus, the real optical TF is rather flat with magnitude~ 1 dB, the phase shift is 180 degree,

 and the modifiable TF (LISO model) is plot on fig1. This plot has not taken the gain from the slider into account yet.

Quote:

Incomprehensible.

Why is the optical TF not (kinda) flat?

Why does the PZT actuator completely ignored?

You need to talk to me tomorrow afternoon when I am in ATF.

Quote:

I determined the OLG TF of the whole PMC loop, and TFs from servo paths and optical path.

 

We want to modify the PMC servo to optimize the PMC loop, so we have to know what are the TFs from part where we can modify,

and where we can't (optical path).

 

The whole TF is measured before, but I remeasured again just to make sure that there won't be any problem from the laser.

How I measure the whole TF is [here].

 

 I measured the OLG TF from the PMC servo. The results agree well with the LISO model, see fig 1.

Then,

 Optical TF = Whole TF - Servo TF.

The Optical TF won't be modified. It will be used to compute the whole TF after the PMC servo modification. 

The measurement at low frequency does not look nice because the signal was suppressed by the gain.

But the TF around UGF still looks fine to work with.

 

 

 

  383   Thu Nov 4 21:13:32 2010 taraNotesPMCTF from PMC servo

I got the calibration from [here]

1) DC ext channel on PMC servo: 32.82 MHz/ V

The DC gain between DC ext channel and the voltage at PZT is 27.65 dB (x24.13),

so the Actuator gain will be 32.82/24.13 = 1.36 MHz/ V;

 The plot on fig1 is the Transfer function of the PZT actuator in MHz/ Volt.

 

The liso plot, [fig1] offset by 30.5 dB, match the result from the measurement.

This means that the gain from AD602 is 30.5 dB, even though the gain slider says 30dB.

 

Assuming that from DC to 100kHz, the TF from optic is flat.

The OLG TF measurement must equal The TF from servo(From LISO) + gain slider(30.5 dB) + PZT(LISO) + optics(flat offset)

The offset in the plot is 25.5 dB. With the 30.5 dB from gain slider, TF from optics is -5dB flat, with 180 degree phase shift see fig2. [add calibration from Hz -> V] [plot2]

The result from previous entry which gives the optic's TF to be flat at 1 dB is wrong because I did not use the whole TF from the servo

when I compare the model and the measurement, so I missed -6 dB from AD797.

 

 

 

Quote:

What are the units of the vert axes?

Separate the open loop gain into three part:

- Optical Gain, Unit [V/m] or [V/Hz], usually flat or simple low path shape

- Servo Filter Gain, Unit [V/V], various shape

- Actuator Gain, Unit [m/V] or [Hz/V], flat or low path filter like up to kHz~100kHz (depending on the time constant of the RC filter),
mechanical resonances above that freq region, which usually determin the highest UGF.

You can change the servo gain by modifying the circuit.

You can change the optical gain by changing the amount of the light in the cavity / on the PD as well as changing the cavity finesse etc.

You can change the actuator gain by replacing the actuator.

Quote:

Sorry for the confusion, PZT actuator is included in the optical TF. 

The plot on fig2 below shows the TF of PZT part, offset by 1 dB to match the misnomer optical path TF.

Thus, the real optical TF is rather flat with magnitude~ 1 dB, the phase shift is 180 degree,

 and the modifiable TF (LISO model) is plot on fig1. This plot has not taken the gain from the slider into account yet.

Quote:

Incomprehensible.

Why is the optical TF not (kinda) flat?

Why does the PZT actuator completely ignored?

You need to talk to me tomorrow afternoon when I am in ATF.

Quote:

I determined the OLG TF of the whole PMC loop, and TFs from servo paths and optical path.

 

We want to modify the PMC servo to optimize the PMC loop, so we have to know what are the TFs from part where we can modify,

and where we can't (optical path).

 

The whole TF is measured before, but I remeasured again just to make sure that there won't be any problem from the laser.

How I measure the whole TF is [here].

 

 I measured the OLG TF from the PMC servo. The results agree well with the LISO model, see fig 1.

Then,

 Optical TF = Whole TF - Servo TF.

The Optical TF won't be modified. It will be used to compute the whole TF after the PMC servo modification. 

The measurement at low frequency does not look nice because the signal was suppressed by the gain.

But the TF around UGF still looks fine to work with.

 

 

 

 

  384   Fri Nov 5 21:23:27 2010 taraNotesPMCSlope of error signal from PMC loop vs RF adjustment

I measured the slope of the error signal vs RF voltage, the result is plotted below

 To increase the overall gain of the PMC loop, one thing we can do is changing the slope of the error signal.

This will increase the gain on the optical path of the loop.

So I measured the slope of the error signal, this information will allow me to know how much

gain I would get from each RF setting. The slope increases as the RF voltage increases, until V_RF ~ 8 V.

The error signal does not change at all when V_RF on the slider is between 8 to 10 [Max] V, and

there is no saturation in the signal.

 

Note: I use the oscilloscope to measure the slope around the center of the error signal, by

measureing dt and dV to get dV/dt around the center, (this can be converted to dV/dHz by the sideband)

but the result has large deviation, so I measure the pk-pk in stead, and divide that by the

cavity FWHM = 3.8 MHz which corresponds to the peak-peak of the signal. to get the average slope.

It will be lower than the actual value

but I'll keep it for now.

 

  385   Tue Nov 9 15:05:00 2010 taraSummaryPMCTF plot for each stage in PMC loop

I plot the TF from each stage in the PMC loop and plot below.

 

1)  Servo (+ gain slider)[V/V], From the mixer output to the output of PA85. The amplitude can be added upto 30.5 dB by the gain slider setup

 

2) PZT [V/V]. From PA85 V output to V at PZT. This includes the last R in the servo (R44 = 64.3k Ohm) and C_pzt (0.23 uF). 

 

 3) Opt [V/V]. This includes the PMC and the frequency discriminator part up to the signal to the mixer.

The PMC converts V -> Hz [1.36 MHz/V]. The PMC pole is 1.9 MHz, so I

assume that it is flat at the region of interest (1-100kHz). The frequency discriminator convert Hz->V, and assuming flat response for now.

Thus the total unit of this part is [V/V] too. I'll separate this part into PMC and+ RFPD later.

 

 

  387   Wed Nov 10 01:06:40 2010 taraSummaryPMCPMC OLG TF with different RF/gain settings

I measure the OLG TF of the PMC with 3 different RF and gain slider settings. I plot the OLG TF of each setup and identify their UGF.

 

 I increase the RF as a first step to optimize PMC loop w/o modifying the circuit. This will increase the TF of the optical path.

The setting are

      

set RF V Gain slider (read out/acutal) UGF [Hz]
b 5.6 15 / 17.5 775
c 5.7 11 / 11.5 520
d 5.7 13 / 14 630

 

 

 

First I  adjust the RF power to reach where I can adjust the stability by changing the gain slider.

RF V above (6 or 7) the gain is too large, even with smallest gain slider, the signal is not stable and the PMC_RCTRANSPD drops from maximum.

So RF V ends up around 5.5 V. this makes the gain slider sit around 10 -15 where I obtain maximum stability. 

The gain slider should not to be set too low because of stability problem. The voltage supply for the opamp should be > +10V.

The gain slider setups are chosen to obtain the maximum stability and maximum power out put (PMC_RCTRANSPD.)

\

c and d have the same RF V, I change the gain to see if there would be any significant change in the performance, and

the data will be used for RF V calibration (how much gain we got from RF V adj).

 

Now we have some room to increase the gain once we lower the power, but

I have to understand why increasing the gain slider makes signal unstable.

The phase margin seems to be ok.  It might be the slope of the TF at UGF that causes instability.

  388   Wed Nov 10 20:04:13 2010 taraSummaryPMCoptical gain vs Vrf for side bands

 I checked that the optical gain in PMC loop increases as the power in the sideband increases. The result is 10.7 dB/V.

 

This measurement is for checking how much gain (in optical path) will we get from changing power in the side bands.

The excitation is sent to EXT DC channel on PMC. Reference signal is at HV mon, response is picked up at Mix mon.

This TF includes PZT and OPT paths, PZT TF should remain the same independent from the side band power.

 

I vary the RF voltage, and adjust the gain slider for maximum stability.  The gain setup should not matter

in the TF part we are measuring as long as the loop is stable.

 

I measured the gain at 3 different frequencies, 290.8 Hz, 1.035 kHz, 5.09 kHz where the TF look reasonable and smooth.

(The loop UGF is ~ 500-900 Hz, Thus the data at 1k and 5 kHz are nicer than that of 290 Hz)

 the slopes from each fit are

 

290 Hz 10.3 dB/V
1.035 kHz 10.72 dB/V
5.09 kHz 10.84 dB/V

 

The results are fairly linear in our region (RF between 4.8 to 5.9 V). The gain slider for this voltage range is between 13 - 20 dB.

At higher RF voltage, PMC_RCTRANSPD starts to drop significantly.

At lower RF voltage, the gain is too low.

 

This means we can increase the gain in OPT TF up to 10 dB by adjusting RF voltage (increase side band power)

  389   Wed Nov 10 22:36:59 2010 taraSummaryPMCcurrent PMC's OLG TF

The current plot for PMC's OLG TF is plotted below. The RF V is 6V, Gain slider is 14 dB.

 

The UGF is 820 Hz with phase margin (PM) = 180 - 53 = 127 degree.

 

At higher gain slider setup, the system starts to oscillate. One possible cause is the peak near 10^4 Hz which

might be the PZT's resonance frequency.

Without the notch the total gain we can increase will be limited by the peak.

I'll make a notch to damp it down.

The current spec will be ~20dB notch at 12.5 kHz, FWHM ~1kHz

 

From current setup, the optical TF should be + 16.5 dB flat, and the gain added by the gain slider is +14 dB.

previous setup we have opt TF = -5 dB and +30 dB from gain slider.

So we have improved the overall gain by ~5 dB and to UGF increased from 530 to 830 Hz.

 

  438   Mon Dec 20 22:52:55 2010 ranaHowToPMCnuts

 The RefCav pole is 37 kHz, not 37 MHz.

To minimize the RFAM, you just look at the PMC REFL PD with the PMC unlocked and adjust the waveplate to minimize the peak. Before doing this, make sure that there is no signal on the PD with the light blocked.

  439   Thu Dec 23 22:26:14 2010 ranaHowToPMCnuts

Ah right, that's embarassing. I'll try that.

Quote:

 The RefCav pole is 37 kHz, not 37 MHz.

To minimize the RFAM, you just look at the PMC REFL PD with the PMC unlocked and adjust the waveplate to minimize the peak. Before doing this, make sure that there is no signal on the PD with the light blocked.

 

  513   Thu Feb 24 15:55:55 2011 FrankNotesPMCPMC transPD calibration corrected

corrected the PMC transPD calibration. Old values for EGUF/EGUL fields in the record were 74.1/-74.1.
The corrected values are 133/-133. Value now reflects what i measure with the Thorlabs power meter.

Changed both entries in the database file.

  619   Wed Jun 29 15:47:40 2011 JenneDailyProgressPMCLISO models

Just a thought....

If you're going to post LISO models (the .fil files), it might be handy to also include a sketch of the circuit, or a link to the circuit.

  620   Wed Jun 29 15:59:51 2011 JenneDailyProgressPMCLISO models

Quote:

Just a thought....

If you're going to post LISO models (the .fil files), it might be handy to also include a sketch of the circuit, or a link to the circuit.

 Already done. Sorry about that.

  622   Thu Jun 30 03:25:13 2011 KojiDailyProgressPMCneed help improving LISO models

For EOM HV:

You need a single zero (or double zero) in order to make the bend of the magnitude curve at high freq.
However, this adds the phase advance at around the cut off freq although you actually have the phase delay.
This means that you need additional double pole just above the measurement freq. This pole may have relatively
high Q so that it can cancel the phase advance by the zero.

 

For EOM circuit:

A zero is missing at around 10^5 Hz. Also a pole or several poles are necessary to realize the magnitude curve and the phase delay at the high freq edge.

 

Filter1:

Limit the freq range from 10^5 instead of rediculous 10^-9.

 

PZT:

Replace one or two single poles by a double pole.

  753   Thu Dec 8 15:59:21 2011 FrankSummaryPMCrealignment

started realigning everything from scratch and calibrate all channels right. PMC optical power channels need re-calibration.

input beam to PMC: 28.9mW
PMC transmitted beam: 23.4mw
transmission trough curved mirror: 1.63mW

--> only 81% visibility (87% including back mirror leakage), but should be enough for what we want to do. Don't know the loss mechanism (didn't investigate)

  754   Thu Dec 8 20:28:06 2011 taraSummaryPMCrealignment

A reminder for Frank about the setup, 

  • The AOM's case on RCAV beam path is not screwed down to the body, so it will be blocking the beam.
  • The height for Faraday isolator behind the PMC is not correct, i think only ~80% of the power is transmitted. I haven't had it fixed yet
  • When I measured the visibility of RCAV, I scanned the cavity and minimize the dip as seen on the REFL RFPD. I got sth ~90% transmission, but when I measured the actual tranmitted power, the visibility is lower than that, maybe only~ 75%.
  • There is some weird reflection on ACAV RFPD, I'm not sure if it comes from the window or not.
  755   Thu Dec 8 21:06:10 2011 FrankSummaryPMCrealignment

thanks, for the info.

I only did the PMC so far as i has to fix the daq and add the new channels. What's the problem with beam height of the isolator? Is the beam too low or the mount too high? Do you know?

Quote:

A reminder for Frank about the setup, 

  • The AOM's case on RCAV beam path is not screwed down to the body, so it will be blocking the beam.
  • The height for Faraday isolator behind the PMC is not correct, i think only ~80% of the power is transmitted. I haven't had it fixed yet
  • When I measured the visibility of RCAV, I scanned the cavity and minimize the dip as seen on the REFL RFPD. I got sth ~90% transmission, but when I measured the actual tranmitted power, the visibility is lower than that, maybe only~ 75%.
  • There is some weird reflection on ACAV RFPD, I'm not sure if it comes from the window or not.

 

  759   Fri Dec 9 06:32:24 2011 TaraSummaryPMCrealignment

The V-block's height is a bit too high. The beam height is very close to 3".

Quote:

thanks for the info.

I only did the PMC so far as i had to fix the daq and add the new channels. What's the problem with beam height of the isolator? Is the beam too low or the mount too high? Do you know?

 

 

 

  783   Thu Jan 12 16:04:05 2012 TaraSummaryPMCIsolator base, EOM base's height

As mention in the previous corresponding entry, the height of the base for the faraday isolator is not correct. I removed the thing from the table and measure its height again in order to have it fixed. It has to be cut by 3/128 inch from the base (see figure below). The groove for the isolator is well leveled. I got the same height for both ends. I'll bring it back to machine shop tomorrow.

faraday_base.jpg

There are other mechanical parts I need to fix:

  • Broadband EOM's base: Frank noticed that it is a bit too high, and the 4- axis stage height has to be adjusted close to minimum which is not good for mechanical stability.
  • New design for EOM base: If we decide to go for two EOMs for 1)adding side band, and 2) feedback, we need some space for installing the second extra EOM. With the current EOM base design, it takes up to much space along the beam path, so I might need to make a new EOM base.
  • RFPDs' base: Now they are only a plastic post. We will need a sturdier design.
  • Base for dual periscope

I'll try to have these parts before we open the chamber to change the seismic stage.

  982   Sat Jun 9 01:49:52 2012 taraNotesPMCPMC servo was acting strange

 Today when Sarah and I tried to align the beam to PMC,  we lost PMC lock and could not bring it back. So we investigated it. The cause of the lost lock is not yet exactly concluded, but we can lock pmc back at ~ 40mW with usual stability.

 What we did before we lost lock:

  • We realigned EAOM in front of PMC. Since we replaced the laser head, the beam misaligned a bit and clipped/ scattered at EAOM. This turns out to be irrelevant with the problem (see details below).

What we did to check what was wrong with the PMC servo:

  • Made sure that the power input to PMC did not exceed  80 mW, so the RFPD for PMC was not destroyed (It was not saturated either).
  • Check the PZT response, by scanning the DC offset. By doing this we still see HOMs showing up on ccd behind the PMC, so the PZT is working fine.
  • Measured error signal from mixer out while scanning the cavity. The error signal had sine wave around 30 Hz added into it, so the signal was error signal + sine wave (30Hz) with amplitude larger than of pk-pk level of error signal (when the alignment was still bad).
  • So I disconnected RF signal, terminated the input with 50ohm, the fluctuation was still there. It was gone after I disconnected LO singal.
  • I checked the signal from LO, nothing was wrong with it.
  • Then I tried to align the beam as best I could without locking the PMC. Once the alignment was good enough, the 30 Hz fluctuation amplitude was smaller than pk-pk signal of the error signal. However when I locked the PMC, it was not very stable. A light tap on the table could kick the PMC out of lock.
  • I tried to reverse all the setup back to original and measured the error signal. With 20mW power input, the error signal was totally fine.IMG_1343.JPG
  • Then I increased more power to PMC, by adjusting the half wave plate in front of the first Faraday Isolator. The shape of the error signal changed as the power increase, but I could still optimize it by adjusting the phase shift (I don't know why would the phase change with the power it should be independent from each other). However, at 60mW input power to PMC(this corresponds to ~110+ mW at the 21.5 MHz EOM) the error signal turned bad. It was distorted, and the peaks from sidebands were gone. It could not be adjusted by changing RF power to EOM or phase shift.     So it has to do with the power. I'm not sure if the alignment of the EOM will be the cause of this behavior, but I aligned it quite well. There was no obvious beam clipped or scattered light on the EOM openings.

IMG_1345.JPG

Current status:

  • PMC is locked with 40mW input, gain 15 dB.
  • The origin of 30 Hz modulation at mixer out is not yet verified, but it disappeared after I investigated the problem.
  • PMC lock is stable, tapping on the table won't kick it out of lock
  1048   Mon Sep 17 19:06:36 2012 taraNotesPMCstainless steel pmc

I got PMC drawing from Dmass, this will be similar to gyro's steel PMC. I'll submit the work to machine shop soon.

The drawing is on svn full PMC assemble can be found at ATF:1543.There are spare mirrors in PSL that can be used. I still have to look for a PZT.

The round trip length is 0.33 cm. this corresponds to FSR = 454.45 MHz. If I want to be able to scan through 2 FSR, the displacement range of the PZT will be dL = 2*FSR * L / f, where L = 0.33m, f = c/lambda.  dL ~ 1um. 

  1052   Mon Sep 24 16:41:19 2012 taraNotesPMCstainless steel pmc

[with Zach and Dmass] We discussed about the stainless steel pmc design  and here are the list of what should be modified.

The drawing can be found, on svn.

pmc_endcap_v2,

  •  the hole for the beam exit can be larger (x1.3) so that the exit beam can pass without clipping. It should not be larger than the pzt
  •  [Important]the thickness of the PZT, thickness of the back mirror, end cap,  will determine the optical path of the PMC (with the beam centered at the input/output mirrors), see pmc_spacer_v2. Make sure to get the thickness right, so the beam is centered on all mirrors.

 pmc_clamp

  • the clamp for the input / output window can have a little larger opening to avoid clipping the beam. The through hole diameter can be 0.9 in stead of 0.8".

pmc_base

  • The height should be corrected for 3" beam height, measured from the table to the center of the mirror (the previous one was designed for 4" beam height. The size of the ball bearing has to be specified (Dmass said it was for 3 mm radius).

Materials

  • find the ruby/ sapphire bearings for the 3-point mount sapphire ball.
  • Other parts of the PMC (spacer, pmc clamp, end cap) will be made from stainless steel, the base will be made from brass.
  • press fit slot and press fit cone will be made from hardened steel dowel pin from McMaster

assembly

  • make sure the assembly has the right beam height (3" for CTN)
  • make sure to glue (with epoxy) the mirror, pzt, end cap carefully so all the parts are parallel, no tilt, no yaw.
  • order ruby or sapphire ball

PZT can be ordered from www.pi.ws.

The requirements for PZT from (LIGO-xx), are (A) pzt range = 2.7 FSR, for 0 - 375 V, (B) resonant frequency at 10kHz or above.

Zach is using model P-016.10H. The displacement is 15 um (with 1000V), OD = 16mm, ID = 8mm, L = 15mm, resonant frequency = 67kHz.  Assuming the pzt is linear, the displacement will be 5.6 um for 375V, this corresponds to 11 FSR for our cavity (FSR = 454 MHz). I don't know if this will cause some locking problem or not, or it might just give us an extra gain in the pmc loop.

If I follow the requirement, the displacment of 5um @ 1000V will be enough for us (model P-016.00H), but the length of the PZT will be 7 mm, and I think we have to fix the drawing accordingly.

pzt_snap.png

Above, an excerpt from the pzt catalog, the full one can be found HERE.

 

 

  1077   Thu Nov 15 00:33:01 2012 taraNotesPMCstainless steel pmc

Kriten sent me solidwork part files for the steel pmc.  I'm checking all the parts and will decide what material we want to use.

She reported that a ss pmc will have the first body mode at 780 Hz, while an aluminum one will have the first body mode at 1kHz. But we have to take thermal expansion, stiffness into account. here are some material properties

 

  Stainless steel AL
Thermal expansion coeff x10^-6 16 22.2
Young modulus    [GPa] 180 69
density   x10^3 kg/m^3 7.8 - 8

2.7

I think the thermal expansion will be a problem, but their thermal expansion coefficients are not that different. I don't know about stiffness of the body. I'll ask someone about this. Otherwise Al might be a better material if we look for higher resonant frequency.

  1078   Thu Nov 15 18:59:17 2012 taraNotesPMCstainless steel pmc

The PMC round trip is ~ 0.32m. The end mirror has ROC = 1.0m. The spotsize is 384 micron.  The end mirror has radius ~2.5 mm. The clipping loss will be ~ 1*10^-43 on the curve mirror, and much smaller at the flat mirrors. The number seems very small but I think it is correct.

 This is just a simple integration for power of the beam P(a) where a = radius of the mirror (2.5mm). The total loss on all three mirrors per one trip is definitely way below 1ppm.

[add calculation]IMG_1982.jpg

  1084   Tue Nov 27 13:13:51 2012 kristenDailyProgressPMCANSYS result for PMC body mode

I made a simulation for PMC body mode, and found out that for Al PMC, the first body mode is 1kHz. And 780 Hz for stainless steel pmc.

 

November 27, 2012

 It is desirable for the first body mode of the PMC to be at or above 1000 Hz in order to provide consistent length for the cavity.

 

 ANSYS Summary

  1. Geometry
    • For any given test, all parts of the assembly were changed to be the same material.  Materials tested include fused silica, aluminum, and stainless steel, and material will be specified per test.
  2. Connections > Contacts
    • Most contacts determined by ANSYS were sufficient.  However, the contacts between the press-fit slots or cones and the ball bearings were adjusted for accuracy.  The "Pinball Region" was changed from "Program Controlled" to "Radius", and the radius set to between 0.1 and 0.3 meter.  This is to ensure that ANSYS recognizes these two objects are resting on each other.
  3. Analysis Settings - Supports
    • The PMC assembly was modified so that the constraints could be more accurately modeled.  Split lines were added to the bottom of the PMC base to model the force applied by the dog clamps, and these small 0.5"x0.5" squares were defined as "Fixed Supports" in the ANSYS model.
    • The entire base was labeled as a frictionless support, because it is sitting on a table. 
  4. Results
    • The first body mode when the PMC is made entirely out of stainless steel is 865Hz
    • The first body mode when the PMC is made entirely out of aluminum is 881Hz

 

First_Mode_-_PMC.png

Above you can see the first mode shape of the PMC.  The colors represent the displacement - deep blue indicates no motion, while red indicates the greatest amount of motion.  The animation of this mode shape shows the PMC spacer rocking transversely on the PMC base.  The PMC base does not move at all.

  1. Changes to geometry (December 3rd, 2012)
    • Holes were cut through the PMC spacer to try to increase the first body mode frequency.  New geometry is shown in the figure below
    • holes_in_spacer_pic.png
    • There was no increase in the first body mode frequency - when made out of stainless steel, ANSYS reported the first body mode of this to be at 855 Hz

 

 

 One question that came up is whether ANSYS is importing the geometry file at the correct size.  According to the scale on the screen, it is the right size.  However, when the material is changed to resemble fused silica, the lowest body mode is 998 Hz, which is about an order of magnitude lower than expected.  This indicates some other error, possibly in importing the structure into ANSYS.

 /more to come

 

 

  1086   Mon Dec 3 16:57:27 2012 taraDailyProgressPMCANSYS result for PMC body mode

Quote:

 

 

First_Mode_-_PMC.png

Above you can see the first mode shape of the PMC.  The colors represent the displacement - deep blue indicates no motion, while red indicates the gr

 

 This does not look like a longitudinal mode. Do you have the frequency for the first longitudinal mode(along cavity length)? the first longitudinal mode should look like this ( this model has no fixed boundary condition, just a block in space).

cavity_eigen.png

  1087   Tue Dec 18 19:07:24 2012 taraDailyProgressPMCANSYS result for PMC body mode

Kristen and Norna came to ATF for impact-hammering of the metal PMC in the gyro setup

LINK

  1088   Mon Jan 7 13:54:29 2013 KristenSummaryPMCModal Frequency Testing for PMC

The PMC was tested & lowest resonant frequency was 330 Hz;  FEA model was adjusted to new frequency of 441 Hz

Results from December 18, 2012

The PMC in 058B W. Bridge was secured with several dog clamps to the laser table.  This table is not as stiff as the table in the Modal Lab in Downs, but was thought to be sufficient for this test.  Testing was done with the B&K system, using a laser vibrometer for the accelerometer and the small 8206 B&K hammer for excitation.  Below is a representation of the axis for this test, to understand where the PMC was excited and measured.

PMC_Measurement_Diagram.JPG

 

Measurements and excitations were approximately at the center of the corresponding face, as indicated in the image.

Below is a graph of the results of these measurements.  You can see that the lowest resonant frequency is at 330 Hz.

Experimental_Modal_Data_-_Dec_18.JPG 

 

Next Steps:

Next I will update the ANSYS model to be more accurate, hopefully showing about 330 Hz as the lowest mode.

FEA Model in ANSYS:

Briefly: the previous model reported in the elog was changed by refining the mesh on the slots/cones and the bearings.  This would allow for that portion to behave more accurately.  The contacts were left as Program-controlled (any other control seemed to overestimate the contact, raising the predicted resonant frequencies). 

Below is an image of the lowest mode, at 441 Hz.  The arrow indicates the motion - the mode is roughly a transverse flagpole mode.

ANSYS_PMC_Mode_441.JPG

Now that the model has been made more accurate, steps can be taken to raise the resonant frequency. While the initial goal that was mentioned to me of 1kHz is improbable, there are certainly ways to raise the frequency and damp the modes that are problematic.

 

 

  1089   Wed Jan 16 16:48:39 2013 ranaSummaryPMCModal Frequency Testing for PMC

  We are interested in the longitudinal mode along the Y direction. That is the only one which is problematic for the servo. Please remeasure so that you excite Y and measure Y and then model the first longitudinal mode.

The other modes are interesting, but they're not the main thing we care about.

  1097   Thu Jan 31 14:00:00 2013 Kristen HoltzNotesPMCPMC Longitudinal Testing and Modal Analysis

Longitudinal Mode frequency @ 420 Hz

 

Monday, January 28, 2013

Tests of resonant frequency specifically for longitudinal mode done on PMC because the piezo will only affect this length.  Originally the PMC spacer was constrained in motion by clamps on the PMC base, as shown below.

PMCphoto_circclamps.JPG

 Data was taken with an oscilloscope and laser vibrometer - the B&K system was not functioning correctly - and the PMC spacer was excited by hitting it with a marker.  The PMC was hit near the endcap, along the long axis of the PMC, as shown in the below image.

PMC_Excitation_Diagram_1-28-13.JPG

 

The results in the time domain are shown below and indicate a resonant frequency of 450 Hz.  A next step is to fit this data to a decaying sine wave.

PMC_ringdown_Jan28.JPG

When the above clamps were loosened to allow for more motion, the frequency dropped to closer to 350 Hz.

PMC_unconstrainedringdown_Jan28.JPG

 

  1126   Sat Mar 23 12:52:48 2013 EvanNotesPMCEigenfrequencies of PMC body: silica and stainless steel

I asked Comsol for the eigenfrequencies of a simplified PMC body. The outer dimensions are as in the design document (6.89″ × 2.375″ × 2.00″), and the borehole has a uniform diameter of 1.188″ (instead of stepping down to a smaller diameter part-way through the body).

Comsol says the lowest mode for silica is at 8.3 kHz, and for stainless steel the lowest mode is at 7.2 kHz. For this simulation the body is assumed to be completely free; I didn't add 3-point contacts or anything like that.

  1127   Mon Mar 25 16:10:19 2013 EvanNotesPMCEigenfrequencies of PMC body: silica and stainless steel

Quote:

I asked Comsol for the eigenfrequencies of a simplified PMC body. The outer dimensions are as in the design document (6.89″ × 2.375″ × 2.00″), and the borehole has a uniform diameter of 1.188″ (instead of stepping down to a smaller diameter part-way through the body).

Comsol says the lowest mode for silica is at 8.3 kHz, and for stainless steel the lowest mode is at 7.2 kHz. For this simulation the body is assumed to be completely free; I didn't add 3-point contacts or anything like that.

 The lowest longitudinal mode for silica is 16.4 kHz, and for steel is 14.2 kHz.

  1131   Wed Mar 27 01:52:34 2013 taraNotesPMCPMC Longitudinal Testing and Modal Analysis

I use COMSOL to find the first longitudinal mode of a stainless steel PMC,  it is about 16 kHz. I'll find an analytical solution and compare them to make sure that the FEA result gives us a reasonable answer or not.

The FEA result in psl:1088 does not show the right body mode of the PMC. The frequency of 440 Hz is from some weird mode as seen from the figure in the entry. Evan checked the body mode of a simplified steel PMC, and I also check independently. Our results agree quite well that the first longitudinal mode is at ~16kHz.

pmc_eigen.png

However, this does not answer what we measured in PSL:1097, where the longitudinal motion is around 300Hz. I checked the body frequency of the base blocked and it is even higher than the PMC body modes' frequencies (this should be expected since the base is even bulkier).

Note: I just learned from Zach that the PMC in GYRO setup does not have 3-point support. It just sits on the base block. But this has not given me any clues about the possible modes yet.

 I'm writing some background and requirement for the PMC[coming soon]

 

  1134   Sun Mar 31 03:03:28 2013 taraNotesPMCPMC Longitudinal Testing and Modal Analysis

[see PSL:1135]

I compared results between COMSOL and analytical solution. The first longitudinal mode from both results are comparable.

Peter sent me a note from Dennis about PMC longitudinal mode calculation. Dennis mentioned about a book by Young&Roark (here), so I looked it up and see how to estimate body mode frequencies of a simple block/beam.  I tried a simple geometry, a 0.1x0.1x0.175 (m) block. According to the book, cf situation 7b, table16.1 page 771, the first longitudinal mode is

f1 = (1.57/2*pi) * sqrt ( E/ rho*L^2), ), rho is the mass density of the material (2202 kg/m^3, for SiO2), E is the Young's modulus (72 GPa), L is the length of the block ( I use L = 0.175/2 because 7b situation is a uniform bar vibrates along its longitudinal axis, with upper end fixed, lower end free. This is similar to a whole beam resonate freely on both end because its center will be fix. Thus, to use the formula for our case, we have to use half length of the beam).

The analytical solution and COMSOL give f1 ~ 16 kHz.

psl_log2.png

 It is very strange that, according to COMSOL simulation, when the cross sectional area of the block is changed to 0.01x0.01 m^2 instead of 0.1x0.1 m^2, the frequency of the longitudinal mode does not change that much (still close to 16kHz. However, from the analytical solution, the frequency should drop by a factor of 10 ( around 165 Hz).

I'm going to think about this a bit more, but at this point, I think my COMSOL model is not correct. Might be some kind of bdy conditions that I'm missing.

psl_log.png

 

 

 

  1135   Sun Mar 31 14:42:05 2013 EvanNotesPMCPMC Longitudinal Testing and Modal Analysis

I think the analytical formula in terms of rho is going to be (1.57/2*pi) * sqrt(E / rho * L^2), since the Roark formula is (1.57/2*pi) * sqrt(A* E * g / w * L^2) and the weight per unit length is w = m * g / L = rho * A * g. With your values for L, A, E, and rho, this gives f1 = 16 kHz. Since A does not appear in the analytical formula, this also explains why changing the area in the Comsol model doesn't change the frequency.

Quote:

I compared results between COMSOL and analytical solution. The first longitudinal mode from both results differ by an order of magnitude!!

Peter sent me a note from Dennis about PMC longitudinal mode calculation. Dennis mentioned about a book by Young&Roark (here), so I looked it up and see how to estimate body mode frequencies of a simple block/beam.  I tried a simple geometry, a 0.1x0.1x0.175 (m) block. According to the book, cf situation 7b, table16.1 page 771, the first longitudinal mode is

f1 = (1.57/2*pi) * sqrt ( AE/ rho*L^2), where A is the cross section area (0.1x0.1), rho is the mass density of the material (2202 kg/m^3, for SiO2), E is the Young's modulus (72 GPa), L is the length of the block ( I use L = 0.175/2 because 7b situation is a uniform bar vibrates along its longitudinal axis, with upper end fixed, lower end free. This is similar to a whole beam resonate freely on both end because its center will be fix. Thus, to use the formula for our case, we have to use half length of the beam).

The analytical solution gives f1 = 1.6 kHz ,while COMSOL result is ~ 16 kHz.

psl_log2.png

 It is very strange that, according to COMSOL simulation, when the cross sectional area of the block is changed to 0.01x0.01 m^2 instead of 0.1x0.1 m^2, the frequency of the longitudinal mode does not change that much (still close to 16kHz. However, from the analytical solution, the frequency should drop by a factor of 10 ( around 165 Hz).

I'm going to think about this a bit more, but at this point, I think my COMSOL model is not correct. Might be some kind of bdy conditions that I'm missing.

psl_log.png

 

 

 

 

  1136   Sun Mar 31 20:06:16 2013 taraNotesPMCPMC Longitudinal Testing and Modal Analysis

Quote:

I think the analytical formula in terms of rho is going to be (1.57/2*pi) * sqrt(E / rho * L^2), since the Roark formula is (1.57/2*pi) * sqrt(A* E * g / w * L^2) and the weight per unit length is w = m * g / L = rho * A * g. With your values for L, A, E, and rho, this gives f1 = 16 kHz. Since A does not appear in the analytical formula, this also explains why changing the area in the Comsol model doesn't change the frequency.

 

 

 good catch! Thanks. Then both analytical and FEA results are the same. So our COMSOL results for PMC should be valid, the first body for a stainless steel PMC, see psl:1131,at 16 kHz is reasonable.

  1137   Mon Apr 1 20:59:19 2013 taraNotesPMCPMC Longitudinal Testing and Modal Analysis

I calculated some requirement for the beam jitter at the output of the PMC. A rough estimate shows that we need the angular stability at the PMC about half nano radian so that the frequency noise of the beam locked to the refcav is less than 10-2 Hz/rtHz.

==Background==

PMC also reduces beam jitters from the laser, so that the beam alignment to the cavity is kept centered. Since the laser is locked to the reference cavity, any misalignment of the input beam will cause the beam to sense the change of the cavity length.

So vibration that shakes the PMC will change the alignment of the output beam. With stiff material, the seismic induced deformation of the PMC will be reduced.

==Calculation==

  • calculate the ray tracing matrices from the PMC to the cavity. I assume that only the angle of the output beam changes due to PMC sagging, because of a long distance from the PMC to the refcav, with several mirrors in between. This gives me the position and the angle of the beam going to the cavity.
  • find out what is the change of the cavity length (dL), when the input beam is translated by dx, with angle theta.
  • convert displacement noise to frequency nosie (dL -> df), as a rough estimate I choose the requirement for df to be less than 10-2 Hz/rtHz (about the level of the estimated coating noise). This step is not really necessary, but I feel that it is easier to compare the noise in Hz/rtHz unit rather than m/rtHz.
  • The required angular stability at the PMC is ~ 0.5 nano rad. This number seems to be too strict. I will double check it.

==next==

Eavn is working on COMSOL to find out the angular tilt of the output beam due to PMC sagging. Optimum support points will be determined to minimize beam jitter due to seismic.

  1138   Thu Apr 4 11:44:14 2013 EvanNotesPMC270 Hz clamped PMC twisting mode

I ran another Comsol simulation with a simplified version of the PMC spacer. This time I put fixed constraints on two circular regions on the sides of the PMC near where it was clamped for the ringdown measurement. Comsol says the spacer has a mode where it twists about these clamp points, and the frequency of the mode is 270 Hz.

  1141   Thu Apr 4 23:55:12 2013 EvanNotesPMCPMC Longitudinal Testing and Modal Analysis

 

These are plots of the sagging of the front and back mirrors as a function of the longitudinal positions of the mounting holes (these positions are measured from the back of the PMC). The first plot is a coarse search, and the second is more targeted toward a region of lower sagging.

I generated these plots by taking Tara's Comsol model of the PMC body, assigning fixed displacement to the three mounting holes, and assigning a body load to the PMC body equal to the weight of the steel. Then, I extracted the displacements of four points on the front edge and four points on the back edge of the PMC borehole (these edges are where the faces of the mirrors will make contact with the body). I then took some cross-products with these points in order to get the unit normals that would result when the mirrors are placed against the deformed body. I then compute the angle between the deformed unit normals and the undeformed unit normals to get the sag of the mirrors in radians.

I'm a bit uneasy about how precision is handled in the Comsol/Matlab combination used to generate these plots. The Comsol GUI has no problem reporting displacements all the way down to 10^-24 meters, but anything smaller than 10^-15 meters or so gets truncated to exactly 0 when the results are reported in Matlab. When propagated through to the sagging computation, this means any sagging smaller than 10^-8 radians or so also gets rounded to exactly 0. You can see in the second set of plots that there are large swaths of exactly the same light blue and periwinkle, which seems to indicate a low level of precision in the computation. There's probably some obvious Comsol/Matlab setting that I'm missing, but I haven't been able to find it so far.

Regardless, it appears there is an optimum range of hole placements for the PMC body: 10 cm for the front holes and 3 cm for the back holes, give or take a centimeter or so.

Quote:

I calculated some requirement for the beam jitter at the output of the PMC. A rough estimate shows that we need the angular stability at the PMC about half nano radian so that the frequency noise of the beam locked to the refcav is less than 10-2 Hz/rtHz.

==Background==

PMC also reduces beam jitters from the laser, so that the beam alignment to the cavity is kept centered. Since the laser is locked to the reference cavity, any misalignment of the input beam will cause the beam to sense the change of the cavity length.

So vibration that shakes the PMC will change the alignment of the output beam. With stiff material, the seismic induced deformation of the PMC will be reduced.

==Calculation==

  • calculate the ray tracing matrices from the PMC to the cavity. I assume that only the angle of the output beam changes due to PMC sagging, because of a long distance from the PMC to the refcav, with several mirrors in between. This gives me the position and the angle of the beam going to the cavity.
  • find out what is the change of the cavity length (dL), when the input beam is translated by dx, with angle theta.
  • convert displacement noise to frequency nosie (dL -> df), as a rough estimate I choose the requirement for df to be less than 10-2 Hz/rtHz (about the level of the estimated coating noise). This step is not really necessary, but I feel that it is easier to compare the noise in Hz/rtHz unit rather than m/rtHz.
  • The required angular stability at the PMC is ~ 0.5 nano rad. This number seems to be too strict. I will double check it.

==next==

Eavn is working on COMSOL to find out the angular tilt of the output beam due to PMC sagging. Optimum support points will be determined to minimize beam jitter due to seismic.

  1145   Mon Apr 8 17:44:20 2013 EvanNotesPMCAbout PMCs

[Rana, Tara, Evan, Eric, Nic] 

We are designing a PMC, to do that we should be able to answer some fundamental questions about a PMC.

Why do we want a PMC?

  • Intensity stabilization(is it?)
  • Filtering of beam profile
  • Alignment reference
  • Reference for waist size and position
  • Jitter suppression
  • Polarization filtering

What should we consider in the design of the cavity?

  • High finesse eventually causes the transmission to drop
  • Cavity g should be chosen so that higher-order PMC modes are well outside the bandwidth of the TEM00 mode
  • Finesse should be chosen so that laser intensity noise is suppressed below the shot noise limit at frequencies of interest
  • Number of mirrors - determines whether or not we get polarization filtering
    • In a 3-mirror cavity, when one polarization is resonant, the other will be antiresonant. In a 4-mirror cavity, both will resonate simultaneously (with small differences in transmission intensity and phase).

What should we consider in the design of the spacer?

  • Acoustic pickup (probably dominates over seismic pickup at frequencies we are interested in)
  • Steel or silica:
    • Longitudinal mode frequencies are comparable
    • Silica is harder to machine
  • Vacuum can?
  • Dimensions:
    • A shorter PMC will have higher vibrational modes
    • A longer PMC has more filtering
    • A spacer that is too thin will have easily excited bending modes

Other:

  • 15 MHz is too low for PDH modulation, because the bandwidth of the resulting loop is too low
  • For a resonant PD, we want a low Q (a few)
  • 3 mirror or 4 mirror design?

 

  1146   Tue Apr 9 15:39:16 2013 taraNotesPMCAbout PMCs

Considerations for PMC design:

  1. Stiffness(Acoustic susceptibility) & heavy material: With heavier material, the pmc motion on the support becomes smaller.(RXA: please quantify with a formula)
  2. Filtering factor (Finesse/FSR/Cavity pole), g-factor: Filter out intensity noise around 10 MHz (RXA: please quantify with a formula)
  3. Design for thermal expansion cancellation between the spacer and the end cap: So that the PMC is less sensitive to ambient temperature
  4.  3 or 4 mirrors?  3 is polarization selective. For general lab use with power less than 1 W,  3 mirror design should be good. (RXA: I don't follow this logic at all)

RXA: In general, all of these considerations need some sort of quantitative detail. Make a DeBra Matrix so that we can evaluate. 

  1148   Sun Apr 14 23:35:03 2013 EvanNotesPMCPMC eigenfrequencies, now with endcap

I added an endcap to Tara's steel PMC Comsol model and looked at the eigenmoedes for a 3-point contact. The lowest mode is a rolling mode at 2.0 kHz, followed by other modes at 3.0 kHz and 3.5 kHz. The first longitudinal stretching mode is at 16 kHz. The rectangular part of the spacer for this steel PMC has dimensions 5" x 2.6 " x 2" and a cavity length of 32 cm (first picture).

I also looked at a beefed up version of the spacer, with dimensions 10" x 4.6" x 2" and a cavity length of 78 cm (second picture). The lowest mode is again a rolling mode at 1.4 kHz, followed by other modes at 2.0 kHz, 2.2 kHz, and so on. The first longitudinal stretching mode is at 9.0 kHz. So it looks like if we want a longer cavity, we can almost double two of the spacer dimensions without shifting the resonances down significantly.

If we use a 10" x 4.6" x 2" spacer but go with a 4-mirror bow-tie design (third picture), we can get something closer to a 1.1 m cavity length. Comsol gives a lowest mode at 1.4 kHz, followed by modes at 2.4 kHz, 2.6 kHz, etc.

  1149   Mon Apr 15 10:59:35 2013 taraNotesPMCDebra matrix for PMC design

Quote:

Considerations for PMC design:

  1. Stiffness(Acoustic susceptibility) & heavy material: With heavier material, the pmc motion on the support becomes smaller.(RXA: please quantify with a formula)
  2. Filtering factor (Finesse/FSR/Cavity pole), g-factor: Filter out intensity noise around 10 MHz (RXA: please quantify with a formula)
  3. Design for thermal expansion cancellation between the spacer and the end cap: So that the PMC is less sensitive to ambient temperature
  4.  3 or 4 mirrors?  3 is polarization selective. For general lab use with power less than 1 W,  3 mirror design should be good. (RXA: I don't follow this logic at all)

RXA: In general, all of these considerations need some sort of quantitative detail. Make a DeBra Matrix so that we can evaluate. 

 Some requirements for the PMC:

==Cavity pole==

 For intensity filtering. The modulation frequencies for the refcavs is ~ 15-25 MHz, we want the intensity fluctuation at this frequency to be shot noise limited.  We have to determine what should be the frequency pole. Intensity noise around 1MHz - 30MHz will be ~ 1/f^2, see the paper by Harb etal, eq1 and fig9, get the paper from psl:1156. Under the assumption that RIN remains constant, at 20MHz the laser will already by shot noise limited (@ 1mW input).  laser intensity noise / shot noise ~ 0.16. (laser intensity noise here means intensity noise from spontaneous emission/ pump-source intensity noise/ dipole fluctuation noise/ noise from intra cavity losses, any thing except shot noise)

laser_rin.jpg

  Thie pole can change with the cavity length and Finesse, [ Finesse = FSR/(2*cavity Pole)] , so our choices for mirror reflectivity, cavity length will affect this number as well. So for a fixed set of mirrors (fixed finesse), longer perimeter means lower cavity pole, but the cavity will be more susceptible to acoustic coupling.

==First longitudinal body mode==

  It should be at high frequency ( for high UGF servo). The shorter the length, the higher the frequency. See PSL:1134.

== g-factor==

 For a stable cavity, g factor has to be between 0 and 1.  Another reason: We should choose g-factor such that HOMs do not coincide with other cavity axial modes (FSR apart). For a ring cavity with 2 curve mirror R1,and R2, g = (1- p/R1) x (1 - p/R2) where p is the round trip length. (For 3-mirror cavity, g = (1 - p/(R))^2 . See HOM calculation.

==Stiffness==

 we want a solid, bulk shape PMC, not thin long one. This will make the PMC less susceptible to acoustic noise.

==Higher order mode suppression== 

Other transverse modes will be suppressed by a factor of (1-r)^2 / (1 +r^2 -2rcos(2*pi* dfmn/ FSR)  where dfmn is the gouy phase shift of m+n mode, r =r1*r2*r3.. (reflectivity of each mirror in the cavity) see evan's note. Transverse modes of the output of the NPRO can be found by scanning the PMC and measure the transmitted beam. Other modes beside TEM00, will be reflected back from the refcav and incident on the RFPD. This will cause the mode mismatch and increase shot noise level. Usually, higher r (higher Finesse), will suppress more HOMs.

==Build up power==:

= Pin x Finesse/ pi. CVI mirrorsfor high damage threshold power have maximum power for cw around 10MW/cm2. So I use this number as an upper limit for the power threshold. Assuming the power input is ~ 30 mW, average spotsize is 350 um. This gives ~ 8W/cm2. So Finesse can be up to ~ 3e6.  (10 MW/cm2 > (Finesse/pi) x 8 W/cm2) .

 

Some assumptions:

  • Losses(scatter/absorption) on each mirror is ~ 100 ppm. It seems that a super polished mirrors in vacuum has ~ 10 ppm loss. This comes from a Finesse measurement of the previous 8" refcavs, see psl:1046. The calculation shows that loss in one cavity is 25 ppm (for 2 mirrors), and 160ppm for another cavity. Since the PMC mirrors will be in air, and probably not as good as refcav mirrors, dust in air might accumulate over time and causes extra loss on the mirrors, 100 ppm loss assumption might be ok for this calculation.
  • PZT range is about 15um @1000V, as shown in the catalog, see PSL 1052 for the details, (we can drive it with ~0-300 V, so ~ 4um displacement),see PSL:1052

 

Let's see some of the designs that are available. Then we can decide which one we should modify to suit our requirement.

  1. Design1 iLIGO PMC: Isosceles triangular PMC, fused silica, perimeter = 0.42m, flat-curve (1m ROC)-flat mirrors. Round Trip = 0.42m See T-080195,here (it says the pole is 7 MHz).
  2. Design2 (Dmass' PMC): stainless steel PMC, perimeter =0.4m , same mirrors as those of design1, so its finesse is the same.
  3. Design3, AdvLIGO PMC style (4 mirrors, bow-tie): stainless steel (see PSL:)
  Cavity pole /FSR/ Finesse g-factor Stiffness  1st Longitudinal body mode  Approximate dimension(height x width  x length)  Note
Design1  cav pole = 7MHz / FSR=714MHz / Finesse =50 0.34    14 kHz  2" x 2.4" x 7.1"  The values are for p-pol, waist radius = 370um.
Design2  cav pole =  9MHz  /FSR = 925MHz / Finesse = 50  0.46    16.6kHz [PSL:1134]  2 x 2.6 x 6  assuming similar mirrors from design 1, w0 = 353 um.
Design3            
             
             
             

 

  1150   Tue Apr 16 13:24:46 2013 EvanNotesPMCDebra matrix for PMC design

For a 3-mirror cavity with a single curved mirror, the g-factor is (1-p/R)^2; there is no factor of 2 in the denominator because for a ring cavity the overall cavity length is equal to the round-trip length.

Also, I think we should shoot for a transmission of at least 90%. If this is going to be for general lab use, then there will probably be situations where people want a good power throughput. The input power might be as high as 2 W if used, e.g., at the 40m with one of those Innolight Mephistos.

  1161   Mon Apr 29 09:17:20 2013 EvanNotesPMCChoice of modulation frequency for PMC

I computed the occurrence of higher-order modes up to order m + n = 20 as a function of g factor for a ring cavity.

In the first set of plots of plots, I've fixed the cavity half-length L and chosen several values of modulation frequency fPDH. In the second set of plots, I've fixed fPDH and chosen several values of L. Green is the carrier, red is the lower sideband, and blue is the upper sideband. The takeaway messages from these plots are that

  1. there are two or three "best" regions to place g: near 0.06, near 0.46, or near 0.54 (although 0.06 is sort of close to instability);
  2. the locations of these regions are independent of the modulation frequency, at least for the frequency range we are interested in; and
  3. a lower modulation frequency widens these best regions.

So I think we should go for as low a crystal frequency as possible that is consistent with having shot-noise limited intensity and a high loop speed. I know the number 20 MHz has been thrown around as the lowest reasonable PDH frequency, but I don't understand quantitatively why this is.

  1162   Mon Apr 29 23:13:36 2013 EvanNotesPMCChoice of modulation frequency for PMC

Quote:

I computed the occurrence of higher-order modes up to order m + n = 20 as a function of g factor for a ring cavity.

In the first set of plots of plots, I've fixed the cavity half-length L and chosen several values of modulation frequency fPDH. In the second set of plots, I've fixed fPDH and chosen several values of L. Green is the carrier, red is the lower sideband, and blue is the upper sideband. The takeaway messages from these plots are that

  1. there are two or three "best" regions to place g: near 0.06, near 0.46, or near 0.54 (although 0.06 is sort of close to instability);
  2. the locations of these regions are independent of the modulation frequency, at least for the frequency range we are interested in; and
  3. a lower modulation frequency widens these best regions.

So I think we should go for as low a crystal frequency as possible that is consistent with having shot-noise limited intensity and a high loop speed. I know the number 20 MHz has been thrown around as the lowest reasonable PDH frequency, but I don't understand quantitatively why this is.

 This and some other PMC design issues are now in the SVN trunk under docs/modecleaner_design/

  1165   Wed May 1 01:45:55 2013 taraNotesPMCDebra matrix for PMC design

Considerations for PMC design is corrected and updated

  1166   Wed May 1 11:57:02 2013 ZachNotesPMCDebra matrix for PMC design

I can't take it anymore: what the $#@& is a Debra matrix??

Quote:

Considerations for PMC design is corrected and updated

 

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