RSE Configuration Specify l_1, l_2, l_3 mirror r,t s -> Finesses f_rf

Transcription

1 Optical design considerations for the 40m Upgrade PRELIMINARY! æ goals of 40 m upgrade æ arm optical parameters æ noise æ recycling cavity parameters æ radii of curvature, spot sizes æ mode cleaner æ seismic noise æ imperfect optics æ core optics size æ upgrade tasks æ SEM mirror control - later! A. Weinstein LIGO, 40m upgrade, 10è6è99 1

2 goals of 40 m upgrade æ The primary goal of the 40 m upgrade is to demonstrate a scheme for using resonant sideband extraction èrseè, in a broadband conæguration, to provide the low power recycling cavity èprcè power gain characteristic of a narrow-band LIGO IFO while retaining the shot-noise performance of a broader-band LIGO IFO. æ in the coming 1-2 years, the lab will be upgraded to LIGO-like standards. æ At the same time, a control scheme will be developed for the signal mirror, for broad-band RSE operation. æ The plan is to be ready to prototype an RSE scheme by æ The 40m laboratory will continue to be used for testing and staging of other LIGO detector innovations; physicist training; and education and outreach. æ More information: talk.ps A. Weinstein LIGO, 40m upgrade, 10è6è99 2

3 arm optical parameters The LIGO-like IFO conæguration is a power-recycled Michelson IFO with Fabry-Perot arms èprm-fpè, with no ësignal" mirror èsmè in the dark port. RSE Configuration Specify l_1, l_2, l_3 mirror r,t s -> Finesses f_rf MC RF RM l 1 BS PSL l 2 l 3 SM SPD APD A. Weinstein LIGO, 40m upgrade, 10è6è99 3

4 Ground-rules: æ ITM, ETM, and RM mirrors have losses of 50 ppm; the BS mirror has losses of 100 ppm èmore precisely, the losses in the PRC due to beam passing through the BS and ITM substrates, and the PRC pickoæ, should all sum to 100 ppmè. æ The ETM has a tranmission of 15 ppm for monitoring. æ We want the arm cavities to be over-coupled. æ We want the PRC to be overcoupled, reæecting 1è of the incident laser light èfor control and stability purposesè. æ All the rest of the light is lost in the IFO: out the asymmetric port, out the ETM for monitoring, out the pickoæ port, or lost due to scattering or absorbtion. æ We assume 6 watts of laser light A. Weinstein LIGO, 40m upgrade, 10è6è99 4

5 arm optical parameters, 2 æ With these ground-rules, the design of such an IFO is driven by one parameter only, which we can choose to be any one of: 10 5 Cavity paramters, 40m 10 4 Finesse Storage time, usec fpole arm Arm power gain PRC power gain hshot/ T ITM æ Note that LIGO I operates with: T ITM = 0:03, Finesse = 204, ç s = 1734 usec, f pole = 91 Hz, G arm = 130, G prc = 60, h shot è0è = 7.4e-24. æ èall shot-noise strain sensitivity numbers quoted here are uncertain as absolute numbers, but their ratios are meaningfulè. A. Weinstein LIGO, 40m upgrade, 10è6è99 5

6 Contrasting parameters æ To compare and contrast conægurations, choose f pole as our driving parameter. æ Most LIGO-like: choose f pole = 91 Hz. æ This requires T ITM ' 100 ppm, ç L arms æ Diæcult to control such low transmission and high ænesse with realistic optics. æ Also, G prc ç 1 in that case; decidedly non-ligo-like, and defeats our purpose èdemonstrate reduction in G prc using RSEè. æ So back oæ, consider a much higher f pole. Let's consider f pole = 2000 Hz, which leads to: T ITM = 6298 ppm, T RM = , ænesse = 976, ç s = 79 usec, G arm = 611, G prc = 13.8, h shot è0è = 3.4e-22. æ Such a high G prc, with a high-powered LIGO-II laser, will lead to signiæcant PRC losses, and thermal lensing eæects. We need to reduce it. =è RSE A. Weinstein LIGO, 40m upgrade, 10è6è99 6

7 Contrasting parameters 2 æ We can reduce G prc by reducing f pole to, say, 500 Hz. This leads to: T ITM = 1489 ppm, T RM = , ænesse = 3915, ç s = 318 usec, G arm = 2314, G prc = 3.7, h shot è0è = 1.6e-22. æ Now G prc has been reduced by a factor of 4, but the bandwidth of the IFO at high frequencies has shrunk due to the smaller f pole. æ Now we add the RSE signal mirror èsmè in the asymmetric port. æ The carrier is absent at the asymmetric port, so it doesn't see the SM. But the GW signal exits through the port, and it does see the SM. æ The compound mirror composed of the ITMèSM is in resonance for the carrier and the GW signal, producing a larger transmittance, and thus, a larger f pole. æ We can choose a T SM which reproduces f pole = 2000 and h shot è0è = 3.4e-22 while keeping ænesse, ç s, G arm, G prc at their f pole = 500 values èt SM = will do itè. A. Weinstein LIGO, 40m upgrade, 10è6è99 7

8 RSE shot noise sensitivity RSE Therm + Seis Arm cavity Displacement sensitivity (m/rthz) Arm finesse = 3916 PRC Gain = 3.71 Arm Gain = T1 = ppm T3 = 1489 ppm T4 = 15 ppm T7 = ppm Frequency (Hz) æ The value of h shot è0è is, unfortunately, characteristic of the broad-band èf pole = 2000 Hzè conæguration; but we assume that, below f pole, we are dominated by other noise sources, anyway, so we're not losing any sensitivity there. æ That's not exactly true, for the 40m with the parameters we've chosen; it may be that we'll be shot-noise limited all the way down to 150 Hz. But that does not change the signiæcance of the experiment. In fact, it will make it easier for us to demonstrate the expected change in the shot-noise limited response as one makes use of RSE. A. Weinstein LIGO, 40m upgrade, 10è6è99 8

9 Goal of the experiment æ First, establish shot-noise limited response of a LIGO-like IFO èwithout RSEè with, say, f pole = 2000 Hz. æ Then, reconægure for f pole = 500 Hz, with a factor 4 smaller G prc, but loss of sensitivity at high f. æ Add RSE to bring high-f sensitivity back to f pole = 2000 Hz, level, but with G prc at f pole = 500 Hz level. A. Weinstein LIGO, 40m upgrade, 10è6è99 9

10 noise Noise curves for most of the expected noise sources, with a LIGO-like conæg with f pole = 2000 Hz. h noise for 40m shot radiation internal suspension seismic SQL total noise h noise (1/Hz 1/2 ) The noise is dominated by: Frequency (hz) æ the seismic ëwall" below ç 75 Hz, æ the shot-noise limit from 300 Hz through the knee at 2000 Hz and on up æ the suspension thermal noise in the region from 75 Hz to 300 Hz. The exact location of these curves depends upon accurate modelling, and I claim no such thing at this time. A. Weinstein LIGO, 40m upgrade, 10è6è99 10

11 Noise modelling æ Suspension noise: assume test masses of 4" diameter èok, 10 cmè, 8.9 cm thickness; a suspension phi = 2e-7 * f èviscous dampingè, f susp = Hz. æ Can increase the test masses to reduce this noise. See the discussion of pros and cons, below. æ See also discussions of the seismic noise, internal thermal noise, and radiation pressure, below. æ We see that we are shot-noise limited above 300 Hz; we choose f pole values of 500 Hz and 2000 Hz to stay clear of all other noise sources. æ In the ægure below, we show ëoptical readout noise" èphoton shot noise and radiation pressure noiseè for LIGO-like conægurations with f pole = 500, 1000, 1500, and 2000 Hz, along with the RSE curve designed to bring f pole from 500! 2000 Hz, and the noise curve for all other sources. A. Weinstein LIGO, 40m upgrade, 10è6è99 11

12 RSE shot noise sensitivity RSE Therm + Seis Arm cavity Displacement sensitivity (m/rthz) Arm finesse = 3916 PRC Gain = 3.71 Arm Gain = T1 = ppm T3 = 1489 ppm T4 = 15 ppm T7 = ppm Frequency (Hz) æ RSE curve matches the f pole = 2000 Hz curve above ç75 Hz, bue follows the f pole = 500 Hz curve in the radiation pressure noise nominated region below that. This is because the radiation pressure noise is due to the carrier power in the arms, not the signal power out the dark port. æ Radiation pressure noise will not be a dominant source of noise for the 40 m with 4" optics, or for LIGO with 10" optics. A. Weinstein LIGO, 40m upgrade, 10è6è99 12

13 recycling cavity parameters æ PRC dimensions: prior to the start of the recycling experiment, Logan and Rakhmanov carefully evaluated the PRC lengths èligo-t960013è. Including the paths through the optical substrates, they found: L inline = = m L perp = = m L prc = è L in + L perp èè2 = m dl = è L in - L perp è = m = Schnupp asymmetry where the ærst number is distance from RM reæective face to BS reæective face, the second is from BS reæective face to ITM reæective face, and the third is the correction due to paths through fused silica. During upgrade installation, these numbers will, of course, all be remeasured carefully. æ Modulation frequency: the lowest modulation frequency for which the carrier èat arm resonanceè and sidebands are in resonance in the PRC is: f mod = cè4l + n * cè2l = cè4l = 32.7 MHz æ Placed on beam AFTER the mode cleaner. A. Weinstein LIGO, 40m upgrade, 10è6è99 13

14 recycling cavity parameters æ Sideband power gain out the dark port èapdè: G AP D sb = t 2 RM sin2 æ è1, r RM r ITM è1, L BS è cos æè 2 where æ = 2çf mod dl=c f pole èhzè G AP D sb è0.542 mè opt. asym èmè G AP D sb èopt. asymè Sideband parameters, 40m APD (0.542m) G sb G sb APD (opt) dl (opt, m) T ITM A. Weinstein LIGO, 40m upgrade, 10è6è99 14

15 radii of curvature, spot sizes æ FP cavity design is driven by g-factor g = g 1 g 2 g 1 = è1, R ITM =L arm è, g 2 = è1, R ETM =L arm è æ Spot size at the end mirrors, for FP cavity with L = 1 m, versus g 1 and g 2 : mirror spot size for FP cavities g g 1 æ structure near the g=1 hyperbolas are spurious. æ White space means unstable FP resonator cavities. 45 æ line is for symmetric cavities. A. Weinstein LIGO, 40m upgrade, 10è6è99 15

16 FP cavity 2 æ Circles correspond to present 40 m conæguration èred, è1,0.38èè, 40 m upgrade conæg ègreen, è.577,.577èè, LIGO arms conæg èmagenta, è0.46,0.72èè, and LIGOè40m PRC conæg èblack, è1,1èè. æ Stability requires g é 1; expect better performance for symmetric cavities èg 1 = g 2 è, small g ç 1=3è. A. Weinstein LIGO, 40m upgrade, 10è6è99 16

17 Mode matching æ Modematching study: minimize mode mismatch due to imperfect radii of curvature of ITM, ETM mirrors: MM =ç æ!0! 0 ç 2 + ç æz0 2z 0 ç 2 æ! 0, z 0 are beam spot size and Rayleigh length for nominal radii of curvature, æ! 0, æz 0 due to sagitta error è0.001 m,1 è 0.1 Mode mismatch vs g, symmetric cavity Mode mismatch / dsag = g = g 1 * g 2, g 1 = g 2 A. Weinstein LIGO, 40m upgrade, 10è6è99 17

18 Arm parameters æ We choose a stable èg = 1è3è, symmetric arm cavity. The beam waist is in the middle of the m arms. Location R curv èmè spot èmmè waist 3.54 ETM ITM BS RM æ LIGO arms have g = 1è3, but is a bit oæset from symmetric, with g 1 = è1-4000è14500è, g 2 = è1-4000è7407è, to keep the spot size at the ETM such that less than 1ppm of the light falls out of the 24cm aperture è5.257 w ETM é apertureè. This is NOT a problem at the 40 m with 4" optics! æ Like LIGO and present 40m, the PRC is nearly unstable, with g ç 1. I don't know how to avoid this, or what its consequences are. A. Weinstein LIGO, 40m upgrade, 10è6è99 18

19 Mode cleaner æ Requirements of the 40 m upgrade with respect to initial laser pointing accuracy, jitter, higher order mode rejection, etc, have not been quantiæed! æ But, a new PSL with pre-mode-cleaner èpmcè, and an improved æxed-spacer 1 meter mode cleaner, will certainly improve things! æ I hope we can use the existing 1 meter fused silica spacer currently in use at the 40m, as well as the existing spring mounts. I don't know anything about this, at present! æ To provide the most suppression at high frequencies èeg, at f RF = 32.7 MHzè, keep cavity pole f pole as small as possible, ie, mirror T as small as possible. æ But not too small: to be roughly insensitive to uncertainties in losses, keep T ç Losses. Also, very small T means that even the desired TEM 00 mode is lost, with transmissivity ç 1. æ Want optimal coupling for TEM 00 mode; so, approximately, T 1 = T Losses. A. Weinstein LIGO, 40m upgrade, 10è6è99 19

20 Mode cleaner 2 æ Choose T 2 = 400 ppm, T 1 = 500 ppm; This gives T 00 = 0.8, f pole = 12 khz, suppression of 2e-7 at 32.7 MHz. æ Now optimize the èsymmetricè cavity g-factor to stay away from any HOM resonances. æ Transmission for 16 lowest HOMs: 10 0 Mode cleaner transmittances for first 16 HOMs Transmittance T mn g factor æ Look for a broad minimum. æ We choose g cav = A. Weinstein LIGO, 40m upgrade, 10è6è99 20

21 Mode cleaner 3 æ Here is an optical design for a stable, symmetric cavity that provides good rejection of higher order modes Mode cleaner transmittances L MC = 1 m 10 1 T mirror = ppm g cav = FSR = 150 MHz Finesse= 6282 Transmittance T mn fpole = 12 khz t s = 14 usec w MC = 560 um T 00 = mode m+n æ Want to grade the transmission of the mirrors to be higher at larger radii, to increase suppression of HOMs which have é r é' waist p n + m + 1. æ I do not know how to set, or address, the specs on pointing accuracy, jitter, etc. æ I have to learn how to design telescopes for matching PSL $ MC and MC $ IFO. æ Output mode cleaner? A. Weinstein LIGO, 40m upgrade, 10è6è99 21

22 seismic noise æ The æve existing core-optics chambers èbs, SV, SE, EV, EEè have 4-stage, 3-legèstage seismic stacks, ætted with viton springs. æ We plan to replace the viton springs with LIGO metal springs and æurel seats. æ We hope that this will reduce the amount of vitonèæurel in the vacuum system èmaybe not?è. In any case, we expect that after the rebuild and bakeout, the seismic stacks, and thus the 40m vacuum, will be signiæcantly cleaner. Our main concern is contamination of the mirror surfaces, NOT water vapor or other residual gas. æ As a side beneæt, the seismic isolation will be much better. A. Weinstein LIGO, 40m upgrade, 10è6è99 22

23 Seismic noise Here is the expected contribution to the horizontal displacement, x rms èfè, from seismic motion Horizontal Displacement of a 40m Test Mass (very approximate) metal springs viton springs envelope x(f) in m/sqrt(hz) Frequency (hz) The smooth curve is an envelope function that is èmore-or-lessè greater than the metal spring curve, everywhere, and is thus ëconservative": x rms = 1 æ 10,8 meters 1 + èf=10è 12:5 h strain = è2=l arm èx rms èfè A. Weinstein LIGO, 40m upgrade, 10è6è99 23

24 Sesmic noise modelling details æ I crudely estimate the masses of the stack: top optical table and plate, 275 kg; leg elements, 75 kg each èto be measured carefully when we disassemble!è. æ The damped metal springs can support a maximum load of 100 lbs or 45 kg. We put in as many springs as we need to hold the weight, and no more. This translates to the following numbers of springs for each stage of the 3 legs, from top to bottom èso multiply by 3 to get the total per stageè: 2,4,6,7. Total: 57 springs per stack. æ The spring constant for the damped metal springs at 100 Hz is k = 379 lbsèin, or 67.7 kgècm. æ The resonant p frequency for stage i, in Hz, is f i = N springs N legs kg=m=è2çè where g = acceleration due to gravity. We get, for the stages from top to bottom: 6.1, 9.1, 10.8, 12.3 Hz. ècf. Viton springs: 21.6, 29.0, 35.5, 38.3 Hz. æ Each stage has a simple pole transfer function, T i = f 2 i =èf 2 i, f 2 + if 2 i =Q iè; where we take Q = 300 èa total guessè. A. Weinstein LIGO, 40m upgrade, 10è6è99 24

25 Sesmic noise modelling details 2 æ The stack transfer function is the product: T 1 T 2 T 3 T 4. æ Then we have the pendulum transfer function, a simple pole with f = 0.74 Hz and Q = 3. æ Then we have the seismic spectrum itself. I don't know the spectrum at the 40m site èdo you?è. I use the ëhanford site noisy, wè microseismic peak", and MUTLIPLY BY 10. æ The product of these spectra give the curves shown above. x mirr èfè = x seis èfèt 1 èfèt 2 èfèt 3 èfèt 4 èfèt pend èfè A. Weinstein LIGO, 40m upgrade, 10è6è99 25

26 imperfect optics æ The desire to operate at arm cavity pole frequencies far below the arm FSR drives us to small ITM transmissivities, of same order as losses è50 ppmè. æ This suggests that small optical imperfections in the ITMs can lead to big changes in the IFO operation. æ FFT èbochner, LIGO-P980004è is designed to address this question with a full simulation of the èdcè E-æelds in the IFO, with realistically-deformed mirror maps. æ At the moment, I don't know how to make those mirror maps, so I've only run FFT with perfect optics. A. Weinstein LIGO, 40m upgrade, 10è6è99 26

27 Output of FFT, 40m RMS deformation 0 çè1800 çè1200 çè 800 çè 400 RMS deformation ènmè R RM èèè 68.4 Opt. Asymm ècmè 45.5 Mod Depth Gamma 0.36 Gprc, Carr, TEM Garm, Carr, TEM GAP D, Carr, TEM00 5e-3 GAP D, Carr, Total 6e-3 1-C 1.6e-3 Gprc, SB, TEM GAP D, SB, TEM GAP D, SB, Total 0.95 Rref, Total fpole èhzè 2022 hsnè0è è1e-22è 1.8 A. Weinstein LIGO, 40m upgrade, 10è6è99 27

28 core optics size æ Current 40 m optics are 4" diameter, 3.5" thick. æ We want to be able to use existing LIGO designs for the suspension controllers. æ LIGO has two types of suspension controllers: SOS for 3" optics èmode cleaner, etcè, packaged as two controllers per rack-mounted crate; and LOS for 10" optics ècore opticsè, packaged as one controller per rack-mounted crate. æ Per noise studies shown above, 3" optics will give unacceptably large suspension thermal and radiation pressure noise. æ We want to keep the size of the optic as small as is possible while giving acceptable suspension thermal and radiation pressure noise. 4" optics give acceptable noise. æ Smaller optics cost less. æ Smaller optics suspensions take up less real-estate in the already-cramped 40m chambers. This is perhaps the most important consideration driving us towards smaller optics. A. Weinstein LIGO, 40m upgrade, 10è6è99 28

29 æ We hope that the 4" optics can make use of the SOS controllers; this has to be spec-ed. æ We hope that the scaling down of a LIGO LOS mechanical system to support a 4" optic will be simple and straightforward. æ Beam spot sizes are of order 4 mm; there is thus negligable clipping, diæraction, or other edge eæects. æ The following output from the FFT program shows the beam spot on a FP arm end mirror. The mirror aperture extends almost to the edge of the mesh area A. Weinstein LIGO, 40m upgrade, 10è6è99 29

30 Interesting structure! upgrade tasks èdue to ænite thickness of BS? No!è èimperfect convergence?è A. Weinstein LIGO, 40m upgrade, 10è6è99 30

31 upgrade tasks æ Itemized list of tasks associated with upcoming bake-out, seismic stack rebuild, vacuum control upgrade: bakeout.txt æ Itemized list of upgrade tasks: wbs.txt æ Milestones: milestones.txt æ Work on control system design: in collaboration with Jim Mason, Ken Strain, etc. A. Weinstein LIGO, 40m upgrade, 10è6è99 31