LIGO II Interferometer Reference Design
Version history:
The configuration of the LIGO II interferometers starts with the LIGO I design -- a power-recycled Michelson interferometer with Fabry-Perot cavities in the arms -- and adds signal recycling. The initial focus is on a design that optimizes the sensitivity to detection of neutron star binary inspirals (NBI), which also tends to give the best overall broadband performance; the design is not required to be frequency tunable in situ, but it may have some useful tunability about the optimal point. The third interferometer may later be designed to have improved narrowband performance over a tunable range of something like 500-1000 Hz.

Top Level Parameters

Test Mass material. In the critical frequency region around 100 Hz, the thermal noise of the test masses either dominates or is a significant part of the noise budget. These noise sources are predominantly governed by materials properties, and there are two materials that stand out for consideration: fused silica (as in LIGO I) and sapphire. A sapphire-based design gives better performance in terms of the NBI figure of merit, but there are significant technical barriers and unknowns in the development of sapphire. Thus the baseline design calls for sapphire test masses, but a silica-based design-- with its not too much poorer performance -- will continue to be pursued as a viable fallback. For either material, any additional mechanical loss arising from the multi-layer dielectric coatings is not yet accounted for.

Test Mass size and mass. To reduce the effect of radiation pressure (quantum and technical) we wish to make the mass as large as possible. The practical limit currently looks to be at 40 kg for sapphire (still requiring development), and very similar for silica. The aspect ratio is determined through optimization of the test mass thermal noise (internal friction and thermoelastic).

Beam size. To reduce the thermal noise due to thermoelastic damping in the test masses, the beam size on the test masses should be made as large as possible. The extent to which the beam size can be increased is limited by factors such as diffraction loss, mirror figure and surface errors, and mode stability, all of which have not yet been fully analyzed. Currently we use a 6 cm beam radius (1/e2 intensity) for sapphire and 5.5 cm for fused silica, motivated by some study of stability under thermal distortions, and by consideration of polishing capability.

Low frequency cutoff and sensitivity. The seismic cutoff frequency is the frequency at which seismic noise, steeply falling with frequency as filtered by the seismic isolation and suspension subsystems, moves the test masses by the same amount as the predominant fundamental noise source, be it quantum radiation pressure or thermal noise. The seismic cutoff frequency for LIGO II, which is thus the lower GW band frequency, is specified to be 10 Hz. This choice is based partly on the NBI range figure of merit, and partly on considerations of technical feasibility. The NBI range does not in fact change significantly for seismic cutoff frequencies from 10-20 Hz. The isolation provided by the seismic and suspension subsystems, however, permits a 10 Hz cutoff without calling for undo sacrifices or complications in the design, and so we choose to preserve strain sensitivity down to 10 Hz. The specified noise level at 10 Hz is based on the expected level of fundamental noise sources, namely quantum radiation pressure and suspension thermal noise. Their estimated levels will change somewhat as the interferometer design is advanced, but for the purposes of establishing a low-frequency sensitivity level, we fix the seismic noise of each test mass to be (no more than) 10-19 m/rtHz at 10 Hz.
 
 
 
  Sapphire Fused Silica
Fabry-Perot arm length 4000 m
Laser wavelength 1064 nm
Optical power at interferometer input 125 W 80 W
Power recycling factor 17 17
FP Input mirror transmission 0.5%  0.5%
Arm cavity power 830 kW 530 kW
Power on beamsplitter 2.1 kW 1.35 kW
Signal recycling mirror transmission 7% 8%
Signal recycling mirror tuning phase 0.12 rad 0.095 rad
Test Mass mass 40 kg 40 kg
Test Mass diameter 31.4 cm 38.8 cm
Neutron star binary inspiral range (Bench) 201 Mpc 165 Mpc
Stochastic GW sensitivity (Bench units) 4.4 x 10-9 1.8 x 10-9

The plot below shows the strain sensitivity vs. frequency for the two designs; this is calculated by the program BENCH, using v. 1.6 as a basis, but including the correlated quantum noise (Buonanno & Chen, gr-qc/0102012) in place of Bench's shot noise and radiation pressure noise terms. The parameters given throughout this reference design are used in the file IFOModel.m.

Strain sensitivity comparison of sapphire and silica based designs:

Design description

Prestabilized Laser

The laser design approach is expected to be similar to that of LIGO I, in that it will be based on a commercially engineered and produced Nd:YAG laser, frequency and amplitude stabilized by LIGO. The laser design will be either an injection-locked high-power oscillator, or a master oscillator-power amplifier. The level of frequency noise required by the prestabilization is TBD, pending establishment of the final interferometer frequency stability requirements and a study of the stabilization heirarchy. There is currently no indication that we will require significantly better performance than in the LIGO I PSL, except perhaps for frequencies above ~1kHz, where there is a clear path to improvement. The relative intensity noise spec is still under review, but is driven at low frequencies but technical radiation pressure on the test masses. The requirement at higher frequencies (> 100 Hz) may turn out to be looser, depending on the choice of the GW readout scheme. The RIN is specified only at the mode cleaner output (interferometer input), as the implementation will use a photodetector looking at a sample of the mode cleaner transmission, likely located in the vacuum system. Given this, the RIN requirement applies not precisely to the PSL itself, but to the PSL & IO subsystems.

Primary requirements

Power in TEM00 mode (silica TMs) 180 Watts (120 W)
Frequency Noise TBD
Relative Intensity Noise (at mode cleaner output), f > 10 Hz 3 x 10-9 /Hz1/2

Input Optics

The input mode cleaner may either have the same length as in LIGO I (12-15 m), or be extended to twice the length by moving the input HAM chamber close to the edge of the LVEA; this option will be decided on the basis of the cost of the hardware modification and the performance benefits of increased length. The level of frequency stability required of the mode cleaner is TBD, pending establishment of the final interferometer frequency stability requirements and a study of the stabilization heirarchy. Requirements on the beam pointing fluctuations at the MC output are similarly TBD. Both sapphire and fused silica are being considered for the mode cleaner mirror substrate material.

Primary requirements & design parameters

Power in TEM00 mode, at mode cleaner output (silica TMs) 125 Watts (80 W)
Frequency Noise TBD
Beam pointing noise TBD
Mode cleaner length 12-15 m, or 25-30 m

Seismic Isolation

The seismic isolation system will use the 'STIFF' design concept (E010016-00.pdf), in which all 12 rigid-body degrees-of-freedom of a two-stage system are actively stabilized using seismometers and geophones as motion sensors, and feedback control. The system supports an optics table, to which the suspensions are mounted. The isolation system also provides actuation capability to compensate for tidal stretching of the arms, and coarse actuation for initial or re-alignment or long term drift compensation. The origin of the BSC displacement requirement is described above; the HAM requirement results from some rough estimates of the allowed motion of the mode cleaner mirrors and the power- and signal-recycling mirrors.

Primary requirements & design parameters

Test mass (BSC) displacement at 10 Hz (w/ suspension) 10-19 m/Hz1/2
HAM optics displacement at 10 Hz (w/ suspension) 3 x 10-17 m/Hz1/2
Optics table motion (BSC & HAM, 10 Hz) 2 x 10-13 m/Hz1/2
Optics table rms motion (BSC & HAM) f = 1-10 Hz: ~10-12 m

f = 0.1-1 Hz: 10-8-10-6 m

Suspensions

The suspensions for LIGO II are multiple pendulum designs, and are essentially the next-generation of the GEO 600 suspensions. The key features of the design (T000012-00.pdf) are: Suspensions in the BSCs will use a 4-stage pendulum, while HAM suspensions use a 3-stage design since there is less vertical clearance. Not all HAM suspensions may require the triple pendulum; suspension requirements for auxilliary suspended optics, such as mode-matching telescope mirrors, are TBD.

Primary requirements & design parameters

Suspension thermal noise at 10 Hz (BSC/test masses) 10-19 m/Hz1/2
Suspension thermal noise at 10 Hz (HAM) 3 x 10-17 m/Hz1/2
Isolation at 10 Hz, BSC/quad 5 x 10-7 (w/ damping)

5 x 10-8 (w/o damping)
Isolation at 10 Hz, HAM/triple 3 x 10-5 (w/ damping)
Pendulum frequency, last stage 0.65 Hz
Intrinsic loss of suspension fiber 3.3 x 10-8
Suspension fiber breaking stress 750 MPa
Number of wires suspending test mass 4
Fiber design: fused silica ribbon, cross section 1 mm x 0.1 mm
Mirror mass 30 kg (BSC), 7 kg (HAM)

Core Optics Components

The baseline design calls for sapphire test masses, and fused silica recycling mirrors and beamsplitter. The test mass dimensions for sapphire are chosen by assuming a 40kg mass, and finding the shape which minimizes the thermoelastic and internal thermal noise. The beamsplitter diameter comes from rough estimates of aperture clipping loss. For fused silica test masses, the diameter must be increased to get sufficient mass that radiation pressure is not an overwhelming noise source.

Primary requirements & design parameters

  Sapphire Fused Silica
Effective mirror Q 2 x 108 3 x 107
Youngs modulus, J/m3 4 x 1011 7 x 1010
Poisson ratio 0.23 0.17
Substrate density, kg/m3 3983 2200
Substrate thermal expansion coeff., /K 5.5 x 10-6 5.1 x 10-7
Substrate specific heat, J/kg/K 770 772
Substrate thermal conductivity, W/m-K 33 1.38
Test mass diameter, cm 31.4 38.8
Test mass thickness, cm 13 15.4
TM mass, kg 40 40
Beamsplitter diameter, cm 35 35
Beamsplitter thickness TBD
Recycling mirror diameter, cm ~26 ~26
Substrate absorption (ITMs), ppm/cm 40 - 80 0.5
Radius of curvature, ITM & ETM, Hot 54 km 38 km
Coating absorption 0.5 ppm
Surface figure deviation 1 nm rms
Microroughness 0.2 nm rms
Optical homogeneity 40 nm P-V
Average power loss per mirror 37.5 ppm
Contrast defect/beamsplitter loss 300 ppm

Auxiliary Optics Support

The AOS subsystem contains a handful of relatively unrelated optical functions. The optical levers, the initial alignment system, and the beam reducing telescopes will be minor extensions of their LIGO I predecessors. More beam dumps and increased light baffling may be required to adequately control scattered light given the higher optical power levels.

» Active thermal compensation

A new component of LIGO II is active thermal compensation of the core optics to counter-act thermal lensing that would otherwise limit power buildup in the interferometer. The idea is to deposit additional heat away from the center of an optic, such as to lower the thermal gradient in the region of the beam diameter. The additional heat would come either from a ring heater mounted in proximity to the optic, or from a scanned external laser beam that is strongly absorbed in the optic (or possibly a combination of the two). The two input test masses, and possibly the beamsplitter, would be thermally compensated. The required degree of compensation is currently under investigation; it depends strongly on the interferometer's sensing system (see below) and the need to maintain power buildup of light components in the power-recycled Michelson. For fused silica, initial modeling indicates that an order of magnitude reduction in the optical path distortion is required. For sapphire, with its much higher thermal conductivity, active thermal compensation may not be necessary if the substrate absorption can be controlled.

» Output mode cleaner

Another new element of LIGO II is an output mode cleaner, now included in the reference design. The benefit of the output mode cleaner is to substantially reduce the carrier power at the output port, and thus also reduce the local-oscillator power required for optimal signal detection. There are two potential designs, dependent on the GW readout technique chosed. If RF sidebands are used, then the output mode cleaner will like be a copy of the input mode cleaner, as it must pass efficiently both the carrier and sidebands. If DC readout is used, the output mode cleaner would be a short, rigid cavity, mounted in one of the output HAM chambers.

Interferometer Sensing & Control

The scope of the ISC subsystem is very similar to that in LIGO I, with the addition of the signal recycling mirror degrees-of-freedom that must be sensed and controlled. At this point there is no baseline sensing scheme for the interferometer, but there seem to be several viable techniques to choose from. Once a GW readout scheme is baselined, requirements for the laser amplitude and frequency noise can be determined.

Primary requirements & design parameters

Number of controlled lengths 5
Number of controlled angles 8 x 2 = 16
Main photodetector quantum efficiency 90%