What is LIGO?
Billingsley: LIGO is fundamentally a Michelson interferometer for detecting gravitational waves. We start with roughly six watts of power out of the laser and input optics systems. This light is input coupled through a 97-percent reflector, known as the recycling mirror, into a Y-shaped recycling cavity (also called the near-Michelson) formed by the recycling mirror, beamsplitter, and each input mirror (Figure 1). The split beam is coupled through an input test mass into each 4-km-long Fabry Perot cavity, which is the cavity formed between each input test mass and end test mass. The Fabry Perot cavities serve to recirculate the light so that there is a sufficient power buildup to give us great enough contrast to detect a gravitational wave signal when the beams interfere. If you picture just a single photon bouncing back and forth in the Fabry Perot cavity, it will make roughly a hundred round trips before returning to the recycling cavity.
Figure 1. The Y-shaped recycling cavity consists of the recycling mirror and both input mirrors. The Fabry Perot cavities are the 4-km-long arms of the interferometer. The power generated in the recycling cavity is 100 W and is built up to 4 kw in the Fabry Perot.
King: The power leaving the pre-stabilized laser is 8.5 W single mode. By the time the beam is injected into the interferometer, it's 6 W. In the recycling cavity, it's 100 W. Because of the further power recycling of the Fabry-Perot cavities, the recirculating power in the interferometer is about 4 kW.
Why did LIGO switch to the Nd:YAG from the argon ion?
King: The LIGO baseline concept was to utilize argon ion lasers, emitting 5 W of single-frequency, single-mode light at 514.5 nm. With enhanced and advanced LIGO interferometers in mind, each requiring higher laser power, the decision was made in 1995-96 to switch to Nd:YAG because of rapid improvements in the field of solid state laser technology. Other considerations included intrinsically better performance in the areas of frequency and intensity noise.
How does this affect the smoothness criteria for the mirror surfaces?
Billingsley: The smoothness criterion for mirror surfaces depends on the wavelength you're using. It was l/600 at the argon ion wavelength, which was the original design for LIGO. Measurements of optical flats are often performed at 632 nm and at that wavelength the specification would be l/800. For Nd:YAG, our current design, it's l/1300.
In switching from argon ion to Nd:YAG, you do lose a little sensitivity due to the longer wavelength, but you gain a lot because the YAG is scaleable to higher powers. With higher power, you can decrease shot noise, which is the limiting noise source at high frequency, meaning you're simply limited by the quantum mechanics of your system, that is, the number of photons available for detection.
Where did you get the Nd:YAG for LIGO?
King: The 10-W Nd:YAG laser was developed by Lightwave Electronics (Mountain View, CA). They had to meet strict requirements on frequency and intensity noise as well as laser reliability. If they met those requirements then we would take that laser and build a system around it to meet the stricter requirements of the LIGO detector. This subsystem is called the prestabilized laser (Figure 2).
Figure 2. The Hanford 2k interferometer pre-stabilized laser. (a) Lightwave laser; (b) reference cavity vacuum chamber; and (c) pre-modecleaner. The reference cavity is an 8-inch-long fused-silica fixed-spacer cavity with mirrors optically contacted at each end. In order for light to resonate in the reference cavity, the separation of the mirrors must be equal to an integer number of half-wavelengths of the incident light. The length of the reference cavity is fixed, so the wavelength of the incident light into the reference cavity is adjusted via frequency actuators. This serves to frequency stabilize the laser.
One requirement that we placed on Lightwave Electronics was that the output power in a circular TEM00 mode had to be greater than or equal to 10 W with the simultaneous power in all higher order modes less than 1 W. Other requirements included: the power drift in a 24-hour period had to be less than 1 percent peak to peak and less than 3 percent over a 500-hour period; the laser frequency drift should not be more than 50 MHz per hour and less than 1 GHz per month. The laser should be 99.7 percent linearly polarized. For reliability, the mean time between failures had to be greater than 10,000 hours and the minimum time between beam adjustments 2,500 hours. There are also requirements on the beam geometry, pertaining to relative pointing fluctuations, which is the change in spot size divided by the spot size.
Our job is to take the 10-W Lightwave laser and stabilize the intensity to 1 part in 10 million, which may go to 5 parts in a billion, and simultaneously to stabilize the frequency fluctuations to 1 part in 10 million. The pre-stabilized laser must deliver these previously unheard-of levels of performance all the time, day in, day out.
Tell us about the frequency stabilization.
King: We've designed and fabricated the control servos that frequency stabilize the Lightwave laser to our reference cavity. In a collaborative effort with Stanford University, we've developed a pre-modecleaner to passively filter the laser intensity at high frequencies and to spatially filter the beam.
We have a three-tiered frequency stabilization strategy, each of which involves stabilizing to progressively quieter frequency reference cavities. Locally we stabilize to an eight-inch-long, fused-silica fixed-spacer cavity, which gets us down to a frequency stability of 10-3. The next stage in the frequency stabilization scheme requires us to stabilize to the suspended 12-m modecleaner, which gets us down to 10-5. The last cavity we stabilize to is the LIGO interferometer, which should get us down to 10-7.
Tell us about the mirrors.
Billingsley: The reflecting mirrors are 25 cm in diameter, 10 cm thick, except the beamsplitter, which is only 4 cm thick. These are some of the most perfect optics in the world. Over the central 80 mm, their RMS deviation from a perfect radius is less than 0.8 nm and often measured at 0.5 or 0.6 nm. If you happen to think of optical surfaces in terms of waves of flatness, this is equivalent to l/1200 at 632.8 nanometers, which is phenomenal.
They're not flat?
Billingsley: Of course the beamsplitter is flat, but the rest are concave, with very long radii of curvature. Our shortest radius of curvature is 7.4 km, which is a great flat mirror for most people. Our longest radius of curvature is 14.9 km.
How do you measure something like that?
Billingsley: We've had an extensive metrology development program, both in the initial phases to support polishing, and in the final phases to support post-coating metrology. All of these measurements are done with phase-shifting Fizeau interferometers.
When we were first devising LIGO and coming up with specifications, we could only hope for optics of the quality we ended up with. We had found one place, Hughes Danbury (Danbury, CT), that had done this kind of work on a fairly large surface. So we entered into what we call the Pathfinder Program, which was devised to see if (1) any other vendor could do this and (2) was it repeatable?
The Pathfinder Program was a competitive bid. We selected two companies with the capability of world class metrology -- Hughes Danbury Optical Systems (HDOS), and the Division for Telecommunications and Industrial Physics of CSIRO, Australia. And we selected two companies that didn't have high-level metrology -- General Optics (Moorpark, CA), and Research Electro Optics (Boulder, CO), who thought they could meet our spec by means of process alone. We contracted with HDOS and CSIRO, and each polished two optics. GO and REO each polished one optic. We did indeed find most companies approached or exceeded our requirement. We were happy to know that we could design the interferometer around these assumptions and could count on getting optics this good.
Who provided the core optics?
Billingsley: The vendors for the glass blanks are Corning in Canton, New York, and Heraeus Amersil in Duluth, Georgia. For polishing, we have split the work with 32 of the optics being polished by CSIRO and eight being polished by General Optics.
What about the beamsplitter?
Billingsley: The beamsplitter glass itself is fused silica and came from Heraeus. Of course, all of our optics are fused silica. Different manufacturers just have different amounts of trace materials. Suprasil is the grade with the lowest OH content. OH is an absorber at 1064 nm, so we have to worry about thermal lensing in the transmissive optics. We use the Heraeus glass for the beamsplitter and the input test masses where thermal lensing could be a problem. Thermal lensing occurs when the laser beam heats the glass and changes the index of refraction.
The beamsplitter glass from Heraeus is also one of their 3D Suprasil materials, meaning that it is homogeneous in all directions and, thus, well suited for use in beamsplitters where the beam is not going through perpendicular to the optic.
There appears to be a strong correlation between the amount of OH in fused silica and absorption of 1064-nm light. So, we need a limit on the amount of OH in the glass.
What are some of the seismic noise sources that you're worried about?
Barton: The seismic noise spectrum has two major components. One is just a general background, which is much the same everywhere and falls as f -1 below 0.1 Hz and f -2 above that. It's traffic rumbling by, the mini earthquakes, wind-induced vibration, and a lot of other sources. The second major component, particularly for Louisiana, is the so-called microseismic peak, at around 0.2 Hz, which is caused by ocean waves. The site is about 80 miles from the Gulf of Mexico, but the microseismic peak is not a strong function of distance inland. It's more dependent on weather, being particularly bad in hurricane season.
How does LIGO approach seismic isolation?
Barton: We expect to be limited by three noise sources (Figure 3). At high frequencies, 100 Hz and above, we're going to be limited by shot noise, which is basically the counting of photons. In the medium frequency band, between 40 and 100 Hz, the limiting noise source is going to be pendulum thermal noise in the piano wire suspending the test masses. Below that, we expect to be limited by seismic noise.
Figure 3. Binary neutron star systems should emit a signal that starts at low frequencies and then chirps upward. The seismic noise falls very steeply with frequency. The pendulum thermal noise falls less steeply. If seismic noise were eliminated completely, at low frequencies the signal would still be masked by pendulum thermal noise. The seismic noise "wall" can be pushed to the left by decreasing all the resonance frequencies of the system.
The last stage has got to be a pendulum, because it has low thermal noise. A fundamental theorem called the Fluctuation Dissipation Theorem relates mechanical damping to thermal noise. The test masses are hung with fairly ordinary carbon steel piano wire. Most of the restoring force in a pendulum is gravity, which doesn't have thermal noise, so it's only the very small amount of thermal noise in the pendulum flexure that counts. There will still be some thermal noise in the motion of the pendulum if you operate it at room temperature.
The pendulum doesn't have nearly enough seismic isolation to get rid of the seismic noise from the ground. So the seismic isolation depends on the number of stages and the resonance frequency of each stage. For an ideal single stage, the transmitted vibration falls as f -2 above the resonance. So, basically, if you can push the resonance frequency down, the f -2 cuts in earlier and you improve matters for any frequency above that. Ideally, you can get an extra f -2 for each extra stage. The pendulum contributes a useful amount of isolation in the horizontal (f=0.7 Hz ), but not enough, and hardly any in the vertical (f=12 Hz). So we stick that on top of a vibration isolation stack consisting of multiple layers of stainless steel blocks and coil springs (Figure 5a).
All the seismic isolation comes from the isolation stacks themselves. We've got an isolation stack at the center of the L and a stack at the end of each arm. The stacks have a number of resonances between 1 to 15 Hz; above 15 Hz the transmission of vibration plummets. Our requirement at 40 Hz means we need to knock the seismic component down by a factor of 106. If we do that, then we'll be okay.
Basically, we've drawn a line in the sand at about 40 Hz. Above 40 Hz is our signal band. Our servos have steep roll-offs so that by 40 Hz they're putting no significant force on the optic at all, so we're putting our entire trust to the seismic isolation. Anything above 40 Hz that is not an identifiable glitch is a gravity wave candidate. Below 40 Hz, we put on control signals to take out the low frequency, large amplitude seismic components.
Tell us more about the isolation stacks.
Barton: We have two different stack designs. Where we require less seismic isolation performance for the less critical optics such as the mode matching telescope, we have a HAM (horizontal access module) chamber (Figure 4) with a three-layer stack. For the really critical optics, i.e., the beamsplitter and test masses, we have a BSC (basic symmetric chamber) with a four-layer stack to get extra isolation (Figure 5).
The HAM with stack weighs 6,800 pounds and is 8 ft. 5 in. long, 6 ft. 3 in. wide (from flange to flange in each case), and 8 ft. 7 in. tall. The larger chamber, the BSC, is about 9 ft. 5 in. in both horizontal directions and 16 ft. 8 in. feet high. Of the two, the BSC is less convenient to work with because the stack is high off the ground (above the optics that it supports) and the top of the chamber has to be removed to install the stack.
Figure 4. A horizontal access module (HAM) chamber with the stack being worked on inside a portable clean room. In the foreground are two of the support pillars, the air bearings wrapped in tin foil sitting atop the vertical actuation mechanisms, and the ends of the crossbeams. Inside the tank from the bottom up are the support tubes, the support table, the stack, the optical table, and assorted optics and counterweights.
What are the main components of the stacks?
Barton: Each stack is a mixture of layers of springs with stainless steel mass elements -- three layers of springs for the HAM and four for the BSC. From the ground up, we have some support pillars, about two feet high for the HAMs and more like 10 feet high for the BSC. They're all on separate concrete foundations, basically to decouple as much as possible the vacuum tank from the seismic isolation system. The tank itself acts as a microphone for sound vibrations in the air, so you don't want to support anything critical on it. On top of the support pillars goes the actuation mechanism.
For coarse actuation of the stack, there is a vertical stage that consists of a number of scissor jacks with screw supports inside. On top of that is an air bearing that allows the whole thing to be lifted as in a sort of first-year-physics air-puck arrangement. So the whole thing can be floated and moved about a centimeter in the horizontal. This coarse actuation allows you to correct position errors, such as creep of the stack over time.
So there are four of these support pillars and four corresponding actuators. On top of that you have crossbeams that snake around the outside of the tank. Then, from the two crossbeams on either side, support tubes actually penetrate the vacuum tank via compliant bellows, which maintain the vacuum seal but decouple any vibrations in the vacuum tank from the sensitive payload. Inside the vacuum tank itself, on top of the two support tubes, there's a support table.
On top of the support table is the stack itself, or more accurately, four stacks, each acting as one leg of the final payload (Figure 5a). The BSC and HAM have quite different payloads. In the HAM chamber, an optical table (different from the support table) sits directly on the stack and has an array of holes on the top surface to allow a variety of optical components to be attached to it. In the BSC, the four stack legs support a so-called "downtube" (Figure 5) that passes down among the stack legs and through a hole in the support table. There is a breadboard array of holes on the bottom surface for attaching optical components. This upside down arrangement is actually the most natural, given that the most important components are hanging as pendulums.
If you go up to the optical table in the HAM and push, it'll sway back and forth with a frequency of about 1.5 Hz. Including the final pendulum, we can hope for about f -8 of horizontal isolation for the HAM and f -10 for the BSC, above the stack resonant frequencies. For example, in the HAM stack, the lowest resonance is about 1.5 Hz in the horizontal and the highest resonance is about 14 Hz. Above 14 Hz, the transfer function from input to output motion plummets.
How many HAMs and BSCs are there?
Barton: There are six HAMs per interferometer, but two of those are reserved for future expansion and don't have stacks. In the Hanford observatory, which will have one full-length and one half-length interferometer, we've got a total of 12 HAMs, and at Livingston there are six. They're scattered around among the BSCs and mostly contain input/output optics. For example, the input beam comes out of the laser enclosure and is cleaned up in a triangular modecleaner formed by mirrors in two HAM chambers. Then it is expanded by a telescope and sent on to the recycling mirror in a third HAM. Finally, it gets to the beamsplitter, which is in a BSC.
There are five BSCs per interferometer or 15 total. There's one for each beamsplitter and for each of the two input test masses and two end test masses.
What's the frequency range of the gravitational wave signal?
Barton: The anticipated signal from a binary neutron star inspiral and coalescence starts at very low frequencies and chirps upward to around a kilohertz. Our sensitivity is from 40 Hz up to a few kilohertz, with a peak sensitivity at 100 Hz. We'd like to see as low in frequency as possible, but increasing seismic isolation doesn't win you much. The seismic floor in the noise curve is very steep. You can win some by pushing it to the left by decreasing the frequency of all the resonances. As you push it to the left, you expose more of the pendulum thermal noise curve, which is much flatter (Figure 3), and you don't get much more of the binary neutron star inspiral signal.
King: We have installed one of these lasers at Hanford. It's been running almost every day since December 19 of last year until now. During that time we've maintained a constant frequency lock, which was only interrupted because someone switched the laser off or there was a power supply fault.
Barton: It's a great adventure on one of the frontiers of physics. It should prove something fundamental about gravity, and it will become a new sort of telescope that will tell us a lot about the universe.
Peter King received his PhD from the University of Sydney, Australia in 1994, studying high-power optically pumped far-infrared lasers for fusion plasma diagnostics. In 1997 he joined the LIGO project to work on the prestabilized laser.
Garilyn Billingsley is currently overseeing internal IR metrology development and external fabrication subcontracts for the LIGO core optics. Garilynn received her Bachelor of Science in Physics from the Univ. of California in 1984 and worked in aerospace for 11 years before coming to the California Institute of Technology.
Core Optics Manager, LIGO
Phone: (1) 626/395-2184
Mark Barton started in geophysics at the Univ. of Queensland in Australia, and went on to do suspension design at the Japanese gravity wave project TAMA. He has been working on suspensions and seismic isolation for LIGO for two years.
LIGO Seismic Isolation
Phone: (1) 626/395-2973
Fax: (1) 626/304-9834
General company info:
California Institute of Technology
Pasadena, CA 91125