LIGO's Interferometer

Basic Michelson Labeled

Layout of a basic Michelson interferometer.

At their cores, LIGO's interferometers are Michelson Interferometers, the same sort of device that was invented in the 1880's:

  • They are L-shaped (not all interferometers are this shape)
  • Mirrors at the ends of the arms reflect light in order to create an interference pattern called 'fringes'
  • A device called a photodetector measures these fringes, revealing minute details of the objects or phenomenon being studied

But this is where the similarities end. The size and added complexity of LIGO's interferometers are far beyond anything the world's first interferometers could have achieved.

The first most obvious difference between a typical Michelson interferometer and LIGO's interferometers is its scale. With arms 4km (2.5 mi.) long, LIGO's interferometers are by far the largest ever built. (By contrast, the interferometer Michelson and Morley used in their famous experiment to study the "aether" had arms about 1.3m long). The scale of LIGO's instruments is crucial to its search for gravitational waves. The longer the arms of an interferometer, the smaller the meaurements they can make. And having to measure a change in distance 10,000 times smaller than a proton means that LIGO has to be larger and more sensitive than any interferometer ever before constructed.

While 4km-long arms seems pretty huge, if LIGO's interferometers were simple Michelsons, they would still be too short to enable the detection of gravitational waves. And of course there are practical limitations to building such a precision instrument much larger than 4km. So how can LIGO possibly make the measurements it does?

Longer is Better

Basic Michelson with FP labeled

Basic Michelson interferometer with Fabry Perot cavities. Additional mirrors are inserted near the beam splitter to facilitate multiple reflections of the laser, containing it within the interferometer and increasing the distance traveled by the beams. This greatly increases LIGO's sensitivity to the smallest changes in arm length.

The paradox was solved by altering the design of the Michelson to include something called "Fabry Perot cavities". The figure at left shows a basic Michelson design modified to include such cavities. An additional mirror is placed in each arm near the beam splitter (the box on the 45-degree angle), 4km from the mirror at the end of that arm. This 4km-long space comprises the Fabry Perot cavity. After entering the instrument via the beam splitter, the laser in each arm bounces between its two mirrors about 300 times before being merged with the beam from the other arm. These reflections serve two functions:

1. It builds up the laser light within the interferometer, which increases LIGO's sensitivity (more photons also makes LIGO more sensitive)

2. It increases the distance traveled by each laser from 4km to 1200km thereby solving our length problem! (The light in Michelson's original interferometer only traveled 11 meters.)

Since we know that the longer the arms of an interferometer, the more sensitive the instrument is to vibration, this design significantly increases LIGO's sensitivity and enables it to detect changes in arm length much smaller than a proton--the size of changes expected to be caused by a gravitational wave. And thanks to Fabry Perot cavities, LIGO can achieve this sensitivity with arms just 4km long.

There is an analogous effect in optical telescopes. Increasing the focal length of a telescope (also how far the light travels between mirrors or lenses before reaching your eye) not only increases the magnification achievable by any given eyepiece, but it also amplifies the smallest vibrations in the telescope. In a telescope, these vibrations are unwanted. LIGO, on the other hand, was designed to feel them, and and with arms effectively 1200km long, LIGO's interferometers can amplify the smallest conceivable vibrations enough that they are detectable and measurable.

 

We Need More Power!

Length isn't the only limiting factor in LIGO's sensitivity. Laser power is also a consideration. Just as increasing length increases the interferometer's sensitivity, increasing laser power also enhances its performance. While increasing length amplifies tiny changes in arm length, increasing laser power results in increasing the interferometer's resolving power. In other words, the more laser photons merge from each arm, the sharper the fringes that are measured by the photodetctor.

Basic Michelson with FP and PR labeled

Basic Michelson with Fabry Perot cavities and Power Recycling mirror. LIGO's interferometers actually use multiple power recycling mirrors but for simplicity only one is shown in the diagram.

But there's a problem here too. LIGO's laser first enters the interferometer at about 40 Watts, but it needs to operate closer to 750kW if it has any hope of detecting gravitational waves. Here we have another paradox. Just as it would be impossible to build a 1200km-long interferometer, building a laser with this initial power is a practical impossibility.

Once again, LIGO uses mirrors to solve this dilemma. They are called Power Recycling Mirrors. The figure at left shows schematically where a power recycling mirror is located inside each interferometer.

Inside the interferometer, light from the laser passes through the transparent side of a power recycling mirror to the beam splitter and then on to the arms of the interferometer. The beam splitter is like those one-way mirrors in police dramas: half the light comes out, the other half is reflected back into the room. The instrument's alignment and mirror coatings, and even quantum mechanics, ensure that nearly all of the laser light entering the arms follows a path back to the reflective side of the power recycling mirror rather than to the photodetector. As laser power is constantly entering the interferometer, the power recycling mirror continually reflects the laser light that has traveled through the instrument back into the interferometer (hence 'recycling'). This process greatly boosts the power of the laser beam inside the Fabry Perot cavities without the need to generate such a powerful laser beam at the outset.

The boost in power generated by power recycling results in a sharpening of the interference fringes that appear when the two beams are superimposed--fringes which will tell scientists if a gravitational wave has passed. The sharper the fringes, the easier it becomes to identify the tell-tale signs of gravitational waves.

Not Quite There Yet!

Two other modifications make LIGO's interferometers unique and able to make the world's smallest measurements. First, they also possess 'signal recycling' mirrors, which, like power recycling, enhance the signal that is received by the photodetector. And second, LIGO's interferometers were constructed with extraordinary mechanisms to damp out unwanted vibrations (noise) making it easier for scientists to weed out vibrations caused by gravitational waves. LIGO's seismic isolation system is discussed in much greater detail in LIGO Technology.

With these modifications, LIGO's interferometer is known as a Dual Recycled, Fabry-Perot Michelson -- but at its heart, it is still a Michelson interferometer.