Basic_ifo_diagram

Basic schematic of LIGO's interferometers with an incoming gravitational wave depicted as arriving from directly above the detector. (Image: LIGO)

What is an Interferometer?

Interferometers are investigative tools used in many fields of science and engineering. They are called interferometers because they work by merging two or more sources of light to create an interference pattern, which can be measured and analyzed; hence "Interfere-ometer". The interference patterns generated by interferometers contain information about the object or phenomenon being studied. They are often used to make very small measurements that are not achievable any other way. This is why they are so powerful for detecting gravitational waves--LIGO's interferometers are designed to measure a distance 1/10,000th the width of a proton!

Widely used today, interferometers were actually invented in the late 19th century by Albert Michelson. The Michelson Interferometer was used in 1887 in the "Michelson-Morley Experiment", which set out to prove or disprove the existence of "Luminiferous Aether"--a substance at the time thought to permeate the Universe. All modern interferometers have evolved from this first one since it demonstrated how the properties of light can be used to make the tiniest of measurements. The invention of lasers has enabled interferometers to make the smallest conceivable measurements, like those required by LIGO.

Remarkably, the basic structure of LIGO's interferometers differs little from the interferometer that Michelson designed over 125 years ago, but with some added features, described in LIGO's Interferometer.

 

What does an Interferometer Look Like?

Basic Michelson Labeled

Layout of a basic Michelson laser interferometer. (Click for larger image)

Because of their wide application, interferometers come in a variety of shapes and sizes. They are used to measure everything from the smallest variations on the surface of a microscopic organism, to the structure of enormous expanses of gas and dust in the distant Universe, and now, to detect gravitational waves. Despite their different designs and the various ways in which they are used, all interferometers have one thing in common: they superimpose beams of light to generate an interference pattern. The basic configuration of a Michelson laser interferometer is shown at right. It consists of a laser, a beam splitter, a series of mirrors, and a photodetector (the black dot) that records the interference pattern.

 

How Does it Work?

In a Michelson interferometer, a laser beam passes through a 'beam splitter' which as the name suggests, splits the original single beam into two beams. The beam splitter allows half of the light to pass through, while the other half is reflected at 90-degrees from the first. Each beam then travels down an arm of the interferometer, at the end of which, it encounters a mirror. The mirror reflects the beam back toward the beam splitter where the two beams (now coming from the opposite direction) are merged back into a single beam. In 'merging', the light waves from the two beams recombine into one, "interfering" with each other in the process before traveling to a photodetector, which is a device that measures the brightness of the recombined beam. LIGO's interferometers are set up so that, as long as the arms don't change length while the beams are traveling, when the two beams recombine, their light waves actucally cancel each other out and nothing reaches the photodetector. In this scenario, the beams are said to have "totally destructively interfered" with each other.

LIGO is designed this way to make it easier to detect when the arms are NOT staying the same length. If one arm gets longer than the other, one laser beam has to travel farther than the other and it takes longer to return to the beam splitter where it is supposed to recombine with the other beam. Since the beams don’t arrive at the same time, their light waves will be slightly offset when they merge, which  causes them to interfere in a different way than they did when they traveled the same distance. The resulting merged beam will be brighter than it was when the arms were the same length (the waves of light will no-longer totally destructively interfere so some light leaks out). In an interferometer, any change in light intensity indicates that something happened to change the distance traveled by one or both laser beams. Moreover, the interference pattern can be used to calculate precisely how much change in length occurred.

 

What is an Interference Pattern?

To better understand how interferometers work, it helps to understand more about 'interference'. Anyone who has thrown stones into a pond or a pool and watched what happened already knows a lot about interference. When the stones hit the water, they generate concentric waves that move away from the stone's point of entry. And where two or more of those concentric waves intersect, their shapes change, generating new waves that are sometimes larger, sometimes smaller, or they cancel each other out. The new pattern of waves occurring where the two separate waves intersect constitutes an "interference" pattern.

Interference patterns in water

Interference patterns in water. The "interference" occurs in the regions where the expanding circular waves from the different sources intersect. (Credit: Wikimedia commons)

Whats an IFO con and des interference

When the peaks of two waves meet, their peaks add up. When the peaks of one wave meet the valleys of another, they cancel out.  Credit: www.explainthatstuff.com

 

The principles of interference are quite simple to understand. The figure at right shows two specific kinds of interference: total constructive interference and total destructive interference. In total constructive interference, when the peak of one wave merges with the peak of an identical wave, they add together and 'construct' a larger wave. In total destructive interference, the peak of one wave meets the valley of an identical wave, and they totally cancel each other out (they 'destroy' each other).

In nature, the peaks and valleys of one wave will not always perfectly meet the peaks or valleys of another wave like the illustration shows. Regardless of how they merge, the height of the wave resulting from the interference always equals the sum of the heights of the merging waves. When the waves don't meet up perfectly, partial constructive or destructive interference occurs. The animation below illustrates this effect. If you watch closely, you will see that the black wave goes through a full range of heights from twice as high and deep (where total constructive interference occurs) to flat (where total destructive interference occurs) as the red and blue waves pass 'through' each other (interfere). In this example, the black wave is the interference pattern! Note how it continues to change as long as the red and blue waves continue to interact.

 

 

 

 

The changing black wave is the interference pattern created by the red and blue waves as they pass through/interact with each other. [Credit: Wikimedia Commons]

 

 

Parallels with Light

It just so happens that light waves behave just like water waves. When two beams of laser-light merge, they too generate an interference pattern that depends on how well-aligned the light waves are when they combine. Just like water, when the peaks of the waves of one light beam perfectly meet the valleys of another, total destructive interference occurs. In water, the wave disappears; in light, the light too disappears and no light (i.e. darkness) results. Conversely, when the peaks of one beam perfectly meet the peaks of another, total constructive interference occurs. Again relating to water, in water waves the height of the resulting wave is equal to the heights of the two waves added together; in a light beam, the result is a much brighter light. As with water, a full range of interference (which in light means a full range of brightness) from partial to total constructive and destructive can occur depending on how well aligned the waves are when they meet. The parallel with water is easy to visualize, as illustrated in the figure below.

Water vs Light Interference Paralells betwen contstructive and destructive interference in water and with light. [Adapted from www.explainthatstuff.com]

In LIGO's interferometers, what dictates how well-aligned the beams are when they merge is the distance they travel before meeting up again. If the beams travel exactly the same distance, their light waves will be perfectly aligned so that the crests of one laser beam match the troughs of the other laser beam causing total destructive interference (LIGO is deliberately designed to make this happen if no gravitational waves are passing). But if for some reason the lasers don't each travel the same distance, their light waves no longer align when they meet up again. In this case, they will no longer totally destructively interfere with each other. Depending on how the waves from the two beams meet up over time, no light, a little light, or a light as bright as the original laser beam may reach the photodetector. Looking again at the animmation above, if the red and blue waves were coming from the arms of the interferometer, the black wave shows what the photodetector would see as the waves interact: sometimes the photodetector sees a light as bright as both the red and blue wave (i.e., the two arms) combined, and sometimes the photodetector sees no light as the crests of one wave meet up with the troughs of the other.

So, what would cause the lasers to travel different distances?

One cause is gravitational waves!

Gravitational waves cause space itself to stretch in one direction and squeeze in a perpendicular direction simultaneously. The effect on LIGO is this: as the wave passes, one arm of an interferometer lengthens while the other shrinks, then vice versa, and so on. The arms will oscillate this way for as long as it takes the wave to pass.

As the length of each arm varies, the distance traveled by each laser beam also varies. Consequently, the beam in the shorter arm returns to the beam splitter before the beam in the longer arm. Arriving at different times (one before the other, then after, then before again, etc.) causes the beams to shift in and out of alignment as they merge, experiencing varying levels of destructive and constructive interference as long as the arms change lengths, which is for as long as it takes for the gravitational wave to pass. In essence, this results in a flicker of light reaching the photodetector. This process is illustrated in the clip at right from Einstein's Messengers (Credit: United States National Science Foundation).

While in principle the idea seems quite simple, in practice, detecting that flicker is not. The change in arm length caused by a gravitational wave can be as small as 1/10,000th the width of a proton (that's 10-19 m)! Furthermore, finding a gravitational wave flicker amongst all the other flickers LIGO experiences (caused by anything that can shake up the mirrors, like earthquakes or traffic on nearby roads) is another story. LIGO Technology describes in detail how LIGO filters out much of that "noise" to make detecting the tell-tale 'flicker' of light caused by a gravitational wave possible.