Basic schematic of LIGO's interferometers with an incoming gravitational wave depicted as arriving from directly above the detector. (Caltech/MIT/LIGO Lab)
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-meter', or interferometer. 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!
Interferometers were pioneered in the mid-to-late 1800s by many scientists including Hippolyte Fizeau, Martin Hoek, Éleuthère Mascart, George Biddell Airy, and Eduard Ketteler, in their attempts to measure the velocity of light through various media (first and foremost, air and water, then others) and especially through moving media (like flowing water). This work was part of a study to understand the wave properties of light, and their dependence on the medium that light traverses.
As it was believed at the time that all waves require a medium for propagation, scientists such as the famous Augustin-Jean Fresnel proposed the existence of a "luminiferous ether", an amorphous substance permeating everything and serving only as a medium for the propagation of light waves. This theory was a prime target for experimental tests using interferometers. Among the scientists from around the world working on this question were American physicists Albert Michelson and Edward Morley, who invented a self-named optical configuration, the Michelson-Morley Interferometer. Results from their experiments published in 1887 are often cited as the first conclusive experimental evidence against the existence of ether, in favor of light (all electro-magnetic radiation) propagating without a medium - i.e., in vacuum. This discovery was one of the foundation stones of Einstein's theory of special, and later general, relativity, as Einstein identified the vacuum paths along which light propagates, tracing out the very curvature of space-time itself.
As a part of common knowledge and wide use in the late 1960s, the particular interferometric configuration used by Michelson and Morley was deemed to be a natural fit for detecting the effects of gravitational waves on space-time (called 'strain'), given its precise measurement of the phase change of light traveling along two perpendicular arms. As such, the Michelson interferometer’s configuration is a core, critical piece of all of today’s gravitational wave interferometric detectors, including LIGO, Virgo, Geo, and KAGRA.
What does an Interferometer Look Like?
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 (using radio interferometry), 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 laser beam-splitter, a series of mirrors, and a photodetector (the black dot) that records the interference pattern.
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 flat, glassy pond or pool and watched what happened knows about interference. When the stones hit the water, they generate concentric waves that move away from the source. Where two or more of those concentric waves intersect, they interfere with each other. This interference can result in a larger wave, a smaller wave, or no wave at all. The visible pattern occurring where the waves intersect is an interference pattern.
Interference patterns in water. The "interference" occurs in the regions where the waves from the different sources intersect. Similarly, LIGO's interferometer generates an interference pattern by bringing together the laser light waves from the two arms. [Wikimedia commons]
When the peaks of two waves meet, their peaks add up (constructive interference) When the peaks of one wave meet the valleys of another identical wave, they cancel out (in the graphic, it is total destructive interference). [www.explainthatstuff.com]
The principles of interference are simple to understand: Two or more waves interact. You add the heights and depths of the separate waves together as they interact, and the resulting wave is the interference pattern. The figure at right shows two specific kinds of interference: total constructive interference and total destructive interference. Total constructive interference happens when the peaks and troughs of two (or more) identical waves, moving in the same direction, perfectly meet up. When added together, you construct a larger wave, the size of which is equal to the sum of the heights (and depths) of the two waves at each point where they are physically interacting. Total destructive interference occurs when the peaks of one wave meets and matches the troughs of an identical wave moving in the opposite direction. When the two waves move through each other, they cancel each other out.
Of course, in nature, two or more waves are rarely identical, and the peaks and troughs of one wave will rarely perfectly meet the peaks or troughs of another wave like the illustration shows. But no matter how similar or different they are, when the waves intersect, the resulting wave always equals the sum of the heights and depths (amplitude) of the waves at their points of intersection. The animation below illustrates this effect in an ideal setting. Two identical waves, red and blue, are moving through each other in opposite directions, and the black wave shows the resulting interference pattern. In this idealized case, the combined wave experiences a full range of heights from twice as high/deep (total constructive interference) to flat (total destructive interference). Note how it changes as long as the red and blue waves continue to interact. In the real world, the interacting waves would be of different amplitudes (heights) and frequencies (widths) so as they interact, the resulting black wave would be more complex, but the principle of adding the heights/depths of the interacting waves at each point would still apply.
The changing black wave is the interference pattern created by the red and blue waves as they pass through/interact with each other. [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. Moreover, since LIGO reliably generates a laser beam with a single, consistent frequency, total constructive and destructive interference can occur. This means that when the peaks of the waves of one beam perfectly meet the troughs of the other wave, total destructive interference occurs. In water, the result is no wave. In light, the result is no light!
Conversely, when the peaks of one beam perfectly meet the peaks of another, total constructive interference occurs. Again, in water, the height of the resulting wave is equal to the sum of the heights of the two waves. In light, the result is a light intensity equal to the sum of the intensities of the two separate light beams.
Carrying this analogy to the end, in water, as identical waves pass through each other experiencing a full range of interference from partial to total constructive and destructive, the result is a bigger wave, a smaller wave, or no wave. In light, the result is a full range of brightness, from darkness to the sum of intensities of the interacting beams. The alignment of the waves as they interact dictates the resulting wave pattern (amplitude and frequency).
Parallels between constructive and destructive interference in water and with light. (Adapted from www.explainthatstuff.com)
In LIGO's interferometers, what dictates how well-aligned the laser beam waves are when they merge is simply the distance they travel before merging. If each beam travels exactly the same distance along each arm, then when the beams are merged again, their light waves will totally destructively interfere (LIGO is deliberately designed to make this happen if no gravitational waves are passing--no wave, no interference pattern). But if for some reason the lasers don't travel the same distances, their light waves are no longer in sync as they merge. The result? Some light reaches the photodetector. If the beams are traveling different distances because a gravitational wave is passing, thus causing the arms to alternately lengthen and shorten, the photodetector sees a flicker of light, ranging in intensity from no light wherever the waves totally destructively interfere to light nearly as bright as the original laser beam wherever the waves totally constructively interfere. This flicker lasts only as long as the passing gravitational wave is detectable in the interferometer, from a fraction of a second for a binary black hole merger, to tens of seconds for a binary neutron star merger. This process is described in more detail below.
How do Gravitational Waves Affect LIGO's Interferometer?
Gravitational waves cause space itself to stretch in one direction and simultaneously compress in a perpendicular direction. In LIGO, this causes one arm of the interferometer to get longer while the other gets shorter, then vice versa, back and forth as long as the wave is passing. The technical term for this motion is "Differential Arm" motion, or differential displacement, since the arms are simultaneously changing lengths in opposing ways.
As described above, as the lengths of the arms change, so too does the distance traveled by each laser beam. A beam in a shorter arm will return to the beam splitter before a beam in a longer arm--as the wave passes, each arm oscillates between being the shorter arm and the longer arm. When they arrive back at the beamsplitter (where they re-merge), the light waves no longer meet up nicely; they are out of phase. Instead, they shift in and out of alignment for as long as the wave is passing. In simple terms, this shifting alignment results in a flicker of light emerging from the interferometer. This process is illustrated in the clip at right from Einstein's Messengers [Credit: U.S. National Science Foundation (NSF)].
While in principle the idea seems almost 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 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" in order to detect the telltale flicker of light caused by a gravitational wave.
