By Chinmay Pala
Abstract
In this paper, the author explains how the Laser Interferometric Gravitational-wave Observatory (LIGO) detects gravitational waves and goes over the differences between initial LIGO and advanced LIGO. Beginning by explaining the formation of gravitational waves, the author then gives an overview of the history and locations of LIGO. In the main part of the paper, the different structures of LIGO are examined: interferometer, laser, beam splitter, arms, mirrors, vibration isolation systems, and photodetector. In the end, the author compares the vibration isolation systems and mirrors used in the initial LIGO and advanced LIGO.
1.1 Introduction
Gravitational waves are created when two huge masses collide or orbit each other. These waves are ripples in space-time that travel in all directions away from the source, at the speed of light. The gravitational wave is attenuated when it reaches the earth than when it was first created, due to the loss of concentration of energy happening in a larger area compared to the time of origin as shown in Fig 01.
Fig 01: An artist\’s illustration of two black holes spiralling together, creating gravitational waves in the process.
(Image from [2])
These waves can be observed from the earth with a great level of precision, using the Laser Interferometer Gravitational-Wave Observatory (LIGO). There arises a question, what is the use of detecting and observing gravitational waves? “Detecting and analyzing the information carried by gravitational waves is allowing us to observe the Universe in a way never before possible, providing astronomers and other scientists with their first glimpses of literally unseeable wonders.” says an official who works at LIGO. [1,3,4]
1.2 History and Locations of LIGO
In the 1960s, Joseph Weber pioneered the effort to build detectors for finding gravitational waves, using large cylinders of aluminium that vibrate in response to a passing wave. Even though it was not enough to detect a gravitational wave, it was an approach that had not been taken before. In the late 1970s, Kip Thorne created an experimental gravitational wave group at Caltech, led by Drever (in 1979) and Stan Whitcomb (in 1980). In 1980, this group got its first funding from the National Science Foundation (NSF), which helped the organization to construct a prototype of the interferometer, and this fund helped LIGO to start working as an observatory.
A cooperative agreement for the management of LIGO was signed between NSF and Caltech. The location for the interferometer was chosen as Hanford, Washington and Livingston, Louisiana in 1992. With the initial funding, the first generation of LIGO (initial-LIGO) operated for 9 years from 1999 to 2008.
In 1993, it was decided to make an Interferometer in Europe for confirming that it’s not just a regional seismic wave or any other small interference, as Gravitational Waves pass through a large area. So the location was confirmed in Santo Stefano a Macerata in Central Italy which was named as Virgo interferometer. These 3 Interferometers weren\’t enough to cover every part of the earth, to observe if a Gravitational-wave passes. So a 4th interferometer was set up at KAGRA, in Japan whose construction was finished on 4th October 2019, a 5th interferometer named GEO600 situated in Sarstedt South of Hanover, Germany and 6th Interferometer in Maharashtra, India which is scheduled to be operational from 2025.
Fig 2: A map of the global ground-based gravitational wave detector network. [4] 
1.3 Structure of LIGO
This section covers the various components used in LIGO. These structures are- the Interferometer, Laser, Beam Splitter, the Arms, the Mirrors, the Vibration Isolation Systems, and the Photodetector. The difference made in each of these components when it was upgraded to Advanced LIGO will also be looked at.
1.31 The Interferometer
An interferometer is an instrument that is used for merging two or more sources of light to create an interference pattern, which is then measured and analysed by looking at the type of interference. Constructive interference is where both waves align in such a way that it adds up to a bigger wave and destructive interference is when waves align in such a way that they cancel each other out.
Fig 03: constructive interference [5] Fig 04: destructive interference [5] 
The present-day model of an interferometer was taken from its previous model known as ‘The Michelson Interferometer’ which was invented by Albert Abraham Michelson for his Michelson-Morley Experiment in 1887.
The interferometer experiment begins with producing a laser which is then split by the beam splitter that splits the single laser beam into two separate beams, which travel in perpendicular directions with a splitting ratio of 1:1 (50% in one direction and 50% in another). Then this laser light is made to travel through Fabry Perot cavities, where it bounces back and forth 300 times. The beam splitter reflects some photons toward the photodetector, but most of the light gets passed back toward the power recycling mirror. The power recycling mirror reflects the beam to the beam splitter to re-enter the interferometer arms. This makes sure that many photons are going through the interferometer arms at any given time. The beams that go towards the photodetector are combined back and detected by the photodetector which helps in seeing the changes made by the light wave. [6]
Fig 05: Layout of Basic Michelson interferometer with Fabry Perot cavities. (Image From physics world) [7] 
1.32 The Laser and the Beam splitter
The interferometer produces a powerful infrared laser with an output after amplification that reaches 200 Watts (amount of energy it takes to produce a certain amount of light. The higher the wattage, the brighter the light) and emits light with a wavelength of 1064 nanometer, which retains its power using the Power recycling mirror.
A beam splitter is a device used in physics labs and other experiments to split the light in two. So in LIGO after the production of the laser light, it goes through the beam splitter that splits the light and sends each part to each arm as shown in Fig 03. [8]
1.33 The Arms
The long arms of the interferometer are kept at ultra-high vacuum. The ultra-high vacuum consists of 2 cylindrical pipe-like structures made of steel, which are constructed to be perpendicular to each other in the ground and have a precise length of 4 km on each side. The longer the arms of the interferometer, the more helpful it is to find the smallest vibration, hence the distance has to be increased.
Even though 4km seems a large distance, this wasn’t enough to find a gravitational wave. So with the help of Fabry- Perot cavities, the beam bounces back and forth from the two mirrors, 300 times. Resulting in a change in distance travelled by the light from just 4km to 1200km
(). This was considered a breakthrough in the field of observing gravitational waves.
To maintain the accuracy in the result, these arms have to be vacuum because even a small particle could disturb the beam which could drastically affect the obtained result. According to officials at LIGO, it took about 1100 hours to evacuate all the air present inside it to obtain a vacuum using a turbopump, and succeeded by making air pressure of 10-9 torr, which is equal to one-trillionth of earth’s atmosphere. [9]
1.34 The Mirrors
The mirror technology and the optics used at LIGO are made with such precision to get the most accurate result possible. Even a small mistake in any of the optics will result in a huge variation in the obtained result. The more distance the LASER goes, a small change in one point in time leads to a drastic effect. If the angle changes, the laser aim would be off. The laser bounces back and forth 300 times, so a small change of 1 mm would become a huge change of 300 mm.
The optics used at LIGO includes 4 test masses: 2 at the end of both vacuum tubes and 2 near the beam splitter. These test masses help the laser beam to bounce back and forth as explained in part [1.33]. These mirrors are made of pure fused silica glass. In the initial LIGO, the suspension was made of steel wires and that was changed in advanced LIGO to fused silica glass fibres, which is as thin as human hair. The new wires do not produce any internal deflection on an atomic scale, unlike steel wire. As the low coefficient of thermal expansion of fused quartz makes it a useful material for precision mirror substrates.The differences between the mirrors used in the initial LIGO and advanced LIGO are listed below in table-1 [10]
|
Initial LIGO |
Advanced LIGO |
|
Single- stage pendulum design |
Four stage pendulum design |
|
The test mass a has diameter of 25cm (9.8inch) |
The test mass has a diameter of 34cm (13.4 inches) |
|
The test mass weighed 11kg (22 lb) |
The test mass weighs 40kg (88 lb) |
|
The thickness of test mass was 10cm (3.9 inches) |
The thickness of test mass was 20cm (7.8 inches) |
|
– passive isolation system |
passive and active isolation system |
Table 1: Summarizes the difference in test masses used in initial LIGO vs advanced LIGO.[10]
1.35 Vibration Isolation System
An Isolation system is necessary for LIGO’s optics to be in a stable position to give an accurate result, as even a small scale disturbance can make a huge difference due to the high-level sensitivity of LIGO. This system is necessary to isolate the optics from seismic waves and other ground-based noises that can disrupt the detection of a gravitational wave.
Vibration isolation in the initial LIGO consisted of a single staged pendulum that used steel fibres, which caused a lot of disturbance at the atomic level and created thermal noises.
Vibration isolation systems used in a-LIGO can be mainly differentiated as (a) Passive Isolation system and (b) Active isolation system.
A passive isolation system works on the principle of inertia. That means the higher the mass of the whole system, the more stable the test mass (mirror) will be. Inertia counteracts the force that applies to the test mass making it as stable as in Vacuum and stabilizes the test masses using simple harmonic motion.
The passive isolation system has two sides horizontally: the main chain side and the reaction chain side. Each chain contains four masses and they are back to back while looking in perspective of the laser beam. The laser hits on the main chain side as you can see in Fig 4, which shows the main chain test mass as a transparent blue colour.
Active isolation uses sensors to sense the seismic wave or any other disturbance and analyse them. Using this data, the magnet gives out a certain force so that the mirror is in a stable position. The Active system moves the reaction chain in the opposite direction of the force that you\’re trying to correct for. The reaction chain helps the mirror to be stable; it connects with the main chain with an electrostatic force to counteract the motion. Using a physical force directly on the main chain would cause too large a displacement if done in a short interval of time.
Vibration Isolation is not only used in Test masses but also the other optical components that help LIGO to get an accurate result. [7,11,13]
Fig 06: Difference between initial LIGO and advanced LIGO suspensions . [11]
1.36 The Photodetector
The Photodetector is used to detect the light waves coming back after the whole process of going through a beam splitter and travelling a distance of 1200 km. It detects the time variation when both the waves come back and carefully looks through the interference that has happened to the light wave. Figure 7 shows an example of how the light looks when it lands on the photodetector.
If something like a gravitational wave passes, there would be interference in the light wave which reaches back resulting in fluctuations that can be seen on a screen. This data which is generated every day is then transferred to a network of supercomputers for analyzing and archiving. This consists of terabytes of data, which is quite impossible for a normal computer to handle. [12,14]
Fig 07: How light appears when it lands on the output photodetector (image directly provided by Michael Landry of LIGO Hanford)
1.4 Conclusion
This article gives a brief overview of the engineering used at LIGO, showing its importance and the precision it has to use to find a gravitational wave. The author discussed how LIGO evolved from its initial stage to advanced LIGO, which gives more accurate results. Studying more about gravitational waves opens a new field of science that can help one understand more about the history and future of the universe.
1.5 Acknowledgments
I would like to thank Daniel Kolodrubetz for his valuable insights and support from the beginning till the end. As well as all the members of the Polygence organisation for giving an opportunity to do this project which was only possible due to their funding and other external support. I would like to extend my gratitude to my parents for providing me with all the required facilities.
1.6 References
- Chen, Sophia. 2019. What Next for Gravitational Wave Detection?, June, 2019.
https://www.aps.org/publications/apsnews/201906/wave.cfm
- Reddy, Francs., and Felicia Chou. 2016. “NSF’s LIGO has detected Gravitational Waves.” https://www.nasa.gov/feature/goddard/2016/nsf-s-ligo-has-detected-gravitational-waves
- Gregersen, Erik. n.d. “Science.” N.p: Encyclopedia Britannica. https://www.britannica.com/list/6-amazing-facts-about-gravitational-waves-and-ligo
- LIGO Scientific Collaboration. n.d. “Gravitational Waves.” What are Gravitational waves?
https://www.ligo.caltech.edu/page/what-are-gw
- Gibson, George N, n.d. “Types of Interference.” Constructive and Destructive Interference https://www.phys.uconn.edu/~gibson/Notes/Section5_2/Sec5_2.htm
- Hua, Wensheng. June, 2005. Low Frequency Vibration Isolation and Alignment system for Advanced LIGO
- Commissariat, Tushna. 2017. The great detector. N.p.: Physics World. http://live.iop-pp01.agh.sleek.net/physicsworld/reader/#!edition/editions_usa_2017/article/page-22383
- LIGO Scientific Collaboration. n.d. “LIGO’s Laser, Frequency and Power Stability” https://www.ligo.caltech.edu/page/laser
- LIGO Scientific Collaboration. n.d. “Ultra-High Vacuum.” Ultra-HIgh Vacuum.
https://www.ligo.caltech.edu/page/vacuum
- LIGO Scientific Collaboration. n.d. “LIGO Optics.” LIGO Optics
https://www.ligo.caltech.edu/page/optics
- LIGO Scientific Collaboration. n.d. “Vibration Isolation System- Active and Passive Damping.” Vibration Isolation. https://www.ligo.caltech.edu/page/vibration-isolation
- LIGO Scientific Collaboration (August 2014 LSC Author list). 2014. Advanced LIGO. N.p.: LIGO collaboration
- Seismic Isolation of Advanced LIGO; Review of strategy, instrumentation and performance. 32nd https://iopscience.iop.org/article/10.1088/0264-9381/32/18/185003/meta
- The Optical Society. 2017. “Increasing the sensitivity of next-generation gravitational wave detectors.” https://www.sciencedaily.com/releases/2017/02/170210131000.htm
- Hua, Wensheng. June, 2005. Low Frequency Vibration Isolation and Alignment system for Advanced LIGO
About the author
Chinmay Pala is a high-school sophomore studying in Kendriya Vidyalaya, Mahe, India. He worked as a science communicator for various journals, especially for the topic ‘Astronomy’. He is passionate about Physics and Astronomy and believes that nothing should be left undefined or undiscovered. In the future, he wishes to work in the Space sector and take humanity to the next level.