Optics is the branch of physics that studies the behaviour and properties of light , including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible , ultraviolet , and infrared light. Light is a type of electromagnetic radiation , and other forms of electromagnetic radiation such as X-rays , microwaves , and radio waves exhibit similar properties.
180-403: An optical amplifier is a device that amplifies an optical signal directly, without the need to first convert it to an electrical signal. An optical amplifier may be thought of as a laser without an optical cavity , or one in which feedback from the cavity is suppressed. Optical amplifiers are important in optical communication and laser physics . They are used as optical repeaters in
360-438: A 5 σ {\displaystyle 5\sigma } -significance will be achieved by 2025 by combining the measurements of several collaborations. Gravitational waves are constantly passing Earth ; however, even the strongest have a minuscule effect and their sources are generally at a great distance. For example, the waves given off by the cataclysmic final merger of GW150914 reached Earth after travelling over
540-783: A decay in the orbit by about 1 × 10 meters per day or roughly the diameter of a proton . At this rate, it would take the Earth approximately 3 × 10 times more than the current age of the universe to spiral onto the Sun. This estimate overlooks the decrease in r over time, but the radius varies only slowly for most of the time and plunges at later stages, as r ( t ) = r 0 ( 1 − t t coalesce ) 1 / 4 , {\displaystyle r(t)=r_{0}\left(1-{\frac {t}{t_{\text{coalesce}}}}\right)^{1/4},} with r 0 {\displaystyle r_{0}}
720-516: A "cross"-polarized gravitational wave, h × , the effect on the test particles would be basically the same, but rotated by 45 degrees, as shown in the second animation. Just as with light polarization, the polarizations of gravitational waves may also be expressed in terms of circularly polarized waves. Gravitational waves are polarized because of the nature of their source. In general terms, gravitational waves are radiated by large, coherent motions of immense mass, especially in regions where gravity
900-408: A "kick" with amplitude as large as 4000 km/s. This is fast enough to eject the coalesced black hole completely from its host galaxy. Even if the kick is too small to eject the black hole completely, it can remove it temporarily from the nucleus of the galaxy, after which it will oscillate about the center, eventually coming to rest. A kicked black hole can also carry a star cluster with it, forming
1080-471: A billion light-years , as a ripple in spacetime that changed the length of a 4 km LIGO arm by a thousandth of the width of a proton , proportionally equivalent to changing the distance to the nearest star outside the Solar System by one hair's width. This tiny effect from even extreme gravitational waves makes them observable on Earth only with the most sophisticated detectors. The effects of
1260-430: A broad band, or extremely low reflectivity at a single wavelength. Constructive interference in thin films can create a strong reflection of light in a range of wavelengths, which can be narrow or broad depending on the design of the coating. These films are used to make dielectric mirrors , interference filters , heat reflectors , and filters for colour separation in colour television cameras. This interference effect
1440-483: A changing quadrupole moment . That is, the system will give off gravitational waves. In theory, the loss of energy through gravitational radiation could eventually drop the Earth into the Sun . However, the total energy of the Earth orbiting the Sun ( kinetic energy + gravitational potential energy ) is about 1.14 × 10 joules of which only 200 watts (joules per second) is lost through gravitational radiation, leading to
1620-619: A changing index of refraction; this principle allows for lenses and the focusing of light. The simplest case of refraction occurs when there is an interface between a uniform medium with index of refraction n 1 and another medium with index of refraction n 2 . In such situations, Snell's Law describes the resulting deflection of the light ray: n 1 sin θ 1 = n 2 sin θ 2 {\displaystyle n_{1}\sin \theta _{1}=n_{2}\sin \theta _{2}} where θ 1 and θ 2 are
1800-497: A complete relativistic theory of gravitation. He conjectured, like Poincare, that the equation would produce gravitational waves, but, as he mentions in a letter to Schwarzschild in February 1916, these could not be similar to electromagnetic waves. Electromagnetic waves can be produced by dipole motion, requiring both a positive and a negative charge. Gravitation has no equivalent to negative charge. Einstein continued to work through
1980-399: A converging lens has positive focal length, while a diverging lens has negative focal length. Smaller focal length indicates that the lens has a stronger converging or diverging effect. The focal length of a simple lens in air is given by the lensmaker's equation . Ray tracing can be used to show how images are formed by a lens. For a thin lens in air, the location of the image is given by
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#17327724481132160-497: A detailed version of the "sticky bead argument". This later led to a series of articles (1959 to 1989) by Bondi and Pirani that established the existence of plane wave solutions for gravitational waves. Paul Dirac further postulated the existence of gravitational waves, declaring them to have "physical significance" in his 1959 lecture at the Lindau Meetings . Further, it was Dirac who predicted gravitational waves with
2340-439: A distributed amplifier. Lumped amplifiers, where the pump light can be safely contained to avoid safety implications of high optical powers, may use over 1 W of optical power. The principal advantage of Raman amplification is its ability to provide distributed amplification within the transmission fiber, thereby increasing the length of spans between amplifier and regeneration sites. The amplification bandwidth of Raman amplifiers
2520-419: A few nm up to ~80 nm. Typical use of EDFA in telecommunications calls for Conventional , or C-band amplifiers (from ~1525 nm to ~1565 nm) or Long , or L-band amplifiers (from ~1565 nm to ~1610 nm). Both of these bands can be amplified by EDFAs, but it is normal to use two different amplifiers, each optimized for one of the bands. The principal difference between C- and L-band amplifiers
2700-446: A frequency of 0.5 Hz, and a wavelength of about 600 000 km, or 47 times the diameter of the Earth. In the above example, it is assumed that the wave is linearly polarized with a "plus" polarization, written h + . Polarization of a gravitational wave is just like polarization of a light wave except that the polarizations of a gravitational wave are 45 degrees apart, as opposed to 90 degrees. In particular, in
2880-531: A hole in the gain for wavelengths close to that signal by saturation of the inhomogeneously broadened ions. Spectral holes vary in width depending on the characteristics of the optical fiber in question and the power of the burning signal, but are typically less than 1 nm at the short wavelength end of the C-band, and a few nm at the long wavelength end of the C-band. The depth of the holes are very small, though, making it difficult to observe in practice. Although
3060-469: A longer gain fiber. However, this disadvantage can be mitigated by combining gain and the dispersion compensation in a single fiber. A third disadvantage of Raman amplifiers is a fast response time, which gives rise to new sources of noise, as further discussed below. Finally, there are concerns of nonlinear penalty in the amplifier for the WDM signal channels. Note: The text of an earlier version of this article
3240-412: A pair of solar mass neutron stars in a circular orbit at a separation of 1.89 × 10 m (189,000 km) has an orbital period of 1,000 seconds, and an expected lifetime of 1.30 × 10 seconds or about 414,000 years. Such a system could be observed by LISA if it were not too far away. A far greater number of white dwarf binaries exist with orbital periods in this range. White dwarf binaries have masses in
3420-407: A passing gravitational wave, in an extremely exaggerated form, can be visualized by imagining a perfectly flat region of spacetime with a group of motionless test particles lying in a plane, e.g., the surface of a computer screen. As a gravitational wave passes through the particles along a line perpendicular to the plane of the particles, i.e., following the observer's line of vision into the screen,
3600-620: A signal generated by the merger of two black holes was received by the LIGO gravitational wave detectors in Livingston, Louisiana, and in Hanford, Washington. The 2017 Nobel Prize in Physics was subsequently awarded to Rainer Weiss , Kip Thorne and Barry Barish for their role in the direct detection of gravitational waves. In Albert Einstein 's general theory of relativity , gravity
3780-450: A similar structure to Fabry–Pérot laser diodes but with anti-reflection design elements at the end faces. Recent designs include anti-reflective coatings and tilted wave guide and window regions which can reduce end face reflection to less than 0.001%. Since this creates a loss of power from the cavity which is greater than the gain, it prevents the amplifier from acting as a laser. Another type of SOA consists of two regions. One part has
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#17327724481133960-477: A single scalar quantity to represent the electric field of the light wave, rather than using a vector model with orthogonal electric and magnetic vectors. The Huygens–Fresnel equation is one such model. This was derived empirically by Fresnel in 1815, based on Huygens' hypothesis that each point on a wavefront generates a secondary spherical wavefront, which Fresnel combined with the principle of superposition of waves. The Kirchhoff diffraction equation , which
4140-522: A single point on the image, while chromatic aberration occurs because the index of refraction of the lens varies with the wavelength of the light. In physical optics, light is considered to propagate as waves. This model predicts phenomena such as interference and diffraction, which are not explained by geometric optics. The speed of light waves in air is approximately 3.0×10 m/s (exactly 299,792,458 m/s in vacuum ). The wavelength of visible light waves varies between 400 and 700 nm, but
4320-437: A spectrum. The discovery of this phenomenon when passing light through a prism is famously attributed to Isaac Newton. Some media have an index of refraction which varies gradually with position and, therefore, light rays in the medium are curved. This effect is responsible for mirages seen on hot days: a change in index of refraction air with height causes light rays to bend, creating the appearance of specular reflections in
4500-449: A structure of a Fabry-Pérot laser diode and the other has a tapered geometry in order to reduce the power density on the output facet. Semiconductor optical amplifiers are typically made from group III-V compound semiconductors such as GaAs /AlGaAs, InP / InGaAs , InP /InGaAsP and InP /InAlGaAs, though any direct band gap semiconductors such as II-VI could conceivably be used. Such amplifiers are often used in telecommunication systems in
4680-465: A thickness of one-fourth the wavelength of incident light. The reflected wave from the top of the film and the reflected wave from the film/material interface are then exactly 180° out of phase, causing destructive interference. The waves are only exactly out of phase for one wavelength, which would typically be chosen to be near the centre of the visible spectrum, around 550 nm. More complex designs using multiple layers can achieve low reflectivity over
4860-779: A total orbital lifetime that may have been billions of years. In August 2017, LIGO and Virgo observed the first binary neutron star inspiral in GW170817 , and 70 observatories collaborated to detect the electromagnetic counterpart, a kilonova in the galaxy NGC 4993 , 40 megaparsecs away, emitting a short gamma ray burst ( GRB 170817A ) seconds after the merger, followed by a longer optical transient ( AT 2017gfo ) powered by r-process nuclei. Advanced LIGO detectors should be able to detect such events up to 200 megaparsecs away; at this range, around 40 detections per year would be expected. Black hole binaries emit gravitational waves during their in-spiral, merger , and ring-down phases. Hence, in
5040-476: A universal gravitational wave background . North American Nanohertz Observatory for Gravitational Waves states, that they were created over cosmological time scales by supermassive black holes, identifying the distinctive Hellings-Downs curve in 15 years of radio observations of 25 pulsars. Similar results are published by European Pulsar Timing Array, who claimed a 3 σ {\displaystyle 3\sigma } -significance . They expect that
5220-476: A variety of technologies and everyday objects, including mirrors , lenses , telescopes , microscopes , lasers , and fibre optics . Optics began with the development of lenses by the ancient Egyptians and Mesopotamians . The earliest known lenses, made from polished crystal , often quartz , date from as early as 2000 BC from Crete (Archaeological Museum of Heraclion, Greece). Lenses from Rhodes date around 700 BC, as do Assyrian lenses such as
5400-553: A well defined energy density in 1964. After the Chapel Hill conference, Joseph Weber started designing and building the first gravitational wave detectors now known as Weber bars . In 1969, Weber claimed to have detected the first gravitational waves, and by 1970 he was "detecting" signals regularly from the Galactic Center ; however, the frequency of detection soon raised doubts on the validity of his observations as
5580-422: A wide range of doped solid-state materials ( Nd: Yb:YAG, Ti:Sa ) and different geometries (disk, slab, rod) to amplify optical signals. The variety of materials allows the amplification of different wavelength while the shape of the medium can distinguish between more suitable for energy of average power scaling. Beside their use in fundamental research from gravitational wave detection to high energy physics at
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5760-525: A wide range of scientific topics, and discussed light from four different perspectives: an epistemology of light, a metaphysics or cosmogony of light, an etiology or physics of light, and a theology of light, basing it on the works of Aristotle and Platonism. Grosseteste's most famous disciple, Roger Bacon , wrote works citing a wide range of recently translated optical and philosophical works, including those of Alhazen, Aristotle, Avicenna , Averroes , Euclid, al-Kindi, Ptolemy, Tideus, and Constantine
5940-515: A worldwide revolution called the Information Age” and Gilder compared the optical amplifier to the integrated circuit in importance, predicting that it would make possible the Age of Information. Optical amplification WDM systems are the common basis of all local, metro, national, intercontinental and subsea telecommunications networks and the technology of choice for the fiber optic backbones of
6120-591: Is a more comprehensive model of light, which includes wave effects such as diffraction and interference that cannot be accounted for in geometric optics. Historically, the ray-based model of light was developed first, followed by the wave model of light. Progress in electromagnetic theory in the 19th century led to the discovery that light waves were in fact electromagnetic radiation. Some phenomena depend on light having both wave-like and particle-like properties . Explanation of these effects requires quantum mechanics . When considering light's particle-like properties,
6300-427: Is a simple paraxial physical optics model for the propagation of coherent radiation such as laser beams. This technique partially accounts for diffraction, allowing accurate calculations of the rate at which a laser beam expands with distance, and the minimum size to which the beam can be focused. Gaussian beam propagation thus bridges the gap between geometric and physical optics. In the absence of nonlinear effects,
6480-424: Is about 130,000 seconds or 36 hours. The orbital frequency will vary from 1 orbit per second at the start, to 918 orbits per second when the orbit has shrunk to 20 km at merger. The majority of gravitational radiation emitted will be at twice the orbital frequency. Just before merger, the inspiral could be observed by LIGO if such a binary were close enough. LIGO has only a few minutes to observe this merger out of
6660-496: Is absent from Newtonian physics. In gravitational-wave astronomy , observations of gravitational waves are used to infer data about the sources of gravitational waves. Sources that can be studied this way include binary star systems composed of white dwarfs , neutron stars , and black holes ; events such as supernovae ; and the formation of the early universe shortly after the Big Bang . The first indirect evidence for
6840-437: Is also what causes the colourful rainbow patterns seen in oil slicks. Gravitational wave Gravitational waves are transient displacements in a gravitational field – generated by the relative motion of gravitating masses – that radiate outward from their source at the speed of light . They were first proposed by Oliver Heaviside in 1893 and then later by Henri Poincaré in 1905 as
7020-486: Is considered to travel in straight lines, while in physical optics, light is considered as an electromagnetic wave. Geometrical optics can be viewed as an approximation of physical optics that applies when the wavelength of the light used is much smaller than the size of the optical elements in the system being modelled. Geometrical optics , or ray optics , describes the propagation of light in terms of "rays" which travel in straight lines, and whose paths are governed by
7200-418: Is defined by the pump wavelengths utilised and so amplification can be provided over wider, and different, regions than may be possible with other amplifier types which rely on dopants and device design to define the amplification 'window'. Raman amplifiers have some fundamental advantages. First, Raman gain exists in every fiber, which provides a cost-effective means of upgrading from the terminal ends. Second,
7380-491: Is derived using Maxwell's equations, puts the Huygens-Fresnel equation on a firmer physical foundation. Examples of the application of Huygens–Fresnel principle can be found in the articles on diffraction and Fraunhofer diffraction . More rigorous models, involving the modelling of both electric and magnetic fields of the light wave, are required when dealing with materials whose electric and magnetic properties affect
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7560-607: Is generally used where low-noise performance is required. The absorption band is relatively narrow and so wavelength stabilised laser sources are typically needed. The 1480 nm band has a lower, but broader, absorption cross-section and is generally used for higher power amplifiers. A combination of 980 nm and 1480 nm pumping is generally utilised in amplifiers. Gain and lasing in Erbium-doped fibers were first demonstrated in 1986–87 by two groups; one including David N. Payne , R. Mears , I.M Jauncey and L. Reekie, from
7740-491: Is not fully understood, it is not easy to model the gravitational radiation emitted by them. As noted above, a mass distribution will emit gravitational radiation only when there is spherically asymmetric motion among the masses. A spinning neutron star will generally emit no gravitational radiation because neutron stars are highly dense objects with a strong gravitational field that keeps them almost perfectly spherical. In some cases, however, there might be slight deformities on
7920-409: Is not possible with conventional astronomy, since before recombination the universe was opaque to electromagnetic radiation. Precise measurements of gravitational waves will also allow scientists to test more thoroughly the general theory of relativity. In principle, gravitational waves can exist at any frequency. Very low frequency waves can be detected using pulsar timing arrays. In this technique,
8100-407: Is so strong that Newtonian gravity begins to fail. The effect does not occur in a purely spherically symmetric system. A simple example of this principle is a spinning dumbbell . If the dumbbell spins around its axis of symmetry, it will not radiate gravitational waves; if it tumbles end over end, as in the case of two planets orbiting each other, it will radiate gravitational waves. The heavier
8280-472: Is that a longer length of doped fiber is used in L-band amplifiers. The longer length of fiber allows a lower inversion level to be used, thereby giving emission at longer wavelengths (due to the band-structure of Erbium in silica) while still providing a useful amount of gain. EDFAs have two commonly used pumping bands – 980 nm and 1480 nm. The 980 nm band has a higher absorption cross-section and
8460-582: Is that it is a relatively broad-band amplifier with a bandwidth > 5 THz, and the gain is reasonably flat over a wide wavelength range. However, a number of challenges for Raman amplifiers prevented their earlier adoption. First, compared to the EDFAs, Raman amplifiers have relatively poor pumping efficiency at lower signal powers. Although a disadvantage, this lack of pump efficiency also makes gain clamping easier in Raman amplifiers. Second, Raman amplifiers require
8640-455: Is the most deployed fiber amplifier as its amplification window coincides with the third transmission window of silica-based optical fiber. The core of a silica fiber is doped with trivalent erbium ions (Er) and can be efficiently pumped with a laser at or near wavelengths of 980 nm and 1480 nm, and gain is exhibited in the 1550 nm region. The EDFA amplification region varies from application to application and can be anywhere from
8820-415: Is therefore amplified in the same manner as the signals, hence the term Amplified Spontaneous Emission . ASE is emitted by the amplifier in both the forward and reverse directions, but only the forward ASE is a direct concern to system performance since that noise will co-propagate with the signal to the receiver where it degrades system performance. Counter-propagating ASE can, however, lead to degradation of
9000-409: Is to the lens, the further the image is from the lens. With diverging lenses, incoming parallel rays diverge after going through the lens, in such a way that they seem to have originated at a spot one focal length in front of the lens. This is the lens's front focal point. Rays from an object at a finite distance are associated with a virtual image that is closer to the lens than the focal point, and on
9180-437: Is treated as a phenomenon resulting from the curvature of spacetime . This curvature is caused by the presence of mass. (See: Stress–energy tensor ) If the masses move, the curvature of spacetime changes. If the motion is not spherically symmetric, the motion can cause gravitational waves which propagate away at the speed of light . As a gravitational wave passes an observer, that observer will find spacetime distorted by
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#17327724481139360-480: The Book of Optics ( Kitab al-manazir ) in which he explored reflection and refraction and proposed a new system for explaining vision and light based on observation and experiment. He rejected the "emission theory" of Ptolemaic optics with its rays being emitted by the eye, and instead put forward the idea that light reflected in all directions in straight lines from all points of the objects being viewed and then entered
9540-412: The LIGO and Virgo detectors received gravitational wave signals at nearly the same time as gamma ray satellites and optical telescopes saw signals from a source located about 130 million light years away. The possibility of gravitational waves and that those might travel at the speed of light was discussed in 1893 by Oliver Heaviside , using the analogy between the inverse-square law of gravitation and
9720-494: The National Ignition Facility they can also be found in many of today's ultra short pulsed lasers . Doped-fiber amplifiers (DFAs) are optical amplifiers that use a doped optical fiber as a gain medium to amplify an optical signal. They are related to fiber lasers . The signal to be amplified and a pump laser are multiplexed into the doped fiber, and the signal is amplified through interaction with
9900-617: The Nimrud lens . The ancient Romans and Greeks filled glass spheres with water to make lenses. These practical developments were followed by the development of theories of light and vision by ancient Greek and Indian philosophers, and the development of geometrical optics in the Greco-Roman world . The word optics comes from the ancient Greek word ὀπτική , optikē ' appearance, look ' . Greek philosophy on optics broke down into two opposing theories on how vision worked,
10080-646: The University of Southampton and one from AT&T Bell Laboratories, consisting of E. Desurvire, P. Becker, and J. Simpson. The dual-stage optical amplifier which enabled Dense Wave Division Multiplexing (DWDM) was invented by Stephen B. Alexander at Ciena Corporation. Thulium doped fiber amplifiers have been used in the S-band (1450–1490 nm) and Praseodymium doped amplifiers in the 1300 nm region. However, those regions have not seen any significant commercial use so far and so those amplifiers have not been
10260-398: The classical electromagnetic description of light, however complete electromagnetic descriptions of light are often difficult to apply in practice. Practical optics is usually done using simplified models. The most common of these, geometric optics , treats light as a collection of rays that travel in straight lines and bend when they pass through or reflect from surfaces. Physical optics
10440-463: The complexity of the equations of general relativity to find an alternative wave model. The result was published in June 1916, and there he came to the conclusion that the gravitational wave must propagate with the speed of light, and there must, in fact, be three types of gravitational waves dubbed longitudinal–longitudinal, transverse–longitudinal, and transverse–transverse by Hermann Weyl . However,
10620-518: The electrostatic force . In 1905, Henri Poincaré proposed gravitational waves, emanating from a body and propagating at the speed of light, as being required by the Lorentz transformations and suggested that, in analogy to an accelerating electrical charge producing electromagnetic waves , accelerated masses in a relativistic field theory of gravity should produce gravitational waves. In 1915 Einstein published his general theory of relativity ,
10800-454: The emission theory , the idea that visual perception is accomplished by rays emitted by the eyes. He also commented on the parity reversal of mirrors in Timaeus . Some hundred years later, Euclid (4th–3rd century BC) wrote a treatise entitled Optics where he linked vision to geometry , creating geometrical optics . He based his work on Plato's emission theory wherein he described
10980-468: The intromission theory and the emission theory . The intromission approach saw vision as coming from objects casting off copies of themselves (called eidola) that were captured by the eye. With many propagators including Democritus , Epicurus , Aristotle and their followers, this theory seems to have some contact with modern theories of what vision really is, but it remained only speculation lacking any experimental foundation. Plato first articulated
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#173277244811311160-404: The quadrupole moment (or the l -th time derivative of the l -th multipole moment ) of an isolated system's stress–energy tensor must be non-zero in order for it to emit gravitational radiation. This is analogous to the changing dipole moment of charge or current that is necessary for the emission of electromagnetic radiation . Gravitational waves carry energy away from their sources and, in
11340-448: The superposition principle , which is a wave-like property not predicted by Newton's corpuscle theory. This work led to a theory of diffraction for light and opened an entire area of study in physical optics. Wave optics was successfully unified with electromagnetic theory by James Clerk Maxwell in the 1860s. The next development in optical theory came in 1899 when Max Planck correctly modelled blackbody radiation by assuming that
11520-466: The surface normal , a line perpendicular to the surface at the point where the ray hits. The incident and reflected rays and the normal lie in a single plane, and the angle between the reflected ray and the surface normal is the same as that between the incident ray and the normal. This is known as the Law of Reflection . For flat mirrors , the law of reflection implies that images of objects are upright and
11700-400: The 'hum' of various SMBH mergers occurring in the universe. Stephen Hawking and Werner Israel list different frequency bands for gravitational waves that could plausibly be detected, ranging from 10 Hz up to 10 Hz. The speed of gravitational waves in the general theory of relativity is equal to the speed of light in vacuum, c . Within the theory of special relativity ,
11880-567: The African . Bacon was able to use parts of glass spheres as magnifying glasses to demonstrate that light reflects from objects rather than being released from them. The first wearable eyeglasses were invented in Italy around 1286. This was the start of the optical industry of grinding and polishing lenses for these "spectacles", first in Venice and Florence in the thirteenth century, and later in
12060-542: The BICEP2 collaboration claimed that they had detected the imprint of gravitational waves in the cosmic microwave background . However, they were later forced to retract this result. In 2017, the Nobel Prize in Physics was awarded to Rainer Weiss , Kip Thorne and Barry Barish for their role in the detection of gravitational waves. In 2023, NANOGrav, EPTA, PPTA, and IPTA announced that they found evidence of
12240-544: The DFA is essentially a polarization independent amplifier, a small proportion of the dopant ions interact preferentially with certain polarizations and a small dependence on the polarization of the input signal may occur (typically < 0.5 dB). This is called Polarization Dependent Gain (PDG). The absorption and emission cross sections of the ions can be modeled as ellipsoids with the major axes aligned at random in all directions in different glass sites. The random distribution of
12420-460: The EDFA has several peaks that are smeared by the above broadening mechanisms. The net result is a very broad spectrum (30 nm in silica, typically). The broad gain-bandwidth of fiber amplifiers make them particularly useful in wavelength-division multiplexed communications systems as a single amplifier can be utilized to amplify all signals being carried on a fiber and whose wavelengths fall within
12600-447: The EDFA. The SOA has higher noise, lower gain, moderate polarization dependence and high nonlinearity with fast transient time. The main advantage of SOA is that all four types of nonlinear operations (cross gain modulation, cross phase modulation, wavelength conversion and four wave mixing ) can be conducted. Furthermore, SOA can be run with a low power laser. This originates from the short nanosecond or less upper state lifetime, so that
12780-548: The Huygens–Fresnel principle states that every point of a wavefront is associated with the production of a new disturbance, it is possible for a wavefront to interfere with itself constructively or destructively at different locations producing bright and dark fringes in regular and predictable patterns. Interferometry is the science of measuring these patterns, usually as a means of making precise determinations of distances or angular resolutions . The Michelson interferometer
12960-557: The Internet (e.g. fiber-optic cables form a basis of modern-day computer networking ). Almost any laser active gain medium can be pumped to produce gain for light at the wavelength of a laser made with the same material as its gain medium. Such amplifiers are commonly used to produce high power laser systems. Special types such as regenerative amplifiers and chirped-pulse amplifiers are used to amplify ultrashort pulses . Solid-state amplifiers are optical amplifiers that use
13140-582: The SOA family is the vertical-cavity SOA (VCSOA). These devices are similar in structure to, and share many features with, vertical-cavity surface-emitting lasers ( VCSELs ). The major difference when comparing VCSOAs and VCSELs is the reduced mirror reflectivity used in the amplifier cavity. With VCSOAs, reduced feedback is necessary to prevent the device from reaching lasing threshold. Due to the extremely short cavity length, and correspondingly thin gain medium, these devices exhibit very low single-pass gain (typically on
13320-633: The Universe when space expanded by a large factor in a very short amount of time. If this expansion was not symmetric in all directions, it may have emitted gravitational radiation detectable today as a gravitational wave background . This background signal is too weak for any currently operational gravitational wave detector to observe, and it is thought it may be decades before such an observation can be made. Water waves, sound waves, and electromagnetic waves are able to carry energy , momentum , and angular momentum and by doing so they carry those away from
13500-507: The VCSOA to single-channel amplification. Thus, VCSOAs can be seen as amplifying filters. Given their vertical-cavity geometry, VCSOAs are resonant cavity optical amplifiers that operate with the input/output signal entering/exiting normal to the wafer surface. In addition to their small size, the surface normal operation of VCSOAs leads to a number of advantages, including low power consumption, low noise figure, polarization insensitive gain, and
13680-454: The ability to fabricate high fill factor two-dimensional arrays on a single semiconductor chip. These devices are still in the early stages of research, though promising preamplifier results have been demonstrated. Further extensions to VCSOA technology are the demonstration of wavelength tunable devices. These MEMS-tunable vertical-cavity SOAs utilize a microelectromechanical systems ( MEMS ) based tuning mechanism for wide and continuous tuning of
13860-822: The adoption of stimulated brillouin scattering (SBS) suppression/mitigation techniques within the fiber, and improvements in overall amplifier design, including large mode area (LMA) fibers with a low-aperture core, micro-structured rod-type fiber helical core, or chirally-coupled core fibers, and tapered double-clad fibers (T-DCF). As of 2015 high finesse, high power and pulsed fiber amplifiers delivered power levels exceeding those available from commercial solid-state single-frequency sources, and stable optimized performance, opening up new scientific applications. There are several simulation tools that can be used to design optical amplifiers. Popular commercial tools have been developed by Optiwave Systems and VPI Systems. Optical Most optical phenomena can be accounted for by using
14040-476: The amplifier's performance since the ASE can deplete the inversion level and thereby reduce the gain of the amplifier and increase the noise produced relative to the desired signal gain. Noise figure can be analyzed in both the optical domain and in the electrical domain. In the optical domain, measurement of the ASE, the optical signal gain, and signal wavelength using an optical spectrum analyzer permits calculation of
14220-484: The amplitude of the wave, which for light is associated with a brightening of the waveform in that location. Alternatively, if the two waves of the same wavelength and frequency are out of phase, then the wave crests will align with wave troughs and vice versa. This results in destructive interference and a decrease in the amplitude of the wave, which for light is associated with a dimming of the waveform at that location. See below for an illustration of this effect. Since
14400-552: The angle of incidence. Plutarch (1st–2nd century AD) described multiple reflections on spherical mirrors and discussed the creation of magnified and reduced images, both real and imaginary, including the case of chirality of the images. During the Middle Ages , Greek ideas about optics were resurrected and extended by writers in the Muslim world . One of the earliest of these was Al-Kindi ( c. 801 –873) who wrote on
14580-435: The angles between the normal (to the interface) and the incident and refracted waves, respectively. The index of refraction of a medium is related to the speed, v , of light in that medium by n = c / v , {\displaystyle n=c/v,} where c is the speed of light in vacuum . Snell's Law can be used to predict the deflection of light rays as they pass through linear media as long as
14760-443: The astronomical distances to these sources, the effects when measured on Earth are predicted to be very small, having strains of less than 1 part in 10 . Scientists demonstrate the existence of these waves with highly-sensitive detectors at multiple observation sites. As of 2012 , the LIGO and VIRGO observatories were the most sensitive detectors, operating at resolutions of about one part in 5 × 10 . The Japanese detector KAGRA
14940-582: The attached fiber. Such reflections disrupt amplifier operation and in the extreme case can cause the amplifier to become a laser. The erbium doped amplifier is a high gain amplifier. The principal source of noise in DFAs is Amplified Spontaneous Emission (ASE), which has a spectrum approximately the same as the gain spectrum of the amplifier. Noise figure in an ideal DFA is 3 dB, while practical amplifiers can have noise figure as large as 6–8 dB. As well as decaying via stimulated emission, electrons in
15120-490: The birefringence axes. These two combined effects (which in transmission fibers give rise to polarization mode dispersion ) produce a misalignment of the relative polarizations of the signal and pump lasers along the fiber, thus tending to average out the PDG. The result is that PDG is very difficult to observe in a single amplifier (but is noticeable in links with several cascaded amplifiers). The erbium-doped fiber amplifier (EDFA)
15300-513: The case of orbiting bodies, this is associated with an in-spiral or decrease in orbit. Imagine for example a simple system of two masses – such as the Earth–Sun system – moving slowly compared to the speed of light in circular orbits. Assume that these two masses orbit each other in a circular orbit in the x – y plane. To a good approximation, the masses follow simple Keplerian orbits . However, such an orbit represents
15480-412: The constant c is not only about light; instead it is the highest possible speed for any interaction in nature. Formally, c is a conversion factor for changing the unit of time to the unit of space. This makes it the only speed which does not depend either on the motion of an observer or a source of light and/or gravity. Thus, the speed of "light" is also the speed of gravitational waves, and, further,
15660-507: The construction of GEO600 , LIGO , and Virgo . After years of producing null results, improved detectors became operational in 2015. On 11 February 2016, the LIGO-Virgo collaborations announced the first observation of gravitational waves , from a signal (dubbed GW150914 ) detected at 09:50:45 GMT on 14 September 2015 of two black holes with masses of 29 and 36 solar masses merging about 1.3 billion light-years away. During
15840-424: The core. This high-powered light beam excites the erbium ions to their higher-energy state. When the photons belonging to the signal at a different wavelength from the pump light meet the excited erbium ions, the erbium ions give up some of their energy to the signal and return to their lower-energy state. A significant point is that the erbium gives up its energy in the form of additional photons which are exactly in
16020-455: The detection of gravitational waves using laser interferometers. The idea of using a laser interferometer for this seems to have been floated independently by various people, including M.E. Gertsenshtein and V. I. Pustovoit in 1962, and Vladimir B. Braginskiĭ in 1966. The first prototypes were developed in the 1970s by Robert L. Forward and Rainer Weiss. In the decades that followed, ever more sensitive instruments were constructed, culminating in
16200-449: The distance (as if on the surface of a pool of water). Optical materials with varying indexes of refraction are called gradient-index (GRIN) materials. Such materials are used to make gradient-index optics . For light rays travelling from a material with a high index of refraction to a material with a low index of refraction, Snell's law predicts that there is no θ 2 when θ 1 is large. In this case, no transmission occurs; all
16380-432: The doping ions . Amplification is achieved by stimulated emission of photons from dopant ions in the doped fiber. The pump laser excites ions into a higher energy from where they can decay via stimulated emission of a photon at the signal wavelength back to a lower energy level. The excited ions can also decay spontaneously (spontaneous emission) or even through nonradiative processes involving interactions with phonons of
16560-400: The dual-stage optical amplifier ( U.S. patent 5,159,601 ) that was a key to the first dense wave division multiplexing (DWDM) system, that they released in June 1996. This marked the start of optical networking. Its significance was recognized at the time by optical authority, Shoichi Sudo and technology analyst, George Gilder in 1997, when Sudo wrote that optical amplifiers “will usher in
16740-401: The dumbbell, and the faster it tumbles, the greater is the gravitational radiation it will give off. In an extreme case, such as when the two weights of the dumbbell are massive stars like neutron stars or black holes, orbiting each other quickly, then significant amounts of gravitational radiation would be given off. Some more detailed examples: More technically, the second time derivative of
16920-502: The early 1990s the physics community rallied around a concerted effort to predict the waveforms of gravitational waves from these systems with the Binary Black Hole Grand Challenge Alliance . The largest amplitude of emission occurs during the merger phase, which can be modeled with the techniques of numerical relativity. The first direct detection of gravitational waves, GW150914 , came from
17100-485: The effects of strain . Distances between objects increase and decrease rhythmically as the wave passes, at a frequency equal to that of the wave. The magnitude of this effect is inversely proportional to the distance (not distance squared) from the source. Inspiraling binary neutron stars are predicted to be a powerful source of gravitational waves as they coalesce , due to the very large acceleration of their masses as they orbit close to one another. However, due to
17280-426: The exchange of energy between light and matter only occurred in discrete amounts he called quanta . In 1905, Albert Einstein published the theory of the photoelectric effect that firmly established the quantization of light itself. In 1913, Niels Bohr showed that atoms could only emit discrete amounts of energy, thus explaining the discrete lines seen in emission and absorption spectra . The understanding of
17460-537: The existence of gravitational waves came in 1974 from the observed orbital decay of the Hulse–Taylor binary pulsar , which matched the decay predicted by general relativity as energy is lost to gravitational radiation. In 1993, Russell A. Hulse and Joseph Hooton Taylor Jr. received the Nobel Prize in Physics for this discovery. The first direct observation of gravitational waves was made in September 2015, when
17640-586: The eye, although he was unable to correctly explain how the eye captured the rays. Alhazen's work was largely ignored in the Arabic world but it was anonymously translated into Latin around 1200 A.D. and further summarised and expanded on by the Polish monk Witelo making it a standard text on optics in Europe for the next 400 years. In the 13th century in medieval Europe, English bishop Robert Grosseteste wrote on
17820-535: The feud between the two lasted until Hooke's death. In 1704, Newton published Opticks and, at the time, partly because of his success in other areas of physics, he was generally considered to be the victor in the debate over the nature of light. Newtonian optics was generally accepted until the early 19th century when Thomas Young and Augustin-Jean Fresnel conducted experiments on the interference of light that firmly established light's wave nature. Young's famous double slit experiment showed that light followed
18000-426: The final fraction of a second of the merger, it released more than 50 times the power of all the stars in the observable universe combined. The signal increased in frequency from 35 to 250 Hz over 10 cycles (5 orbits) as it rose in strength for a period of 0.2 second. The mass of the new merged black hole was 62 solar masses. Energy equivalent to three solar masses was emitted as gravitational waves. The signal
18180-474: The focus to be smeared out in space. In particular, spherical mirrors exhibit spherical aberration . Curved mirrors can form images with a magnification greater than or less than one, and the magnification can be negative, indicating that the image is inverted. An upright image formed by reflection in a mirror is always virtual, while an inverted image is real and can be projected onto a screen. Refraction occurs when light travels through an area of space that has
18360-401: The form of fiber-pigtailed components, operating at signal wavelengths between 850 nm and 1600 nm and generating gains of up to 30 dB. The semiconductor optical amplifier is of small size and electrically pumped. It can be potentially less expensive than the EDFA and can be integrated with semiconductor lasers, modulators, etc. However, the performance is still not comparable with
18540-448: The frequency tunability of ultrafast solid-state lasers (e.g. Ti:sapphire ). By using a noncollinear interaction geometry optical parametric amplifiers are capable of extremely broad amplification bandwidths. In the 21st century high power fiber lasers were adopted as an industrial material processing tool, and were expanding into other markets including the medical and scientific markets. One key enhancement enabling penetration into
18720-446: The gain is nonresonant, which means that gain is available over the entire transparency region of the fiber ranging from approximately 0.3 to 2 μm. A third advantage of Raman amplifiers is that the gain spectrum can be tailored by adjusting the pump wavelengths. For instance, multiple pump lines can be used to increase the optical bandwidth, and the pump distribution determines the gain flatness. Another advantage of Raman amplification
18900-423: The gain medium by multiplexing a pump wavelength with signal wavelength, while a lumped Raman amplifier utilises a dedicated, shorter length of fiber to provide amplification. In the case of a lumped Raman amplifier, a highly nonlinear fiber with a small core is utilised to increase the interaction between signal and pump wavelengths, and thereby reduce the length of fiber required. The pump light may be coupled into
19080-404: The gain medium is reached. In some condition, the width ( FWHM ) of the pulse is reduced. Due to the inhomogeneous portion of the linewidth broadening of the dopant ions, the gain spectrum has an inhomogeneous component and gain saturation occurs, to a small extent, in an inhomogeneous manner. This effect is known as spectral hole burning because a high power signal at one wavelength can 'burn'
19260-415: The gain of the amplifier will be reduced. This effect is known as gain saturation – as the signal level increases, the amplifier saturates and cannot produce any more output power, and therefore the gain reduces. Saturation is also commonly known as gain compression. To achieve optimum noise performance DFAs are operated under a significant amount of gain compression (10 dB typically), since that reduces
19440-777: The gain reacts rapidly to changes of pump or signal power and the changes of gain also cause phase changes which can distort the signals. This nonlinearity presents the most severe problem for optical communication applications. However it provides the possibility for gain in different wavelength regions from the EDFA. "Linear optical amplifiers" using gain-clamping techniques have been developed. High optical nonlinearity makes semiconductor amplifiers attractive for all optical signal processing like all-optical switching and wavelength conversion. There has been much research on semiconductor optical amplifiers as elements for optical signal processing, wavelength conversion, clock recovery, signal demultiplexing, and pattern recognition. A recent addition to
19620-427: The gain window. An erbium-doped waveguide amplifier (EDWA) is an optical amplifier that uses a waveguide to boost an optical signal. A relatively high-powered beam of light is mixed with the input signal using a wavelength selective coupler (WSC). The input signal and the excitation light must be at significantly different wavelengths. The mixed light is guided into a section of fiber with erbium ions included in
19800-402: The glass matrix. These last two decay mechanisms compete with stimulated emission reducing the efficiency of light amplification. The amplification window of an optical amplifier is the range of optical wavelengths for which the amplifier yields a usable gain. The amplification window is determined by the spectroscopic properties of the dopant ions, the glass structure of the optical fiber, and
19980-411: The gloss of surfaces such as mirrors, which reflect light in a simple, predictable way. This allows for the production of reflected images that can be associated with an actual ( real ) or extrapolated ( virtual ) location in space. Diffuse reflection describes non-glossy materials, such as paper or rock. The reflections from these surfaces can only be described statistically, with the exact distribution of
20160-596: The gravitational equivalent of electromagnetic waves . In 1916, Albert Einstein demonstrated that gravitational waves result from his general theory of relativity as ripples in spacetime . Gravitational waves transport energy as gravitational radiation , a form of radiant energy similar to electromagnetic radiation . Newton's law of universal gravitation , part of classical mechanics , does not provide for their existence, instead asserting that gravity has instantaneous effect everywhere. Gravitational waves therefore stand as an important relativistic phenomenon that
20340-505: The implied rate of energy loss of the Milky Way would drain our galaxy of energy on a timescale much shorter than its inferred age. These doubts were strengthened when, by the mid-1970s, repeated experiments from other groups building their own Weber bars across the globe failed to find any signals, and by the late 1970s consensus was that Weber's results were spurious. In the same period, the first indirect evidence of gravitational waves
20520-416: The incident rays came. This is called retroreflection . Mirrors with curved surfaces can be modelled by ray tracing and using the law of reflection at each point on the surface. For mirrors with parabolic surfaces , parallel rays incident on the mirror produce reflected rays that converge at a common focus . Other curved surfaces may also focus light, but with aberrations due to the diverging shape causing
20700-418: The indexes of refraction and the geometry of the media are known. For example, the propagation of light through a prism results in the light ray being deflected depending on the shape and orientation of the prism. In most materials, the index of refraction varies with the frequency of the light, known as dispersion . Taking this into account, Snell's Law can be used to predict how a prism will disperse light into
20880-537: The initial radius and t coalesce {\displaystyle t_{\text{coalesce}}} the total time needed to fully coalesce. More generally, the rate of orbital decay can be approximated by where r is the separation between the bodies, t time, G the gravitational constant , c the speed of light , and m 1 and m 2 the masses of the bodies. This leads to an expected time to merger of Compact stars like white dwarfs and neutron stars can be constituents of binaries. For example,
21060-436: The interaction between light and matter that followed from these developments not only formed the basis of quantum optics but also was crucial for the development of quantum mechanics as a whole. The ultimate culmination, the theory of quantum electrodynamics , explains all optics and electromagnetic processes in general as the result of the exchange of real and virtual photons. Quantum optics gained practical importance with
21240-426: The interaction of light with the material. For instance, the behaviour of a light wave interacting with a metal surface is quite different from what happens when it interacts with a dielectric material. A vector model must also be used to model polarised light. Numerical modeling techniques such as the finite element method , the boundary element method and the transmission-line matrix method can be used to model
21420-503: The interactions with phonons of the glass, while inhomogeneous broadening is caused by differences in the glass sites where different ions are hosted. Different sites expose ions to different local electric fields, which shifts the energy levels via the Stark effect . In addition, the Stark effect also removes the degeneracy of energy states having the same total angular momentum (specified by
21600-483: The invention of the compound optical microscope around 1595, and the refracting telescope in 1608, both of which appeared in the spectacle making centres in the Netherlands. In the early 17th century, Johannes Kepler expanded on geometric optics in his writings, covering lenses, reflection by flat and curved mirrors, the principles of pinhole cameras , inverse-square law governing the intensity of light, and
21780-491: The inventions of the maser in 1953 and of the laser in 1960. Following the work of Paul Dirac in quantum field theory , George Sudarshan , Roy J. Glauber , and Leonard Mandel applied quantum theory to the electromagnetic field in the 1950s and 1960s to gain a more detailed understanding of photodetection and the statistics of light. Classical optics is divided into two main branches: geometrical (or ray) optics and physical (or wave) optics. In geometrical optics, light
21960-401: The kind of oscillations associated with gravitational waves as produced by a pair of masses in a circular orbit . In this case the amplitude of the gravitational wave is constant, but its plane of polarization changes or rotates at twice the orbital rate, so the time-varying gravitational wave size, or 'periodic spacetime strain', exhibits a variation as shown in the animation. If the orbit of
22140-528: The lattice of the gain medium produces photons coherent with the incoming photons. Parametric amplifiers use parametric amplification. The principle of optical amplification was invented by Gordon Gould on November 13, 1957. He filed US Patent US80453959A on April 6, 1959, titled "Light Amplifiers Employing Collisions to Produce Population Inversions" (subsequently amended as a continuation in part and finally issued as U.S. patent 4,746,201A on May 4, 1988). The patent covered “the amplification of light by
22320-504: The laws of reflection and refraction at interfaces between different media. These laws were discovered empirically as far back as 984 AD and have been used in the design of optical components and instruments from then until the present day. They can be summarised as follows: When a ray of light hits the boundary between two transparent materials, it is divided into a reflected and a refracted ray. The laws of reflection and refraction can be derived from Fermat's principle which states that
22500-449: The light is modelled as a collection of particles called " photons ". Quantum optics deals with the application of quantum mechanics to optical systems. Optical science is relevant to and studied in many related disciplines including astronomy , various engineering fields, photography , and medicine (particularly ophthalmology and optometry , in which it is called physiological optics). Practical applications of optics are found in
22680-422: The light is reflected. This phenomenon is called total internal reflection and allows for fibre optics technology. As light travels down an optical fibre, it undergoes total internal reflection allowing for essentially no light to be lost over the length of the cable. A device that produces converging or diverging light rays due to refraction is known as a lens . Lenses are characterized by their focal length :
22860-550: The long distance fiber-optic cables which carry much of the world's telecommunication links. There are several different physical mechanisms that can be used to amplify a light signal, which correspond to the major types of optical amplifiers. In doped fiber amplifiers and bulk lasers, stimulated emission in the amplifier's gain medium causes amplification of incoming light. In semiconductor optical amplifiers (SOAs), electron – hole recombination occurs. In Raman amplifiers , Raman scattering of incoming light with phonons in
23040-489: The masses is elliptical then the gravitational wave's amplitude also varies with time according to Einstein's quadrupole formula . As with other waves , there are a number of characteristics used to describe a gravitational wave: The speed, wavelength, and frequency of a gravitational wave are related by the equation c = λf , just like the equation for a light wave . For example, the animations shown here oscillate roughly once every two seconds. This would correspond to
23220-443: The mathematical rules of perspective and described the effects of refraction qualitatively, although he questioned that a beam of light from the eye could instantaneously light up the stars every time someone blinked. Euclid stated the principle of shortest trajectory of light, and considered multiple reflections on flat and spherical mirrors. Ptolemy , in his treatise Optics , held an extramission-intromission theory of vision:
23400-449: The merger of two black holes. A supernova is a transient astronomical event that occurs during the last stellar evolutionary stages of a massive star's life, whose dramatic and catastrophic destruction is marked by one final titanic explosion. This explosion can happen in one of many ways, but in all of them a significant proportion of the matter in the star is blown away into the surrounding space at extremely high velocities (up to 10% of
23580-494: The merits of Aristotelian and Euclidean ideas of optics, favouring the emission theory since it could better quantify optical phenomena. In 984, the Persian mathematician Ibn Sahl wrote the treatise "On burning mirrors and lenses", correctly describing a law of refraction equivalent to Snell's law. He used this law to compute optimum shapes for lenses and curved mirrors . In the early 11th century, Alhazen (Ibn al-Haytham) wrote
23760-400: The nature of Einstein's approximations led many (including Einstein himself) to doubt the result. In 1922, Arthur Eddington showed that two of Einstein's types of waves were artifacts of the coordinate system he used, and could be made to propagate at any speed by choosing appropriate coordinates, leading Eddington to jest that they "propagate at the speed of thought". This also cast doubt on
23940-483: The noise figure. For the electrical measurement method, the detected photocurrent noise is evaluated with a low-noise electrical spectrum analyzer, which along with measurement of the amplifier gain permits a noise figure measurement. Generally, the optical technique provides a more simple method, though it is not inclusive of excess noise effects captured by the electrical method such multi-path interference (MPI) noise generation. In both methods, attention to effects such as
24120-405: The object and image distances are positive if the object and image are on opposite sides of the lens. Incoming parallel rays are focused by a converging lens onto a spot one focal length from the lens, on the far side of the lens. This is called the rear focal point of the lens. Rays from an object at a finite distance are focused further from the lens than the focal distance; the closer the object
24300-424: The observation of events involving exotic objects in the distant universe that cannot be observed with more traditional means such as optical telescopes or radio telescopes ; accordingly, gravitational wave astronomy gives new insights into the workings of the universe. In particular, gravitational waves could be of interest to cosmologists as they offer a possible way of observing the very early universe. This
24480-401: The optical explanations of astronomical phenomena such as lunar and solar eclipses and astronomical parallax . He was also able to correctly deduce the role of the retina as the actual organ that recorded images, finally being able to scientifically quantify the effects of different types of lenses that spectacle makers had been observing over the previous 300 years. After the invention of
24660-400: The order of a few percent) and also a very large free spectral range (FSR). The small single-pass gain requires relatively high mirror reflectivity to boost the total signal gain. In addition to boosting the total signal gain, the use of the resonant cavity structure results in a very narrow gain bandwidth; coupled with the large FSR of the optical cavity, this effectively limits operation of
24840-437: The order of the Sun , and diameters in the order of the Earth. They cannot get much closer together than 10,000 km before they will merge and explode in a supernova which would also end the emission of gravitational waves. Until then, their gravitational radiation would be comparable to that of a neutron star binary. When the orbit of a neutron star binary has decayed to 1.89 × 10 m (1890 km), its remaining lifetime
25020-416: The orientation of the ellipsoids in a glass produces a macroscopically isotropic medium, but a strong pump laser induces an anisotropic distribution by selectively exciting those ions that are more aligned with the optical field vector of the pump. Also, those excited ions aligned with the signal field produce more stimulated emission. The change in gain is thus dependent on the alignment of the polarizations of
25200-412: The output facet. Typical parameters: In a Raman amplifier, the signal is intensified by Raman amplification . Unlike the EDFA and SOA the amplification effect is achieved by a nonlinear interaction between the signal and a pump laser within an optical fiber. There are two types of Raman amplifier: distributed and lumped. A distributed Raman amplifier is one in which the transmission fiber is utilised as
25380-441: The paper was rewritten with the opposite conclusion and published elsewhere. In 1956, Felix Pirani remedied the confusion caused by the use of various coordinate systems by rephrasing the gravitational waves in terms of the manifestly observable Riemann curvature tensor . At the time, Pirani's work was overshadowed by the community's focus on a different question: whether gravitational waves could transmit energy . This matter
25560-478: The particles will follow the distortion in spacetime, oscillating in a " cruciform " manner, as shown in the animations. The area enclosed by the test particles does not change and there is no motion along the direction of propagation. The oscillations depicted in the animation are exaggerated for the purpose of discussion – in reality a gravitational wave has a very small amplitude (as formulated in linearized gravity ). However, they help illustrate
25740-676: The path taken between two points by a ray of light is the path that can be traversed in the least time. Geometric optics is often simplified by making the paraxial approximation , or "small angle approximation". The mathematical behaviour then becomes linear, allowing optical components and systems to be described by simple matrices. This leads to the techniques of Gaussian optics and paraxial ray tracing , which are used to find basic properties of optical systems, such as approximate image and object positions and magnifications . Reflections can be divided into two types: specular reflection and diffuse reflection . Specular reflection describes
25920-402: The peak gain wavelength of the amplifier. SOAs have a more rapid gain response, which is in the order of 1 to 100 ps. For high output power and broader wavelength range, tapered amplifiers are used. These amplifiers consist of a lateral single-mode section and a section with a tapered structure, where the laser light is amplified. The tapered structure leads to a reduction of the power density at
26100-510: The physicality of the third (transverse–transverse) type that Eddington showed always propagate at the speed of light regardless of coordinate system. In 1936, Einstein and Nathan Rosen submitted a paper to Physical Review in which they claimed gravitational waves could not exist in the full general theory of relativity because any such solution of the field equations would have a singularity. The journal sent their manuscript to be reviewed by Howard P. Robertson , who anonymously reported that
26280-511: The propagation of light in systems which cannot be solved analytically. Such models are computationally demanding and are normally only used to solve small-scale problems that require accuracy beyond that which can be achieved with analytical solutions. All of the results from geometrical optics can be recovered using the techniques of Fourier optics which apply many of the same mathematical and analytical techniques used in acoustic engineering and signal processing . Gaussian beam propagation
26460-455: The pump and signal lasers – i.e. whether the two lasers are interacting with the same sub-set of dopant ions or not. In an ideal doped fiber without birefringence , the PDG would be inconveniently large. Fortunately, in optical fibers small amounts of birefringence are always present and, furthermore, the fast and slow axes vary randomly along the fiber length. A typical DFA has several tens of meters, long enough to already show this randomness of
26640-497: The quantum number J). Thus, for example, the trivalent erbium ion (Er) has a ground state with J = 15/2, and in the presence of an electric field splits into J + 1/2 = 8 sublevels with slightly different energies. The first excited state has J = 13/2 and therefore a Stark manifold with 7 sublevels. Transitions from the J = 13/2 excited state to the J= 15/2 ground state are responsible for the gain at 1500 nm wavelength. The gain spectrum of
26820-408: The rate of spontaneous emission, thereby reducing ASE. Another advantage of operating the DFA in the gain saturation region is that small fluctuations in the input signal power are reduced in the output amplified signal: smaller input signal powers experience larger (less saturated) gain, while larger input powers see less gain. The leading edge of the pulse is amplified, until the saturation energy of
27000-416: The rays (or flux) from the eye formed a cone, the vertex being within the eye, and the base defining the visual field. The rays were sensitive, and conveyed information back to the observer's intellect about the distance and orientation of surfaces. He summarized much of Euclid and went on to describe a way to measure the angle of refraction , though he failed to notice the empirical relationship between it and
27180-423: The reflected light depending on the microscopic structure of the material. Many diffuse reflectors are described or can be approximated by Lambert's cosine law , which describes surfaces that have equal luminance when viewed from any angle. Glossy surfaces can give both specular and diffuse reflection. In specular reflection, the direction of the reflected ray is determined by the angle the incident ray makes with
27360-415: The same distance behind the mirror as the objects are in front of the mirror. The image size is the same as the object size. The law also implies that mirror images are parity inverted, which we perceive as a left-right inversion. Images formed from reflection in two (or any even number of) mirrors are not parity inverted. Corner reflectors produce reflected rays that travel back in the direction from which
27540-439: The same phase and direction as the signal being amplified. So the signal is amplified along its direction of travel only. This is not unusual – when an atom "lases" it always gives up its energy in the same direction and phase as the incoming light. Thus all of the additional signal power is guided in the same fiber mode as the incoming signal. An optical isolator is usually placed at the output to prevent reflections returning from
27720-407: The same side of the lens as the object. The closer the object is to the lens, the closer the virtual image is to the lens. As with mirrors, upright images produced by a single lens are virtual, while inverted images are real. Lenses suffer from aberrations that distort images. Monochromatic aberrations occur because the geometry of the lens does not perfectly direct rays from each object point to
27900-447: The scientific market was improvement in high finesse fiber amplifiers, which became able to deliver single frequency linewidths (<5 kHz) together with excellent beam quality and stable linearly polarized output. Systems meeting these specifications steadily progressed from a few watts of output power initially, to tens of watts and later hundreds of watts. This power increase was achieved with developments in fiber technology, such as
28080-405: The simple equation 1 S 1 + 1 S 2 = 1 f , {\displaystyle {\frac {1}{S_{1}}}+{\frac {1}{S_{2}}}={\frac {1}{f}},} where S 1 is the distance from the object to the lens, θ 2 is the distance from the lens to the image, and f is the focal length of the lens. In the sign convention used here,
28260-464: The singularities in question were simply the harmless coordinate singularities of the employed cylindrical coordinates. Einstein, who was unfamiliar with the concept of peer review, angrily withdrew the manuscript, never to publish in Physical Review again. Nonetheless, his assistant Leopold Infeld , who had been in contact with Robertson, convinced Einstein that the criticism was correct, and
28440-457: The source. Gravitational waves perform the same function. Thus, for example, a binary system loses angular momentum as the two orbiting objects spiral towards each other – the angular momentum is radiated away by gravitational waves. The waves can also carry off linear momentum, a possibility that has some interesting implications for astrophysics . After two supermassive black holes coalesce, emission of linear momentum can produce
28620-464: The spectacle making centres in both the Netherlands and Germany. Spectacle makers created improved types of lenses for the correction of vision based more on empirical knowledge gained from observing the effects of the lenses rather than using the rudimentary optical theory of the day (theory which for the most part could not even adequately explain how spectacles worked). This practical development, mastery, and experimentation with lenses led directly to
28800-411: The speed of any massless particle. Such particles include the gluon (carrier of the strong force), the photons that make up light (hence carrier of electromagnetic force), and the hypothetical gravitons (which are the presumptive field particles associated with gravity; however, an understanding of the graviton, if any exist, requires an as-yet unavailable theory of quantum gravity). In August 2017,
28980-414: The speed of light). Unless there is perfect spherical symmetry in these explosions (i.e., unless matter is spewed out evenly in all directions), there will be gravitational radiation from the explosion. This is because gravitational waves are generated by a changing quadrupole moment , which can happen only when there is asymmetrical movement of masses. Since the exact mechanism by which supernovae take place
29160-418: The spontaneous emission accompanying the input signal are critical to accurate measurement of noise figure. Gain is achieved in a DFA due to population inversion of the dopant ions. The inversion level of a DFA is set, primarily, by the power of the pump wavelength and the power at the amplified wavelengths. As the signal power increases, or the pump power decreases, the inversion level will reduce and thereby
29340-538: The stimulated emission of photons from ions, atoms or molecules in gaseous, liquid or solid state.” In total, Gould obtained 48 patents related to the optical amplifier that covered 80% of the lasers on the market at the time of issuance. Gould co-founded an optical telecommunications equipment firm, Optelecom Inc. , that helped start Ciena Corp with his former head of Light Optics Research, David Huber and Kevin Kimberlin . Huber and Steve Alexander of Ciena invented
29520-421: The subject of as much development as the EDFA. However, Ytterbium doped fiber lasers and amplifiers, operating near 1 micrometre wavelength, have many applications in industrial processing of materials, as these devices can be made with extremely high output power (tens of kilowatts). Semiconductor optical amplifiers (SOAs) are amplifiers which use a semiconductor to provide the gain medium. These amplifiers have
29700-444: The superposition principle can be used to predict the shape of interacting waveforms through the simple addition of the disturbances. This interaction of waves to produce a resulting pattern is generally termed "interference" and can result in a variety of outcomes. If two waves of the same wavelength and frequency are in phase , both the wave crests and wave troughs align. This results in constructive interference and an increase in
29880-403: The surface called "mountains", which are bumps extending no more than 10 centimeters (4 inches) above the surface, that make the spinning spherically asymmetric. This gives the star a quadrupole moment that changes with time, and it will emit gravitational waves until the deformities are smoothed out. Many models of the Universe suggest that there was an inflationary epoch in the early history of
30060-472: The telescope, Kepler set out the theoretical basis on how they worked and described an improved version, known as the Keplerian telescope , using two convex lenses to produce higher magnification. Optical theory progressed in the mid-17th century with treatises written by philosopher René Descartes , which explained a variety of optical phenomena including reflection and refraction by assuming that light
30240-440: The term "light" is also often applied to infrared (0.7–300 μm) and ultraviolet radiation (10–400 nm). The wave model can be used to make predictions about how an optical system will behave without requiring an explanation of what is "waving" in what medium. Until the middle of the 19th century, most physicists believed in an "ethereal" medium in which the light disturbance propagated. The existence of electromagnetic waves
30420-421: The timing of approximately 100 pulsars spread widely across our galaxy is monitored over the course of years. Detectable changes in the arrival time of their signals can result from passing gravitational waves generated by merging supermassive black holes with wavelengths measured in lightyears. These timing changes can be used to locate the source of the waves. Using this technique, astronomers have discovered
30600-428: The transmission fiber in the same direction as the signal (co-directional pumping), in the opposite direction (contra-directional pumping) or both. Contra-directional pumping is more common as the transfer of noise from the pump to the signal is reduced. The pump power required for Raman amplification is higher than that required by the EDFA, with in excess of 500 mW being required to achieve useful levels of gain in
30780-500: The upper energy level can also decay by spontaneous emission, which occurs at random, depending upon the glass structure and inversion level. Photons are emitted spontaneously in all directions, but a proportion of those will be emitted in a direction that falls within the numerical aperture of the fiber and are thus captured and guided by the fiber. Those photons captured may then interact with other dopant ions, and are thus amplified by stimulated emission. The initial spontaneous emission
30960-495: The wavelength and power of the pump laser. Although the electronic transitions of an isolated ion are very well defined, broadening of the energy levels occurs when the ions are incorporated into the glass of the optical fiber and thus the amplification window is also broadened. This broadening is both homogeneous (all ions exhibit the same broadened spectrum) and inhomogeneous (different ions in different glass locations exhibit different spectra). Homogeneous broadening arises from
31140-400: Was a famous instrument which used interference effects to accurately measure the speed of light. The appearance of thin films and coatings is directly affected by interference effects. Antireflective coatings use destructive interference to reduce the reflectivity of the surfaces they coat, and can be used to minimise glare and unwanted reflections. The simplest case is a single layer with
31320-666: Was completed in 2019; its first joint detection with LIGO and VIRGO was reported in 2021. Another European ground-based detector, the Einstein Telescope , is under development. A space-based observatory, the Laser Interferometer Space Antenna (LISA), is also being developed by the European Space Agency . Gravitational waves do not strongly interact with matter in the way that electromagnetic radiation does. This allows for
31500-653: Was discovered. In 1974, Russell Alan Hulse and Joseph Hooton Taylor, Jr. discovered the first binary pulsar , which earned them the 1993 Nobel Prize in Physics . Pulsar timing observations over the next decade showed a gradual decay of the orbital period of the Hulse–Taylor pulsar that matched the loss of energy and angular momentum in gravitational radiation predicted by general relativity. This indirect detection of gravitational waves motivated further searches, despite Weber's discredited result. Some groups continued to improve Weber's original concept, while others pursued
31680-540: Was emitted by objects which produced it. This differed substantively from the ancient Greek emission theory. In the late 1660s and early 1670s, Isaac Newton expanded Descartes's ideas into a corpuscle theory of light , famously determining that white light was a mix of colours that can be separated into its component parts with a prism . In 1690, Christiaan Huygens proposed a wave theory for light based on suggestions that had been made by Robert Hooke in 1664. Hooke himself publicly criticised Newton's theories of light and
31860-467: Was predicted in 1865 by Maxwell's equations . These waves propagate at the speed of light and have varying electric and magnetic fields which are orthogonal to one another, and also to the direction of propagation of the waves. Light waves are now generally treated as electromagnetic waves except when quantum mechanical effects have to be considered. Many simplified approximations are available for analysing and designing optical systems. Most of these use
32040-554: Was seen by both LIGO detectors in Livingston and Hanford, with a time difference of 7 milliseconds due to the angle between the two detectors and the source. The signal came from the Southern Celestial Hemisphere , in the rough direction of (but much farther away than) the Magellanic Clouds . The confidence level of this being an observation of gravitational waves was 99.99994%. A year earlier,
32220-439: Was settled by a thought experiment proposed by Richard Feynman during the first "GR" conference at Chapel Hill in 1957. In short, his argument known as the " sticky bead argument " notes that if one takes a rod with beads then the effect of a passing gravitational wave would be to move the beads along the rod; friction would then produce heat, implying that the passing wave had done work . Shortly after, Hermann Bondi published
32400-593: Was taken from the public domain Federal Standard 1037C . An optical parametric amplifier allows the amplification of a weak signal-impulse in a nonlinear medium such as a noncentrosymmetric nonlinear medium (e.g. Beta barium borate (BBO)) or even a standard fused silica optical fiber via the Kerr effect . In contrast to the previously mentioned amplifiers, which are mostly used in telecommunication environments, this type finds its main application in expanding
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