Slow light is the propagation of an optical pulse or other modulation of an optical carrier at a very low

group velocity The group velocity of a wave is the velocity with which the overall envelope shape of the wave's amplitudes—known as the ''modulation'' or ''envelope'' of the wave—propagates through space. For example, if a stone is thrown into the middl ...

. Slow light occurs when a propagating pulse is substantially slowed by the interaction with the medium in which the propagation takes place. Group velocities below c were known to be possible as far back as 1880, but could not be realized in a useful manner until 1991, when Stephen Harris and collaborators demonstrated

electromagnetically induced transparency Electromagnetically induced transparency (EIT) is a coherent optical nonlinearity which renders a medium transparent within a narrow spectral range around an absorption line. Extreme dispersion is also created within this transparency "window" ...

in trapped strontium atoms. Reduction of the speed of light by a factor of 165 was reported in 1995. In 1998, Danish physicist Lene Vestergaard Hau led a combined team from

Harvard University Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of highe ...

and the

Rowland Institute for Science The Rowland Institute for Science was founded by Edwin H. Land, founder of Polaroid Corporation, as a nonprofit, privately endowed basic research organization in 1980. The institute merged with Harvard University on July 1, 2002, and is now called ...

which realized much lower group velocities of light. They succeeded in slowing a beam of light to about 17 meters per second. In 2004, researchers at

UC Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant uni ...

first demonstrated slow light in a

semiconductor A semiconductor is a material which has an electrical conductivity value falling between that of a conductor, such as copper, and an insulator, such as glass. Its resistivity falls as its temperature rises; metals behave in the opposite way ...

, with a group velocity 9.6 kilometers per second. Hau and her colleagues later succeeded in stopping light completely, and developed methods by which it can be stopped and later restarted. In 2005, IBM created a

microchip An integrated circuit or monolithic integrated circuit (also referred to as an IC, a chip, or a microchip) is a set of electronic circuits on one small flat piece (or "chip") of semiconductor material, usually silicon. Large numbers of tiny ...

that can slow down light, fashioned out of fairly standard materials, potentially paving the way toward commercial adoption.

Background

When light propagates through a material, it travels slower than the vacuum speed, . This is a change in the

phase velocity The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, ...

of the light and is manifested in physical effects such as

refraction In physics, refraction is the redirection of a wave as it passes from one medium to another. The redirection can be caused by the wave's change in speed or by a change in the medium. Refraction of light is the most commonly observed phenomen ...

. This reduction in speed is quantified by the ratio between and the phase velocity. This ratio is called the

refractive index In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, ...

of the material. Slow light is a dramatic reduction in the

of light, not the phase velocity. Slow light effects are not due to abnormally large refractive indices, as will be explained below. The simplest picture of

light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 t ...

given by classical physics is of a

wave In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (re ...

or disturbance in the

electromagnetic field An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical ...

. In a

vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or " void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often ...

Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits ...

predict that these disturbances will travel at a specific speed, denoted by the symbol . This well-known physical constant is commonly referred to as the

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit fo ...

. The postulate of the constancy of the speed of light in all inertial reference frames lies at the heart of

special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The law ...

and has given rise to a popular notion that the "speed of light is always the same". However, in many situations light is more than a disturbance in the electromagnetic field. Light traveling within a medium is no longer a disturbance solely of the electromagnetic field, but rather a disturbance of the field and the positions and velocities of the charged particles (

electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have n ...

s) within the material. The motion of the electrons is determined by the field (due to the

Lorentz force In physics (specifically in electromagnetism) the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge moving with a velocity in an elect ...

) but the field is determined by the positions and velocities of the electrons (due to

Gauss' law In physics and electromagnetism, Gauss's law, also known as Gauss's flux theorem, (or sometimes simply called Gauss's theorem) is a law relating the distribution of electric charge to the resulting electric field. In its integral form, it s ...

and Ampère's law). The behavior of a disturbance of this combined electromagnetic-charge density field (i.e. light) is still determined by Maxwell's equations, but the solutions are complicated because of the intimate link between the medium and the field. Understanding the behavior of light in a material is simplified by limiting the types of disturbances studied to

sinusoidal A sine wave, sinusoidal wave, or just sinusoid is a mathematical curve defined in terms of the '' sine'' trigonometric function, of which it is the graph. It is a type of continuous wave and also a smooth periodic function. It occurs often i ...

functions of time. For these types of disturbances Maxwell's equations transform into algebraic equations and are easily solved. These special disturbances propagate through a material at a speed slower than called the

. The ratio between and the phase velocity is called the

index of refraction In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...

of the material (). The index of refraction is not a constant for a given material, but depends on temperature, pressure, and upon the frequency of the (sinusoidal) light wave. This latter leads to an effect called

dispersion Dispersion may refer to: Economics and finance *Dispersion (finance), a measure for the statistical distribution of portfolio returns *Price dispersion, a variation in prices across sellers of the same item *Wage dispersion, the amount of variatio ...

. A human eye perceives the intensity of the sinusoidal disturbance as the

brightness Brightness is an attribute of visual perception in which a source appears to be radiating or reflecting light. In other words, brightness is the perception elicited by the luminance of a visual target. The perception is not linear to luminance, ...

of the light and the frequency as the

color Color (American English) or colour (British English) is the visual perceptual property deriving from the spectrum of light interacting with the photoreceptor cells of the eyes. Color categories and physical specifications of color are associ ...

. If a light is turned on or off at a specific time or otherwise modulated, then the amplitude of the sinusoidal disturbance is also time-dependent. The time-varying amplitude does not propagate at the phase velocity but rather at the

. The group velocity depends not only on the refractive index of the material, but also the way in which the refractive index changes with frequency (i.e. the

derivative In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. ...

of refractive index with respect to frequency). Slow light refers to a very low group velocity of light. If the dispersion relation of the refractive index is such that the index changes rapidly over a small range of frequencies, then the group velocity might be very low, thousands or millions of times less than , even though the index of refraction is still a typical value (between 1.5 and 3.5 for glasses and semiconductors).

Ways to achieve slow light

There are many mechanisms which can generate slow light, all of which create narrow spectral regions with high

, i.e. peaks in the

dispersion relation In the physical sciences and electrical engineering, dispersion relations describe the effect of dispersion on the properties of waves in a medium. A dispersion relation relates the wavelength or wavenumber of a wave to its frequency. Given t ...

. Schemes are generally grouped into two categories: material dispersion and waveguide dispersion. Material dispersion mechanisms such as

(EIT), coherent population oscillation (CPO), and various

four-wave mixing Four-wave mixing (FWM) is an intermodulation phenomenon in nonlinear optics, whereby interactions between two or three wavelengths produce two or one new wavelengths. It is similar to the third-order intercept point in electrical systems. Four-wave ...

(FWM) schemes produce a rapid change in refractive index as a function of optical frequency, i.e. they modify the temporal component of a propagating wave. This is done by using a nonlinear effect to modify the dipole response of a medium to a signal or "probe" field. Waveguide dispersion mechanisms such as

photonic crystals A photonic crystal is an optical nanostructure in which the refractive index changes periodically. This affects the propagation of light in the same way that the structure of natural crystals gives rise to X-ray diffraction and that the atomic ...

, coupled resonator optical waveguides (CROW), and other micro-resonator structures modify the spatial component (k-vector) of a propagating wave. Slow light can also be achieved by exploiting the dispersion properties of planar waveguides realized with single negative metamaterials (SNM) or double negative metamaterials (DNM). A predominant figure of merit of slow light schemes is the ''Delay-Bandwidth Product'' (DBP). Most slow light schemes can actually offer an arbitrarily long delay for a given device length (length/delay = signal velocity) at the expense of

bandwidth Bandwidth commonly refers to: * Bandwidth (signal processing) or ''analog bandwidth'', ''frequency bandwidth'', or ''radio bandwidth'', a measure of the width of a frequency range * Bandwidth (computing), the rate of data transfer, bit rate or thr ...

. The product of the two is roughly constant. A related figure of merit is the ''fractional delay'', the time a pulse is delayed divided by the total time of the pulse. Plasmon induced transparency – an analog of EIT – provides another approach based on the destructive interference between different resonance modes. Recent work has now demonstrated this effect over a broad transparency window across a frequency range greater than 0.40 THz.

Potential use

Optical switches which make use of slow light in photonic crystals could produce faster data transmission in fiber optic cables, while having significantly lower power requirements. Slow light can also be used to control delays in optical networks, permitting more orderly traffic flow. In addition, slow light can be used to build

interferometer Interferometry is a technique which uses the '' interference'' of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber o ...

s that are far more sensitive to frequency shift than conventional interferometers. This property can be used to build better, smaller frequency sensors and compact high resolution spectrometers. Other potential applications include optical quantum memory.

In fiction

The description of "luminite" in

Maurice Renard Maurice Renard (28 February 1875, Châlons-en-Champagne – 18 November 1939, Rochefort-Sur-Mer) was a French writer. Career Renard authored the archetypal mad scientist novel '' Le Docteur Lerne, sous-dieu'' r. Lerne - Undergod(1908), wh ...

's novel, ''Le maître de la lumière'' (''The Master of Light'', 1933), might be one of the earliest mentions of slow light. Subsequent fictional works that address slow light are noted below. *The slow light experiments are mentioned in

Dave Eggers Dave Eggers (born March 12, 1970) is an American writer, editor, and publisher. He wrote the 2000 best-selling memoir ''A Heartbreaking Work of Staggering Genius''. Eggers is also the founder of ''Timothy McSweeney's Quarterly Concern'', a lite ...

's novel ''

You Shall Know Our Velocity ''You Shall Know Our Velocity!'' is a 2002 novel by Dave Eggers. It was Eggers's debut novel, following the success of his memoir ''A Heartbreaking Work of Staggering Genius'' (2000). The plot follows Will and Hand, two childhood friends who set ...

'' (2002), in which the speed of light is described as a "Sunday crawl". *On

Discworld ''Discworld'' is a comic fantasy"Humorous Fantasy" in David Pringle, ed., ''The Ultimate Encyclopedia of Fantasy'' (pp.31-33). London, Carlton,2006. book series written by the English author Terry Pratchett, set on the Discworld, a flat ...

, where

Terry Pratchett Sir Terence David John Pratchett (28 April 1948 – 12 March 2015) was an English humourist, satirist, and author of fantasy novels, especially comical works. He is best known for his '' Discworld'' series of 41 novels. Pratchett's first no ...

novel series A book series is a sequence of books having certain characteristics in common that are formally identified together as a group. Book series can be organized in different ways, such as written by the same author, or marketed as a group by their pub ...

takes place, light travels only a few hundred miles per hour due to Discworld's "embarrassingly strong" magic field. *"Slow glass" is a fictional material in

Bob Shaw Robert Shaw (31 December 1931 – 11 February 1996) was a science fiction writer and fan from Northern Ireland, noted for his originality and wit. He won the Hugo Award for Best Fan Writer in 1979 and 1980. His short story "Light of Other Days" ...

's short story "

Light of Other Days "Light of Other Days" is a science fiction short story by Bob Shaw. It was originally published in August 1966 in ''Analog Science Fiction and Fact.'' The story uses the idea of "slow glass": glass through which light takes years to pass. Bob Sha ...

" (''

Analog Analog or analogue may refer to: Computing and electronics * Analog signal, in which information is encoded in a continuous variable ** Analog device, an apparatus that operates on analog signals *** Analog electronics, circuits which use analog ...

'', 1966), and several subsequent stories. The glass, which delays the passage of light by years or decades, is used to construct windows, called ''scenedows'', that enable city dwellers, submariners and prisoners to watch "live" countryside scenes. "Slow glass" is a material where the delay light takes in passing through the glass is attributed to photons passing "...through a spiral tunnel coiled outside the radius of capture of each atom in the glass." Shaw later reworked the stories into the novel ''Other Days, Other Eyes'' (1972). *"Slow Light" (2022) is a short film made by Kijek/Adamski with two animation techniques. It's a story of a boy who is born blind and suddenly at the age of seven sees a light. A medical examination reveals that his eyes are so dense that it takes seven years for the light to reach the retina and hence for the image to reach his consciousness.The consequence of the eye defect translates into the mental immaturity of the man, lack of understanding of the present and belated reflections on long-gone facts. The man is never mature enough for his age and constantly lingers on the past.

Notes

References