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Silicon photonics is the study and application of
photonic Photonics is a branch of optics that involves the application of generation, detection, and manipulation of light in form of photons through emission, transmission, modulation, signal processing, switching, amplification, and sensing. Though ...
systems which use
silicon Silicon is a chemical element with the symbol Si and atomic number 14. It is a hard, brittle crystalline solid with a blue-grey metallic luster, and is a tetravalent metalloid and semiconductor. It is a member of group 14 in the periodic ta ...
as an optical medium. The silicon is usually patterned with sub-micrometre precision, into microphotonic components. These operate in the
infrared Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from around ...
, most commonly at the 1.55 micrometre
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, t ...
used by most fiber optic telecommunication systems. The silicon typically lies on top of a layer of silica in what (by analogy with a similar construction in microelectronics) is known as silicon on insulator (SOI). Silicon photonic devices can be made using existing semiconductor fabrication techniques, and because silicon is already used as the substrate for most integrated circuits, it is possible to create hybrid devices in which the
optical 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, ultravio ...
and
electronic Electronic may refer to: *Electronics, the science of how to control electric energy in semiconductor * ''Electronics'' (magazine), a defunct American trade journal *Electronic storage, the storage of data using an electronic device *Electronic co ...
components are integrated onto a single microchip. Consequently, silicon photonics is being actively researched by many electronics manufacturers including IBM and
Intel Intel Corporation is an American multinational corporation and technology company headquartered in Santa Clara, California. It is the world's largest semiconductor chip manufacturer by revenue, and is one of the developers of the x86 seri ...
, as well as by academic research groups, as a means for keeping on track with Moore's Law, by using optical interconnects to provide faster
data transfer Data transmission and data reception or, more broadly, data communication or digital communications is the transfer and reception of data in the form of a digital bitstream or a digitized analog signal transmitted over a point-to-point or ...
both between and within microchips. The propagation 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 te ...
through silicon devices is governed by a range of nonlinear optical phenomena including the Kerr effect, the Raman effect,
two-photon absorption Two-photon absorption (TPA or 2PA) or two-photon excitation or non-linear absorption is the simultaneous absorption of two photons of identical or different frequencies in order to excite a molecule from one state (usually the ground state) to a hi ...
and interactions between photons and free charge carriers. The presence of nonlinearity is of fundamental importance, as it enables light to interact with light, thus permitting applications such as wavelength conversion and all-optical signal routing, in addition to the passive transmission of light. Silicon
waveguide A waveguide is a structure that guides waves, such as electromagnetic waves or sound, with minimal loss of energy by restricting the transmission of energy to one direction. Without the physical constraint of a waveguide, wave intensities de ...
s are also of great academic interest, due to their unique guiding properties, they can be used for communications, interconnects, biosensors, and they offer the possibility to support exotic nonlinear optical phenomena such as soliton propagation.


Applications


Optical communications

In a typical optical link, data is first transferred from the electrical to the optical domain using an electro-optic modulator or a directly modulated laser. An electro-optic modulator can vary the intensity and/or the phase of the optical carrier. In silicon photonics, a common technique to achieve modulation is to vary the density of free charge carriers. Variations of electron and hole densities change the real and the imaginary part of the refractive index of silicon as described by the empirical equations of Soref and Bennett. Modulators can consist of both forward-biased
PIN diode A pin is a device used for fastening objects or material together. Pin or PIN may also refer to: Computers and technology * Personal identification number (PIN), to access a secured system ** PIN pad, a PIN entry device * PIN, a former Dutch ...
s, which generally generate large phase-shifts but suffer of lower speeds, as well as of reverse-biased PN junctions. A prototype optical interconnect with microring modulators integrated with germanium detectors has been demonstrated. Non-resonant modulators, such as Mach-Zehnder interferometers, have typical dimensions in the millimeter range and are usually used in telecom or datacom applications. Resonant devices, such as ring-resonators, can have dimensions of few tens of micrometers only, occupying therefore much smaller areas. In 2013, researchers demonstrated a resonant depletion modulator that can be fabricated using standard Silicon-on-Insulator Complementary Metal-Oxide-Semiconductor (SOI CMOS) manufacturing processes. A similar device has been demonstrated as well in bulk CMOS rather than in SOI. On the receiver side, the optical signal is typically converted back to the electrical domain using a semiconductor
photodetector Photodetectors, also called photosensors, are sensors of light or other electromagnetic radiation. There is a wide variety of photodetectors which may be classified by mechanism of detection, such as photoelectric or photochemical effects, or ...
. The semiconductor used for carrier generation has usually a band-gap smaller than the photon energy, and the most common choice is pure germanium. Most detectors utilize a PN junction for carrier extraction, however, detectors based on
metal–semiconductor junction In solid-state physics, a metal–semiconductor (M–S) junction is a type of electrical junction in which a metal comes in close contact with a semiconductor material. It is the oldest practical semiconductor device. M–S junctions can either ...
s (with germanium as the semiconductor) have been integrated into silicon waveguides as well. More recently, silicon-germanium
avalanche photodiode An avalanche photodiode (APD) is a highly sensitive semiconductor photodiode detector that exploits the photoelectric effect to convert light into electricity. From a functional standpoint, they can be regarded as the semiconductor analog of phot ...
s capable of operating at 40 Gbit/s have been fabricated. Complete transceivers have been commercialized in the form of active optical cables. Optical communications are conveniently classified by the reach, or length, of their links. The majority of silicon photonic communications have so far been limited to telecom and datacom applications, where the reach is of several kilometers or several meters respectively. Silicon photonics, however, is expected to play a significant role in computercom as well, where optical links have a reach in the centimeter to meter range. In fact, progress in computer technology (and the continuation of Moore's Law) is becoming increasingly dependent on faster
data transfer Data transmission and data reception or, more broadly, data communication or digital communications is the transfer and reception of data in the form of a digital bitstream or a digitized analog signal transmitted over a point-to-point or ...
between and within
microchips 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 M ...
. Optical interconnects may provide a way forward, and silicon photonics may prove particularly useful, once integrated on the standard silicon chips. In 2006,
Intel Intel Corporation is an American multinational corporation and technology company headquartered in Santa Clara, California. It is the world's largest semiconductor chip manufacturer by revenue, and is one of the developers of the x86 seri ...
Senior Vice President - and future CEO -
Pat Gelsinger Patrick Paul Gelsinger (; born March 5, 1961) is an American business executive and engineer currently serving as CEO of Intel. Based mainly in Silicon Valley since the late 1970s, Gelsinger graduated from Stanford University with a master's deg ...
stated that, "Today, optics is a niche technology. Tomorrow, it's the mainstream of every chip that we build." The first microprocessor with optical input/output (I/O) was demonstrated in December 2015 using an approach known as "zero-change" CMOS photonics. This first demonstration was based on a 45 nm SOI node, and the bi-directional chip-to-chip link was operated at a rate of 2×2.5 Gbit/s. The total energy consumption of the link was calculated to be of 16 pJ/b and was dominated by the contribution of the off-chip laser. Some researchers believe an on-chip
laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fi ...
source is required. Others think that it should remain off-chip because of thermal problems (the quantum efficiency decreases with temperature, and computer chips are generally hot) and because of CMOS-compatibility issues. One such device is the hybrid silicon laser, in which the silicon is bonded to a different
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. ...
(such as indium phosphide) as the lasing medium. Other devices include all-silicon Raman laser or an all-silicon Brillouin lasers wherein silicon serves as the lasing medium. In 2012, IBM announced that it had achieved optical components at the 90 nanometer scale that can be manufactured using standard techniques and incorporated into conventional chips. In September 2013, Intel announced technology to transmit data at speeds of 100 gigabits per second along a cable approximately five millimeters in diameter for connecting servers inside data centers. Conventional PCI-E data cables carry data at up to eight gigabits per second, while networking cables reach 40 Gbit/s. The latest version of the USB standard tops out at ten Gbit/s. The technology does not directly replace existing cables in that it requires a separate circuit board to interconvert electrical and optical signals. Its advanced speed offers the potential of reducing the number of cables that connect blades on a rack and even of separating processor, storage and memory into separate blades to allow more efficient cooling and dynamic configuration. Graphene photodetectors have the potential to surpass germanium devices in several important aspects, although they remain about one order of magnitude behind current generation capacity, despite rapid improvement. Graphene devices can work at very high frequencies, and could in principle reach higher bandwidths. Graphene can absorb a broader range of wavelengths than germanium. That property could be exploited to transmit more data streams simultaneously in the same beam of light. Unlike germanium detectors, graphene photodetectors do not require applied voltage, which could reduce energy needs. Finally, graphene detectors in principle permit a simpler and less expensive on-chip integration. However, graphene does not strongly absorb light. Pairing a silicon waveguide with a graphene sheet better routes light and maximizes interaction. The first such device was demonstrated in 2011. Manufacturing such devices using conventional manufacturing techniques has not been demonstrated.


Optical routers and signal processors

Another application of silicon photonics is in signal routers for optical communication. Construction can be greatly simplified by fabricating the optical and electronic parts on the same chip, rather than having them spread across multiple components. A wider aim is all-optical signal processing, whereby tasks which are conventionally performed by manipulating signals in electronic form are done directly in optical form. An important example is all- optical switching, whereby the routing of optical signals is directly controlled by other optical signals. Another example is all-optical wavelength conversion. In 2013, a
startup company A startup or start-up is a company or project undertaken by an entrepreneur to seek, develop, and validate a scalable business model. While entrepreneurship refers to all new businesses, including self-employment and businesses that never intend ...
named "Compass-EOS", based in
California California is a state in the Western United States, located along the Pacific Coast. With nearly 39.2million residents across a total area of approximately , it is the most populous U.S. state and the 3rd largest by area. It is also the m ...
and in
Israel Israel (; he, יִשְׂרָאֵל, ; ar, إِسْرَائِيل, ), officially the State of Israel ( he, מְדִינַת יִשְׂרָאֵל, label=none, translit=Medīnat Yīsrāʾēl; ), is a country in Western Asia. It is situated ...
, was the first to present a commercial silicon-to-photonics router.


Long range telecommunications using silicon photonics

Silicon microphotonics can potentially increase the
Internet The Internet (or internet) is the global system of interconnected computer networks that uses the Internet protocol suite (TCP/IP) to communicate between networks and devices. It is a '' network of networks'' that consists of private, pub ...
's bandwidth capacity by providing micro-scale, ultra low power devices. Furthermore, the power consumption of datacenters may be significantly reduced if this is successfully achieved. Researchers at Sandia, Kotura, NTT, Fujitsu and various academic institutes have been attempting to prove this functionality. A 2010 paper reported on a prototype 80 km, 12.5 Gbit/s transmission using microring silicon devices.


Light-field displays

As of 2015, US startup company
Magic Leap Magic Leap, Inc. is an American technology company that released a head-mounted virtual retinal display, called ''Magic Leap One'', which superimposes 3D computer-generated imagery over real world objects, by "projecting a digital light field ...
is working on a light-field chip using silicon photonics for the purpose of an augmented reality display.


Physical properties


Optical guiding and dispersion tailoring

Silicon is
transparent Transparency, transparence or transparent most often refer to: * Transparency (optics), the physical property of allowing the transmission of light through a material They may also refer to: Literal uses * Transparency (photography), a still, ...
to
infrared light Infrared (IR), sometimes called infrared light, is electromagnetic radiation (EMR) with wavelengths longer than those of visible light. It is therefore invisible to the human eye. IR is generally understood to encompass wavelengths from arou ...
with wavelengths above about 1.1 micrometres. Silicon also has a very high
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, or ...
, of about 3.5. The tight optical confinement provided by this high index allows for microscopic
optical waveguide An optical waveguide is a physical structure that guides electromagnetic waves in the optical spectrum. Common types of optical waveguides include optical fiber waveguides, transparent dielectric waveguides made of plastic and glass, liquid light ...
s, which may have cross-sectional dimensions of only a few hundred nanometers. Single mode propagation can be achieved, thus (like
single-mode optical fiber In fiber-optic communication, a single-mode optical fiber (SMF), also known as fundamental- or mono-mode, is an optical fiber designed to carry only a single mode of light - the transverse mode. Modes are the possible solutions of the Helmholtz ...
) eliminating the problem of modal dispersion. The strong dielectric boundary effects that result from this tight confinement substantially alter the optical dispersion relation. By selecting the waveguide geometry, it is possible to tailor the dispersion to have desired properties, which is of crucial importance to applications requiring ultrashort pulses. In particular, the ''group velocity dispersion'' (that is, the extent to which group velocity varies with wavelength) can be closely controlled. In bulk silicon at 1.55 micrometres, the group velocity dispersion (GVD) is ''normal'' in that pulses with longer wavelengths travel with higher group velocity than those with shorter wavelength. By selecting a suitable waveguide geometry, however, it is possible to reverse this, and achieve ''anomalous'' GVD, in which pulses with shorter wavelengths travel faster. Anomalous dispersion is significant, as it is a prerequisite for soliton propagation, and
modulational instability In the fields of nonlinear optics and fluid dynamics, modulational instability or sideband instability is a phenomenon whereby deviations from a periodic waveform are reinforced by nonlinearity, leading to the generation of spectral-sidebands and t ...
. In order for the silicon photonic components to remain optically independent from the bulk silicon of the
wafer A wafer is a crisp, often sweet, very thin, flat, light and dry biscuit, often used to decorate ice cream, and also used as a garnish on some sweet dishes. Wafers can also be made into cookies with cream flavoring sandwiched between them. They ...
on which they are fabricated, it is necessary to have a layer of intervening material. This is usually
silica Silicon dioxide, also known as silica, is an oxide of silicon with the chemical formula , most commonly found in nature as quartz and in various living organisms. In many parts of the world, silica is the major constituent of sand. Silica is ...
, which has a much lower refractive index (of about 1.44 in the wavelength region of interest), and thus light at the silicon-silica interface will (like light at the silicon-air interface) undergo total internal reflection, and remain in the silicon. This construct is known as silicon on insulator. It is named after the technology of silicon on insulator in electronics, whereby components are built upon a layer of insulator in order to reduce parasitic capacitance and so improve performance.


Kerr nonlinearity

Silicon has a focusing Kerr nonlinearity, in that 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, or ...
increases with optical intensity. This effect is not especially strong in bulk silicon, but it can be greatly enhanced by using a silicon waveguide to concentrate light into a very small cross-sectional area. This allows nonlinear optical effects to be seen at low powers. The nonlinearity can be enhanced further by using a slot waveguide, in which the high refractive index of the silicon is used to confine light into a central region filled with a strongly nonlinear
polymer A polymer (; Greek '' poly-'', "many" + ''-mer'', "part") is a substance or material consisting of very large molecules called macromolecules, composed of many repeating subunits. Due to their broad spectrum of properties, both synthetic a ...
. Kerr nonlinearity underlies a wide variety of optical phenomena. One example is four wave mixing, which has been applied in silicon to realise
optical parametric amplification An optical parametric amplifier, abbreviated OPA, is a laser light source that emits light of variable wavelengths by an optical parametric amplification process. It is essentially the same as an optical parametric oscillator, but without the optic ...
, parametric wavelength conversion, and frequency comb generation., Kerr nonlinearity can also cause
modulational instability In the fields of nonlinear optics and fluid dynamics, modulational instability or sideband instability is a phenomenon whereby deviations from a periodic waveform are reinforced by nonlinearity, leading to the generation of spectral-sidebands and t ...
, in which it reinforces deviations from an optical waveform, leading to the generation of spectral-sidebands and the eventual breakup of the waveform into a train of pulses. Another example (as described below) is soliton propagation.


Two-photon absorption

Silicon exhibits
two-photon absorption Two-photon absorption (TPA or 2PA) or two-photon excitation or non-linear absorption is the simultaneous absorption of two photons of identical or different frequencies in order to excite a molecule from one state (usually the ground state) to a hi ...
(TPA), in which a pair of
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they a ...
s can act to excite an electron-hole pair. This process is related to the Kerr effect, and by analogy with
complex 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, or ...
, can be thought of as the imaginary-part of a
complex Complex commonly refers to: * Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe ** Complex system, a system composed of many components which may interact with each ...
Kerr nonlinearity. At the 1.55 micrometre telecommunication wavelength, this imaginary part is approximately 10% of the real part. The influence of TPA is highly disruptive, as it both wastes light, and generates unwanted
heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is ...
. It can be mitigated, however, either by switching to longer wavelengths (at which the TPA to Kerr ratio drops), or by using slot waveguides (in which the internal nonlinear material has a lower TPA to Kerr ratio). Alternatively, the energy lost through TPA can be partially recovered (as is described below) by extracting it from the generated charge carriers.


Free charge carrier interactions

The free charge carriers within silicon can both absorb photons and change its refractive index. This is particularly significant at high intensities and for long durations, due to the carrier concentration being built up by TPA. The influence of free charge carriers is often (but not always) unwanted, and various means have been proposed to remove them. One such scheme is to implant the silicon with
helium Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic table. ...
in order to enhance carrier recombination. A suitable choice of geometry can also be used to reduce the carrier lifetime. Rib waveguides (in which the waveguides consist of thicker regions in a wider layer of silicon) enhance both the carrier recombination at the silica-silicon interface and the
diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemica ...
of carriers from the waveguide core. A more advanced scheme for carrier removal is to integrate the waveguide into the intrinsic region of a
PIN diode A pin is a device used for fastening objects or material together. Pin or PIN may also refer to: Computers and technology * Personal identification number (PIN), to access a secured system ** PIN pad, a PIN entry device * PIN, a former Dutch ...
, which is reverse biased so that the carriers are attracted away from the waveguide core. A more sophisticated scheme still, is to use the diode as part of a circuit in which
voltage Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to ...
and
current Currents, Current or The Current may refer to: Science and technology * Current (fluid), the flow of a liquid or a gas ** Air current, a flow of air ** Ocean current, a current in the ocean *** Rip current, a kind of water current ** Current (stre ...
are out of phase, thus allowing power to be extracted from the waveguide. The source of this power is the light lost to two photon absorption, and so by recovering some of it, the net loss (and the rate at which heat is generated) can be reduced. As is mentioned above, free charge carrier effects can also be used constructively, in order to modulate the light.


Second-order nonlinearity

Second-order nonlinearities cannot exist in bulk silicon because of the
centrosymmetry In crystallography, a centrosymmetric point group contains an inversion center as one of its symmetry elements. In such a point group, for every point (x, y, z) in the unit cell there is an indistinguishable point (-x, -y, -z). Such point group ...
of its crystalline structure. By applying strain however, the inversion symmetry of silicon can be broken. This can be obtained for example by depositing a
silicon nitride Silicon nitride is a chemical compound of the elements silicon and nitrogen. is the most thermodynamically stable and commercially important of the silicon nitrides, and the term "silicon nitride" commonly refers to this specific composition. It ...
layer on a thin silicon film. Second-order nonlinear phenomena can be exploited for optical modulation,
spontaneous parametric down-conversion Spontaneous parametric down-conversion (also known as SPDC, parametric fluorescence or parametric scattering) is a nonlinear instant optical process that converts one photon of higher energy (namely, a pump photon), into a pair of photons (namely, ...
, parametric amplification, ultra-fast optical signal processing and mid-infrared generation. Efficient nonlinear conversion however requires
phase matching Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform *Phase space, a mathematica ...
between the optical waves involved. Second-order nonlinear waveguides based on strained silicon can achieve
phase matching Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform *Phase space, a mathematica ...
by dispersion-engineering. So far, however, experimental demonstrations are based only on designs which are not phase matched. It has been shown that
phase matching Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform *Phase space, a mathematica ...
can be obtained as well in silicon double slot waveguides coated with a highly nonlinear organic cladding and in periodically strained silicon waveguides.


The Raman effect

Silicon exhibits the Raman effect, in which a photon is exchanged for a photon with a slightly different energy, corresponding to an excitation or a relaxation of the material. Silicon's Raman transition is dominated by a single, very narrow frequency peak, which is problematic for broadband phenomena such as
Raman amplification Raman amplification "Raman effect"
. ''
Raman lasers. Early studies of Raman amplification and Raman lasers started at UCLA which led to demonstration of net gain Silicon Raman amplifiers and silicon pulsed Raman laser with fiber resonator (Optics express 2004). Consequently, all-silicon Raman lasers have been fabricated in 2005.


The Brillouin effect

In the Raman effect, photons are red- or blue-shifted by optical phonons with a frequency of about 15 THz. However, silicon waveguides also support
acoustic phonon In physics, a phonon is a collective excitation in a periodic, elastic arrangement of atoms or molecules in condensed matter, specifically in solids and some liquids. A type of quasiparticle, a phonon is an excited state in the quantum mechanical ...
excitations. The interaction of these acoustic phonons with light is called Brillouin scattering. The frequencies and mode shapes of these acoustic phonons are dependent on the geometry and size of the silicon waveguides, making it possible to produce strong Brillouin scattering at frequencies ranging from a few MHz to tens of GHz. Stimulated Brillouin scattering has been used to make narrowband optical amplifiers as well as all-silicon Brillouin lasers. The interaction between photons and acoustic phonons is also studied in the field of
cavity optomechanics Cavity optomechanics is a branch of physics which focuses on the interaction between light and mechanical objects on low-energy scales. It is a cross field of optics, quantum optics, solid-state physics and materials science. The motivation f ...
, although 3D optical cavities are not necessary to observe the interaction. For instance, besides in silicon waveguides the optomechanical coupling has also been demonstrated in fibers and in chalcogenide waveguides.


Solitons

The evolution of light through silicon waveguides can be approximated with a cubic Nonlinear Schrödinger equation, which is notable for admitting sech-like soliton solutions. These optical solitons (which are also known in
optical fiber An optical fiber, or optical fibre in Commonwealth English, is a flexible, transparent fiber made by drawing glass ( silica) or plastic to a diameter slightly thicker than that of a human hair. Optical fibers are used most often as a mea ...
) result from a balance between self phase modulation (which causes the leading edge of the pulse to be redshifted and the trailing edge blueshifted) and anomalous group velocity dispersion. Such solitons have been observed in silicon waveguides, by groups at the universities of Columbia,
Rochester Rochester may refer to: Places Australia * Rochester, Victoria Canada * Rochester, Alberta United Kingdom *Rochester, Kent ** City of Rochester-upon-Medway (1982–1998), district council area ** History of Rochester, Kent ** HM Prison ...
, and Bath.


References

{{DEFAULTSORT:Silicon photonics Nonlinear optics Photonics Silicon