silicon photonics

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.{{cite journal

|last1 = Soref

|first1 = Richard A.

|last2 = Bennett

|first2 = Brian R.

|date = 1987

|title = Electrooptical effects in silicon

|journal = IEEE Journal of Quantum Electronics

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|archive-date = 2 December 2020

|archive-url = https://web.archive.org/web/20201202224441/https://zenodo.org/record/1232209

|url-status = live

}} Modulators can consist of both forward-biased PIN diodes, which generally generate large phase-shifts but suffer of lower speeds,{{cite journal

|doi = 10.1109/JLT.2003.818167

|title = Electrooptic Modulation of Silicon-on-Insulator Submicrometer-Size Waveguide Devices

|journal = Journal of Lightwave Technology

|year = 2003

|volume = 21

|issue = 10

|pages = 2332–2339

| bibcode = 2003JLwT...21.2332B |last1 = Barrios

|first1 = C.A.

|last2 = Almeida

|first2 = V.R.

|last3 = Panepucci

|first3 = R.

|last4 = Lipson

|first4 = M.

}} as well as of reverse-biased p–n junctions.{{cite journal

|doi = 10.1364/OE.15.000660

|last1 = Liu

|first1 = Ansheng

|last2 = Liao

|first2 = Ling

|last3 = Rubin

|first3 = Doron

|last4 = Nguyen

|first4 = Hat

|last5 = Ciftcioglu

|first5 = Berkehan

|last6 = Chetrit

|first6 = Yoel

|last7 = Izhaky

|first7 = Nahum

|last8 = Paniccia

|first8 = Mario

|s2cid = 24984744

|title = High-speed optical modulation based on carrier depletion in a silicon waveguide

|journal = Optics Express

|year = 2007

|volume = 15

|issue = 2

|pages = 660–668 |pmid = 19532289

|bibcode = 2007OExpr..15..660L

|doi-access = free

}}

A prototype optical interconnect with microring modulators integrated with germanium detectors has been demonstrated.{{cite journal

|doi = 10.1364/OE.17.015248

|pmid = 19688003

|title = Integrated GHz silicon photonic interconnect with micrometer-scale modulators and detectors

|journal = Optics Express

|year = 2009

|volume = 17

|issue = 17

|pages = 15248–15256

| bibcode = 2009OExpr..1715248C |arxiv = 0907.0022 |last1 = Chen

|first1 = Long

|last2 = Preston

|first2 = Kyle

|last3 = Manipatruni

|first3 = Sasikanth

|last4 = Lipson

|first4 = Michal

|s2cid = 40101121

}}

{{cite news

|title = Intel cranks up next-gen chip-to-chip play

|publisher = The Register

|author = Vance, Ashlee

|author-link=Ashlee Vance

|url = https://www.theregister.co.uk/2007/01/27/intel_silicon_modulator/print.html

|accessdate = 26 July 2009

|archive-date = 4 October 2012

|archive-url = https://web.archive.org/web/20121004045117/http://www.theregister.co.uk/2007/01/27/intel_silicon_modulator/print.html

|url-status = live

}}

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 only tens of micrometers, therefore occupying 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.{{Cite journal | last1 = Shainline | first1 = J. M. | last2 = Orcutt | first2 = J. S. | last3 = Wade | first3 = M. T. | last4 = Nammari | first4 = K. | last5 = Moss | first5 = B. | last6 = Georgas | first6 = M. | last7 = Sun | first7 = C. | last8 = Ram | first8 = R. J. | last9 = Stojanović | first9 = V. | last10 = Popović | first10 = M. A. | s2cid = 16603677 | doi = 10.1364/OL.38.002657 | title = Depletion-mode carrier-plasma optical modulator in zero-change advanced CMOS | journal = Optics Letters | volume = 38 | issue = 15 | pages = 2657–2659 | year = 2013 | pmid = 23903103|bibcode = 2013OptL...38.2657S }} A similar device has been demonstrated as well in bulk CMOS rather than in SOI.{{cite web |url=http://www.kurzweilai.net/major-silicon-photonics-breakthrough-could-allow-for-continued-exponential-growth-in-microprocessors |title=Major silicon photonics breakthrough could allow for continued exponential growth in microprocessors |publisher=KurzweilAI |date=8 October 2013 |access-date=8 October 2013 |archive-date=8 October 2013 |archive-url=https://web.archive.org/web/20131008130226/http://www.kurzweilai.net/major-silicon-photonics-breakthrough-could-allow-for-continued-exponential-growth-in-microprocessors |url-status=live }}{{Cite journal | last1 = Shainline | first1 = J. M. | last2 = Orcutt | first2 = J. S. | last3 = Wade | first3 = M. T. | last4 = Nammari | first4 = K. | last5 = Tehar-Zahav | first5 = O. | last6 = Sternberg | first6 = Z. | last7 = Meade | first7 = R. | last8 = Ram | first8 = R. J. | last9 = Stojanović | first9 = V. | last10 = Popović | first10 = M. A. | s2cid = 6228126 | doi = 10.1364/OL.38.002729 | title = Depletion-mode polysilicon optical modulators in a bulk complementary metal-oxide semiconductor process | journal = Optics Letters | volume = 38 | issue = 15 | pages = 2729–2731 | year = 2013 | pmid = 23903125|bibcode = 2013OptL...38.2729S }}

On the receiver side, the optical signal is typically converted back to the electrical domain using a semiconductor photodetector. The semiconductor used for carrier generation usually had a band-gap smaller than the photon energy, and the most common choice is pure germanium.{{cite journal |last1=Kucharski |first1=D. |last2=Guckenberger |first2=D. |last3=Masini |first3=G. |last4=Abdalla |first4=S. |last5=Witzens |first5=J. |last6=Sahni |first6=S. |display-authors=1 |year=2010 |title=10 Gb/s 15mW optical receiver with integrated Germanium photodetector and hybrid inductor peaking in 0.13µm SOI CMOS technology |journal= Solid-State Circuits Conference Digest of Technical Papers (ISSCC) |pages=360–361}}{{cite journal|year = 2006|title=CMOS photonics using germanium photodetectors|journal=ECS Transactions|volume=3|issue=7|pages=17–24|doi=10.1149/1.2355790|last1=Gunn|first1=Cary|last2=Masini|first2=Gianlorenzo|last3=Witzens|first3=J.|last4=Capellini|first4=G.|bibcode=2006ECSTr...3g..17G|s2cid=111820229 }} Most detectors use a p–n junction for carrier extraction, however, detectors based on metal–semiconductor junctions (with germanium as the semiconductor) have been integrated into silicon waveguides as well.{{cite journal

|doi = 10.1364/OE.15.009843

|pmid = 19547334

|title = High speed and high responsivity germanium photodetector integrated in a Silicon-On-Insulator microwaveguide

|journal = Optics Express

|year = 2007

|volume = 15

|issue = 15

|pages = 9843–9848

| bibcode = 2007OExpr..15.9843V |last1 = Vivien

|first1 = Laurent

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|first2 = Mathieu

|last3 = Fédéli

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|last4 = Marris-Morini

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|last5 = Damlencourt

|first5 = Jean François

|last6 = Mangeney

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|first9 = Eric

|last10 = Le Roux

|first10 = Xavier

|last11 = Pascal

|first11 = Daniel

|last12 = Laval

|first12 = Suzanne

|doi-access = free

}} More recently, silicon-germanium avalanche photodiodes capable of operating at 40 Gbit/s have been fabricated.{{cite journal

|doi = 10.1038/nphoton.2008.247

|title = Monolithic germanium/silicon avalanche photodiodes with 340 GHz gain–bandwidth product

|journal = Nature Photonics

|year = 2008

|volume = 3

|issue = 1

|pages = 59–63

|bibcode = 2009NaPho...3...59K|last1 = Kang

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}}{{cite news

|title = Intel trumpets world's fastest silicon photonic detector

|publisher = The Register

|author = Modine, Austin

|url = https://www.theregister.co.uk/2008/12/08/intel_world_record_apd_research/

|date = 8 December 2008

|access-date = 10 August 2017

|archive-date = 10 August 2017

|archive-url = https://web.archive.org/web/20170810133155/https://www.theregister.co.uk/2008/12/08/intel_world_record_apd_research/

|url-status = live

}}

Complete transceivers have been commercialized in the form of active optical cables.{{cite journal|author = Narasimha, A.|title = A 40-Gb/s QSFP optoelectronic transceiver in a 0.13 µm CMOS silicon-on-insulator technology|year = 2008|journal = Proceedings of the Optical Fiber Communication Conference (OFC)|page = OMK7|url = http://www.opticsinfobase.org/abstract.cfm?URI=OFC-2008-OMK7|isbn = 978-1-55752-859-9|access-date = 14 September 2012|archive-date = 16 April 2023|archive-url = https://web.archive.org/web/20230416232644/https://opg.optica.org/abstract.cfm?URI=OFC-2008-OMK7|url-status = live}}

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{{cite book

| last = Doerr

| first = Christopher R.

| editor-last = Yamada

| editor-first = Koji

| display-authors = etal

| title = Photonic Integration and Photonics-Electronics Convergence on Silicon

| journal = Frontiers in Physics

| volume = 3

| year = 2015

| publisher = Frontiers Media SA

| doi = 10.3389/fphy.2015.00037

| page = 7

| chapter = Silicon photonic integration in telecommunications

| bibcode= 2015FrP.....3...37D

| doi-access = free

}}

and datacom applications,{{cite conference

| title = Monolithic Silicon Photonics at 25Gb/s

| first = Jason

| last = Orcutt

| year = 2016

| conference = Optical Fiber Communication Conference

| publisher = OSA

| pages = Th4H.1

| doi = 10.1364/OFC.2016.Th4H.1

|display-authors=etal

}}{{cite conference

| title = Recent Progress in Silicon Photonics R&D and Manufacturing on 300mm Wafer Platform

| first = Boeuf

| last = Frederic

| year = 2015

| conference = Optical Fiber Communication Conference

| publisher = OSA

| pages = W3A.1

| doi = 10.1364/OFC.2015.W3A.1

|display-authors=etal

}} 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 between and within microchips.{{cite journal

|doi = 10.1109/MCISE.2003.1166548

|title = Beyond Moore's Law: the interconnect era

|journal = Computing in Science & Engineering

|year = 2003

|volume = 5

|issue = 1

|pages = 20–24

|author = Meindl, J. D.

|bibcode = 2003CSE.....5a..20M

|s2cid = 15668981

}} Optical interconnects may provide a way forward, and silicon photonics may prove particularly useful, once integrated on the standard silicon chips.{{cite journal

|doi = 10.1364/JON.6.000063

|title = Silicon photonics for compact, energy-efficient interconnects

|journal = Journal of Optical Networking

|year = 2006

|volume = 6

|issue = 1

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}}{{cite conference

|author = Orcutt, J. S.

|title = Demonstration of an Electronic Photonic Integrated Circuit in a Commercial Scaled Bulk CMOS Process

|conference = Conference on Lasers and Electro-Optics/Quantum Electronics and Laser Science Conference and Photonic Applications Systems Technologies

|year = 2008

|display-authors=etal}} In 2006, Intel Senior Vice President - and future CEO - Pat Gelsinger stated that, "Today, optics is a niche technology. Tomorrow, it's the mainstream of every chip that we build." In 2010 Intel demonstrated a 50 Gbit/s connection made with silicon photonics.{{cite web | url=https://www.anandtech.com/show/3834/intels-silicon-photonics-50g-silicon-photonics-link | title=Intel's 50Gbps Silicon Photonics Link: The Future of Interfaces }}

The first microprocessor with optical input/output (I/O) was demonstrated in December 2015 using an approach known as "zero-change" CMOS photonics.{{cite journal

|last1 = Sun

|first1 = Chen

|display-authors = etal

|date = 2015

|title = Single-chip microprocessor that communicates directly using light

|url = https://escholarship.org/uc/item/4dh1v4px

|journal = Nature

|volume = 528

|issue = 7583

|pages = 534–538

|doi = 10.1038/nature16454

|pmid = 26701054

|bibcode = 2015Natur.528..534S

|s2cid = 205247044

|access-date = 2 July 2019

|archive-date = 23 June 2020

|archive-url = https://web.archive.org/web/20200623032459/https://escholarship.org/uc/item/4dh1v4px

|url-status = live

}} This is known as fiber-to-the-processor.{{cite web | url=https://spectrum.ieee.org/silicon-photonics-stumbles-at-the-last-meter | title=Silicon Photonics Stumbles at the Last Meter - IEEE Spectrum }}

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 source is required.{{cite conference

| title = Semiconductor lasers on silicon

| first = John E

| last = Bowers

| year = 2014

| conference = 2014 International Semiconductor Laser Conference\

| publisher = IEEE

| pages = 29

}} 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 (such as indium phosphide) as the lasing medium.{{cite web

|url = http://techresearch.intel.com/articles/Tera-Scale/1448.htm

|title = Hybrid Silicon Laser – Intel Platform Research

|publisher = Intel

|accessdate = 14 July 2009

|archive-date = 28 June 2009

|archive-url = https://web.archive.org/web/20090628011649/http://techresearch.intel.com/articles/Tera-Scale/1448.htm

|url-status = live

}} Other devices include all-silicon Raman laser{{cite journal

|title = An all-silicon Raman laser

|doi = 10.1038/nature03273

|journal = Nature

|pmid = 15635371

|year = 2005

|volume = 433

|issue = 7023

|pages = 292–294

| bibcode = 2005Natur.433..292R |last1 = Rong

|first1 = H

|last2 = Liu

|first2 = A

|last3 = Jones

|first3 = R

|last4 = Cohen

|first4 = O

|last5 = Hak

|first5 = D

|last6 = Nicolaescu

|first6 = R

|last7 = Fang

|first7 = A

|last8 = Paniccia

|first8 = M

|s2cid = 4407228

}} or an all-silicon Brillouin lasers{{Cite journal|last1=Otterstrom|first1=Nils T.|last2=Behunin|first2=Ryan O.|last3=Kittlaus|first3=Eric A.|last4=Wang|first4=Zheng|last5=Rakich|first5=Peter T.|date=2018-06-08|title=A silicon Brillouin laser|journal=Science|volume=360|issue=6393|pages=1113–1116|doi=10.1126/science.aar6113|pmid=29880687|issn=0036-8075|bibcode=2018Sci...360.1113O|arxiv=1705.05813|s2cid=46979719}} 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.{{cite web |url=http://www.gizmag.com/ibm-silicon-nanophotonics/25446/ |title=IBM integrates optics and electronics on a single chip |publisher=Gizmag.com |date=13 December 2012 |author=Borghino, Dario |access-date=20 April 2013 |archive-date=22 April 2013 |archive-url=https://web.archive.org/web/20130422010438/http://www.gizmag.com/ibm-silicon-nanophotonics/25446/ |url-status=live }} 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.{{cite web |last=Simonite |first=Tom |url=http://www.technologyreview.com/news/518941/intels-laser-chips-could-make-data-centers-run-better |title=Intel Unveils Optical Technology to Kill Copper Cables and Make Data Centers Run Faster | MIT Technology Review |publisher=Technologyreview.com |accessdate=4 September 2013 |archive-date=5 September 2013 |archive-url=https://web.archive.org/web/20130905013254/http://www.technologyreview.com/news/518941/intels-laser-chips-could-make-data-centers-run-better/ |url-status=live }}

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.Orcutt, Mike (2 October 2013) [https://www.technologyreview.com/2013/10/02/176263/graphene-could-make-data-centers-and-supercomputers-more-efficient/ "Graphene-Based Optical Communication Could Make Computing More Efficient] {{Webarchive|url=https://web.archive.org/web/20210510194440/https://www.technologyreview.com/2013/10/02/176263/graphene-could-make-data-centers-and-supercomputers-more-efficient/ |date=10 May 2021 }}. MIT Technology Review.

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.{{cite journal

|doi = 10.1109/JSSC.2006.884388

|title = A Fully Integrated 20-Gb/s Optoelectronic Transceiver Implemented in a Standard 0.13- μm CMOS SOI Technology

|journal = IEEE Journal of Solid-State Circuits

|year = 2006

|volume = 41

|issue = 12

|pages = 2945–2955

|last1 = Analui

|first1 = Behnam

|last2 = Guckenberger

|first2 = Drew

|last3 = Kucharski

|first3 = Daniel

|last4 = Narasimha

|first4 = Adithyaram

|bibcode = 2006IJSSC..41.2945A

|s2cid = 44232146

}} 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.{{cite journal

|doi = 10.1364/OPEX.12.004094

|title = All optical switching and continuum generation in silicon waveguides

|journal = Optics Express

|year = 2004

|volume = 12

|issue = 17

|pages = 4094–4102

| bibcode = 2004OExpr..12.4094B |last1 = Boyraz

|first1 = ÖZdal

|last2 = Koonath

|first2 = Prakash

|last3 = Raghunathan

|first3 = Varun

|last4 = Jalali

|first4 = Bahram

|pmid = 19483951

|s2cid = 29225037

|doi-access = free

}} An important example is all-optical switching, whereby the routing of optical signals is directly controlled by other optical signals.{{cite journal

|doi = 10.1038/nphoton.2008.31

|title = High-throughput silicon nanophotonic wavelength-insensitive switch for on-chip optical networks

|journal = Nature Photonics

|year = 2008

|volume = 2

|issue = 4

|pages = 242–246

|last1 = Vlasov

|first1 = Yurii

|last2 = Green

|first2 = William M. J.

|last3 = Xia

|first3 = Fengnian

}} Another example is all-optical wavelength conversion.{{cite journal

|doi = 10.1364/OE.15.012949

|pmid = 19550563

|title = Broad-band continuous-wave parametric wavelength conversion in silicon nanowaveguides

|journal = Optics Express

|year = 2007

|volume = 15

|issue = 20

|pages = 12949–12958

| bibcode = 2007OExpr..1512949F |last1 = Foster

|first1 = Mark A.

|last2 = Turner

|first2 = Amy C.

|last3 = Salem

|first3 = Reza

|last4 = Lipson

|first4 = Michal

|author4-link=Michal Lipson

|author5-link=Alexander Gaeta

|last5 = Gaeta

|first5 = Alexander L.

|s2cid = 12219167

|doi-access = free

}}

In 2013, a startup company named "Compass-EOS", based in California and in Israel, was the first to present a commercial silicon-to-photonics router.{{cite web |url=https://venturebeat.com/2013/03/12/after-six-years-of-planning-compass-eos-takes-on-cisco-to-make-blazing-fast-routers/ |title=After six years of planning, Compass-EOS takes on Cisco to make blazing-fast routers |publisher=venturebeat.com |date=12 March 2013 |accessdate=25 April 2013 |archive-date=5 May 2013 |archive-url=https://web.archive.org/web/20130505002536/http://venturebeat.com/2013/03/12/after-six-years-of-planning-compass-eos-takes-on-cisco-to-make-blazing-fast-routers/ |url-status=live }}

Silicon microphotonics can potentially increase the Internet'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,{{cite book

|title = Optical Fiber Communication Conference

|year = 2010

|issue = OMI7

|pages = OMI7

|author = Zortman, W. A.

|chapter = Power Penalty Measurement and Frequency Chirp Extraction in Silicon Microdisk Resonator Modulators

|doi = 10.1364/OFC.2010.OMI7

|isbn = 978-1-55752-885-8

|s2cid = 11379237

}} 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.{{cite journal

|doi = 10.1364/OE.18.015544

|pmid = 20720934

|title = First demonstration of long-haul transmission using silicon microring modulators

|journal = Optics Express

|year = 2010

|volume = 18

|issue = 15

|pages = 15544–15552

| bibcode = 2010OExpr..1815544B

|last1 = Biberman

|first1 = Aleksandr

|last2 = Manipatruni

|first2 = Sasikanth

|last3 = Ophir

|first3 = Noam

|last4 = Chen

|first4 = Long

|last5 = Lipson

|first5 = Michal

|last6 = Bergman

|first6 = Keren

|s2cid = 19421366

|doi-access = free

}}

As of 2015, US startup company Magic Leap is working on a light-field chip using silicon photonics for the purpose of an augmented reality display.{{Cite web|title = Can Magic Leap Do What It Claims with $592 Million?|url = http://www.technologyreview.com/news/538146/magic-leap-needs-to-engineer-a-miracle/|accessdate = 2015-06-13|publisher = MIT Technology Review|last = Bourzac|first = Katherine|date = 2015-06-11|archive-date = 14 June 2015|archive-url = https://web.archive.org/web/20150614005122/http://www.technologyreview.com/news/538146/magic-leap-needs-to-engineer-a-miracle/|url-status = live}}

Silicon photonics has been used in artificial intelligence inference processors that are more energy efficient than those using conventional transistors. This can be done using Mach-Zehnder interferometers (MZIs) which can be combined with nanoelectromechanical systems to modulate the light passing though it, by physically bending the MZI which changes the phase of the light.{{cite web |url=https://hc32.hotchips.org/assets/program/conference/day2/HotChips2020_ML_Inference_Lightmatter.pdf |title=Silicon Photonics for Artificial Intelligence Acceleration |website=hotchips.org |first=Carl |last=Ramey |accessdate=2023-07-01}}{{cite web |url=https://www.eetimes.com/optical-compute-promises-game-changing-ai-performance/ |title=Optical Compute Promises Game-Changing AI Performance |first=Sally |last=Ward-Foxton |date= August 24, 2020 |work=EE Times |accessdate=2023-07-01}}{{cite web |url=https://www.eetimes.com/how-does-optical-computing-work/ |title=How Does Optical Computing Work? |first=Sally |last=Ward-Foxton |date= August 24, 2020 |work=EE Times |accessdate=2023-07-01}}

Silicon is transparent to infrared light with wavelengths above about 1.1 micrometres.{{cite web

|url = http://www.rdg.ac.uk/infrared/library/infraredmaterials/ir-infraredmaterials-si.aspx

|title = Silicon (Si)

|publisher = University of Reading Infrared Multilayer Laboratory

|accessdate = 17 July 2009

|archive-date = 14 May 2016

|archive-url = http://arquivo.pt/wayback/20160514092507/http://www.rdg.ac.uk/infrared/library/infraredmaterials/ir-infraredmaterials-si.aspx

|url-status = live

}} Silicon also has a very high refractive index, of about 3.5. The tight optical confinement provided by this high index allows for microscopic optical waveguides, which may have cross-sectional dimensions of only a few hundred nanometers. Single mode propagation can be achieved, thus (like single-mode optical fiber) 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.{{cite journal

|doi = 10.1364/OL.31.001295

|pmid = 16642090

|title = Dispersion tailoring and soliton propagation in silicon waveguides

|journal = Optics Letters

|year = 2006

|volume = 31

|issue = 9

|pages = 1295–1297

| bibcode = 2006OptL...31.1295Y |last1 = Yin

|first1 = Lianghong

|last2 = Lin

|first2 = Q.

|last3 = Agrawal

|first3 = Govind P.

|s2cid = 43103486

}}{{cite journal

|doi = 10.1364/OE.14.004357

|pmid = 19516587

|title = Tailored anomalous group-velocity dispersion in silicon channel waveguides

|journal = Optics Express

|year = 2006

|volume = 14

|issue = 10

|pages = 4357–4362

| bibcode = 2006OExpr..14.4357T |last1 = Turner

|first1 = Amy C.

|last2 = Manolatou

|first2 = Christina

|last3 = Schmidt

|first3 = Bradley S.

|last4 = Lipson

|first4 = Michal

|last5 = Foster

|first5 = Mark A.

|last6 = Sharping

|first6 = Jay E.

|last7 = Gaeta

|first7 = Alexander L.

|s2cid = 41508892

|doi-access = free

}}{{Cite journal|last1=Talukdar|first1=Tahmid H.|last2=Allen|first2=Gabriel D.|last3=Kravchenko|first3=Ivan|last4=Ryckman|first4=Judson D.|date=2019-08-05|title=Single-mode porous silicon waveguide interferometers with unity confinement factors for ultra-sensitive surface adlayer sensing|journal=Optics Express|language=EN|volume=27|issue=16|pages=22485–22498|doi=10.1364/OE.27.022485|pmid=31510540|issn=1094-4087|bibcode=2019OExpr..2722485T|osti=1546510|doi-access=free}} Anomalous dispersion is significant, as it is a prerequisite for soliton propagation, and modulational instability.{{cite book

|last = Agrawal

|first = Govind P.

|year = 1995

|title = Nonlinear fiber optics

|place = San Diego (California)

|publisher = Academic Press

|edition =2nd

|isbn = 0-12-045142-5

}}

In order for the silicon photonic components to remain optically independent from the bulk silicon of the wafer on which they are fabricated, it is necessary to have a layer of intervening material. This is usually silica, which has a much lower refractive index (of about 1.44 in the wavelength region of interest{{cite journal

|doi = 10.1364/JOSA.55.001205

|title = Interspecimen Comparison of the Refractive Index of Fused Silica

|journal = Journal of the Optical Society of America

|year = 1965

|volume = 55

|issue = 10

|pages = 1205–1209

|author = Malitson, I. H.

|bibcode = 1965JOSA...55.1205M

}}), 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.{{cite journal

|title = Frontiers of silicon-on-insulator

|journal = Journal of Applied Physics

|year = 2003

|volume = 93

|page = 4955

| bibcode = 2003JAP....93.4955C |doi = 10.1063/1.1558223

|issue = 9 |last1 = Celler

|first1 = G. K.

|last2 = Cristoloveanu

|first2 = Sorin

}} Silicon photonics have also been built with silicon nitride as the material in the optical waveguides.{{cite web | url=https://ieeexplore.ieee.org/document/7537452 | title=Silicon photonics: Silicon nitride versus silicon-on-insulator | date=March 2016 | pages=1–3 }}{{cite journal | url=https://ieeexplore.ieee.org/document/8472140 | title=Silicon Nitride in Silicon Photonics | date=2018 | doi=10.1109/JPROC.2018.2861576 | last1=Blumenthal | first1=Daniel J. | last2=Heideman | first2=Rene | last3=Geuzebroek | first3=Douwe | last4=Leinse | first4=Arne | last5=Roeloffzen | first5=Chris | journal=Proceedings of the IEEE | volume=106 | issue=12 | pages=2209–2231 }}

Silicon has a focusing Kerr nonlinearity, in that the refractive index 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.{{cite journal

|doi = 10.1364/OE.15.005976

|title = Nonlinear silicon-on-insulator waveguides for all-optical signal processing

|journal = Optics Express

|year = 2007

|volume = 15

|issue = 10

|pages = 5976–5990

| bibcode = 2007OExpr..15.5976K

|pmid=19546900|last1 = Koos

|first1 = C

|last2 = Jacome

|first2 = L

|last3 = Poulton

|first3 = C

|last4 = Leuthold

|first4 = J

|last5 = Freude

|first5 = W

|s2cid = 7069722

|hdl = 10453/383

|hdl-access = free

}}

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,{{cite journal

|title = Broad-band optical parametric gain on a silicon photonic chip

|journal = Nature

|year = 2006

|volume = 441

|issue = 7096

|pages = 960–3

|pmid = 16791190

|doi = 10.1038/nature04932

| bibcode = 2006Natur.441..960F |last1 = Foster

|first1 = M. A.

|last2 = Turner

|first2 = A. C.

|last3 = Sharping

|first3 = J. E.

|last4 = Schmidt

|first4 = B. S.

|last5 = Lipson

|first5 = M

|last6 = Gaeta

|first6 = A. L.

|s2cid = 205210957

}} parametric wavelength conversion, and frequency comb generation.,{{cite journal|last1=Griffith|first1=Austin G.|last2=Lau|first2=Ryan K.W.|last3=Cardenas|first3=Jaime|last4=Okawachi|first4=Yoshitomo|last5=Mohanty|first5=Aseema|last6=Fain|first6=Romy|last7=Lee|first7=Yoon Ho Daniel|last8=Yu|first8=Mengjie|last9=Phare|first9=Christopher T.|last10=Poitras|first10=Carl B.|last11=Gaeta|first11=Alexander L.|last12=Lipson|first12=Michal|title=Silicon-chip mid-infrared frequency comb generation|journal=Nature Communications|date=24 February 2015|volume=6|pages=6299|doi=10.1038/ncomms7299|arxiv = 1408.1039 |bibcode = 2015NatCo...6.6299G|pmid=25708922|s2cid=1089022}}{{cite journal|last1=Kuyken|first1=Bart|last2=Ideguchi|first2=Takuro|last3=Holzner|first3=Simon|last4=Yan|first4=Ming|last5=Hänsch|first5=Theodor W.|last6=Van Campenhout|first6=Joris|last7=Verheyen|first7=Peter|last8=Coen|first8=Stéphane|last9=Leo|first9=Francois|last10=Baets|first10=Roel|last11=Roelkens|first11=Gunther|last12=Picqué|first12=Nathalie|title=An octave-spanning mid-infrared frequency comb generated in a silicon nanophotonic wire waveguide|journal=Nature Communications|date=20 February 2015|volume=6|pages=6310|doi=10.1038/ncomms7310|arxiv = 1405.4205 |bibcode = 2015NatCo...6.6310K|pmid=25697764|pmc=4346629}}

Kerr nonlinearity can also cause modulational instability, 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.{{cite journal

|title = Modulation instability in silicon photonic nanowires

|journal = Optics Letters

|year = 2006

|volume = 31

|pages = 3609–11

|pmid=17130919

| bibcode = 2006OptL...31.3609P |doi = 10.1364/OL.31.003609

|issue = 24 |last1 = Panoiu

|first1 = Nicolae C.

|last2 = Chen

|first2 = Xiaogang

|last3 = Osgood Jr.

|first3 = Richard M.

}} Another example (as described below) is soliton propagation.

Silicon exhibits two-photon absorption (TPA), in which a pair of photons can act to excite an electron-hole pair. This process is related to the Kerr effect, and by analogy with complex refractive index, can be thought of as the imaginary-part of a complex Kerr nonlinearity. At the 1.55 micrometre telecommunication wavelength, this imaginary part is approximately 10% of the real part.{{cite journal

|doi = 10.1364/OL.32.002031

|pmid = 17632633

|title = Impact of two-photon absorption on self-phase modulation in silicon waveguides: Free-carrier effects

|journal = Optics Letters

|year = 2006

|volume = 32

|issue = 14

|pages = 2031–2033

|last1 = Yin

|first1 = Lianghong

|last2 = Agrawal

|first2 = Govind P.

|s2cid = 10937266

|bibcode = 2007OptL...32.2031Y

}}

The influence of TPA is highly disruptive, as it both wastes light, and generates unwanted heat.{{cite news

|author = Nikbin, Darius

|title = Silicon photonics solves its "fundamental problem"

|publisher = IOP publishing

|url = http://optics.org/cws/article/research/25379

|date = 20 July 2006

|access-date = 27 July 2009

|archive-date = 31 May 2008

|archive-url = https://web.archive.org/web/20080531024216/http://optics.org/cws/article/research/25379

|url-status = live

}} It can be mitigated, however, either by switching to longer wavelengths (at which the TPA to Kerr ratio drops),{{cite journal

|title = Two-photon absorption and Kerr coefficients of silicon for 850– {{convert|2200|nmi|km|abbr=on}}

|journal = Applied Physics Letters

|year = 2007

|volume = 90

|page = 191104

| bibcode = 2007ApPhL..90b1104R |doi = 10.1063/1.2430400

|issue = 2 |last1 = Rybczynski

|first1 = J.

|last2 = Kempa

|first2 = K.

|last3 = Herczynski

|first3 = A.

|last4 = Wang

|first4 = Y.

|last5 = Naughton

|first5 = M. J.

|last6 = Ren

|first6 = Z. F.

|last7 = Huang

|first7 = Z. P.

|last8 = Cai

|first8 = D.

|last9 = Giersig

|first9 = M.

|s2cid = 122887780

}} 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.{{cite conference

|author = Tsia, K. M.

|title = Energy Harvesting in Silicon Raman Amplifiers

|conference = 3rd IEEE International Conference on Group IV Photonics

|year = 2006

}}

The free charge carriers within silicon can both absorb photons and change its refractive index.{{cite journal

|doi = 10.1109/JQE.1987.1073206

|title = Electrooptical Effects in Silicon

|journal = IEEE Journal of Quantum Electronics

|year = 1987

|volume = 23

|issue = 1

|pages = 123–129

|bibcode = 1987IJQE...23..123S

|last1 = Soref

|first1 = R.

|last2 = Bennett

|first2 = B.

|url = https://zenodo.org/record/1232209

|access-date = 2 July 2019

|archive-date = 2 December 2020

|archive-url = https://web.archive.org/web/20201202224441/https://zenodo.org/record/1232209

|url-status = live

}} 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 in order to enhance carrier recombination.{{cite journal

|doi = 10.1364/OL.31.001714

|pmid = 16688271

|title = Nonlinear absorption and Raman gain in helium-ion-implanted silicon waveguides

|journal = Optics Letters

|year = 2006

|volume = 31

|issue = 11

|pages = 1714–1716

| bibcode = 2006OptL...31.1714L |last1 = Liu

|first1 = Y.

|last2 = Tsang

|first2 = H. K.

|author-link2=Hon Ki Tsang

}} 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 of carriers from the waveguide core.{{cite journal

|title = Lifetime of photogenerated carriers in silicon-on-insulator rib waveguides

|journal = Applied Physics Letters

|year = 2005

|volume = 86

|issue = 1

|page = 071115

| bibcode = 2005ApPhL..86a1115Z |doi = 10.1063/1.1846145 |last1 = Zevallos l.

|first1 = Manuel E.

|last2 = Gayen

|first2 = S. K.

|last3 = Alrubaiee

|first3 = M.

|last4 = Alfano

|first4 = R. R.

|s2cid = 37590490

}}

A more advanced scheme for carrier removal is to integrate the waveguide into the intrinsic region of a PIN diode, which is reverse biased so that the carriers are attracted away from the waveguide core.{{cite journal

|doi = 10.1364/OPEX.13.000519

|pmid = 19488380

|title = Net continuous wave optical gain in a low loss silicon-on-insulator waveguide by stimulated Raman scattering

|journal = Optics Express

|year = 2005

|volume = 13

|issue = 2

|pages = 519–525

| bibcode = 2005OExpr..13..519J |last1 = Jones

|first1 = Richard

|last2 = Rong

|first2 = Haisheng

|last3 = Liu

|first3 = Ansheng

|last4 = Fang

|first4 = Alexander W.

|last5 = Paniccia

|first5 = Mario J.

|last6 = Hak

|first6 = Dani

|last7 = Cohen

|first7 = Oded

|s2cid = 6804621

|doi-access = free

}} A more sophisticated scheme still, is to use the diode as part of a circuit in which voltage and current 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.{{cite book

|year = 2007

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|chapter = High Speed Carrier Injection 18 Gb/S Silicon Micro-ring Electro-optic Modulator

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}}

Second-order nonlinearities cannot exist in bulk silicon because of the centrosymmetry 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 layer on a thin silicon film.{{cite journal|last1=Jacobsen|first1=Rune S.|last2=Andersen|first2=Karin N.|last3=Borel|first3=Peter I.|last4=Fage-Pedersen|first4=Jacob|last5=Frandsen|first5=Lars H.|last6=Hansen|first6=Ole|last7=Kristensen|first7=Martin|last8=Lavrinenko|first8=Andrei V.|last9=Moulin|first9=Gaid|last10=Ou|first10=Haiyan|last11=Peucheret|first11=Christophe|last12=Zsigri|first12=Beáta|last13=Bjarklev|first13=Anders|title=Strained silicon as a new electro-optic material|journal=Nature|volume=441|issue=7090|year=2006|pages=199–202|issn=0028-0836|doi=10.1038/nature04706|pmid=16688172|bibcode = 2006Natur.441..199J |s2cid=205210888}}

Second-order nonlinear phenomena can be exploited for optical modulation, spontaneous parametric down-conversion, parametric amplification, ultra-fast optical signal processing and mid-infrared generation. Efficient nonlinear conversion however requires phase matching between the optical waves involved. Second-order nonlinear waveguides based on strained silicon can achieve phase matching by dispersion-engineering.{{cite journal|last1=Avrutsky|first1=Ivan|last2=Soref|first2=Richard|title=Phase-matched sum frequency generation in strained silicon waveguides using their second-order nonlinear optical susceptibility|journal=Optics Express|volume=19|issue=22|pages=21707–16|year=2011|issn=1094-4087|doi=10.1364/OE.19.021707|pmid=22109021|bibcode = 2011OExpr..1921707A |doi-access=free}}

So far, however, experimental demonstrations are based only on designs which are not phase matched.{{cite journal|last1=Cazzanelli|first1=M.|last2=Bianco|first2=F.|last3=Borga|first3=E.|last4=Pucker|first4=G.|last5=Ghulinyan|first5=M.|last6=Degoli|first6=E.|last7=Luppi|first7=E.|last8=Véniard|first8=V.|last9=Ossicini|first9=S.|last10=Modotto|first10=D.|last11=Wabnitz|first11=S.|last12=Pierobon|first12=R.|last13=Pavesi|first13=L.|title=Second-harmonic generation in silicon waveguides strained by silicon nitride|journal=Nature Materials|volume=11|issue=2|year=2011|pages=148–154|issn=1476-1122|doi=10.1038/nmat3200|pmid=22138793|bibcode = 2012NatMa..11..148C |hdl=11379/107111|hdl-access=free}}

It has been shown that phase matching can be obtained as well in silicon double slot waveguides coated with a highly nonlinear organic cladding{{cite journal|last1=Alloatti|first1=L.|last2=Korn|first2=D.|last3=Weimann|first3=C.|last4=Koos|first4=C.|last5=Freude|first5=W.|last6=Leuthold|first6=J.|title=Second-order nonlinear silicon-organic hybrid waveguides|journal=Optics Express|volume=20|issue=18|pages=20506–15|year=2012|issn=1094-4087|doi=10.1364/OE.20.020506|pmid=23037098|bibcode=2012OExpr..2020506A|url=https://publikationen.bibliothek.kit.edu/1000032089|doi-access=free|access-date=2 July 2019|archive-date=29 February 2020|archive-url=https://web.archive.org/web/20200229063030/https://publikationen.bibliothek.kit.edu/1000032089|url-status=live}}

and in periodically strained silicon waveguides.{{cite journal|last1=Hon|first1=Nick K.|last2=Tsia|first2=Kevin K.|last3=Solli|first3=Daniel R.|last4=Jalali|first4=Bahram|title=Periodically poled silicon|journal=Applied Physics Letters|volume=94|issue=9|year=2009|page=091116|issn=0003-6951|doi=10.1063/1.3094750|arxiv = 0812.4427 |bibcode = 2009ApPhL..94i1116H |s2cid=28598739}}

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, but is beneficial for narrowband devices such as 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.

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 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.{{Cite journal|last1=Rakich|first1=Peter T.|last2=Reinke|first2=Charles|last3=Camacho|first3=Ryan|last4=Davids|first4=Paul|last5=Wang|first5=Zheng|date=2012-01-30|title=Giant Enhancement of Stimulated Brillouin Scattering in the Subwavelength Limit|journal=Physical Review X|volume=2|issue=1|pages=011008|doi=10.1103/PhysRevX.2.011008|issn=2160-3308|bibcode=2012PhRvX...2a1008R|doi-access=free|hdl=1721.1/89020|hdl-access=free}}{{Cite journal|last1=Shin|first1=Heedeuk|last2=Qiu|first2=Wenjun|last3=Jarecki|first3=Robert|last4=Cox|first4=Jonathan A.|last5=Olsson|first5=Roy H.|last6=Starbuck|first6=Andrew|last7=Wang|first7=Zheng|last8=Rakich|first8=Peter T.|date=December 2013|title=Tailorable stimulated Brillouin scattering in nanoscale silicon waveguides|journal=Nature Communications|volume=4|issue=1|pages=1944|doi=10.1038/ncomms2943|issn=2041-1723|pmc=3709496|pmid=23739586|bibcode=2013NatCo...4.1944S|arxiv=1301.7311}} Stimulated Brillouin scattering has been used to make narrowband optical amplifiers{{Cite journal|last1=Kittlaus|first1=Eric A.|last2=Shin|first2=Heedeuk|last3=Rakich|first3=Peter T.|date=2016-07-01|title=Large Brillouin amplification in silicon|journal=Nature Photonics|volume=10|issue=7|pages=463–467|doi=10.1038/nphoton.2016.112|issn=1749-4885|arxiv=1510.08495|bibcode=2016NaPho..10..463K|s2cid=119159337}}{{Cite journal|last1=Van Laer|first1=Raphaël|last2=Kuyken|first2=Bart|last3=Van Thourhout|first3=Dries|last4=Baets|first4=Roel|date=2015-03-01|title=Interaction between light and highly confined hypersound in a silicon photonic nanowire|journal=Nature Photonics|volume=9|issue=3|pages=199–203|doi=10.1038/nphoton.2015.11|issn=1749-4885|arxiv=1407.4977|bibcode=2015NaPho...9..199V|s2cid=55218097}}{{Cite journal|last1=Van Laer|first1=Raphaël |last2=Bazin|first2=Alexandre|last3=Kuyken|first3=Bart|last4=Baets|first4=Roel|last5=Thourhout|first5=Dries Van|date=2015-01-01|title=Net on-chip Brillouin gain based on suspended silicon nanowires|journal=New Journal of Physics|volume=17|issue=11|pages=115005|doi=10.1088/1367-2630/17/11/115005|issn=1367-2630|arxiv=1508.06318|bibcode=2015NJPh...17k5005V|s2cid=54539825 }} as well as all-silicon Brillouin lasers. The interaction between photons and acoustic phonons is also studied in the field of cavity optomechanics, although 3D optical cavities are not necessary to observe the interaction.{{Cite journal|last1=Van Laer|first1=Raphaël|last2=Baets|first2=Roel|last3=Van Thourhout|first3=Dries|date=2016-05-20|title=Unifying Brillouin scattering and cavity optomechanics|journal=Physical Review A|volume=93|issue=5|pages=053828|doi=10.1103/PhysRevA.93.053828|arxiv=1503.03044|bibcode=2016PhRvA..93e3828V|s2cid=118542296}} For instance, besides in silicon waveguides the optomechanical coupling has also been demonstrated in fibers{{Cite journal|last1=Kobyakov|first1=Andrey|last2=Sauer|first2=Michael|last3=Chowdhury|first3=Dipak|date=2010-03-31|title=Stimulated Brillouin scattering in optical fibers|journal=Advances in Optics and Photonics|volume=2|issue=1|pages=1|doi=10.1364/AOP.2.000001|issn=1943-8206|bibcode=2010AdOP....2....1K}} and in chalcogenide waveguides.{{Cite journal|last1=Levy|first1=Shahar|last2=Lyubin|first2=Victor|last3=Klebanov|first3=Matvei|last4=Scheuer|first4=Jacob|last5=Zadok|first5=Avi|s2cid=11976822|date=2012-12-15|title=Stimulated Brillouin scattering amplification in centimeter-long directly written chalcogenide waveguides|journal=Optics Letters|volume=37|issue=24|pages=5112–4|doi=10.1364/OL.37.005112|pmid=23258022|issn=1539-4794|bibcode=2012OptL...37.5112L}}

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.{{cite book

|title = Solitons: an introduction

|publisher = Cambridge University Press

|year = 1989

|isbn = 0-521-33655-4

|author1=Drazin, P. G. |author2=Johnson, R. S.

|name-list-style=amp }} These optical solitons (which are also known in optical fiber) 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, and Bath.

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