Soliton Propagation in Optical Fibers

Soliton Propagation in Optical FibersRussell HermanUNC WilmingtonMarch 21, 20031OutlineHistory Optical FibersTransmissionCommunicationsLinear Wave PropagationNonlinear Schrdinger EquationSolitonsOther Fiber Characteristics

2Geometric OpticsReflectionRefractionTotal Internal Reflection

3Internal Reflection in WaterDaniel Colladon1826 velocity of sound in waterIntroduced Compressed air1841 Beam in jet of waterJohn Tyndall1853 Royal Institute talks1854 needed demoFaraday suggested demoSir Francis Bolton 1884 Illuminated Fountains, London

4Internal Reflection in GlassGlass Egypt 1600 BCEMedievel glass blowers1842 Jacques BabinetLight Guided in Glass Rods1880s William Wheeler Patent for Light Pipes in HomesMost glass is a mixture of silica obtained from beds of fine sand or from pulverized sandstone; an alkali to lower the melting point, usually a form of soda or, for finer glass, potash; lime as a stabilizer; and cullet (waste glass) to assist in melting the mixture. The properties of glass are varied by adding other substances, commonly in the form of oxides, e.g., lead, for brilliance and weight; boron, for thermal and electrical resistance; barium, to increase the refractive index, as in optical glass; cerium, to absorb infrared rays; metallic oxides, to impart color; and manganese, for decolorizing. -http://www.infoplease.com/ce6/society/A0858420.html5Spun Glass FibersRene de Reamur First in 18th CenturyCharles Vernon Boys Measurement of Delicate Forces Mass on thread1887 First quartz fibersRadiomicrometer measured candle heat over 2 miHerman HammesfahrGlass Blower, American Patent for glass fibersGlass Fabric - Dresses for 1892 Worlds Fair - $30,000Not Practical scratched, fibers easily brokeOwens-Illinois Glass Company1931 Mass Production glass woolJoint venture with Corning Glass Works => Owens-Corning Fiberglass1935 Woven into Clothing without breaking!

Image TransmissionFirst Facsimile 1840sAlexander Graham Bell 1875 TelautographHenry C. Saint-Rene 1895 First Bundle of glass rodsJohn Logie BairdMechanical TV inventor, London1925 First Public Demo of TVBundle of Fibers, 8 lines/frameClarence W. HansellGE, RCA 300 Patents1930 Bundling of fibers to transmit imagesHeinrich LammMedical Student - MunichFirst transmitted fiber optic image - 1930

Light LeakageBrian OBrien, Opt. Soc. Am., RochesterAbraham Van HeelNetherlands, Periscopes, ScramblersMetal Coating, Lacquer, Cladding Hard clean, smooth, no touching1952Holger Moller HansenGastroscope, 1951 Patent, rejectedAvram Hirsch Goldbogen Mike Todd, 1950Cinerama 3 camerasClad Optical FibersHopkins and KapanyBasil HirshowitzGastroentologist1956 First endoscope at U. MichiganLawrence E. CurtissUndergraduate1956 First glass-clad fiber, tube+rod$5500J. Wilbur HicksImage Scramblers at AO => CIA

Wireless CommunicationOptical TelegraphsSemaphoresBells Photophone 1880Used Selenium, 700 ftWireless Marconi 1898Communication Satellites Arthur C. Clarke 1945John R. Pierce 1950sOptical Communication ConcernsRadio CompetitionBandwidthTransparencyPipes and Switches - Telephones

Wireless World, October 1945, pages 305-308 Bells Photophone

On Bell's Photophone...

"The ordinary man...will find a little difficulty in comprehending how sunbeams are to be used. Does Prof. Bell intend to connect Boston and Cambridge...with a line of sunbeams hung on telegraph posts, and, if so, what diameter are the sunbeams to be...?...will it be necessary to insulate them against the weather...?...until (the public) sees a man going through the streets with a coil of No. 12 sunbeams on his shoulder, and suspending them from pole to pole, there will be a general feeling that there is something about Prof. Bell's photophone which places a tremendous strain on human credulity."

New York Times Editorial, 30 August 1880Source: International Fiber Optics & Communications, June, 1986, p.29

http://www.alecbell.org/Invent-Photophone.html BandwidthC.W. Hansell RCA 1920s transatlantic 57 kHz, 5.26 km1925 20 MHz, 15 m Vacuum TubesSouth America in Daytime lower costTelephone EngineersHigher frequency & multiplexing (24-phone channels)1939 500 MHz C.W. HansellAimed for TV demandsWWII microwaves passed 1 GHzRelay Towers 50 mi apart vs Coaxial Cables in 50sNext? Alec Harvey Reeves, 1937 ITT Paris/ 1950s STL digital signals to lessen noise problemsTelepathy?Shorter Wavelengths Weather problemsWaveguidesHollow PipesBCsCutoff Wavelength100 MHz Wavelength = 3 m => 1.5 waveguideGHz 10 cmBell Circular, hollow, D=5 cm for 60 GHz/5 m 1950 Stewart E Miller1956 Holmdel 3.2 km leakage from bends/kinks1958 50.8 mm, 80,000 conversations, 35-75 GHz, digitized => 160 million bits/sMaxwells Equations

Wave Equation

Vaccum -Linear and Homogeneous Medium -

Waveguides add BCs => modes and cutoff frequencyFiber Modes

Cylindrical Symmetry

Central Core + Cladding Normalized FrequencyorRadial Equation

SolutionsBCs => Eigenvalue Problem for bmj

Single Mode Condition (HE11)

Ex:

Still Needed: coherent beams, clean fiber materialLASERsCharles H. TownesCoherent Microwave Oscillator MASER 1951With Arthur L.Schawlow (Bell Labs) LASERTheodore Maiman 1960Hughes Research Ruby laserPRL rejected paper!Ali Javan 19601.15 micrometer He-Ne LaserFirst gas laser First continuous beam laserLater: Bell Labs 633 nm versionVisible, stable, coherent

Other LasersSemiconductor Laser 1962Short endurance at -196 CCommunications problemsRuby 25 mi could not seeHe-Ne 1.6 mi large spread in good weatherGeorg Goubau 1958Beam Waveguides15 cm x 970 m with 10 lensesRudolf Kompfner/Stewart E. Miller 1963models of waveguidesHollow Optical Light Pipes, Fiber OpticsThe Transparency ProblemLight Pipes Confocal WaveguidesImpossible tolerancesFibers mode problemMultimodes messyPulse SpreadingAntoni Karbowiak/Len Lewin/Charles K. Kao, STLMultimode Calculations 1960sRescaled microwave results by 100,000Needed .001 mm too fine to see or handleThe Transparency SolutionC.K. Kao and George Hockham Single mode fiberRods in air, energy along surface, low absorption loss0.1-0.2 microns thickAdded Cladding! 1% index change => O(10) increased diameterEasier to focus light on coreNew Problem light travels in core => optical lossesPaper loss can be < 20 dB/km 1965-6Robert Maurer Corning first low loss fibersNonlinear Wave Equation

Isotropic Nonlinear -

Third harmonic generation, four wave mixing, nonlinear refractionIn Silica -

Basic Propagation Equation

Assumptions:PNL smallPolarization along length scalarQuasimonochromatic small widthInstantaneous responseNeglect molecular vibrationsAmplitude Equation

GVD Group Velocity Dispersion= 0 near 1.27 mm>0 Normal dispersion