Soliton Propagation in Optical Fibers Russell Herman UNC

Soliton Propagation in Optical Fibers Russell Herman UNC Wilmington March 21, 2003

Outline • History – Optical Fibers – Transmission – Communications • • Linear Wave Propagation Nonlinear Schrödinger Equation Solitons Other Fiber Characteristics

Geometric Optics • Reflection • Refraction • Total Internal Reflection

Internal Reflection in Water • Daniel Colladon – 1826 velocity of sound in water – Introduced Compressed air – 1841 Beam in jet of water • John Tyndall – 1853 Royal Institute talks – 1854 needed demo • Faraday suggested demo • Sir Francis Bolton – 1884 Illuminated Fountains, London

Internal Reflection in Glass • Glass – Egypt 1600 BCE • Medievel glass blowers • 1842 Jacques Babinet – Light Guided in Glass Rods • 1880 s William Wheeler – Patent for Light Pipes in Homes Most 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/ce 6/society/A 0858420. html

Spun Glass Fibers • Rene de Reamur – First in 18 th Century • Charles Vernon Boys – Measurement of Delicate Forces – Mass on thread – 1887 First quartz fibers – Radiomicrometer – measured candle heat over 2 mi • Herman Hammesfahr – Glass Blower, American Patent for glass fibers – Glass Fabric - Dresses for 1892 World’s Fair - $30, 000 – Not Practical – scratched, fibers easily broke • Owens-Illinois Glass Company – 1931 Mass Production – glass wool • Joint venture with Corning Glass Works => Owens-Corning Fiberglass – 1935 Woven into Clothing – without breaking!

Image Transmission • First Facsimile – 1840’s • Alexander Graham Bell – 1875 Telautograph • Henry C. Saint-Rene’ – 1895 – First Bundle of glass rods • John Logie Baird – Mechanical TV inventor, London – 1925 First Public Demo of TV – Bundle of Fibers, 8 lines/frame • Clarence W. Hansell – GE, RCA – 300 Patents – 1930 Bundling of fibers to transmit images • Heinrich Lamm – Medical Student - Munich – First transmitted fiber optic image - 1930

Light Leakage • Brian O’Brien, – Opt. Soc. Am. , Rochester • Abraham Van Heel – Netherlands, Periscopes, Scramblers – Metal Coating, Lacquer, … • Cladding Hard – clean, smooth, no touching – 1952 • Holger Moller Hansen – Gastroscope, 1951 Patent, rejected • Avram Hirsch Goldbogen – Mike Todd, 1950 – Cinerama – 3 cameras

Clad Optical Fibers • Hopkins and Kapany • Basil Hirshowitz – Gastroentologist – 1956 First endoscope at U. Michigan • Lawrence E. Curtiss – Undergraduate – 1956 First glass-clad fiber, tube+rod – $5500 • J. Wilbur Hicks – Image Scramblers at AO => CIA

Wireless Communication • Optical Telegraphs – Semaphores • Bell’s Photophone 1880 – Used Selenium, 700 ft • “Wireless” – Marconi 1898 • Communication Satellites – Arthur C. Clarke 1945 – John R. Pierce 1950 s • Optical Communication Concerns – Radio Competition – Bandwidth – Transparency • Pipes and Switches - Telephones Wireless World, October 1945, pages 305 -308

Bell’s Photophone On Bell's Photophone. . . http: //www. alecbell. org/Invent-Photophone. html "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 1880 Source: International Fiber Optics & Communications, June, 1986, p. 29

Bandwidth • C. W. Hansell – RCA – 1920 s transatlantic 57 k. Hz, 5. 26 km – 1925 – 20 MHz, 15 m – Vacuum Tubes • South America in Daytime – lower cost • Telephone Engineers – Higher frequency & multiplexing (24 -phone channels) • 1939 – 500 MHz – C. W. Hansell – Aimed for TV demands • WWII – microwaves passed 1 GHz • Relay Towers – 50 mi apart vs Coaxial Cables in 50 s • Next? – Alec Harvey Reeves, – 1937 ITT Paris/ 1950 s STL – digital signals to lessen noise problems – Telepathy? – Shorter Wavelengths – Weather problems

Waveguides • Hollow Pipes – – – BCs Cutoff Wavelength 100 MHz – Wavelength = 3 m => 1. 5 waveguide GHz – 10 cm Bell Circular, hollow, D=5 cm for 60 GHz/5 m – 1950 – Stewart E Miller • 1956 – Holmdel – 3. 2 km – leakage from bends/kinks • 1958 – 50. 8 mm, 80, 000 conversations, 35 -75 GHz, digitized => 160 million bits/s

Maxwell’s Equations

Wave Equation Vaccum - Linear and Homogeneous Medium - Waveguides – add BCs => modes and cutoff frequency

Fiber Modes or Cylindrical Symmetry Central Core + Cladding Normalized Frequency

Radial Equation Solutions BCs => Eigenvalue Problem for bmj Single Mode Condition (HE 11) Ex: Still Needed: coherent beams, clean fiber material

LASERs • Charles H. Townes – Coherent Microwave Oscillator – MASER – 1951 – With Arthur L. Schawlow (Bell Labs) – LASER • Theodore Maiman 1960 – Hughes Research – Ruby laser – PRL rejected paper! • Ali Javan 1960 – 1. 15 micrometer He-Ne Laser – First gas laser – First continuous beam laser – Later: Bell Labs 633 nm version • Visible, stable, coherent

Other Lasers • Semiconductor Laser 1962 – Short endurance at -196 C • Communications problems – Ruby – 25 mi – could not see – He-Ne – 1. 6 mi – large spread in good weather • Georg Goubau 1958 – Beam Waveguides – 15 cm x 970 m with 10 lenses • Rudolf Kompfner/Stewart E. Miller 1963 – models of waveguides – Hollow Optical Light Pipes, Fiber Optics

The Transparency Problem • Light Pipes – Confocal Waveguides – Impossible tolerances • Fibers – mode problem – Multimodes messy – Pulse Spreading • Antoni Karbowiak/Len Lewin/Charles K. Kao, STL – Multimode Calculations 1960 s – Rescaled microwave results by 100, 000 – Needed. 001 mm – too fine to see or handle

The Transparency Solution • C. K. Kao and George Hockham – Single mode fiber – Rods in air, energy along surface, low absorption loss – 0. 1 -0. 2 microns thick – Added Cladding! – 1% index change => O(10) increased diameter – Easier to focus light on core – New Problem – light travels in core => optical losses – Paper – loss can be < 20 d. B/km 1965 -6 • Robert Maurer Corning first low loss fibers

Nonlinear Wave Equation Isotropic – Nonlinear - In Silica - Third harmonic generation, four wave mixing, nonlinear refraction

Basic Propagation Equation Assumptions: • PNL small • Polarization along length – scalar • Quasimonochromatic – small width • Instantaneous response • Neglect molecular vibrations

Amplitude Equation GVD – Group Velocity Dispersion = 0 near 1. 27 mm >0 Normal dispersion <0 Anomalous dispersion (Higher f moves slower)

Nonlinear Schrödinger Equation Balance between dispersion and nonlinearity

Optical Solitons • Hasegawa and Tappert – 1973 • Mollenauer, et. al. – 1980 – 7 ps, 1. 2 W, 1. 55 mm, single mode – 700 m

Optical Losses

Solitons • John Scott Russell 1834 – ". . . I followed it on horseback, and overtook it still rolling on at a rate of some eight or nine miles per hour, preserving its original figure some 30 feet long and a foot to a foot and a half in height. " - J. S. Russell • Airy, 50 yr dispute • Rayleigh and Bussinesq 1872 • Korteweg and de. Vries 1895

Recreation in 1995 in Glasgow

Inverse Scattering Method • • • Kruskal and Zabusky - 1965 Gardner, Greene, Kruskal, Muira – 1967 Zahkarov and Shabat – NLS – 70’s …. Sine-Gordon, Toda Lattice, Relativity, etc. AKNS – Ablowitz, Kaup, Newell, Segur 1974

Two Soliton Solution of the NLS

Other Nonlinear Effects • Soliton Perturbation Theory • Coupled NLS • Dark Solitons – Normal Dispersion Regime • Raman Pumping

Summary • History – Optical Fibers – Transmission – Communications • • • Linear Wave Propagation Nonlinear Schrödinger Equation Solitons Perturbations Other Applications – Soliton Lasers and Switching – Coupled Equations