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

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

3. Geometric Optics Reflection Refraction Total Internal Reflection

4. 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

5. Internal Reflection in Glass Glass – Egypt 1600 BCE Medievel glass blowers 1842 Jacques Babinet –Light Guided in Glass Rods 1880s 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/ce6/society/A0858420.html

6. 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!

7. 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

8. 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

9. 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

10. 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 1950s Optical Communication Concerns –Radio Competition –Bandwidth –Transparency Pipes and Switches - Telephones Wireless World, October 1945, pages 305-308

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

12. Bandwidth C.W. Hansell – RCA –1920s transatlantic 57 kHz, 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 50s Next? –Alec Harvey Reeves, – 1937 ITT Paris/ 1950s STL –digital signals to lessen noise problems –Telepathy? –Shorter Wavelengths – Weather problems

13. 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

14. Maxwell’s Equations

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

16. Fiber Modes Cylindrical Symmetry Central Core + Cladding Normalized Frequency or

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

18. 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

19. 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

20. 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 1960s –Rescaled microwave results by 100,000 –Needed.001 mm – too fine to see or handle

21. 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 dB/km 1965-6 Robert Maurer Corning first low loss fibers

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

23. Basic Propagation Equation Assumptions: P NL small Polarization along length – scalar Quasimonochromatic – small width Instantaneous response Neglect molecular vibrations

24. Amplitude Equation GVD – Group Velocity Dispersion = 0 near 1.27  m >0 Normal dispersion <0 Anomalous dispersion (Higher f moves slower)

25. Nonlinear Schrödinger Equation Balance between dispersion and nonlinearity

26. Optical Solitons Hasegawa and Tappert – 1973 Mollenauer, et. al. – 1980 –7 ps, 1.2 W, 1.55 mm, single mode – 700 m

27. Optical Losses

28. 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 deVries 1895

29. Recreation in 1995 in Glasgow

30. 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

31. Two Soliton Solution of the NLS

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

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