Soliton Propagation in Optical Fibers

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Soliton Propagation in Optical Fibers

• Russell Herman
• UNC Wilmington
• March 21, 2003

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Outline

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

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Geometric Optics

• Reflection
• Refraction
• Total Internal Reflection

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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

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Internal Reflection in Glass
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.h
tml

• Glass Egypt 1600 BCE
• Medievel glass blowers
• 1842 Jacques Babinet
• Light Guided in Glass Rods
• 1880s William Wheeler
• Patent for Light Pipes in Homes

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Spun Glass Fibers

• Rene de Reamur First in 18th 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 Worlds Fair -
  30,000
• Not Practical scratched, fibers easily broke
• Owens-Illinois Glass Company
• 1931 Mass Production glass wool
• Joint venture with Corning Glass Works gt
  Owens-Corning Fiberglass
• 1935 Woven into Clothing without breaking!

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Image Transmission

• First Facsimile 1840s
• 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

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Light Leakage

• Brian OBrien,
• 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

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Clad Optical Fibers

• Hopkins and Kapany
• Basil Hirshowitz
• Gastroentologist
• 1956 First endoscope at U. Michigan
• Lawrence E. Curtiss
• Undergraduate
• 1956 First glass-clad fiber, tuberod
• 5500
• J. Wilbur Hicks
• Image Scramblers at AO gt CIA

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Wireless Communication

• Optical Telegraphs
• Semaphores
• Bells 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
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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
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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

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Waveguides

• Hollow Pipes
• BCs
• Cutoff Wavelength
• 100 MHz Wavelength 3 m gt 1.5 waveguide
• GHz 10 cm
• Bell Circular, hollow, D5 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 gt 160 million bits/s

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Maxwells Equations
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Wave Equation
Vaccum -
Linear and Homogeneous Medium -
Waveguides add BCs gt modes and cutoff frequency
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Fiber Modes
or
Cylindrical Symmetry
Central Core Cladding Normalized Frequency
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Radial Equation
Solutions
BCs gt Eigenvalue Problem for bmj
Single Mode Condition (HE11)
Ex
Still Needed coherent beams, clean fiber material
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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

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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

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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

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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 gt O(10)
  increased diameter
• Easier to focus light on core
• New Problem light travels in core gt optical
  losses
• Paper loss can be lt 20 dB/km 1965-6
• Robert Maurer Corning first low loss fibers

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

• Assumptions
• PNL small
• Polarization along length scalar
• Quasimonochromatic small width
• Instantaneous response
• Neglect molecular vibrations

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Amplitude Equation
GVD Group Velocity Dispersion 0 near 1.27
mm gt0 Normal dispersion lt0 Anomalous dispersion
(Higher f moves slower)
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Nonlinear Schrödinger Equation
Nonlinear Schrödinger Equation
Balance between dispersion and nonlinearity
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Optical Solitons

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

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Optical Losses
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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

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Recreation in 1995 in Glasgow
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Inverse Scattering Method

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

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Two Soliton Solution of the NLS
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Other Nonlinear Effects

• Soliton Perturbation Theory
• Coupled NLS
• Dark Solitons Normal Dispersion Regime
• Raman Pumping

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Summary

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

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