EE 230: Optical Fiber Communication Lecture 6

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EE 230 Optical Fiber Communication Lecture 6
Nonlinear Processes in Optical Fibers
From the movie Warriors of the Net
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Polarization

• In molecules, PµaEßE2?E3
• In materials, PX(o)X(1)EX(2)E2X(3)E3
• If multiple electric fields are applied, every
  possible cross term is generated.
• At sufficiently high values of E, quadratic or
  higher terms become important and nonlinear
  effects are induced in the fiber.

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Polarization
Distortion of an electron cloud in response to an
E-field
Molecules and their dipole moments
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Non-linear Polarization
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Nonlinear Effects

• Stimulated Raman scattering
• Stimulated Brillouin scattering
• Four-wave Mixing
• Self-phase Modulation
• Cross-phase Modulation

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Index of Refraction
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Imaginary part of index absorption

• For a sample of absorbance A and thickness d, the
  imaginary part of the refractive index is equal
  to

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Index of Refraction vs Wavelength
Refractive Index for various materials
Refractive index vs Frequency for silica
Wave slowing in a medium of higher Index
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Nonlinear index of refraction

• Real part of index is best described as a power
  series
• nn1n2(P/Aeff)
• Term in parentheses is the intensity. For silica
  fiber, n2?2.6x10-11 µm2/mW

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Interaction Length

• where a (in cm-1) is the loss coefficient of the
  fiber. 0.1 dB/km2.3x10-7 cm-1.

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Nonlinear parameter

• Propagation constant is power-dependent

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Propagation in Single Mode Fiber
Geometrical optics is not useful for single mode
fiber, must be handled by full E M
treatment Think of guiding as diffraction
constrained by refraction Fields are
evanescently damped in the cladding
Understanding Fiber Optics-Hecht
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Effective Length and effective area
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Single Mode Gaussian Approximation
Fundamentals of Photonics - Saleh and Teich
Fiber Optic Communiocation Systems - Agrawal
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Gaussian Pulse Mode Field Diameter
w0/a0.651.619V-3/22.879V-6 for V between 1.2
and 2.4. Otherwise, use w0/a(ln V)-1/2
Fiber Optics Communication Technology-Mynbaev
Scheiner
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Mitigation

• If P is high in a fiber application, the
  nonlinear component of the index is minimized by
  increasing the effective area of the fiber.
  Fiber designed for this purpose is called LEAF
  fiber (Large Effective Area).

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Phase modulation

• Self-modulation fNL ?PLeff
• Cross-modulation fNL 2?PotherLeff
• Effect of these phase changes is a frequency
  chirp (frequency changes during pulse),
  broadening pulse and reducing bit rate-length
  product

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Self Phase Modulation
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Pulse Spreading due to Self Phase Modulation
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Gaussian Pulse in a Kerr Medium
Phase change of gaussian pulse
Instantaneous frequency shift
Instantaneous Frequency chirp
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Solitons
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Nonlinear scattering

• Signal photon scatters off oscillation that is
  present in the material, gains or loses frequency
  equivalent to that of the material oscillation
• At high powers, beating of signal frequency and
  scattered frequency generates frequency component
  at the difference that drives the material
  oscillations

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Stimulated Brillouin Scattering

• Sound waves represent alternating regions of
  compressed material and expanded material
• Index of refraction increases with density of
  polarizable electrons and thus with compression
• Scattering is induced by index discontinuities

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SBS, continued

• Transfer of energy into acoustic wave results in
  backwards scattering in fiber
• Brillouin frequency shift equal to 2nv/?, where n
  is the mode index and v is the speed of sound in
  the material
• For fiber, scattered light is 11 GHz lower in
  frequency than signal wavelength (speed of sound
  is 5.96 km/s)

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Stimulated Raman scattering

• Oscillations are Si-O bonds in the glass,
  frequency 3.3x1013 Hz
• Scattered photon can come off decreased by that
  amount (Stokes) or increased by that amount
  (anti-Stokes)
• Stokes shift scatters 1550 nm light up to 1870 nm
  light

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Raman shift in silica

• Spectrum shows major peaks at 1100, 800, and 450
  cm-1
• Those vibrational oscillations occur at 33, 24,
  and 13.5 THz
• Raman gain spectrum shows maximum at 12-14, 18,
  24, and 33 THz

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Four-wave Mixing
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Taylor Series expansion of ß(?)

• Through the cubic term
• where

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Importance of Taylor Series terms

• Group velocity Vg, dispersion D, and dispersion
  slope S

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Four-Wave Mixing Phase-Matching Requirement

• Phase mismatch M needs to be small for FWM to
  occur significantly

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FWM in a WDM system

• ?1?2? (power lost from one signal wavelength)
• ?3?? where ? is the difference in frequency
  between adjacent channels
• ?4?-?
• Substitute in phase mismatch expression to get
  Mß2?2
• Want ß2 to be big to minimize FWM!

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Four Wave Mixing