Optical Fiber Communications

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Optical Fiber Communications

• Lecture 10

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Topics

• Single Mode Fiber
• Mode Field Diameter
• Propagation Modes in Single Mode Fiber
• Graded Index Fiber

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Single Mode Fiber

• Single Mode fiber are constructed by
• letting dimensions of core diameter be a few
  wavelengths and
• by having small index difference between core and
  cladding
• In practice core cladding index difference varies
  between 0.1 and 1.0 percent
• Typical single mode fiber may have a core radius
  of 3 micron and NA 0.1 at wavelength 0.8 micron

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Mode Field Diameter

• Geometric distribution of light in propagation
  mode is important when predicting performance
  characteristics.
• Mode Field Diameter (MFD) is analogues to core
  diameter in multimode fibers except not all light
  that propagates is carried in the core
• Many models for characterizing MFD with main
  consideration of how to approximate electric
  field distribution

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MFD

• Assume electric field distribution to be Gaussian
• Where r is radius, Eo is field at zero radius,
  and Wo is the width of the electric field
  distribution
• Take width 2Wo of MFD to be 2e-1radius of optical
  electric field (e-2 of optical power)

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MFD

• The MFD width 2Wo can be defined for LP01 mode as

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Propagation Modes in Single Mode Fiber

• In single mode fiber there are two independent
  degenerate propagation modes
• These modes are similar but their polarization
  planes are orthogonal
• Electric field of light propagating along the
  fiber is linear superposition of these two
  polarization mode

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Fig. 2-24 Polarizations of fundamental mode
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contd

• Choose one of the modes to have its transverse
  electric field along x direction and the other in
  y direction
• In ideal fiber, two modes are degenerate with
  equal propagation constants and will maintain
  polarization state injected into the fiber
• In actual fiber there are imperfections, such as
  asymmetrical lateral stress, noncircular cores
  and variations in refractive index profiles
• These imperfections break circular symmetry

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contd

• The modes propagate with different phase
  velocities and the difference between their
  effective refractive indices is called
  birefringence
• Or
• If light is injected into the fiber so that both
  modes are excited, then one will be delayed in
  phase

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contd

• When this phase difference is an integral mpi,
  the two mode will beat at this point and input
  polarization state will be reproduced.
• The length over which this beating occurs is the
  fiber beat length

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Example

• A single mode optical fiber has a beat length of
  8 cm at 1300nm, the modal birefringence
• Or

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Graded Index Fiber Structure

• In graded index fiber, core refractive index
  decreases continuously with increasing radial
  distance r from center of fiber and constant in
  cladding
• Alpha defines the shape of the index profile
• As Alpha goes to infinity, above reduces to step
  index
• The index difference is

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contd

• NA is more complex that step index fiber since it
  is function of position across the core
• Geometrical optics considerations show that light
  incident on fiber core at position r will
  propagate only if it within NA(r)
• Local numerical aperture is defined as
• And

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contd

• Number of bound modes

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Examples

• If a 9.5 micron, find n2 in order to design a
  single mode fiber, if n11.465.
• Solution,
• The longer the wavelength, the larger refractive
  index difference is needed to maintain single
  mode condition, for a given fiber

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Examples

• Compute the number of modes for a fiber whose
  core diameter is 50 micron. Assume that n11.48
  and n21.46. Wavelength 0.8 micron.
• Solution
• For large V, the total number of modes supported
  can be estimated as

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Example

• What is the maximum core radius allowed for a
  glass fiber having n11.465 and n21.46 if the
  fiber is to support only one mode at wavelength
  of 1250nm.
• Solution

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HW

• Due 2/11/08
• 2-2
• 2-8
• 2-11
• 2-18
• 2-19
• 2-21
• 2-24
• 2-25
• 2-27
• 2-28