16.711 Lecture 3 Optical fibers

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16.711 Lecture 3 Optical fibers
Last lecture

• Geometric optic view of waveguide, numeric
  aperture
• Symmetric planar dielectric Slab waveguide
• Modal and waveguide dispersion in palnar
  waveguide
• Rectangular waveguide, effective index method

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16.711 Lecture 3 Optical fibers
Today

• Fiber modes
• Fiber Losses
• Dispersion in single-mode fibers
• Dispersion induced limitations
• Dispersion management
• The Graded index fibers

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16.711 Lecture 3 Optical fibers
Fiber modes --- single mode and multi-mode fibers
V-number
Number of modes when Vgtgt2.41
Normalized propagation constant
for V between 1.5 2.5.
Mode field diameter (MFD)
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16.711 Lecture 3 Optical fibers
Examples --- single mode and multi-mode fibers
1. Calculate the number of allowed modes in a
multimode step index fiber, a 100 ?m, core
index of 1.468 and a cladding index of 1.447 at
the wavelength of 850nm.
Solution
2. What should be the core radius of a single
mode fiber that has the core index of 1.468 and
the cladding index of 1.447 at the wavelength of
1.3?m.
Solution
a lt 2.1?m
3. Calculate the mode field diameter of a single
mode fiber that has the core index of 1.458 and
the cladding index of 1.452 at the wavelength of
1.3?m.
Solution
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16.711 Lecture 3 Optical fibers
Fiber loss

• Material absorption

silica electron resonance lt0.4?m OH vibrational
resonance 2.73 ?m Harmonic and combination
tones 1.39 ?m 1.24 ?m, 0.95 ?m

• Rayleigh scattering

Local microscopic fluctuations in density
C 0.8dB/km ?m4
0.14dB loss _at_ 1.55?m

• Bending loss and Bending radius

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16.711 Lecture 3 Optical fibers
Dispersions in single mode fiber

• Material dispersion

Example --- material dispersion
Calculate the material dispersion effect for LED
with line width of 100nm and a laser with a line
width of 2nm for a fiber with dispersion
coefficient of Dm 22pskm-1nm-1 at 1310nm.
Solution
for the LED
for the Laser
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16.711 Lecture 3 Optical fibers
Dispersions in single mode fiber

• Waveguide dispersion

Example --- waveguide dispersion
n2 1.48, and delta n 0.2 percent. Calculate
Dw at 1310nm.
Solution
for V between 1.5 2.5.
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16.711 Lecture 3 Optical fibers

• chromatic dispersion (material plus waveduide
  dispersion)

• material dispersion is determined by the
  material composition of a fiber.

• waveguide dispersion is determined by the
  waveguide index profile of a fiber

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16.711 Lecture 3 Optical fibers

• Polarization mode dispersion

• fiber is not perfectly symmetric, inhomogeneous.
• refractive index is not isotropic.

• dispersion flattened fibers
• Use waveguide geometry and index profiles to
  compensate the material dispersion

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16.711 Lecture 3 Optical fibers

• Dispersion induced limitations

• For RZ bit With no intersymbol interference

• For NRZ bit With no intersymbol interference

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16.711 Lecture 3 Optical fibers
Dispersion induced limitations

• Optical and Electrical Bandwidth

• Bandwidth length product

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16.711 Lecture 3 Optical fibers
Dispersion induced limitations
Example --- bit rate and bandwidth
Calculate the bandwidth and length product for an
optical fiber with chromatic dispersion
coefficient 8pskm-1nm-1 and optical bandwidth for
10km of this kind of fiber and linewidth of 2nm.
Solution

• Fiber limiting factor absorption or dispersion?

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16.711 Lecture 3 Optical fibers
Dispersion Management

• Pre compensation schemes

1. Prechirp

Gaussian Pulse
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16.711 Lecture 3 Optical fibers
Dispersion Management

• Pre compensation schemes

1. Prechirp

Prechirped Gaussian Pulse
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16.711 Lecture 3 Optical fibers
Dispersion Management

1. Prechirp

With T1/T0 sqrt(2), the transmission distance
is
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16.711 Lecture 3 Optical fibers
Dispersion Management
Examples
1. Whats the dispersion limited transmission
distance for a 1.55?m light wave system making
use of direct modulation at 10Gb/s? D
17ps(km-nm). Assume that frequency chirping
broadens the guassian-shape by a factor of 6 from
its transform limited width.
Solution
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16.711 Lecture 3 Optical fibers
Dispersion compensation fiber or dispersion
shifted fiber

• Why dispersion compensation fiber

• for long haul fiber optic communication.
• Alloptical solution

• Approaches

• longer wavelength has a larger index.

make the waveguide weakly guided so that longer
wavelength has a lower index.
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16.711 Lecture 3 Optical fibers
The Graded index fibers

• Approaches

Only valid for paraxial approximation
General case Intermode dispersion
Calculate the BL product of a grade index filber
of 50?m core with refractive index of n1 1.480
and n2 1.460. At 1.3 ?m.
Solution