1. 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

2. 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

3. 16.711 Lecture 3 Optical fibers
Fiber modes --- single mode and multi-mode fibers
V-number
Number of modes when V>>2.41
Normalized propagation constant
for V between 1.5 – 2.5.
Mode field diameter (MFD)

4. 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 and a cladding index of at the wavelength of 850nm.
Solution:
2. What should be the core radius of a single mode fiber that has the core index of and the cladding index of at the wavelength of 1.3m.
Solution:
a < 2.1m
3. Calculate the mode field diameter of a single mode fiber that has the core index of and the cladding index of at the wavelength of 1.3m.
Solution:

5. 16.711 Lecture 3 Optical fibers
Fiber loss
Material absorption
silica electron resonance <0.4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 1.55m
Bending loss and Bending radius

6. 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

7. 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.

8. 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

9. 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

10. 16.711 Lecture 3 Optical fibers
Dispersion induced limitations
For RZ bit With no intersymbol interference
For NRZ bit With no intersymbol interference

11. 16.711 Lecture 3 Optical fibers
Dispersion induced limitations
Optical and Electrical Bandwidth
Bandwidth length product

12. 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?

13. 16.711 Lecture 3 Optical fibers
Dispersion Management
Pre compensation schemes
Prechirp
Gaussian Pulse:

14. 16.711 Lecture 3 Optical fibers
Dispersion Management
Pre compensation schemes
Prechirp
Prechirped Gaussian Pulse:

15. 16.711 Lecture 3 Optical fibers
Dispersion Management
Prechirp
With T1/T0 = sqrt(2), the transmission distance is:

16. 16.711 Lecture 3 Optical fibers
Dispersion Management
Examples:
1. What’s 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:

17. 16.711 Lecture 3 Optical fibers
Dispersion compensation fiber or dispersion shifted fiber
Why dispersion compensation fiber:
for long haul fiber optic communication.
All–optical solution
Approaches
longer wavelength has a larger index.
make the waveguide weakly guided so that longer wavelength has a lower index.

18. 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 = and n2 = At 1.3 m.
Solution: