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# 16.711 Lecture 3 Optical fibers

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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 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 < 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:

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 loss @ 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 = 1.480 and n2 = 1.460. At 1.3 m. Solution: