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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 V>>2.41 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 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 1.3m. Solution: a < 2.1m 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 1.3m. Solution:

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**16.711 Lecture 3 Optical fibers**

Fiber loss Material absorption silica electron resonance <0.4m 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 1.55m 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 Prechirp Gaussian Pulse:

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**16.711 Lecture 3 Optical fibers**

Dispersion Management Pre compensation schemes Prechirp Prechirped Gaussian Pulse:

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**16.711 Lecture 3 Optical fibers**

Dispersion Management Prechirp With T1/T0 = sqrt(2), the transmission distance is:

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**16.711 Lecture 3 Optical fibers**

Dispersion Management Examples: 1. What’s the dispersion limited transmission distance for a 1.55m 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. All–optical 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 50m core with refractive index of n1 = and n2 = At 1.3 m. Solution:

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