16 711 Lecture 3 Optical fibers Last lecture
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
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
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)
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 850 nm. 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:
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. 8 d. B/km m 4 0. 14 d. B loss @ 1. 55 m • Bending loss and Bending radius
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 100 nm and a laser with a line width of 2 nm for a fiber with dispersion coefficient of Dm = 22 pskm-1 nm-1 at 1310 nm. Solution: for the LED for the Laser
16. 711 Lecture 3 Optical fibers Dispersions in single mode fiber • Waveguide dispersion Example --- waveguide dispersion n 2 = 1. 48, and delta n = 0. 2 percent. Calculate Dw at 1310 nm. Solution: for V between 1. 5 – 2. 5.
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
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
16. 711 Lecture 3 Optical fibers • Dispersion induced limitations • For RZ bit With no intersymbol interference • For NRZ bit With no intersymbol interference
16. 711 Lecture 3 Optical fibers Dispersion induced limitations • Optical and Electrical Bandwidth • Bandwidth length product
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 8 pskm-1 nm-1 and optical bandwidth for 10 km of this kind of fiber and linewidth of 2 nm. Solution: • Fiber limiting factor absorption or dispersion?
16. 711 Lecture 3 Optical fibers Dispersion Management • Pre compensation schemes 1. Prechirp Gaussian Pulse:
16. 711 Lecture 3 Optical fibers Dispersion Management • Pre compensation schemes 1. Prechirped Gaussian Pulse:
16. 711 Lecture 3 Optical fibers Dispersion Management 1. Prechirp With T 1/T 0 = sqrt(2), the transmission distance is:
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 10 Gb/s? D = 17 ps(km-nm). Assume that frequency chirping broadens the guassian-shape by a factor of 6 from its transform limited width. Solution:
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.
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 n 1 = 1. 480 and n 2 = 1. 460. At 1. 3 m. Solution:
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