Presentation on theme: "Lecture 3 Optical fibers"— Presentation transcript:
1 16.711 Lecture 3 Optical fibers Last lectureGeometric optic view of waveguide, numeric apertureSymmetric planar dielectric Slab waveguideModal and waveguide dispersion in palnar waveguideRectangular waveguide, effective index method
2 16.711 Lecture 3 Optical fibers TodayFiber modesFiber LossesDispersion in single-mode fibersDispersion induced limitationsDispersion managementThe Graded index fibers
3 16.711 Lecture 3 Optical fibers Fiber modes --- single mode and multi-mode fibersV-numberNumber of modes when V>>2.41Normalized propagation constantfor V between 1.5 – 2.5.Mode field diameter (MFD)
4 16.711 Lecture 3 Optical fibers Examples --- single mode and multi-mode fibers1. 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 < 2.1m3. 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:
5 16.711 Lecture 3 Optical fibers Fiber lossMaterial absorptionsilica electron resonance <0.4mOH vibrational resonance ~ 2.73 mHarmonic and combination tones ~1.39 m1.24 m, 0.95 mRayleigh scatteringLocal microscopic fluctuations in densityC~ 0.8dB/km m40.14dB 1.55mBending loss and Bending radius
6 16.711 Lecture 3 Optical fibers Dispersions in single mode fiberMaterial dispersionExample --- material dispersionCalculate 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 LEDfor the Laser
7 16.711 Lecture 3 Optical fibers Dispersions in single mode fiberWaveguide dispersionExample --- waveguide dispersionn2 = 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 dispersionfiber 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 limitationsFor RZ bit With no intersymbol interferenceFor NRZ bit With no intersymbol interference
12 16.711 Lecture 3 Optical fibers Dispersion induced limitationsExample --- bit rate and bandwidthCalculate 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?
15 16.711 Lecture 3 Optical fibers Dispersion ManagementPrechirpWith T1/T0 = sqrt(2), the transmission distance is:
16 16.711 Lecture 3 Optical fibers Dispersion ManagementExamples: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:
17 16.711 Lecture 3 Optical fibers Dispersion compensation fiber or dispersion shifted fiberWhy dispersion compensation fiber:for long haul fiber optic communication.All–optical solutionApproacheslonger 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 fibersApproachesOnly valid for paraxial approximationGeneral case Intermode dispersionCalculate the BL product of a grade index filber of 50m core with refractive index of n1 = and n2 = At 1.3 m.Solution: