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Intermode Dispersion (MMF) Group Delay = L / vg L v gmin n1 n 2 L c L v gmax vgmin c/n1. (Fundamental) vgmax c/n2. (Highest order mode) /L - 50 ns / km Depends on length! Intramode Dispersion (SMF) Dispersion in the fundamental mode Group Delay = L / vg Group velocity vg depends on Refractive index = n(l) V-number= n(l) = (n1 n2)/n1 = (l) Material Dispersion Waveguide Dispersion Profile Dispersion Material Dispersion All excitation sources are inherently non-monochromatic and emit within a spectrum ∆l of wavelengths. Waves in the guide with different free space wavelengths travel at different group velocities due to the wavelength dependence of n1. The waves arrive at the end of the fiber at different times and hence result in a broadened output pulse. Dm l L Dm = material dispersion coefficient, ps nm-1 km-1 Waveguide Dispersion Waveguide dispersion: The group velocity vg(01) of the fundamental mode depends on the V-number which itself depends on the source wavelength l even if n1 and n2 were constant. Even if n1 and n2 were wavelength independent (no material dispersion), we will still have waveguide dispersion by virtue of vg(01) depending on V and V depending inversely on l. Waveguide dispersion arises as a result of the guiding properties of the waveguide which imposes a nonlinear -lm relationship. Dw l L Dw = waveguide dispersion coefficient Dw depends on the waveguide structure, ps nm-1 km-1 Chromatic Dispersion Material dispersion coefficient (Dm) for the core material (taken as SiO2), waveguide dispersion coefficient (Dw) (a = 4.2 mm) and the total or chromatic dispersion coefficient Dch (= Dm + Dw) as a function of free space wavelength, l Chromatic = Material + Waveguide (Dm Dw )l L Dispersion coefficient (ps km-1 nm-1) 20 Dm 10 SiO2-13.5%GeO2 0 a (mm) Dw 4.0 3.5 3.0 –10 2.5 –20 1.2 1.3 1.4 1.5 1.6 l (mm) Material and waveguide dispersion coefficients in an optical fiber with a core SiO 2-13.5%GeO2 for a = 2.5 to 4 mm. © 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Polarization Dispersion n different in different directions due to induced strains in fiber in manufacturing, handling and cabling. n/n < 10-6 Dpol L Dpol = polarization dispersion coefficient Typically Dpol = 0.1 - 0.5 ps nm-1 km-1/2 Self-Phase Modulation Dispersion : Nonlinear Effect At sufficiently high light intensities, the refractive index of glass n is n = n + CI where C is a constant and I is the light intensity. The intensity of light modulates its own phase. For 1 ps km-1 Imax 3 W cm-2. n is 310-7. 2a 10 mm, A 7.8510-7 cm2. Optical power 23.5 W in the core Zero Dispersion Shifted Fiber Dispersion Material Dispersion Zero at 1.55 mm 0 1.2 mm Total Dispersion 1.4 mm 1.6 mm l Total dispersion is zero in the Er-optical amplifier band around 1.55 mm Waveguide Dispersion Zero-dispersion shifted fiber Disadvantage: Cross talk (4 wave mixing) Nonzero Dispersion Shifted Fiber For Wavelength Division Multiplexing (WDM) avoid 4 wave mixing: cross talk. We need dispersion not zero but very small in Er-amplifer band (1525-1620 nm) Dch = 0.1 - 6 ps nm-1 km-1. Nonzero dispersion shifted fibers Nonzero Dispersion Shifted Fiber Nonzero dispersion shifted fiber (Corning) Fiber with flattened dispersion slope Dispersion Flattened Fiber Dispersion flattened fiber example. The material dispersion coefficient (Dm) for the core material and waveguide dispersion coefficient (Dw) for the doubly clad fiber result in a flattened small chromatic dispersion between l1 and l2. Dispersion and Maximum Bit Rate 0.5 B 1/ 2 Return-to-zero (RTZ) bit rate or data rate. Nonreturn to zero (NRZ) bit rate = 2 RTZ bitrate Output optical power T = 4 1 0.61 0.5 t A Gaussian output light pulse and some tolerable intersymbol interference between two consecutive output light pulses (y-axis in relative units). At time t = from the pulse center, the relative magnitude is e -1/2 = 0.607 and full width root mean square (rms) spread isrms = 2. © 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Dispersion and Maximum Bit Rate Maximum Bit Rate 0.25 0.59 B 1/2 BL 0.25L Dispersion 1/2 Dch l1/2 L 0.25 0.59 Dch l Dch l1/2 Bit Rate = constant inversely proportional to dispersion inversely proportional to line width of laser (single frequency lasers!) Electrical signal (photocurrent) 1 0.707 Fiber Sinusoidal signal Photodetector Emitter t Optical Input f = Modulation frequency Pi = Input light power Optical Output Po = Output light power 1 kHz 1 MHz 1 GHz 1 MHz 1 GHz f fel Sinusoidal electrical signal Po / Pi 0.1 0.05 0 t 0 t 1 kHz fop f An optical fiber link for transmitting analog signals and the effect of dispersion in the fiber on the bandwidth, fop. © 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Relationships between dispersion parameters, maximum bit rates and bandwidths. RZ = Return to zero pulses. NRZ = Nonreturn to zero pulses. B is the maximum bit rate for NRZ pulses. Dispersed pulse shape Gaussian with rms deviation Rectangular with full width T 1/2 = FWHM width = 0.4251/2 B (RZ) 0.25/ B (NRZ) 0.5/ fop fel 0.75B = 0.19/ 0.71fop = 0.13/ = 0.29T = 0.291/2 0.25/ 0.5/ 0.69B = 0.17/ 0.73fop = 0.13/ Example: Bit rate and dispersion Consider an optical fiber with a chromatic dispersion coefficient 8 ps km-1 nm-1 at an operating wavelength of 1.5 mm. Calculate the bit rate distance product (BL), and the optical and electrical bandwidths for a10 km fiber if a laser diode source with a FWHP linewidth l1/2 of 2 nm is used. Solution For FWHP dispersion, 1/2/L = |Dch|l1/2 = (8 ps km-1 nm-1)(2 nm) = 16 ps km-1 Assuming a Gaussian light pulse shape, the RTZ bit rate distance product (BL) is BL = 0.59L/t1/2 = 0.59/(16 ps km-1) = 36.9 Gb s-1 km. The optical and electrical bandwidths for a 10 km distance is fop = 0.75B = 0.75(36.9 Gb s-1 km) / (10 km) = 2.8 GHz. fel = 0.70fop = 1.9 GHz. Combining intermodal and intramodal dispersions Consider a graded index fiber with a core diameter of 30 mm and a refractive index of 1.474 at the center of the core and a cladding refractive index of 1.453. Suppose that we use a laser diode emitter with a spectral linewidth of 3 nm to transmit along this fiber at a wavelength of 1300 nm. Calculate, the total dispersion and estimate the bit-rate distance product of the fiber. The material dispersion coefficient Dm at 1300 nm is 7.5 ps nm-1 km-1. How does this compare with the performance of a multimode fiber with the same core radius, and n1 and n2? Solution The normalized refractive index difference = (n1n2)/n1 = (1.4741.453)/1.474 = 0.01425. Modal dispersion for 1 km is intermode = Ln12/[(20)(31/2)c] = 2.910-11 s 1 or 0.029 ns. The material dispersion is 1/2 = LDm l1/2 = (1 km)(7.5 ps nm-1 km-1)(3 nm) = 0.0225 ns Assuming a Gaussian output light pulse shaper, intramode = 0.4251/2 = (0.425)(0.0225 ns) = 0.0096 ns Total dispersion is 2 2 rms intermode intramode 0.0292 0.00962 0.030 ns B = 0.25/rms = 8.2 Gb Comparison of typical characteristics of multimode step-index, single-mode step-index, and graded-index fibers. (Typical values combined from various sources; 1997 Property = (n1n2)/n1 Core diameter (mm) Cladding diameter (mm) NA Bandwidth distance or Dispersion Mu ltimode step-index fiber 0.02 100 140 0.3 20 - 100 MHzkm. Attenuation of light 4 - 6 dB km-1 at 850 nm 0.7 - 1 dB km -1 at 1.3 mm Typical light source Light emi tting diode (LED ) Short haul or subscriber local network communications Typical applications Single-mode step- index Graded Index 0.003 8.3 (MFD = 9 .3 mm) 125 0.1 < 3.5 ps km-1 nm-1 at 1.3 mm > 100 Gb s-1 km in common use 1.8 dB km-1 at 850 nm 0.34 dB km-1 at 1.3 mm 0.2 dB km-1 at 1.55 mm Lasers, single mode injection lasers Long haul commu nications 0.015 62.5 125 0.26 300 MHz km - 3 GHz km at 1.3 mm 3 dB km-1 at 850 nm 0.6 - 1 dB km -1 at 1.3 mm 0.3 dB km-1 at 1.55 mm LED, lasers Local and wide-area networks. Medium haul communications Dispersion Compensation Total dispersion = DtLt + DcLc = (10 ps nm-1 km-1)(1000 km) + (100 ps nm-1 km-1)(80 km) = 2000 ps/nm for 1080 km or 1.9 ps nm-1 km-1 Dispersion Compensation and Management Compensating fiber has higher attenuation. Doped core. Need shorter length More susceptible to nonlinear effects. Use at the receiver end. Different cross sections. Splicing/coupling losses. Compensation depends on the temperature. Manufacturers provide transmission fiber spliced to inverse dispersion fiber for a well defined D vs. l Dispersion Managed Fiber The inverse dispersion slope of dispersion managed fiber cancels the detrimental effect of dispersion across the a wide spectrum of wavelength. More DWDM channels expected in ultralong haul transmission. (Courtesy of OFS Division of Furukawa.) Attenuation Attenuation = Absorption + Scattering Attenuation coefficient is defined as the fractional decrease in the optical power per unit distance. is in m-1. Pout = Pinexp(L) Pin 1 dB 10log L Pout dB 10 4.34 ln(10) Lattice Absorption (Reststrahlen Absorption) A solid with ions Ex Light direction k z Lattice absorption through a crystal. The field in the wave oscillates the ions which consequently generate "mechanical" waves in the crystal; energy is thereby transferred from the wave to lattice vibrations. © 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Rayleigh Scattering Rayleigh scattering involves the polarization of a small dielectric particle or a region that is much smaller than the light wavelength. The field forces dipole oscillations in the particle (by polarizing it) which leads to the emission of EM waves in "many" directions so that a portion of the light energy is directed away from the incident beam. 2 8 3 2 R 4 n 1 T kBTf 3l = isothermal compressibility (at Tf) Tf = fictive temperature (roughly the softening temperature of glass) where the liquid structure during the cooling of the fiber is frozen to become the glass structure Example: Rayleigh scattering limit What is the attenuation due to Rayleigh scattering at around thel = 1.55 mm window given that pure silica (SiO2) has the following properties: Tf = 1730°C (softening temperature); T = 710-11 m2 N-1 (at high temperatures); n = 1.4446 at 1.5 mm. Solution We simply calculate the Rayleigh scattering attenuation using 8 3 2 R 4 (n 1) 2 T kBTf 3l 8 3 2 2 11 23 R (1.4446 1) (7 10 )(1.38 10 )(1730 273) 6 4 3(1.55 10 ) R = 3.27610-5 m-1 or 3.27610-2 km-1 Attenuation in dB per km is dB = 4.34R = (4.34)(3.73510-2 km-1) = 0.142 dB km-1 This represents the lowest possible attenuation for a silica glass core fiber at 1.55 mm. Corning low-water-peak fiber has no OH- peak E-band is available for communications with this fiber [Photonics Spectra, April 2002 p.69] Bending Loss Field distribution Microbending Escaping wave Cladding < Core c R Sharp bends change the local waveguide geometry that can lead to waves escaping. The zigzagging ray suddenly finds itself with an incidence angle that gives rise to either a transmitted wave, or to a greater cladding penetration; the field reaches the outside medium and some light energy is lost. © 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Microbending Loss R R exp exp 3/ 2 Rc Bending loss for three different fibers. The cut-off wavelength is 1.2 mm. All three are operating at l = 1.5 mm. Example: Microbending loss It is found that for a single mode fiber with a cut-off wavelength lc = 1180 nm, operating at 1300 nm, the microbending loss reaches 1 dB m-1 when the radius of curvature of the bend is roughly 6 mm for = 0.00825, 12 mm for = 0.00550 and 35 mm for = 0.00275. Explain these findings? Solution: Maybe later? WDM Illustration