What about the loss in optical fiber? Why and to what degree do optical signals gets distorted as they propagate along a fiber? Fiber links are limited by in path length by attenuation and pulse distortion.
3.1 Attenuation Three transmission windows: 1 st window: 800 900 nm (low cost) nd window: around 1300 nm (low disp.) 3 rd window: around 1500 nm (low loss)
3.1 Attenuation Losses occurring in glass fibers can be classified as absorption, scattering, and geometric effects. Absorption: - Intrinsic absorption due to strong electronic and molecular transition bands, mainly in UV and infrared - Impurities: OH ion and transition-metal ions Rayleigh Scattering: It arise from microscopic variations in the material density from compositional fluctuations, and from structural inhomogeneities or defects occurring during fiber manufacture. Fig.3.3 Geometric effect: bending losses
3.1.1 Attenuation Unit db is a convenient measure of the relative power levels in a communications system. P 1 P P 3 P 4 x x Loss between P1 and P in db is: Power level in cascaded system Fractional transmission efficiency between P1 and P is: db P = 10 log10 P1 Fractional transmission efficiency for the cascaded system: Total loss for the cascaded system: P P 1 P P P P P P 4 3 3 1 P 4 P4 P3 P P 4 P 3 P db = 10log10 = 10log10 = 10log10 + 10log10 + 10log10 P1 P3 P P1 P3 P P1 Obviously, total loss (in db) is just the sum of the loss (in db) of the individual cascaded elements. This illustrates the major advantage of the db scale.
3.1.1 Attenuation Unit Optical power in dbm: P P( dbm) = 10log ( unit : dbm) 1mW Optical power decreases exponentially with distance α Pz ( ) = P(0) e 1 P(0) α p = ln z P ( z ) p z α p : Attenuation coefficient ( unit: km -1 ) z : path length For simplicity, express attenuation coefficient in units of db/km : Convert to db from km -1 : 10 P(0) α( db / km) = log 4.343 p (3 1 c) z = α P( z)
3.1 Attenuation Example Consider a 30-km long optical fiber that has an attenuation of 0.8dB/km at 1300 nm. Find the loss of the fiber in db and fractional transmission efficiency Example A system has -3 db of loss. Compute its transmission efficiency. Example 3- (p93) Consider a 30-km long optical fiber that has an attenuation of 0.8dB/km at 1300 nm. Suppose we want to find the optical output power P out if 00 μ W of optical power is launched into the fiber:
Fiber links are limited by in path length by attenuation and pulse distortion. 3. Signal distortion in optical waveguides Optical signal becomes increasingly distorted as it travels along a fiber. Dispersion Pulse spread Signal distortion Intramodal dispersion : Intermodal dispersion : Material dispersion Waveguide dispersion Multimode dispersion Material dispersion: arise from the variation of the refractive index of the core material as a function of wavelength - Spectral width of optical source - n(λ) group velocity Waveguide dispersion: since 0% of the light propagating in the cladding travels faster than the light confined to the core. The arises the dependence of the group velocity on the ratio between core radius and the wavelength (a /λ ), i.e., fiber designs.
3..1 Information Capacity Determination Information capacity is specified by the Bandwidth distance product in MHz.km
3.. Group Delay Optical source: has spectral width σ λ Material dispersion : n (λ) group velocity Phase velocity: Group velocity: V p V g ω = β dω = dβ
3.. Group Delay As signal propagates along the fiber, each spectral component can be assumed to travel independently and to undergo a Group delay or time delay For a distance L traveled by the pulse, the group delay is: τ g L L λ dβ = = = L (3 13) V dω/ dβ πc dλ g The amount of pulse spreading arises from Group Delay Variation dτ g L dβ d β In terms of λ : δτ = δλ = λ + λ δλ (3 15 a) dλ πc dλ dλ Dispersion: D 1 dτ g d 1 π c = = = β (3 17) Ld λ d λ V g λ β = d β dω β : GVD (group velocity dispersion) Dispersion: is a result of material dispersion and waveguide dispersion Unit of Dispersion : ps/(nm.km)
3..3 Material Dispersion π n( λ) β = λ (3 18) τ L dn mat n c = d (3 19) dτmat σλl dn λ σ mat σ λ σ LD ( ) (3 0) λ mat λ dλ = c dλ = σ λ : Spectral width of a source σ mat : Pulse spread Problem 3-4 (p109) Consider a typical GaAlAs LED having a spectral width of 40 nm at an 800-nm peak output so that σ λ /λ= 5 percent. As can be seen from Fig. 3-13 the material dispersion at 800 nm is about 110ps/nm.km, find the pulse spread per km.
3..3 Material Dispersion Material Dispersion
τ Chapter 3 Signal Degradation in Optical Fibers 3..4 Waveguide dispersion: Assumption: consider n is independent of λ Steps to find pulse spread: find β find group delay τ find variation of group delay with wavelength dτ /dλ pulse spread dτ σ σ λ dλ b: normalized propagation constant is defined as For small value of Δ, we have: wg b β / k n n n 1 ( ) β / k n 1 ua b = 1 = (3 1) V n n (3 ) L d kb = n + n Δ (3 4) c dk β nkb ( Δ+ 1) (3 3) V= NA πa/ λ Question 3-14 ( ) L dvb = n + n Δ (3 5) c dv In Eq. 3-5, 1 st term is constant (no dispersion) and nd term represents the group delay arising from waveguide dispersion. τ wg
3..4 Waveguide dispersion: ( ) d Vb Jv ( ua) = b 1 dv Jv+ 1( ua) Jv 1( ua)
3..5 Signal Distortion in Single-Mode Fibers Group delay: τ wg ( ) L d Vb = n + n Δ (3 5) c dv Find the pulse spread σ wg for a spectral width σ λ of a laser source: d τ wg V d τ wg nl Δ λ d ( Vb) σwg σλ = σλ = σ V = D ( ) (3 6) wg λ σλl dλ λ dv cλ dv Note: there is an error in our book in Eq. (3-6) D wg n d ( Vb) ( λ) = Δ V cλ dv Problem 3-5(p11) Let n=1.48 and Δ= 0. %. At V=.4, from Fig. 3-15 the expression in square bracket is 0.6. At wavelength λ = 130 nm, find the D wg.
3..5 Signal Distortion in Single-Mode Fibers For standard single-mode fused silica-core fiber - At wavelength around 1.3 μm, zero dispersion Fig 3-16 Material dispersion & waveguide dispersion as function of wavelength for stand single-mode fused-silica-core fiber
3..5 Signal Distortion in Single-Mode Fibers Dispersion shifted fiber: a specially designed fiber, shift zero dispersion to 1.5 μm from 1.3 μm.
3..5 Signal Distortion in Single-Mode Fibers
3..5 Signal Distortion in Single-Mode Fibers
3..6 Polarization-Mode Dispersion The effect of fiber birefringence on the polarization states of an optical signal are another source of pulse broadening. A varying birefringence along its length will cause each polarization mode to travel at a slightly different velocity and the resulting difference in propagation time between the two orthogonal polarization modes will result in pulse spreading. This is the polarization mode dispersion (PMD) Δτ pol = L v gx L v gy
3..7 Intermodal Distortion Multi-mode fiber has intermodal distortion. The intermodal distortion is a result of different values of the group delay for each individual mode at a single frequency. This can be obtained from the time difference between the highest an lowest order modes from geometrical optics: δt = T T = mod max min n 1 ΔL c
Simplified modal: a sequence of thin lens The refractive index is lower at the outer edge of the core than in the center of the core Higher-order modes travel faster than lower-order modes Low intermodal delay distortion
Group velocity dispersion includes the material & waveguide dispersions. D ( λ) D + D GVD mat wg σ = D ( λ) σ GVD GVD L λ Total dispersion is the sum of group velocity, polarization dispersion and other dispersion types and the total rms pulse spreading can be approximately written as: D D + D +... σ total GVD pol total = D σ totall λ