OpticalWaveguides,2ndEdition

Intermode Dispersion (MMF) Low order mode High order mode Cladding Core Light pulse t 0 t Spread, (X Broadened light pulse Intensity Intensity Axial (X ! L v gmin L v gmax v gmin < c/n 1 . (Fundamental) v gmax < c/n 2 . (Highest order mode) (X L < n 1 n 2 c (X/L < l0 - 50 ns / km Depends on length! Group Delay X = L / v g Intramode Dispersion (SMF) Group Delay X = L / v g Group velocity v g depends on Refractive index = n(ì) Material Dispersion V-number= n(ì) Waveguide Dispersion ( = (n 1 n 2 )/n 1 = ((ì) Profile Dispersion X t Spread, ² X t 0 ì Spectrum, ² ì ì 1 ì 2 ì o Intensity Intensity Intensity Cladding Core Emitter Very short light pulse v g (ì 2 ) v g (ì 1 ) Input Output Dispersion in the fundamental mode Material Dispersion All excitation sources are inherently non-monochromatic and emit within a spectrum ¨ì of wavelengths. Waves in the guide with different free space wavelengths travel at different group velocities due to the wavelength dependence of n 1 . The waves arrive at the end of the fiber at different times and hence result in a broadened output pulse. X t Spread, ² X t 0 ì Spectrum, ² ì ì 1 ì 2 ì o Intensity Intensity Intensity Cladding Core Emitter Very short light pulse v g (ì 2 ) v g (ì 1 ) Input Output (X L ! D m (ì D m = material dispersion coefficient, ps nm -1 km -1 Waveguide Dispersion Waveguide dispersion: The group velocity v g (01) of the fundamental mode depends on the V-number which itself depends on the source wavelength ì, even if n 1 and n 2 were constant. Even if n 1 and n 2 were wavelength independent (no material dispersion), we will still have waveguide dispersion by virtue of v g (01) depending on V and V depending inversely on ì. Waveguide dispersion arises as a result of the guiding properties of the waveguide which imposes a nonlinear æ-¡ lm relationship. X t Spread, ² X t 0 ì Spectrum, ² ì ì 1 ì 2 ì o Intensity Intensity Intensity Cladding Core Emitter Very short light pulse v g (ì 2 ) v g (ì 1 ) Input Output (X L ! D w (ì D w = waveguide dispersion coefficient D w depends on the waveguide structure, ps nm -1 km -1 0 1.2 1.3 1.4 1.5 1.6 1.1 -30 20 30 10 -20 -10 ì (µm) Dm Dm + Dw D w ì 0 Dispersion coefficient (ps km -1 nm -1 ) Chromatic Dispersion Material dispersion coefficient (D m ) for the core material (taken as SiO 2 ), waveguide dispersion coefficient (D w ) (a = 4.2 µm) and the total or chromatic dispersion coefficient D ch (= D m + D w ) as a function of free space wavelength, ì (X L !(D m + D w )(ì Chromatic = Material + Waveguide Material and waveguide dispersion coefficients in an optical fiber with a core SiO 2 -13.5%GeO 2 for a = 2.5 to 4 µm. 0 ±10 10 20 1.2 1.3 1.4 1.5 1.6 ±20 ì (µm) D m D w SiO 2 -13.5%GeO 2 2.5 3.0 3.5 4.0 a (µm) Dispersion coefficient (ps km -1 nm -1 ) © 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Core z n 1x // x n 1y // y E y E x E x E y E (X = Pulse spread Input light pulse Output light pulse t t (X Intensity Polarization Dispersion n different in different directions due to induced strains in fiber in manufacturing, handling and cabling. on/n · 10 -6 (X ! D pol L D pol = polarization dispersion coefficient Typically D pol = 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. ì Light intensity A Gaussian light intensity spectrum and variation of refractive index due to self-phase modulation. ì n' n n (ì (I n' I max I min For (X < 1 ps km -1 (I max < 3-l0 7 W cm -2 . (n is 3-10 -7 . 2a < 10 µm, A < 7.85-10 -7 cm 2 . Optical power < 23.5 W in the core Zero Dispersion Shifted Fiber Total dispersion is zero in the Er-optical amplifier band around 1.55 µm 0 1.2 µm 1.4 µm 1.6 µm Zero at 1.55 µm Material Dispersion Total Dispersion Dispersion ì Waveguide Dispersion Zero-dispersion shifted fiber Disadvantage: Cross talk (4 wave mixing) Outer Core Outer Cladding Inner Core Inner Cladding End View of Fiber (Not to Scale) Fiber Axis Refractive Index 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) D ch = 0.1 - 6 ps nm -1 km -1 . Nonzero dispersion shifted fibers Wavelength (nm) +10 -10 1300 1400 1500 1600 Dispersion (ps/nm-km) Standard single mode Nonzero dispersion-shifted Reduced Slope Nonzero dispersion-shifted Zero dispersion-shifted Nonzero Dispersion Shifted Fiber Wavelength (nm) +10 -10 1300 1400 1500 1600 Dispersion (ps/nm-km) Standard single mode Nonzero dispersion-shifted Reduced Slope Nonzero dispersion-shifted Zero dispersion-shifted 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 -0.1 -25 -15 -5 15 25 5 0 Radius (µm) Refractive Index change (%) Nonzero dispersion shifted fiber (Corning) 0.6% 0.4% Fiber with flattened dispersion slope 20 -10 -20 -30 10 1.1 1.2 1.3 1.4 1.5 1.6 1.7 0 30 ì (µm) D m D w D ch = D m + D w ì 1 Dispersion coefficient (ps km -1 nm -1 ) ì 2 n r Thin layer of cladding with a depressed index Dispersion Flattened Fiber Dispersion flattened fiber example. The material dispersion coefficient (D m ) for the core material and waveguide dispersion coefficient (D w ) for the doubly clad fiber result in a flattened small chromatic dispersion between ì 1 and ì 2 . t 0 Emitter Very short light pulses Input Output Fiber Photodetector Digital signal Information Information t 0 ~2² X l/2 T t Output Intensity Input Intensity ² X l/2 Dispersion and Maximum Bit Rate B < 0.5 (X 1/ 2 Return-to-zero (RTZ) bit rate or data rate. Nonreturn to zero (NRZ) bit rate = 2 RTZ bitrate t Output optical power (X l/2 T = 4o 1 0.5 0.61 2o A Gaussian output light pulse and some tolerable intersymbol interference between two consecutive output light pulses (y-axis in relative units). At time t = o from the pulse center, the relative magnitude is e -1/2 = 0.607 and full width root mean square (rms) spread is (X rms = 2o. © 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Dispersion and Maximum Bit Rate B < 0.25 o ! 0.59 (X 1/ 2 (X 1/ 2 L ! D ch (ì 1/ 2 Maximum Bit Rate Dispersion BL < 0.25L o ! 0.25 D ch o ì ! 0.59 D ch (ì 1/ 2 Bit Rate = constant inversely proportional to dispersion inversely proportional to line width of laser (single frequency lasers!) t 0 P i = Input light power Emitter Optical Input Optical Output Fiber Photodetector Sinusoidal signal Sinusoidal electrical signal t t 0 f 1 kHz 1 MHz 1 GHz P o / P i f op 0.1 0.05 f = Modulation frequency An optical fiber link for transmitting analog signals and the effect of dispersion in the fiber on the bandwidth, f op . P o = Output light power Electrical signal (photocurrent) f el 1 0.707 f 1 kHz 1 MHz 1 GHz © 1999 S.O. Kasap, Optoelectronics (Prentice Hall) 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 µm. 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 (ì 1/2 of 2 nm is used. Solution For FWHP dispersion, (X 1/2 /L = |D ch |(ì 1/2 = (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/(t 1/2 = 0.59/(16 ps km -1 ) = 36.9 Gb s -1 km. The optical and electrical bandwidths for a 10 km distance is f op = 0.75B = 0.75(36.9 Gb s -1 km) / (10 km) = 2.8 GHz. f el = 0.70f op = 1.9 GHz. Dispersed pulse shape (X 1/2 = FWHM width B (RZ) B' (NRZ) f op f el Gaussian with rms deviation o o = 0.425(X 1/2 0.25/o 0.5/o 0.75B = 0.19/o 0.71f op = 0.13/o Rectangular with full width (T o = 0.29(T = 0.29(X 1/2 0.25/o 0.5/o 0.69B = 0.17/o 0.73f op = 0.13/o 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. Combining intermodal and intramodal dispersions Consider a graded index fiber with a core diameter of 30 µm 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 D m 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 n 1 and n 2 ? Solution The normalized refractive index difference ( = (n 1 n 2 )/n 1 = (1.474 1.453)/1.474 = 0.01425. Modal dispersion for 1 km is o intermode = Ln 1 ( 2 /[(20)(3 1/2 )c] = 2.9-10 -11 s 1 or 0.029 ns. The material dispersion is (X 1/2 = LD m (ì 1/2 = (1 km)(7.5 ps nm -1 km -1 )(3 nm) = 0.0225 ns Assuming a Gaussian output light pulse shaper, o intramode = 0.425(X 1/2 = (0.425)(0.0225 ns) = 0.0096 ns Total dispersion is o rms ! o intermode 2 +o intramode 2 ! 0.029 2 + 0.0096 2 ! 0.030 ns B = 0.25/(X rms = 8.2 Gb Property Multimode step-index fiber Single-mode step-index Graded Index ( = (n 1 n 2 )/n 1 0.02 0.003 0.015 Core diameter (µm) 100 8.3 (MFD = 9.3 µm) 62.5 Cladding diameter (µm) 140 125 125 NA 0.3 0.1 0.26 Bandwidth - distance or Dispersion 20 - 100 MHz km. < 3.5 ps km -1 nm -1 at 1.3 µm > 100 Gb s -1 km in common use 300 MHz km - 3 GHz km at 1.3 µm Attenuation of light 4 - 6 dB km -1 at 850 nm 0.7 - 1 dB km -1 at 1.3 µm 1.8 dB km -1 at 850 nm 0.34 dB km -1 at 1.3 µm 0.2 dB km -1 at 1.55 µm 3 dB km -1 at 850 nm 0.6 - 1 dB km -1 at 1.3 µm 0.3 dB km -1 at 1.55 µm Typical light source Light emitting diode (LED) Lasers, single mode injection lasers LED, lasers Typical applications Short haul or subscriber local network communications Long haul communications Local and wide-area networks. Medium haul communications Comparison of typical characteristics of multimode step-index, single-mode step-index, and graded-index fibers. (Typical values combined from various sources; 1997 Dispersion Compensation Very short light pulse Input Output L t Transmission Fiber ² X ! D t L t L t Dispersion Compensating Fiber Input Output ² X ! D t L t + D c L c ì D t ì D c Transmission Fiber Dispersion Compnesating Fiber Total dispersion = D t L t + D c L c = (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. ì 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 Medium k Attenuation of light in the direction of propagation. z E Attenuation = Absorption + Scattering Attenuation coefficient ¬ is defined as the fractional decrease in the optical power per unit distance. ¬ is in m -1 . P out = P in exp(¬L) ¬ dB ! 1 L 10log P in P out ' + ' ¦ ¬ dB ! 10 ln(10) ¬ ! 4.34¬ z A solid with ions Light direction k E x 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) Lattice Absorption (Reststrahlen Absorption) Rayleigh Scattering Scattered waves Incident wave Through wave A dielectric particle smaller than wavelength 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. ¬ R < 8x 3 3ì 4 n 2 1 ¸ ) 2 ¡ T k B T f ¡ 1 = isothermal compressibility (at T f ) T f = 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 the ì = 1.55 µm window given that pure silica (SiO 2 ) has the following properties: T f = 1730°C (softening temperature); ¡ T = 7-10 -11 m 2 N -1 (at high temperatures); n = 1.4446 at 1.5 µm. Solution We simply calculate the Rayleigh scattering attenuation using ¬ R < 8x 3 3ì 4 (n 2 1) 2 ¡ T k B T f ¬ R < 8x 3 3(1.55 -10 6 ) 4 (1.4446 2 1) 2 (7 -10 11 )(1.38 -10 23 )(1730 + 273) ¬ R = 3.276-10 -5 m -1 or 3.276-10 -2 km -1 Attenuation in dB per km is ¬ dB = 4.34¬ R = (4.34)(3.735-10 -2 km -1 ) = 0.142 dB km -1 This represents the lowest possible attenuation for a silica glass core fiber at 1.55 µm. 0.05 0.1 0.5 1.0 5 10 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 Lattice absorption Rayleigh scattering Wavelength (µm) Illustration of a typical attenuation vs. wavelength characteristics of a silica based optical fiber. There are two communications channels at 1310 nm and 1550 nm. OH - absorption peaks 1310 nm 1550 nm © 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Corning low-water-peak fiber has no OH - peak E-band is available for communications with this fiber [Photonics Spectra, April 2002 p.69] Escaping wave ¿ ¿ ¿'· ¿ ¿ ¿ > ¿ c ¿' Microbending R Cladding Core Field distribution 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) Bending Loss 0 2 4 6 8 10 12 14 16 18 Radius of curvature (mm) l0 1 l0 2 l0 l l l0 l0 2 ¬ B (m -1 ) for 10 cm of bend ì = 633 nm ì = 790 nm V ! 2.08 V ! 1.67 Measured microbending loss for a 10 cm fiber bent by different amounts of radius of curvature R. Single mode fiber with a core diameter of 3.9 µm, cladding radius 48 µm, ( = 0.00275, NA = 0.10, V ! 1.67 and 2.08 (Data extracted and replotted from A.J. Harris and P.F. Castle, IEEE J. Light Wave Technology, Vol. LT14, pp. 34-40, 1986; see original article for discussion of peaks in ¬ B vs. R at 790 nm). ¬ ·exp R R c ' + ' ¦ ·exp R ( 3/ 2 ' + ' ¦ Microbending Loss Example: Microbending loss It is found that for a single mode fiber with a cut-off wavelength ì c = 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? Bending loss for three different fibers. The cut-off wavelength is 1.2 µm. All three are operating at ì = 1.5 µm. WDM Illustration Modulator Modulator Non-linear fiber and amplifiers introduce Intermodulation Modulator Modulator Eight Carriers 100 GHz Spacing Number of carriers and power level must be limited and this reduces range.