Propagation losses in optical fibers

Chapter Dielectric Waveguides and Optical Fibers 1-Fev-017 Propagation losses in optical fibers Charles Kao, Nobel Laureate (009) Courtesy of the Chinese University of Hong Kong S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education 013 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 65

Light Attenuation 1-Fev-017 The attenuation of light in a medium Attenuation = Absorption + Scattering Attenuation coefficient α is defined as the fractional decrease in the optical power per unit distance. α is in m -1. P out = P in exp( αl) α db = 1 10log L P P in out 10 αdb = α = 4. 34α ln(10) From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 66

Attenuation in Optical Fibers Attenuation vs. wavelength for a standard silica based fiber. From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 67

Lattice Absorption (Reststrahlen Absorption) EM Wave oscillations are coupled to lattice vibrations (phonons), vibrations of the ions in the lattice. Energy is transferred from the EM wave to these lattice vibrations. This corresponds to Fundamental Infrared Absorption in glasses From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 68

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. α R 8π 3 3λ 4 ( n 1) β T k B T f β Τ = 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 From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 69

Low-water-peak fiber has no OH - peak E-band is available for communications with this fiber From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 71

Chapter Dielectric Waveguides and Optical Fibers 1-Fev-017 Dispersion in optical fibers Charles Kao, Nobel Laureate (009) Courtesy of the Chinese University of Hong Kong S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education 013 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 7

Spectral width Pulse duration (Temporal and Spatial Coherence) 1-Fev-017 (a) A sine wave is perfectly coherent and contains a well-defined frequency υ o. (b) A finite wave train lasts for a duration t and has a length l. Its frequency spectrum extends over υ = / t. It has a coherence time t and a coherence length λ. (c) White light exhibits practically no coherence. From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 73

Spectral width Pulse duration (Temporal and Spatial Coherence) υ 1 t FWHM spreads From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 74

Spectral width Pulse duration (Temporal and Spatial Coherence) No interference Interference t No interference (a) A B Source Time (b) P c Spatially coherent source Q (c) c An incoherent beam Space (a) Two waves can only interfere over the time interval t. (b) Spatial coherence involves comparing the coherence of waves emitted from different locations on the source. (c) An incoherent beam From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 75

Spectral width Pulse duration (Temporal and Spatial Coherence) t = coherence time l = c t = coherence length For a Gaussian light pulse Spectral width υ 1 t Pulse duration From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 76

Temporal and Spatial Coherence t = coherence time l = c t = coherence length Na lamp, orange radiation at 589 nm has spectral width υ 5 10 11 Hz. t 1/ υ = 10-1 s or ps, and its coherence length l = c t, l = 6 10-4 m or 0.60 mm. He-Ne laser operating in multimode has a spectral width around 1.5 10 9 Hz, t 1/ υ = 1/1.5 10 9 s or 0.67 ns l = c t = 0.0 m or 00 mm. υ 1 t From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 77

Intermode Dispersion (MMF) Group Delay τ = L / v g τ L n 1 n c (Since n 1 and n are only slightly different) From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 78

Intermode Dispersion (MMF) TE 0 θ c θ c TE highest v g min c n 1 sin θ c = τ = c n 1 n n 1 L L v g v v g max min gmax c n 1 τ = L ( n1 n ) c n n 1 τ L n 1 n c τ/l 10 50 ns / km Depends on length! From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 79

Intramode Dispersion (SMF) Dispersion in the fundamental mode Group Delay τ = L / v g Group velocity v g depends on Refractive index = n(λ) V-number = V(λ) = (n 1 n )/n 1 = (λ) Material Dispersion Waveguide Dispersion Profile Dispersion From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 80

Material Dispersion Emitter emits a spectrum λ 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. τ L = D m λ D m = Material dispersion coefficient, ps nm -1 km -1 From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 81

Intramode Dispersion (SMF) Chromatic dispersion in the fundamental mode v g v g1 τ = DL λ Output pulse dispersed δ(t) τ λ 1 λ λ = λ λ 1 Chromatic spread λ τ g1 τ g OR τ D = L λ D = dτ Ldλ Definition of Dispersion Coefficient From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 8 τ τ = τ g1 τ g Dispersion

Emitter Input Very short light pulse Material Dispersion Cladding v g (λ 1 ) Core v g (λ ) Output v g = c / N g Group velocity Depends on the wavelength τ L = D m λ D m = Material dispersion coefficient, ps nm -1 km -1 D m λ d n c dλ From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 83

Wave guide dispersion b hence β depend on V and hence on λ V πa = λ ( n n ) 1/ 1 b 0.996 1.148 V Normalized propagation constant b = (β /k) n n 1 n k = π/λ From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 84

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 λ, even if n 1 and n were constant. Even if n 1 and n 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 λ. Waveguide dispersion arises as a result of the guiding properties of the waveguide which imposes a nonlinear ω vs. β lm relationship. τ L = D w λ Dw = waveguide dispersion coefficient D w depends on the waveguide structure, ps nm -1 km -1 From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 85

Chromatic Dispersion Material dispersion coefficient (D m ) for the core material (taken as SiO ), waveguide dispersion coefficient (D w ) (a = 4. µm) and the total or chromatic dispersion coefficient D ch (= D m + D w ) as a function of free space wavelength, λ Chromatic = Material + Waveguide τ L = (D m + D w ) λ From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 86

What do Negative and Positive D m mean? 1 Silica glass Negative D m Positive D m λ λ 1 1 t N g >N g1 λ 1 v g1 λ v g λ 1 λ Positive D m λ 1 N g <N g1 v g1 v g τ t τ = Positive D m t λ Negative D m D m τ = L λ t τ = Negative λ = λ λ 1 From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 87

Waveguide Dimension and Chromatic Dispersion D w d ( bv ) = n V cλ dv D w 0.05λ a cn D w (ps nm 1 km 1 ) 83.76 λ(µm) [ a(µm)] n Waveguide dispersion depends on the guide properties From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 88

Profile Dispersion Group velocity v g (01) of the fundamental mode depends on, refractive index difference. may not be constant over a range of wavelengths: = (λ) τ L = D p λ D p = Profile dispersion coefficient D p < 0.1 ps nm -1 km -1 Can generally be ignored NOTE Total intramode (chromatic) dispersion coefficient D ch D ch = D m + D w + D p where D m, D w, D p are material, waveguide and profile dispersion coefficients respectively From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 89

Chromatic Dispersion D ch = D m + D w + D p S 0 = Chromatic dispersion slope at λ 0 D ch = τ L = D ch λ S λ λ 0 1 0 4 λ Chromatic dispersion is zero at λ = λ 0 4 From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 90

Is dispersion really zero at λ 0? The cause of τ is the wavelength spread λ at the input τ = f( λ) dτ 1 d τ τ = τ ( λ) τ ( λ0 ) = ( λ) + ( λ) dλ λ! 0 dλ λ 0 d τ = D ch Ldλ +L τ = L = 0 τ = [ LD ch ( λ λ dd ch = dλ 1 1 km S0 ( λ) = = S 0 d dτ λ λ d d 0 )] + ( ) λ 0 ( - -1 0.090ps nm km )( nm) 1.01ps λ From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 91

Polarization Dispersion n different in different directions due to induced strains in fiber in manufacturing, handling and cabling. δn/n < 10-6 τ = D PMD L D PMD = Polarization dispersion coefficient Typically D PMD = 0.1 0.5 ps nm -1 km -1/ From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 9

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. τ L C I c What is the optical power that will give τ/l 0.1 ps km -1? Take C = 10-14 cm W -1 I (c/c)( τ/l) = 3 10 6 W cm - or n 3 10-6 Given a 10 µm, A 7.85 10-7 cm Optical power.35 W in the core In many cases, this dispersion will be less than other dispersion mechanisms From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 93

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 (155-160 nm) D ch = 0.1 6 ps nm -1 km -1. Nonzero dispersion shifted fibers Various fibers named after their dispersion characteristics. The range 1500-1600 nm is only approximate and depends on the particular application of the fiber. From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 94

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 λ 1 and λ. From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 95

Nonzero Dispersion Shifted Fiber: More Examples Refractive Index change (%) 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0. 0.1 0.0 0.6% -0.1-5 -15-5 0 5 15 5 Radius (µm) 0.4% Nonzero dispersion shifted fiber (Corning) Fiber with flattened dispersion slope (schematic) From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 96

Commercial Fibers for Optical Communications Fiber Standard single mode, ITU- T G.65 D ch S 0 D PMD ps nm -1 km -1 ps nm - km -1 ps km -1/ 17 0.093 < 0.5 (1550 nm) (cabled) Some attributes D ch = 0 at λ 0 131 nm, MFD = 8.6-9.5 µm at 1310 nm. λ c 160 nm. Non-zero dispersion shifted fiber, ITU-T G.655 0.1 6 (1530 nm) < 0.05 at 1550 nm < 0.5 (cabled) For 1500-1600 nm range. WDM application MFD = 8 11 µm. Non-zero dispersion shifted fiber, ITU-T G.656 Corning SMF8e+ (Standard SMF) 14 < 0.045 at 1550 nm 18 (1550 nm) < 0.0 (cabled) For 1460-165 nm range. DWDM application. MFD = 7 11 µm (at 1550 nm). Positive D ch. λ c <1310 nm 0.088 < 0.1 Satisfies G.65. λ 0 1317 nm, MFD = 9. µm (at 1310 nm), 10.4 µm (at 1550 nm); λ c 160 nm. OFS TrueWave RS Fiber.6-8.9 0.045 0.0 Satisfies G.655. Optimized for 1530 nm - 165nm. MFD = 8.4 µm (at 1550 nm); λ c 160 nm. OFS REACH Fiber 5.5-8.9 0.045 0.0 Higher performance than G.655 specification. Satisfies G.656. For DWDM from 1460 to 165 nm. λ 0 1405 nm. MFD = 8.6 µm (at 1550 nm) From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 97

Single Mode Fibers: Selected Examples From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 98

Dispersion Compensation 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) = 000 ps/nm for 1080 km D effective = 1.9 ps nm -1 km -1 From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 99

Dispersion Compensation DispersionDvs. wavelength characteristics involved in dispersion compensation. Inverse dispersion fiber enables the dispersion to be reduced and maintained flat over the communication wavelengths. From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 100

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. λ From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 101

Dispersion and Maximum Bit Rate B 0.5 τ 1/ Return-to-zero (RTZ) bit rate or data rate. Nonreturn to zero (NRZ) bit rate = RTZ bitrate From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 10

NRZ and RTZ T Information 1 0 1 1 0 1 0 0 1 NRZ RZ From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 103

Maximum Bit Rate B A Gaussian output light pulse and some tolerable intersymbol interference between two consecutive output light pulses (y-axis in relative units). At time t = σ from the pulse center, the relative magnitude is e 1/ = 0.607 and full width root mean square (rms) spread is τ rms = σ. (The RTZ case) From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 104

Dispersion and Maximum Bit Rate Maximum Bit Rate Dispersion 0.5 0.59 τ 1 / B = = D ch λ1/ σ τ L 1/ BL 0.59 0.59 = τ λ 1/ D ch 1/ Bit Rate Distance is inversely proportional to dispersion inversely proportional to line width of laser (so, we need single frequency lasers!) From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 105

Dispersion and Maximum Bit Rate Maximum Bit Rate B 0.5 σ = 0.59 τ 1/ σ = + σ intermodal σ intramodal ) ( ) ( ) 1 / 1/ intermodal 1/ intramodal ( τ = τ + τ From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 106

Optical Bandwidth An optical fiber link for transmitting analog signals and the effect of dispersion in the fiber on the bandwidth, f op. From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 107

Pulse Shape and Maximum Bit Rate From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 108

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 a 10 km fiber if a laser diode source with a FWHP linewidth λ 1/ of nm is used. Solution For FWHP dispersion, τ 1/ /L = D ch λ 1/ = (8 ps nm -1 km -1 )( nm) = 16 ps km -1 Assuming a Gaussian light pulse shape, the RTZ bit rate distance product (BL) is BL = 0.59L/ τ 1/ = 0.59/(16 ps km -1 ) = 36.9 Gb s -1 km The optical and electrical bandwidths for a 10 km fiber are f op = 0.75B = 0.75(36.9 Gb s -1 km) / (10 km) =.8 GHz f el = 0.70f op = 1.9 GHz From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 109

Chapter Dielectric Waveguides and Optical Fibers 1-Fev-017 Graded Index (GRIN) Fibers Charles Kao, Nobel Laureate (009) Courtesy of the Chinese University of Hong Kong S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education 013 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This publication is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458. From: S.O. Kasap, Optoelectronics and Photonics: Principles and Practices, Second Edition, 013 Pearson Education, USA 110