1 OPTICAL COMMUNICATIONS S

2 Course Program 5 lectures on Fridays  First lecture Friday in Room H-402  13:15-16:30 (15 minutes break in-between) Exercises  Demo exercises during lectures  Homework Exercises must be returned beforehand (will count in final grade) Seminar presentation  27.11, 13:15-16:30 in Room H-402  Topic to be agreed beforehand 2 labworks  Preliminary exercises (will count in final grade) Exam   op

3 Course Schedule 1.Introduction and Optical Fibers (6.11) 2.Nonlinear Effects in Optical Fibers (13.11) 3.Fiber-Optic Components (20.11) 4.Transmitters and Receivers (4.12) 5.Fiber-Optic Measurements & Review (11.12)

4 Lecturers In case of problems, questions... Course lecturers  G. Genty (3  F. Manoocheri (2 lectures)

5 Optical Fiber Concept Optical fibers are light pipes Communications signals can be transmitted over these hair thin strands of glass or plastic Concept is a century old But only used commercially for the last ~25 years when technology had matured

6 Optical fibers have more capacity than other means (a single fiber can carry more information than a giant copper cable!) Price Speed Distance Weight/size Immune from interference Electrical isolation Security Why Optical Fiber Systems?

7 Optical Fiber Applications > 90% of all long distance telephony > 50% of all local telephony Most CATV (cable television) networks Most LAN (local area network) backbones Many video surveillance links Military Optical fibers are used in many areas

8 Optical Fiber Technology Core Cladding Mechanical protection layer An optical fiber consists of two different types of solid glass 1970: first fiber with attenuation (loss) <20 dB/km 1979: attenuation reduced to 0.2 dB/km commercial systems!

9 Optical Fiber Communication Optical fiber systems transmit modulated infrared light TransmitterReceiver Fiber Components Information can be transmitted over very long distances due to the low attenuation of optical fibers

10 Frequencies in Communications 1  m 1 cm 10 cm 1 m 10 m 100 m 1 km 10 km 100 km waveguide coaxial cable wire pairs optical fiber Telephone Data Video Satellite Radar TV Radio Submarine cable Telephone Telegraph wavelength frequency 300 THz 30 GHz 3 GHz 300 MHz 30 Mhz 3 MHz 300 kHz 30 kHz 3 kHz

11 Frequencies in Communications Optical Fiber: > Gb/s Micro-wave ~10 Mb/s Short-wave radio ~100 kb/s Long-wave radio ~4 Kb/s Data rate Increase of communication capacity and rates requires higher carrier frequencies Optical Fiber Communication!

12 Optical fibers are cylindrical dielectric waveguides Cladding diameter 125 µm Cladding (pure silica) Core silica doped with Ge, Al… Core diameter from 9 to 62.5 µm Typical values of refractive indices Cladding: n 2 = (silica: SiO 2 ) Core: n 1 =1.461 (dopants increase ref. index compared to cladding) n1n1 n2n2 Optical Fiber A useful parameter: fractional refractive index difference  = ( n 1 - n 2 ) / n 1 <<1 Dielectric: material which does not conduct electricity but can sustain an electric field

13 Fiber Manufacturing Preform (soot) fabrication  deposition of core and cladding materials onto a rod using vapors of SiCCL 4 and GeCCL 4 mixed in a flame burned Consolidation of the preform  preform is placed in a high temperature furnace to remove the water vapor and obtain a solid and dense rod Drawing in a tower  solid preform is placed in a drawing tower and drawn into a thin continuous strand of glass fiber Optical fiber manufacturing is performed in 3 steps

14 Fiber Manufacturing Step 1Steps 2&3

15 Light Propagation in Optical Fibers Guiding principle: Total Internal Reflection  Critical angle  Numerical aperture Modes Optical Fiber types  Multimode fibers  Single mode fibers Attenuation Dispersion  Inter-modal  Intra-modal

16 Total Internal Reflection n2n2 n1n1 11 22 Snell’s law: n 1 sin  1 = n 2 sin  2 n 1 > n 2 Light is partially reflected and refracted at the interface of two media with different refractive indices: Reflected ray with angle identical to angle of incidence Refracted ray with angle given by Snell’s law 11 Refracted ray with angle: sin  2 = n 1 / n 2 sin  1 Solution only if n 1 / n 2 sin  1 ≤1 Angles  1 &  2 defined with respect to normal! !

17 Total Internal Reflection n2n2 n1n1 11 22 Snell’s law: n 1 sin  1 = n 2 sin  2 n2n2 n1n1 cc n 1 > n 2 sin  c = n 2 / n 1 If  >  c No ray is refracted! For angle  such that  >  C, light is fully reflected at the core-cladding interface: optical fiber principle! n2n2 n1n1  n2n2 n2n2 11

18 Example: n 1 = 1.47 n 2 = 1.46  NA = 0.17 Numerical Aperture n2n2 n1n1 cc  max For angle  such that  <  max, light propagates inside the fiber For angle  such that  >  max, light does not propagate inside the fiber Numerical aperture NA describes the acceptance angle  max for light to be guided

19 Geometrical optics can’t describe rigorously light propagation in fibers Must be handled by electromagnetic theory (wave propagation) Starting point: Maxwell’s equations Theory of Light Propagation in Optical Fiber with

20 Theory of Light Propagation in Optical Fiber We consider only linear propagation: P NL (r,T) negligible  (1) : linear susceptibility

21 Theory of Light Propagation in Optical Fiber

22 Theory of Propagation in Optical Fiber n : refractive index  : absorption

23 Theory of Light Propagation in Optical Fiber Each components of E(x,y,z,t)=U(x,y,z)e j  t must satisfy the Helmoltz equation Assumption: the cladding radius is infinite In cylindrical coodinates the Helmoltz equation becomes x y z ErEr EzEz EφEφ r φ Note: =  / c

24 Theory of Light Propagation in Optical Fiber U = U(r,φ,z)= U(r)U(φ) U(z) Consider waves travelling in the z-direction U(z) =e - j  z U(φ) must be 2 periodic U(φ) =e - j lφ, l=0,±1,±2 …integer  = k 0 n eff is the propagation constant

25 Theory of Propagation in Optical Fiber A light wave is guided only if We introduce

26 Theory of Propagation in Optical Fiber

27 Examples aa K0(r)K0(r)J0(r)J0(r)K0(r)K0(r) K3(r)K3(r)J3(r)J3(r)K3(r)K3(r) a r r l=0l=3

28 Characteristic Equation Boundary conditions at the core-cladding interface give a condition on the propagation constant  (characteristics equation) For each l value there are m solutions for  Each value  lm corresponds to a particualr fiber mode

29 Number of Modes Supported by an Optical Fiber Solution of the characteristics equation U(r, φ,z)=F(r)e - jl  e -j  lm z is called a mode, each mode corresponds to a particular electromagnetic field pattern of radiation The modes are labeled LP lm Number of modes M supported by an optical fiber is related to the V parameter defined as M is an increasing function of V ! If V <2.405, M =1 and only the mode LP 01 propagates: the fiber is said Single-Mode

30 Number of Modes Supported by an Optical Fiber Number of modes well approximated by: If V <2.405, M =1 and only the mode LP 01 propagates: Single-Mode fiber! cladding Example: 2a =50  m n 1 =1.46 V =17.6  =0.005 M =155 =1.3  m

31 Examples of Modes in an Optical Fiber  =  m a =8.335  m n 1 =  =0.034

32 Examples of Modes in an Optical Fiber  =  m a =8.335  m n 1 =  =0.034

33 Cut-Off Wavelength The propagation constant of a given mode depends on the wavelength [  ( )] The cut-off condition of a mode is defined as  2 ( )-k 0 2 n 2 2=  2 ( )- 4  2 n 2 2 /   There exists a wavelength c above which only the fundamental mode LP 01 can propagate Example: 2a =9.2  m n 1 =  = c ~1.2  m

34 Single-Mode Guidance In a single-mode fiber, for wavelengths  > c ~1.26  m only the LP 01 mode can propagate

35 Mode Field Diameter Fiber Optics Communication Technology-Mynbaev & Scheiner The fundamental mode of a single-mode fiber is well approximated by a Gaussian function

36 Step-index single-mode Types of Optical Fibers Refractive index profile Cladding diameter 125 µm Core diameter from 8 to 10 µm n1n1 n2n2 n  n2n2 n1n1 r

37 Step-index multimode Types of Optical Fibers Refractive index profile Cladding diameter from 125 to 400 µm Core diameter from 50 to 200 µm n1n1 n2n2 n  n2n2 n1n1 r

38 Graded-index multimode Types of Optical Fibers Refractive index profile Cladding diameter from 125 to 140 µm Core diameter from 50 to 100 µm n1n1 n2n2 n n2n2 n1n1 r

39 Attenuation Signal attenuation in optical fibers results form 3 phenomena:  Absorption  Scattering  Bending Loss coefficient:   depends on the wavelength For a single-mode fiber,  dB  = nm

40 Scattering and Absorption Short wavelength: Rayleigh scattering  induced by inhomogeneity of the refractive index and proportional to 1/ 4 Absorption  Infrared band  Ultraviolet band 3 Transmission windows  820 nm  1300 nm  1550 nm 4 1st window2nd3rd 820 nm1.3 µm1.55 µm 2 IR absorption Rayleigh Water peaks scattering 0.4  1/ UV absorption Wavelength (µm)

41 Macrodending losses are caused by the bending of fiber Bending of fiber affects the condition  <  C For single-mode fiber, bending losses are important for curvature radii < 1 cm Macrobending Losses

42 Microdending losses are caused by the rugosity of fiber Micro-deformation along the fiber axis results in scattering and power loss Microbending Losses

43 Fundamental mode Higher order mode Attenuation: Single-mode vs. Multimode Fiber Light in higher-order modes travels longer optical paths Multimode fiber attenuates more than single-mode fiber Wavelength (µm) 4 2 MMF SMF

44 Dispersion What is dispersion?  Power of a pulse travelling though a fiber is dispersed in time  Different spectral components of signal travel at different speeds  Results from different phenomena Consequences of dispersion: pulses spread in time 3 Types of dispersion:  Inter-modal dispersion (in multimode fibers)  Intra-modal dispersion (in multimode and single-mode fibers)  Polarization mode dispersion (in single-mode fibers) tt

45 Input pulse Dispersion in Multimode Fibers (inter-modal) t Input pulse Output pulse t In a multimode fiber, different modes travel at different speed temporal spreading (inter-modal dispersion) Inter-modal dispersion limits the transmission capacity The maximum temporal spreading tolerated is half a bit period The limit is usually expressed in terms of bit rate-distance product

46 Dispersion in Multimode Fibers (Inter-modal) n2n2 n1n1 cc L  Slow rayFast ray Fastest ray guided along the core center Slowest ray is incident at the critical angle sin

47 Dispersion in Multimode Fibers Example: n 1 = 1.5 and  = 0.01 →  B L< 10 Mb∙s -1 Capacity of multimode-step index index fibers B×L ≈ 20 Mb/s×km × 

48 Input pulse Fast mode travels a longer physical path Slow mode travels a shorter physical path Dispersion in graded-index Multimode Fibers t Input pulse Output pulse t Temporal spreading is small Capacity of multimode-graded index fibers B×L ≈ 2 Gb/s×km

49 Intra-modal Dispersion In a medium of index n, a signal pulse travels at the group velocity g defined as  Intra-modal dispersion results from 2 phenomena  Material dispersion (also called chromatic dispersion)  Waveguide dispersion Different spectral components of signal travel at different speeds The dispersion parameter D characterizes the temporal pulse broadening  T per unit length per unit of spectral bandwidth  :  T = D ×  × L

50 Material Dispersion Refractive index n depends on the frequency/wavelength of light Speed of light in material is therefore dependent on frequency/wavelength Input pulse, 1 t Input pulse, 2 t t

51 Material Dispersion Refractive index of silica as a function of wavelength is given by the Sellmeier Equation

52 Material Dispersion L Input pulse, 1 t Input pulse, 2 t 1 2  t TT

53 Material Dispersion

54 Waveguide Dispersion The size w 0 of a mode depends on the ratio a /  : Consequence: the relative fraction of power in the core and cladding varies This implies that the group-velocity g also depends on a /  1 2 > 1

55 Total Dispersion Waveguide dispersion shifts the wavelength of zero-dispersion to 1.32  m D Intra-modal <0: normal dispersion region D Intra-modal >0: anomalous dispersion region

56 Dispersion can be changed by changing the refractive index Change in index profile affects the waveguide dispersion Total dispersion is changed n2n2 n1n1 Single-mode Fiber n2n2 n1n1 Dispersion shifted Fiber Single-mode fiber: 1310 nm Dispersion shifted Fiber: 1550 nm Single-mode Fiber Wavelength ( µ m) Dispersion shifted Fiber Tuning Dispersion

57 Dispersion Related Parameters

58 Polarization Mode Dispersion Optical fibers are not perfectly circular In general, a mode has 2 polarizations (degenerescence): x and y Causes broadening of signal pulse x y x

59 Effects of Dispersion: Pulse Spreading Total pulse spreading is determined as the geometric sum of pulse spreading resulting from intra-modal and inter-modal dispersion Examples: Consider a LED  m  =50 nm after L=1 km,  T=5.6 ns D Inter-modal =2.5 ns/km D Intra-modal =100 ps/nm×km Consider a DFB laser 1.5  m  =.2 nm after L=100 km,  T=0.34 ns! D Intra-modal =17 ps/nm×km D Polarization =0.5 ps/ √km

60 Effects of Dispersion: Capacity Limitation Capacity limitation: maximum broadening<half a bit period Example: Consider a DFB laser 1.55  m  =0.2 nm LB<150 Gb/s ×km D =17 ps/nm×km If L=100 km, B Max =1.5 Gb/s

61 Advantage of Single-Mode Fibers No intermodal dispersion Lower attenuation No interferences between multiple modes Easier Input/output coupling Single-mode fibers are used in long transmission systems

62 Summary Attractive characteristics of optical fibers: Low transmission loss Enormous bandwidth Immune to electromagnetic noise Low cost Light weight and small dimensions Strong, flexible material

63 Summary Important parameters:  NA : numerical aperture (angle of acceptance)  V : normalized frequency parameter (number of modes)  c : cut-off wavelength (single-mode guidance)  D : dispersion (pulse broadening) Multimode fiber  Used in local area networks (LANs) / metropolitan area networks (MANs)  Capacity limited by inter-modal dispersion: typically 20 Mb/s x km for step index and 2 Gb/s x km for graded index Single-mode fiber  Used for short/long distances  Capacity limited by dispersion: typically 150 Gb/s x km