Optical Fiber Concept

Transcription

1 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 ~30 years when technology had matured 5 5

2 Why Optical Fiber Systems? 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 6 6

3 Optical Fiber Applications Optical fibers are used in many areas > 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 7 7

4 Optical Fiber Technology An optical fiber consists of two different types of solid glass Core Cladding Mechanical protection layer 970: first fiber with attenuation (loss) <0 db/km 979: attenuation reduced to 0. db/km commercial systems! 8 8

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

6 00 km 0 km km 00 m 0 m m 0 cm cm Frequencies in Communications wire pairs coaxial cable waveguide frequency 3 khz Submarine cable Telephone 30 khz Telegraph 300 khz TV Radio Satellite Radar 3 MHz 30 Mhz 300 MHz 3GHz 30 GHz µm optical fiber wavelength ee Telephone Data Video 300 THz 0 0

7 Frequencies in Communications Data rate Optical Fiber: > Gb/s Micro-wave ~0 Mb/s Short-wave radio ~00 kb/s Long-wave radio ~4 Kb/s Increase of communication capacity and rates requires higher carrier frequencies Optical Fiber Communications!

8 Optical Fiber Optical fibers are cylindrical dielectric waveguides Dielectric: material which does not conduct electricity but can sustain an electric field Cladding diameter 5 µm n Core diameter from 9 to 6.5 µm n Cladding (pure silica) Core silica doped with Ge, Al Typical values of refractive indices Cladding: n.460 (silica: SiO ) Core: n.46 (dopants increase ref. index compared to cladding) A useful parameter: fractional refractive index difference δ (n -n ) /n <<

9 Fiber Manufacturing Optical fiber manufacturing is performed in 3 steps 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 3 3

10 Fiber Manufacturing Step Steps &3 4 4

11 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 5 5

12 Total Internal Reflection 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! Angles θ & θ defined with respect to normal! Snell s law: n sin θ n sin θ θ θ n > n θ n n Refracted ray with angle: sin θ n / n sin θ Solution only if n / n sin θ 6 6

13 Total Internal Reflection Snell s law: If θ >θ sin θ c n / n c No ray n sin θ n sin θ is refracted! θ n θ c n n θ n > n n θ n n n n θ For angle θ such that θ >θ C, light is fully reflected at the core-cladding interface: optical fiber principle! 7 7

14 Numerical Aperture For angle θ such that θ <θ max, light propagates inside the fiber For angle θ such that θ >θ max, light does not propagate inside the fiber n θ max n θ Example: n.47 c n.46 NA 0.7 NA n n n sinθmax n n n δ with δ << n n Numerical aperture NA describes the acceptance angle θ max for light to be guided 8 8

15 Theory of Light Propagation in Optical Fiber Geometrical optics can t describe rigorously light propagation in fibers Must be handled by electromagnetic theory (wave propagation) Starting point: Maxwell s equations E B T () H J + D T () D ρ f (3) B 0 (4) with B µ 0 H + M : Magnetic flux density D ε 0 E + P : Electric flux density J 0 : Current density ρ f 0 : Charge density 9 9

16 Theory of Light Propagation in Optical Fiber Pr,t ( ) P L ( r,t)+ P NL ( r,t) P L P NL + ( r,t) ε 0 χ () ( t t )Er,t ( ) dt : Linear Polarization χ () : linear susceptibility ( r,t): Nonlinear Polarization We consider only linear propagation: P NL (r,t) negligible 0 0

17 Theory of Light Propagation in Optical Fiber Ert (, ) PL (,) r t Ert (,) + µ 0 c t t + i t We now introduce the Fourier transform: E% ω ( r, ω) E(r,t)e dt k Ert (,) k ( i ω ) E% ( r, ω ) k t ω c () And we get: Er %(, ω) Er %(, ω ) + µ 0ε0χ ( ω) ω Er %(, ω) which can be rewritten as ω () Er % (, ω ) + cµ 0ε0χ ( ω) Er (, ω) 0 % c ω i.e. Er % (, ω) ε( ω) Er % (, ω) 0 c -

18 Theory of Propagation in Optical Fiber αc ε(ω) n + i + () ω with n R χ (ω) and α [ ] f ti i d ω cn(ω) I χ () (ω) [ ] n: refractive index α: absorption E (r,ω) ( E (r,ω)) E (r,ω) E (r,ω) E (r,ω) D (r,ω) 0 ( ) E (r,ω) + n ω c E (r,ω) 0 : Helmoltz Equation!

19 Theory of Light Propagation in Optical Fiber Each components of E(x,y,z,t)U(x,y,z)e jωt must satisfy the Helmoltz equation n n for r a U + n k 0 U 0 with n n for r > a k 0 π /λ Assumption: the cladding radius is infinite In cylindrical coodinates the Helmoltz equation becomes n n U U U for r a U r + r r + r ϕ + z + n k 0 U 0 with n n for r > a k 0 π /λ 0 Note: λω /c y x E r φ E z z r E φ 3 3

20 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(φ) must be π periodic U(φ) e -j lφ, l0,±,± integer U ( r, ϕ, z) d F + dr r F( r) e df + n dr jlϕ k 0 e jβz β with l 0, ±, ±... Plugging into the Helmoltz Eq. one gets : l r F U(z) e -jβz n n for r a 0 with n n for r > a k0 π / λ0 One can define an effective index of refraction n eff β k 0 n eff is the such that β ω c n, n < n propagation eff eff < n constant 4 4

21 Theory of Propagation in Optical Fiber A light wave is guided only if nk0 β nk 0 We introduce κ n k 0 ( ) β γ β ( n k 0 ) κ + γ k ) 0 ( n n ) k 0 NA : constant! Note : κ,γ 0 κ,γ :real We then get : d F dr + df r dr + κ l F 0 for r a r d F dr + df r dr γ + l F 0 for r > a r 5 5

22 Theory of Propagation in Optical Fiber The solutions of J ( κr ) ( γr ) the equations are of F ( r) J for ρ a l l l : Bessel function of F ( r ) K for ρ > a l K l l st the form : kind with order l : Modified Bessel function of with κ ( n k 0 ) β ( ) γ β n k 0 κ + γ k 0 n ( n ) k 0 NA : constant! st kind with order l 6 6

23 Examples l0 l3 K 0 (γr) J 0 (κr) a K 0 (γr) r K 3 (γr) a J 3 (κr) a K 3 (γr) r F(r) J 0 (κr) for r a K 0 (γr) for r < a F(r) J 3 (κr) for r a K 3 (γr) for r < a 7 7

24 8 Characteristic Equation Boundary conditions at the core-cladding interface give a condition on the propagation constant β (characteristics equation) β solving can be found by The propagation constant g p p g β ( q ) β β l K J n K J lm l l l l + Γ + Κ Γ + Κ ) ( ) ( ) ( ) ( the characteristic equation : can be found by solving The propagation constant ' ' ' ' aκ aγ k n K J n K J l l l l Γ Κ Γ + Κ Γ Γ + Κ Κ Γ Γ + Κ Κ and with ) ( ) ( ) ( ) ( 0 For each l value there are m solutions for β Each value β lm corresponds to a particualr fiber mode 8

25 Number of Modes Supported by an Optical Fiber Solution of the characteristics equation U(r,φ,z)F(r)e -jlϕ e -jβ 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! V ak 0 NA π a λ n n If V <.405, M and only the mode LP 0 propagates: the fiber is said to be Single-Mode 9 9

26 Number of Modes Supported by an Optical Fiber π a λ Number of modes well approximated by: M V /, where V ( n n) n eff n n n core LP 0 LP V Example: a 50 µm n.46 V7.6 δ0.005 M55 λ.3 3 µm If V <.405, M and only the mode LP 0 propagates: Single-Mode fiber! cladding 30 30

27 Examples of Modes in an Optical Fiber λ µm a µm n.4640 δ

28 Examples of Modes in an Optical Fiber λ µm a µm n.4640 δ

29 Cut-Off Wavelength The propagation constant of a given mode depends on wavelength [β (λ)] The cut-off condition of a mode is defined as β (λ)-k 0 n β (λ)-4π n /λ 0 There exists a wavelength λ c above which only the fundamental mode LP 0 can propagate 0 p p g π V <.405 λc na δ. 84an δ λc λc or equivalently a 0.54 n δ n δ π Example: a 9. µm n.4690 δ0.004 λ c ~. µm 33 33

30 Single-Mode Guidance In a single-mode fiber, for wavelengths λ >λ c ~.6 µm only the LP 0 mode can propagate 34 34

31 Mode Field Diameter The fundamental mode of a single-mode fiber is well approximated by a Gaussian function F ( ρ ) Ce ρ w 0 where C is a constant and w the mode size A good approximation for the mode size is obtained from w w a for. < V 3/ 6 V V a for V >. 4 ln( V ) 0 <. 4 Fiber Optics Communication Technology-Mynbaev & Scheiner 35 35

32 Types of Optical Fibers Step-index single-mode n Cladding diameter 5 µm Core diameter from 8 to 0 µm n Refractive index profile n n n δ 0.00 r 36 36

33 Types of Optical Fibers Step-index multimode n Cladding diameter from 5 to 400 µm Core diameter from 50 to 00 µm n Refractive index profile n n n δ 0.0 r 37 37

34 Types of Optical Fibers Graded-index multimode n Cladding diameter from 5 to 40 µm Core diameter from 50 to 00 µm n n Refractive index profile n n r 38 38

35 Attenuation Signal attenuation in optical fibers results form 3 phenomena: Absorption Scattering Bending Loss coefficient: α α depends on wavelength P Out P e in αl P Out 0 0log 0 α L α L P in ln(0) α is usually expressed in units of db/km : α db 4.343α For a single-mode fiber, α db nm 39 39

36 Scattering and Absorption Short wavelength: Rayleigh scattering induced by inhomogeneity of the refractive index and proportional to /λ 4 Absorption Infrared band Ultraviolet band 4 st window nd 3rd 80 nm.3 µm.55 µm IR absorption Rayleigh scattering α /λ 4 Water peaks 0.4 UV absorption 0. 3 Transmission windows 80 nm 300 nm 550 nm Wavelength (µm) 40 40

37 Macrobending Losses Macrodending losses are caused by the bending of fiber Bending of fiber affects the condition θ < θ C For single-mode fiber, bending losses are important for curvature radii < cm 4 4

38 Microbending Losses Microdending losses are caused by the rugosity of fiber Micro-deformation along the fiber axis results in scattering and power loss 4 4

39 Attenuation: Single-mode vs. Multimode Fiber 4 Fundamental mode Higher order mode 0.4 SMF 0. MMF Wavelength (µm) Light in higher-order modes travels longer optical paths Multimode fiber attenuates more than single-mode fiber 43 43

40 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 t t 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) 44 44

41 Dispersion in Multimode Fibers (inter-modal) Input pulse Input pulse Output pulse t 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 / bit period The limit is usually expressed in terms of bit rate x distance 45 45

42 Dispersion in Multimode Fibers (Inter-modal) Fastest ray guided along the core center Slowest ray is incident at the critical angle n n θ c Slow ray θ L T Fast ray n n n L L c n c n L c T T with T v L L FAST FAST SLOW n n v SLOW FAST L n n T L vfast c n SLOW L cosθ L c δ FAST FAST and T SLOW L π sin cos θ L v SLOW SLOW L sin θ n n C θ L 46 46

43 Dispersion in Multimode Fibers If bit rate B b L n i.e. δ < c n B cn or L B < nδ s We must have T < B Example: n.5and δ 0.0 B L<0Mb s - p Capacity of multimode-step index index fibers B L 0 Mb/s km 47 47

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

45 Intra-modal Dispersion In a medium of index n, a signal pulse travels at the group velocity ν defined as: g dωω λ d β v g dβ πc d λ Intra-modal dispersion results from 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 λ: T D λ L d λ d β DIntra modal in units of ps/nm km dλ vg πc dλ 49 49

46 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, λ t Input pulse, λ t t 50 50

47 Material Dispersion Refractive index of silica as a function of wavelength is given by the Sellmeier Equation A λ Aλ A3λ n( λ) λ λ λ λ λ λ with A A A , λ nm , λ nm , λ 6.44 nm 3 5 5

48 5 Material Dispersion λ λ λ β π λ d dn n c d d c v g / λ λ λ Input pulse, λ λ λ T p p t t L Input pulse, λ t λ λ λ λ λ λ d n d c L v d d L D L T g 5

49 Material Dispersion ps/nm/km m) Material (p Material µ Wavelength (µm) D M -000 DMaterial0@.7 µm λ d n DMaterial (units : ps/nm km) c dλλ 53 53

50 Waveguide Dispersion The size w 0 of a mode depends on the ratio a/λ : λ λ >λ w a / V V 6 Consequence: the relative fraction of power in the core and cladding varies This implies that the group-velocity ν g also depends on a/λ D Waveguide d dλ vg λ π nc d λ d w λ 0 where w 0 is the mode size 54 54

51 Total Dispersion D Intra modal D Material + D Waveguide D Intra-modal <0: normal dispersion region D Intra-modal >0: anomalous dispersion region Waveguide dispersion shifts the wavelength of zero-dispersion to.3 µm 55 55

52 Tuning Dispersion Dispersion can be changed by changing the refractive index Change in index profile affects the waveguide dispersion Total dispersion is changed 0 n n 0 Single-mode Fiber n Single-mode Fiber n Dispersion shifted Fiber 0 Single-mode fiber: 30 nm Dispersion shifted Fiber: 550 nm -0 Dispersion shifted Fiber Wavelength (µm) 56 56

53 57 Dispersion Related Parameters s/km of :group delay in units β β ω β d n c eff y g p modal Intra λ π β λ ω ω β λ β λ β ω c d d d d d d v d d D d v g g /km s group velocity dispersion parameter in units of : β λ λ ω λ λ d d d v d g 57

54 Polarization Mode Dispersion Optical fibers are not perfectly circular y x x In general, a mode has polarizations (degenerescence): x and y Causes broadening of signal pulse T L v gx v gy D Polarization L 58 58

55 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 T T Intermodal + T Intra-modal + T Polarization Multimode Fiber : T Single - Mode Fiber : T ( D L) + ( D λ L) Inter modal ( D λ L) + ( D L ) Intra modal Intra modal Polarization Examples: Consider a LED µm λ50 nm after L km, T5.6 ns D Inter-modal.5 ns/km D Intra-modal 00 ps/nm km Consider a DFB laser µm λ.nmafterl00km, T0.34 ns! D Intra-modal 7 ps/nm km D Polarization 0.5 ps/ km 59 59

56 Effects of Dispersion: Capacity Limitation Capacity limitation: maximum broadening</f a bit period T < B For Single - Md Mode Fiber, T LB < D Intra modal λ LD (neglecting polarization effects) Intra modal λ Example: Consider a DFB laser µm λ 0. nm D 7 ps/nm km LB<50 Gb/s km If L00 km, B Max.5 Gb/s 60 60

57 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 6 6

58 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 6 6

59 Summary Important parameters: NA: numerical aperture (angle of acceptance) V: normalized frequency parameter (number of modes) λ 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 0 Mb/s x km for step index and Gb/s x km for graded index Single-mode fiber Used for short/long distances Capacity limited by dispersion: typically 50 Gb/s x km 63 63