Optical Fibre Communication Systems

Transcription

1 Optical Fibre Communication Systems Lecture 2: Nature of Light and Light Propagation Professor Z Ghassemlooy Northumbria Communications Laboratory Faculty of Engineering and Environment The University of Northumbria U.K. Prof. Z Ghassemlooy 1

2 Contents Wave Nature of Light Particle Nature of Light Electromagnetic Wave Reflection, Refraction, and Total Internal Reflection Ray Properties in Fibre Types of Fibre Fibre Characteristics Attenuation Dispersion Bandwidth Distance Product Summary Prof. Z Ghassemlooy 2

3 Wave Nature of Light Newton (1680) believed in the particle theory of light. In reflection and refraction, light behaved as a particle. He explained the straight-line casting of sharp shadows of objects placed in a light beam. But he could not explain the textures of shadows Young (1800) Showed that light interfered with itself. Wave theory: Explains interference, diffraction, and dispersion. The wave theory is also able to account for the fact that the edges of a shadow are not quite sharp. This theory describes: Propagation, reflection, refraction and attenuation Interference Dispersion Diffraction G Ekspong, Stockholm University, Sweden, Prof. Z Ghassemlooy 3

4 Wave Nature of Light - contd. James Clerk Maxwell (1850) - Mathematical theory of electromagnetism led to the view that light is of electromagnetic nature, propagating as a wave from the source to the receiver. Heinrich Hertz (1887) - Discovered experimentally the existence of electromagnetic waves at radio-frequencies. Wave theory does not describe the absorption of light by a photosensitive materials He discovered the photoelectric effect. So what is it? Prof. Z Ghassemlooy 4

5 Wave Nature of Light - contd. Light (electromagnetic wave) shining ona metal surface results in its energy being transferred to the electrons on the surface of the metal and some electron will escape. The released electron are called photo-electron. E photo-electron is related to the f incident light but not its intensity. So light is energetic enough to shift electron(s) or not. The work function The amount of E need by eth EM wave to free an electron from a meta surface (i.e., a E threshold ) Max Planck, Neils Bohr and Albert Einstein Invoked the idea of light being emitted in tiny pulses of energy Prof. Z Ghassemlooy 5

6 Wave Nature of Light - contd. Classical Planck (1900) - Developed a model that explained light as a quantization of energy [Got a Nobel Prize]. Considered the Block Body cavity - E = nhf n = 0, 1, 2, 3.., h = Plancks constant x JS [or x evs], f = frequency of one of the standing wave within a black body. - The energy spectrum of the standing wave within the black body cavity is not continuous as in the classical theory, but take specific values: Quantum E.g., - A standing wave within a black body cavity has a frequency f = 7.25 x Hz (Blue-violet). The energy is: E = n(4.136 x evs)(7.25 x Hz) = n(3 ev), Energy So for n = 1, 2, 3, 4,.. we have E = 3, 6, 9, 12,. But not 1, 2, 4, 5, 7, 8 and so on. Interesting! This contradicted the continuous wave theory of light, where wave DO NOT have distinct constituent! Prof. Z Ghassemlooy 6

7 Wave Nature of Light - contd. Einstein (1905) Used Plank s idea to showed that in the photoelectric effect (light causing electrons to be emitted from a metal surface) light must act as a particle. He came up with this K max = hf - Max. kenetic Energy of an electron Work function Therefore, light must be regarded as having a dual nature; in some cases light acts as a wave in others it acts like a particle. Prof. Z Ghassemlooy 7

8 Particle Nature of Light Light behaviour can be explained in terms of the amount of energy imparted in an interaction with some other medium. In this case, a beam of light is composed of a stream of small lumps or QUANTA of energy, known as PHOTONS. Each photon carries with it a precisely defined amount of energy defined as: W p = h*f Joules (J) where; h = Plank's constant = x J.s, f = Frequency Hz The convenient unit of energy is electron volt (ev), which is the kinetic energy acquired by an electron when accelerated to 1 ev = 1.6 x J. Even although a photon can be thought of as a particle of energy it still has a fundamental wavelength, which is equivalent to that of the propagating wave as described by the wave model. This model of light is useful when the light source contains only a few photons. Prof. Z Ghassemlooy 8

9 Electromagnetic Spectrum Prof. Z Ghassemlooy 9

10 Electromagnetic Radiation Carries energy through space (includes visible light, dental x-rays, radio waves, heat radiation from a fireplace) The wave is composed of a combination of mutually perpendicular electric and magnetic fields the direction of propagation of the wave is at right angles to both field directions, this is known as an ELECTROMAGNETIC WAVE EM wave move through a vacuum at 3.0 x 10 8 m/s ("speed of light") E = v p H = H [c/n] Speed of light in a vacuum c f o - Propagation constant = /v p Prof. Z Ghassemlooy 10

11 The Wave Equation Solutions to Maxwell s equations: phase fronts Plane wave: E e jkr Spherical wave: Wave number in vacuum E e jkr R k 2 Note: k = k nk / n 0 0 k n 0 r 00 r k0 r Prof. Z Ghassemlooy 11

12 Polarization Demonstrates the transverse nature of EM wave. Unpolarized light source: The electric field is vibrating in many directions; all perpendicular to the direction of propagation. Polarized light source: The vibration of the electric field is mostly in one direction. Any direction is possible as long as it's perpendicular to the propagation. Types of polarization - Depending on existence and changes of different electric fields Linear Horizontal (E field changing in parallel with respect to earth s surface) Vertical (E field going up/down with respect to earth s surface) Dual polarized Circular (Ex and Ey) Similar to satellite communications TX and RX must agree on direction of rotation Elliptical Linear polarization is used in WiFi communications Horizontal Diognal Vertical Prof. Z Ghassemlooy 12

13 One Dimensional EM Wave Incident wave E y E r Transmitted wave Reflected wave 0 i t n 1 n 2 z Note that, the phases of three waves, which are independent of z, t, must be equal: t n 1 < n 2 E t At the boundary point i.e., z = 0, we have: Or Prof. Z Ghassemlooy 13

14 Properties of Light Law of Reflection External reflection: n 1 < n 2 External reflection: n 1 > n 2 Law of Refraction - Light beam is bent towards the normal when passing into a medium of higher refractive index. Light beam is bent away from the normal when passing into a medium of lower refractive index. Index of Refraction n = Speed of light in a vacuum / Speed of light in a medium Inverse square law Light intensity diminishes with square of distance from source. Prof. Z Ghassemlooy 14

15 Law of Reflection Considering at time t = 0 within the boundary plane, we have With the reflected and refracted waves being in the plane of incident, and if Then we have Note that, both waves are travelling in the same medium. Therefore have identical wavelength, so = r. Thus i = r Incident angle = Reflection angle Prof. Z Ghassemlooy 15

16 Law of Refraction Considering at time t = 0 within the boundary plane, we have With the reflected and refracted waves being in the plane of incident, and if Then we have So we have Prof. Z Ghassemlooy 16

17 One Dimensional EM Wave Boundary Conditions It applies to the instantaneous values of the fields at the boundary. Note that E = v p H = H(c/n) In each medium, we can write the following equations, assuming that i = r TE: TM: Prof. Z Ghassemlooy 17

18 Reflectance and Transmission The reflection and transmission coefficients: and Reflectance Is the fraction of the power P in the incident wave that is reflected Transmittance Is the fraction of the power P in the incident wave that is transmitted Prof. Z Ghassemlooy 18

19 Phase Changes External Reflection Note that in certain cases we have I.e., a phase change of TE: Phase changes takes place for any angel of incidence TM: Phase change occurs for i > B, where B is the Brewster angle Prof. Z Ghassemlooy 19

20 Phase Changes Internal Reflection For 0 < i < c TE: No phase change TM: Phase change of for i < B For i > c TE: The phase change TM: The phase change Prof. Z Ghassemlooy 20

21 Ref. index Group Velocity A pure single frequency EM wave propagate through a wave guide at a Phase velocity v p c / n However, non-monochromatic waves travelling together will have a velocity known as Group Velocity: v g c / ng Where the fibre group index is: n g dn n d n g n 500 (nm) Prof. Z Ghassemlooy 21

22 Reflection and Refraction of Light Medium 1 Boundary 1 1 n Refracted ray n 2 2 n 1 < n 2 n 2 Medium 2 Incident ray n 1 Using the Snell's law at the boundary we have: n 1 sin 1 = n 2 sin 2 or n 1 cos 1 = n 2 cos 2 1 = The angle of incident n 1 > n 2 Reflected ray Prof. Z Ghassemlooy 22

23 Total Internal Reflection As 1 increases (or 1 decreases) then there is no reflection n 1 > n 2 n 2 The incident angle 1 = c = Critical Angle 1 c n 1 Beyond the critical angle, light ray becomes totally internally reflected n 1 > n 2 n 2 When 1 = 90 o (or c = 0 o ) 1 < c 1 n 1 sin 1 = n 2 Thus the critical angle c sin 1 n n > c n 1 Prof. Z Ghassemlooy 23

24 Ray Propagation in Fibre - Bound Rays > c, > max 5 2 c a 2 Core n 1 Air (n o =1) Cladding n 2 From Snell s Law: n 0 sin = n 1 sin (90 - ) = max when = c Thus, n 0 sin max = n 1 cos c At high frequencies f, since a > light wavelength, lightt launched into the fibre core would propagate as plane TEM wave with v p = / 1 At high frequencies f, since a <, light launched into the fibre will propagate within the cladding, thus unbounded and unguided plane TEM wave with v p = / 2 Therefore, we have n 2 k 0 = 2 < < 1 = n 1 k 0 Prof. Z Ghassemlooy 24

25 Ray Propagation in Fibre - contd. Or n 0 sin max = n 1 (1 - sin 2 c ) 0.5 Since c sin 1 n n 2 1 Then n 0 sin max n1 1 n n n n n n Numerical Aperture ( ) 1 2 NA NA determines the light gathering capabilities of the fibre Prof. Z Ghassemlooy 25

26 Ray Propagation in Fibre - contd. Therefore n 0 sin max = NA Fibre acceptance angle max sin 1 NA n0 Note n 1 n n 1 2 Relative refractive index difference Thus 0.5 NA n1 ( 2) 0.14< NA < 1 Prof. Z Ghassemlooy 26

27 Modes in Fibre A fiber can support: many modes (multi-mode fibre). a single mode (single mode fibre). For the mode to propagate we must have Where m is an integer The total phase change Or For each value of m there will a corresponding value of i, namely m, that satisfies this equation. The dependence of at reflection on is such that we cannot obtain an explicit expression for in terms of m. So the equation must be solved either numerically or graphically. Prof. Z Ghassemlooy 27

28 Modes in Fibre Let s rewrite the equation as: The intersection of the two curve of and defines the values of for which the modes propagates along the waveguide. Note that, we are only interested in < c. Prof. Z Ghassemlooy 28

29 Modes in Fibre Prof. Z Ghassemlooy 29

30 Modes in Fibre Or Prof. Z Ghassemlooy 30

31 Modes in Fibre V Parameter - the number of modes [also known as the normalised frequency] supported in a fiber, which is determined by the indices, operating wavelength and the diameter of the core, given as. or V a NA 0 Note, a mode remains guided provided the following is satisfied n 2 k 0 = 2 < < 1 = n 1 k 0 Prof. Z Ghassemlooy 31

32 Modes in Fibre The number of TE or TM modes propagating is given by: For V < /2, then N m = 1, i.e., only one mode (m = 0, the lowest order) will propagate. In practice there will be two modes of TE 0 and TM 0. V < corresponds to a single mode fiber. By reducing the radius of the fiber, V goes down, and it becomes impossible to reach a point when only a single mode can be supported. Prof. Z Ghassemlooy 32

33 Modes in Fibre Problem: Consider a symmetric planar dielectric waveguide of 100 um thick with core and cladding refractive indices of 1.54 and 1.5, respectively. Determine the number of possible modes at a operating wavelength of 1300 nm. Solution: Prof. Z Ghassemlooy 33

34 Basic Fibre Properties Cylindrical Dielectric Waveguide Low loss Usually fused silica Core Cladding Buffer coating Core refractive index > cladding refractive index Operation is based on total internal reflection Prof. Z Ghassemlooy 34

35 Types of Fibre There are two main fibre types: (1) Step index: Multi-mode Single mode (2) Graded index multi-mode Total number of guided modes M for multi-mode fibres: Multi-mode SI M 0. 5V 2 Multi-mode GI M 0. 25V 2 Prof. Z Ghassemlooy 35

36 Step-index Multi-mode Fibre Input pulse m Output pulse m NA: n 1 = n 2 = 1.46 Advantages: dn=0.04,100 ns/km Allows the use of non-coherent optical light source, e.g. LED's Facilitates connecting together similar fibres Imposes lower tolerance requirements on fibre connectors. Cost effective Disadvantages: Suffer from dispersion (i.e. low bandwidth (a few MHz) High power loss Prof. Z Ghassemlooy 36

37 Graded-index Multi-mode Fibre Input pulse m m n 2 n 1 dn = 0.04,1ns/km Output pulse Advantages: Allows the use of non-coherent optical light source, e.g. LED's Facilitates connecting together similar fibres Imposes lower tolerance requirements on fibre connectors. Reduced dispersion compared with STMMF Disadvantages: Lower bandwidth compared with STSMF High power loss compared with the STSMF Prof. Z Ghassemlooy 37

38 Step-index Single-mode Fibre Input pulse m 8-12 m NA: 0.14 n 1 = n 2 = 1.46 dn = 0.005, 5ps/km Output pulse Advantages: Only one mode is allowed due to diffraction/interference effects. Allows the use high power laser source Facilitates fusion splicing similar fibres Low dispersion, therefore high bandwidth (a few GHz). Low loss (0.1 db/km) Disadvantages: Cost Prof. Z Ghassemlooy 38

39 Single Mode Fiber - Power Distribution Optical power Guided Evanescent Intensity profile of the fundamental mode Prof. Z Ghassemlooy 39

40 Fibre Characteristics The most important characteristics that limit the transmission capabilities are: Attenuation (loss) Dispersion (pulse spreading) Prof. Z Ghassemlooy 40

41 Attenuation (db/km) Attenuation - Standard Fibre 10 5 InGaAsP FP-laser or LED MM-fibre, GaAslaser or LED 80nm SM-fiber, InGaAsP DFB-laser, ~ 1990 Optical amplifiers 180 nm Fourth Generation, 1996, 1.55 m WDM-systems Bandwidth nm 1550 nm Wavelength (nm) c f 2 = x Hz 1300 nm Hz 1550 nm Prof. Z Ghassemlooy 41

42 Attenuation (Loss ) - contd. P i Fibre L P o The output power P o (L)= P i (0).e - pl Fibre attenuation coefficient ( p = scattering + absorption + bending ) p 1 L ln P P o i Or in db/km, fibre attenuation 1 P log o (km 1 p ) L Pi Prof. Z Ghassemlooy 42

43 Fibre Attenuation - contd. In a typical system, the total loss could bas db, before it needs amplification. So, at 0.2 db/km, this corresponds to a distance of km. Stephen Schultz Attenuation along the fibre link can be measured using Optical Time Domain Reflectometer Prof. Z Ghassemlooy 43

44 Fibre Attenuation - contd. Bending loss Radiation loss at bends in the optical fiber Insignificant unless R<1mm Larger radius of curvature becomes more significant if there are accumulated bending losses over a long distance Coupling and splicing loss Misalignment of core centers Tilt Air gaps End face reflections Mode mismatches Prof. Z Ghassemlooy 44

45 Fibre Dispersion Digital data carried composed of a large number of frequencies travelling at a given rate. There is a limit to the highest data rate (frequency) that can be sent down a fibre and be expected to emerge intact at the output. This is because of a phenomenon known as Dispersion (pulse spreading), which limits the "Bandwidth of the fibre. T s i (t) Many modes Cause of Dispersion: Chromatic (Intramodal) Dispersion Modal (Intermodal) Dispersion L s o (t) Output pulse =L/v g Prof. Z Ghassemlooy 45

46 Chromatic (Intramodal) Dispersion It is a result of group velocity being a function of wavelength. In any given mode different spectral components of a pulse traveling through the fibre at different speed. It depends on the light source spectral characteristics. Laser LED (many modes) = 1-2 nm = R.M.S Spectral width = 40 nm wavelength May occur in all fibre, but is the dominant in single mode fibre Main causes: Material dispersion - different wavelengths => different speeds Waveguide dispersion: different wavelengths => different angles Prof. Z Ghassemlooy 46

47 Material Dispersion Prof. Z Ghassemlooy 47

48 Material Dispersion So we can re-write the group velocity as Then we have Due to material dispersion The group delay over a transmission span of L is: Prof. Z Ghassemlooy 48

49 Material Dispersion If the wavelength spread is 0, the we have RMS pulse broadening 2 0 d n mat L 0 ns / km 2 c d 0 Where material dispersion coefficient: 175 D mat 2 0 d n c d 2 0 ps / nm. km D mat nd window Note: Negative sign, indicates that low wavelength components arrives before higher wavelength components Prof. Z Ghassemlooy 49

50 Waveguide Dispersion This results from variation of the group velocity with wavelength for a particular mode. Depends on the size of the fibre. This can usually be ignored in multimode fibres, since it is very small compared with material dispersion. However it is significant in monomode fibres Waveguide dispersion D mat Total dispersion Material dispersion Prof. Z Ghassemlooy 50

51 Chromatic (Intramodal) Dispersion Prof. Z Ghassemlooy 51

52 Modal (Intermodal) Dispersion Lower order modes travel travelling almost parallel to the centre line of the fibre cover the shortest distance, thus reaching the end of fibre sooner. The higher order modes (more zig-zag rays) take a longer route as they pass along the fibre and so reach the end of the fibre later. Mainly in multimode fibres 2 1 c Cladding n 2 Core n 1 Prof. Z Ghassemlooy 52

53 Modal Dispersion - SIMMF The time taken for ray 1 to propagate a length of fibre L gives the minimum delay time: Ln1 tmin c The time taken for the ray to propagate a length L cos tmax of fibre L gives the maximum delay time: c n1 Since n2 sin c cos n Since relative refractive index difference 1 The delay difference ( n n n 1 2) 1 T s t max t min Thus T s Ln cn Prof. Z Ghassemlooy 53

54 Modal Dispersion - SIMMF For 1, ( n n n and NA n1 ( 2) 1 ) 2 L( NA) T s 2cn For a rectangular input pulse, the RMS pulse broadening due to modal dispersion at the output of the fibre is: modal Ln1 3.5c Total dispersion = chromatic dispersion + modal dispersion 1 2 L( NA) 7n C 1 2 T 2 2 [ chrom modal ] 1/ 2 Prof. Z Ghassemlooy 54

55 Modal Dispersion - GIMMF The delay difference Ln T s 1 2c 2 The RMS pulse broadening modalgi 2 Ln C Prof. Z Ghassemlooy 55

56 Dispersion - Consequences I- Frequency Limitation (Bandwidth) T L = L B L L = L 2 > L 1 Maximum frequency limitation of signal, which can be sent along a fibre Intersymbol interference (ISI), which is unacceptable in digital systems which depend on the precise sequence of pulses Intersymbol interference II- Distance: A given length of fibre, has a maximum frequency (bandwidth) which can be sent along it. To increase the bandwidth for the same type of fibre one needs to decrease the length of the fibre. Prof. Z Ghassemlooy 56

57 Bandwidth Limitations Maximum channel bandwidth B: For non-return-to-zero (NRZ) data format: B = B T /2 For return-to-zero (RZ) data format: B = B T Where the maximum bit rate B T = 1/T, and T = bit duration. For zero pulse overlap at the output of the fibre B T <= 1/2 where is the pulse width. For MMSF: B T (max) = 1/2T s For a Gaussian shape pulse:b T 0.2/ rms where rms is the RMS pulse width. For MMSF: B T (max) =0.2/ modal or B T (max) =0.2/ T Total dispersion Prof. Z Ghassemlooy 57

58 Bandwidth Distance Product (BDP) The BDP is the bandwidth of a kilometer of fibre and is a constant for any particular type of fibre. B opt * L = B T * L (MHzkm) For example, A multimode fibre has a BDP of 20 MHz.km, then:- - 1 km of the fibre would have a bandwidth of 20 MHz - 2 km of the fibre would have a bandwidth of 10 MHz Typical B.D.P. for different types of fibres are: Multimode 6-25 MHz.km Single Mode MHz.km Graded Index MHZ.km Prof. Z Ghassemlooy 58

59 Bit rate B (Gbps) Bandwidth Distance Product 100 Source spectral width < 1 nm Source spectral width = 1 nm ,000 Distance L (km) D mat = 17 ps/km.nm Prof. Z Ghassemlooy 59

60 Controlling Dispersion For single mode fibre: Wavelength 1300: - Dispersion is very small - Loss is high compared to 1550 nm wavelength Wavelength 1550: - Dispersion is high compared with 1300 nm - Loss is low Limitation due to dispersion can be removed by moveing zero-diepersion point from 1300 nm to 1550 nm. How? By controlling the waveguide dispersion. Fibre with this property are called Dispersion-Shifted Fibres Prof. Z Ghassemlooy 60

61 Controlling Dispersion Dispersion-Shifted Fibre Standard Dispersion shifted Dispersion flattened Basic idea Change the refractive index profile in cladding and core Thus introducing negative dispersion Wavelength m) ( Prof. Z Ghassemlooy 61

62 References Prof. Z Ghassemlooy 62

63 Summary Nature of light : Particle and wave Light is part of EM spectrum Phase and group velocities Reflection, refraction and total internal reflection etc. Types of fibre Attenuation and dispersion Prof. Z Ghassemlooy 63