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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. http://soe.unn.ac.uk/ocr Prof. Z Ghassemlooy 1 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 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 the interference where the light intensity can be enhanced in some places and diminished in other places behind a screen with a slit or several slits. The wave theory is also able to account for the fact that the edges of a shadow are not quite sharp. G Ekspong, Stockholm This theory describes: Propagation, reflection, University, Sweden, 1999. refraction and attenuation Prof. Z Ghassemlooy 3 Wave Nature of Light - contd. James Clerk Maxwell (1850) His 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 1900-20 Max Planck, Neils Bohr and Albert Einstein Invoked the idea of light being emitted in tiny pulses of energy Prof. Z Ghassemlooy 4 Wave Nature of Light - contd. Planck (1900) - Developed a model that explained light as a quantization of energy. 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. Planck (1900) - Developed a model that explained light as a quantization of energy. 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 5 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: Wp = h*f Joules (J) where; h = Plank's constant = 6.626 x 10-34 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 10-19 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 6 Electromagnetic Spectrum Prof. Z Ghassemlooy 7 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 108 m/s ("speed of light") E E (r , )e j ( t z ) H H (r , )e j ( t z ) Speed of light in a vacuum c f - Propagation constant = /vp Prof. Z Ghassemlooy 8 The Wave Equation Solutions to Maxwell’s equations: phase fronts Plane wave: Ee jk r Spherical wave: Wave number in vacuum k e jkR E R 2 k n k0 k 0 r 0 0 r k0 0 / n n r Note: k = Prof. Z Ghassemlooy 9 One Dimensional EM Wave • For most purposes, a travelling light wave can be presented as a one-dimensional, scalar wave provided it has a direction of propagation. • Such a wave is usually described in terms of the electric field E. Wavelength A plane wave propagating in the direction of z is: Eo z E ( z, t ) Eo sin( t z ) Phase 2 vp The propagation constant Phase velocity v p c / n n = Propagation medium refractive index Prof. Z Ghassemlooy 10 Polarization Light is a transverse, electromagnetic wave, where the transverse nature of it can be demonstrated through polarization. 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. Horizontal Vertical Prof. Z Ghassemlooy Diognal 11 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 dn ng n d 1.49 Ref. index Where the fibre group index is: ng 1.46 n 1.44 500 Prof. Z Ghassemlooy (nm)1700 1900 12 Properties of Light Law of Reflection The angle of Incidence = The angle of reflection 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 13 Reflection and Refraction of Light Medium 1 1 1 2 n1 Boundary 1 n2 Incident ray 2 1 1 1 n1 Reflected ray Medium 2 n1 < n2 2 Refracted n2 ray n1 > n2 Using the Snell's law at the boundary we have: n1 sin 1 = n2 sin 2 or n1 cos 1 = n2 cos 2 1 = The angle of incident Prof. Z Ghassemlooy 14 Total Internal Reflection • As 1 increases (or 1 decreases) then there is no reflection c n1 • Beyond the critical angle, light ray becomes totally internally reflected When 1 = 90o (or c = 0o) Thus the critical angle n2 1 • The incident angle 1 = c = Critical Angle n1 sin 1 = n2 n1 > n2 n1 > n2 1<c n2 1 1> 1 n2 c sin n1 Prof. Z Ghassemlooy c n1 15 Ray Propagation in Fibre - Bound Rays > c, > max 5 2 c 3 2 a 2 1 4 Core n1 Air (no =1) Cladding n2 From Snell’s Law: n0 sin = n1 sin (90 - ) At high frequencies f , since a > light wavelength , lightt launched into the fibre core would propagate as plane TEM wave with vp = /1 = max when = c Thus, n0 sin max = n1 cos c At high frequencies f , since a < , light launched into the fibre will propagate within the cladding, thus unbounded and unguided plane TEM wave with vp = /2 Therefore, we have n2k0 = 2 < < 1 = n1k0 Prof. Z Ghassemlooy 16 Ray Propagation in Fibre - contd. n0 sin max = n1 (1 - sin2 c)0.5 Or Since 1 n2 c sin n1 n 2 n0 sin max n1 1 2 n1 Then n12 n22 0.5 0.5 n12 2 0.5 n2 Numerical Aperture ( NA) NA determines the light gathering capabilities of the fibre Prof. Z Ghassemlooy 17 Ray Propagation in Fibre - contd. Therefore n0 sin max = NA Fibre acceptance angle Note n1 n2 NA max sin 1 n0 Relative refractive index difference n1 Thus NA n1 (2) 0.5 Prof. Z Ghassemlooy 0.14< NA < 1 18 Modes in Fibre A fiber can support: – many modes (multi-mode fibre). – a single mode (single mode fibre). The number of modes (V) [also known as the normalised frequency] supported in a fiber is determined by the indices, operating wavelength and the diameter of the core, given as. a V NA or V< 2.405 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 19 Basic Fibre Properties Cylindrical Dielectric Core Cladding Buffer coating Waveguide Low loss Usually fused silica Core refractive index > cladding refractive index Operation is based on total internal reflection Prof. Z Ghassemlooy 20 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 21 Step-index Multi-mode Fibre Input pulse 120-400m 50-200 m Output pulse n1 =1.48-1.5 n2 = 1.46 dn=0.04,100 ns/km 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. • Cost effective Disadvantages: • Suffer from dispersion (i.e. low bandwidth (a few MHz) • High power loss Prof. Z Ghassemlooy 22 Graded-index Multi-mode Fibre 50-100 m Input pulse 120-140m n2 n1 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 23 Step-index Single-mode Fibre Input pulse 100-120m 8-12 m Output pulse n1 =1.48-1.5 n2 = 1.46 dn = 0.005, 5ps/km 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 24 Single Mode Fiber - Power Distribution Optical power Guided Evanescent Intensity profile of the fundamental mode Prof. Z Ghassemlooy 25 Fibre Characteristics • The most important characteristics that limit the transmission capabilities are: • Attenuation (loss) • Dispersion (pulse spreading) Prof. Z Ghassemlooy 26 Attenuation - Standard Fibre SM-fiber, InGaAsP DFB-laser, ~ 1990 Optical amplifiers InGaAsP FP-laser or LED Attenuation (dB/km) 10 MM-fibre, GaAslaser or LED 80nm 180 nm 5 2.0 Fourth Generation, 1996, 1.55 m WDM-systems 1.0 0.5 1300 nm 0.2 0.1 600 800 1200 1000 1400 Wavelength (nm) 1550 nm 1600 1800 c 14 Hz | 14 Hz | Bandwidth f = 1.142 x 10 + 2.2475 10 1300 nm 1550 nm 2 Prof. Z Ghassemlooy 27 Attenuation (Loss ) - contd. Fibre Pi L The output power Po Po (L)= Pi (0).e- pL Fibre attenuation coefficient (p = scattering + absorption + bending) 1 Po p ln L Pi Po 1 Or in dB/km, fibre attenuation log 4.343 p (km 1 ) L Pi Prof. Z Ghassemlooy 28 Fibre Attenuation - contd. • In a typical system, the total loss could bas 20-30 dB, before it needs amplification. So, at 0.2 dB/km, this corresponds to a distance of 100-150 km. Attenuation along the fibre link can be measured using Optical Time Domain Reflectometer Prof. Z Ghassemlooy 29 Fibre Dispersion • Data carried in an optical fibre consists of pulses of light energy consists 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 si(t) Many modes L so(t) Output pulse Cause of Dispersion: • Chromatic (Intramodal) Dispersion • Modal (Intermodal) Dispersion Prof. Z Ghassemlooy 30 Chromatic 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 31 Material Dispersion Refractive index of silica is frequency dependent. Thus different frequency (wavelength) components travel at different speed 2 d n RMS pulse broadening mat L c d2 Where material dispersion 175 coefficient: 100 d n Dm at c d2 ns / km 2nd window 2 ps / nm.km Dmat 0 Note: Negative sign, indicates that low wavelength components arrives before higher wavelength components. Prof. Z Ghassemlooy -100 0.8 1.0 1.2 1.4 1.6 1.7 32 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. 175 Waveguide dispersion 100 Dmat 0 -100 0.8 Total dispersion Material dispersion 1.0 1.2 1.4 1.6 1.7 Prof. Z Ghassemlooy 33 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 Cladding n2 Core n1 c 1 Prof. Z Ghassemlooy 34 Modal Dispersion - SIMMF The time taken for ray 1 to propagate a length of fibre L gives the minimum delay time: Ln1 t min c The time taken for the ray to propagate a length of fibre L gives the maximum delay time: L cos tmax c n1 Since sin c n2 cos n1 The delay difference Ts tmax tmin (n n ) Since relative refractive index 1 2 difference n 1 Thus Ln12 Ts cn2 Prof. Z Ghassemlooy 35 Modal Dispersion - SIMMF For 1, (n1n2 ) n2 and NA n1 (2) 0.5 L( NA) 2 Ts 2cn1 For a rectangular input pulse, the RMS pulse broadening due to modal dispersion at the output of the fibre is: Ln1 L( NA) 2 modal 3.5c 7n1C Total dispersion = chromatic dispersion + modal dispersion T [chrom2 modal2 ]1 / 2 Prof. Z Ghassemlooy 36 Modal Dispersion - GIMMF The delay difference Ln12 Ts 2c the RMS pulse broadening Ln12 m odalGI 34.6C Prof. Z Ghassemlooy 37 Dispersion - Consequences I- Frequency Limitation (Bandwidth) T 1 0 1 0 0 1 L = L1 1 0 1 0 0 1 B L • 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. L = L2 > L1 1 0 1 0 0 1 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 38 Bandwidth Limitations • Maximum channel bandwidth B: • For non-return-to-zero (NRZ) data format: B = BT /2 • For return-to-zero (RZ) data format: B = BT Where the maximum bit rate BT = 1/T, and T = bit duration. • For zero pulse overlap at the output of the fibre BT <= 1/2 where is the pulse width. For MMSF: BT (max) = 1/2Ts • For a Gaussian shape pulse:BT 0.2/rms where rms is the RMS pulse width. For MMSF: BT (max) =0.2/ modal or BT (max) =0.2/ T Total dispersion Prof. Z Ghassemlooy 39 Bandwidth Distance Product (BDP) The BDP is the bandwidth of a kilometer of fibre and is a constant for any particular type of fibre. Bopt * L = BT * 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 500 - 1500 MHz.km Graded Index 100 - 1000 MHZ.km Prof. Z Ghassemlooy 40 Bandwidth Distance Product Bit rate B (Gbps) 100 Source spectral width < 1 nm 10 1 Source spectral width = 1 nm 0.1 1 10 100 1000 10,000 Distance L (km) Dmat = 17 ps/km.nm Prof. Z Ghassemlooy 41 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 42 Controlling Dispersion 20 Dispersion shifted 10 0 Dispersion flattened Standard -10 -20 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Wavelength ( m) Prof. Z Ghassemlooy 43 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 44