Guided Propagation Along the Optical Fiber Xavier Fernando Ryerson Comm. Lab
The Nature of Light Quantum Theory Light consists of small particles (photons) Wave Theory Light travels as a transverse electromagnetic wave Ray Theory Light travels along a straight line and obeys laws of geometrical optics. Ray theory is valid when the objects are much larger than the wavelength (multimode fibers)
Different Theories We will first use ray theory to understand light propagation in multimode fibres Then use electromagnetic wave theory to understand propagation in single mode fibres Quantum theory is useful to learn photo detection and emission phenomena
Step Index Fiber n 1 n 2 n 1 >n 2 Core and Cladding are glass with appropriate optical properties Buffer is plastic for mechanical protection
The Optical Fiber Fiber optic cable functions as a light guide, guiding the light from one end to the other end. Categories based on propagation: Single Mode Fiber (SMF) Multimode Fiber (MMF) Categories based on refractive index profile Step Index Fiber (SIF) Graded Index Fiber (GIF)
Step Index Fiber y y Cladding Core φ r z Fiber axis n 2 n 1 n The step index optical fiber. The central region, the core, has greater refractive index than the outer region, the cladding. The fiber has cylindrical symmetry. We use the coordinates r, φ, z to represent any point in the fiber. Cladding is normally much thicker than shown. 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Single Mode Step Index Fiber r Buffer tube: d = 1mm n n 1 n 2 Protective polymerinc coating Cladding: d = 125-150 µm Core: d = 8-10 µm Only The cross one propagation section of a typical mode is single-mode allowed fiber a given with wavelength. a tight buffer This tube. is (d achieved = diameter) by very small core diameter (8-10 µm) SMF offers highest bit rate, most widely used in telecom 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Ray description of different fibers
Refraction and Reflection When Φ 2 = 90, Φ 1 = Φc is the Critical Angle Snell s Law: n 1 Sin Φ 1 = n 2 Sin Φ 2 Φc=Sin -1 (n 2 /n 1 )
Step Index Multimode Fiber = n 2 n 2 1 2 1 n 2 1 n 2 n 2 1
Step Index Multimode Fiber Guided light propagation can be explained by ray optics When the incident angle is smaller the acceptance angle, light will propagate via TIR Large number of modes possible Each mode travels at a different velocity Modal Dispersion Used in short links, mostly with LED sources
Graded Index Multimode Fiber Core refractive index gradually changes towards the cladding The light ray gradually bends and the TIR happens at different points The rays that travel longer distance also travel faster Offer less modal dispersion compared to Step Index MMF
Step and Graded Index Fibers n 2 O 2 1 3 n 1 n (a) Multimode step index fiber. Ray paths are different so that rays arrive at different times. O O' O'' 3 2 1 2 3 n 2 n 1 n (b) Graded index fiber. Ray paths are different but so are the velocities along the paths so that all the rays arrive at the same time. n 2 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Graded Index Fiber O 2 1 B θ B θ B' c/n a c/n b B' θ B' Ray 2 A θ A M Ray 1 B'' n c n b n a c b a O' We can visualize a graded index fiber by imagining a stratified medium with the layers of refractive indices n a > n b > n c... Consider two close rays 1 and 2 launched from O at the same time but with slightly different launching angles. Ray 1 just suffers total internal reflection. Ray 2 becomes refracted at B and reflected at B'. 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Total Internal Reflection (a) TIR (b) TIR n decreases step by step from one layer to next upper layer; very thin layers. Continuous decrease in n gives a ray path changing continuously. (a) A ray in thinly stratifed medium becomes refracted as it passes from one layer to the next upper layer with lower n and eventually its angle satisfies TIR (b) In a medium where n decreases continuously the path of the ray bends continuously. 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
1999 S.O. Kasap, Optoelectronics (Prentice Hall) Skew Rays Along the fiber 1 Meridio nal ray Fiber axis 3 1, 3 (a) A meridiona ray always crosses the fibe axis. 2 2 1 2 Fiber axis 3 Skew ray 4 5 5 4 1 2 3 (b) A skew ray does not have to cross the fiber axis. It zigzags around the fiber axis. Ray path along the fiber Ray path projected on to a plane normal to fiber axis Illustration of the difference between a meridional ray and a skew ray. Numbers represent reflections of the ray. Skew rays circulate around the core and increase the dispersion
Single Mode Fiber Only one electromagnetic mode is allowed to propagate No modal dispersion Most widely used in long haul high speed links For single mode condition, the V-Number (Normalized Frequency) < Cut-off V 2π a( NA) V = < λ V c
b 1 0.8 0.6 0.4 LP 01 LP 11 LP 21 LP 02 0.2 0 0 1 2 3 4 5 6 2.405 V Normalized propagation constant b vs. V-number for a step index fiber for various LP modes.
1.5 V[d 2 (Vb)/dV 2 ] 1 0.5 0 0 1 2 3 V - number [d 2 (Vb)/dV 2 ] vs. V-number for a step index fiber (after W.A. Gambling et al., The Radio and Electronics Engineer, 51, 313, 1981) 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Field Distribution in the SMF Field of evanescent wave (exponential decay) y n 2 Field of guided wave E(y) m = 0 E(y,z,t) = E(y)cos(ωt β 0 z) Light n 1 n 2 The electric field pattern of the lowest mode traveling wave along the guide. This mode has m = 0 and the lowest θ. It is often referred to as the glazing incidence ray. It has the highest phase velocity along the guide. 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Mode-field Diameter (2W 0 ) In a Single Mode Fiber, E( r) = E exp( r / 2 2 0 w0 ) At r = w o, E(W o )=E o /e Typically W o > a
Cladding Power Vs Normalized Frequency Modes V c = 2.4
Power in the cladding Lower order modes have higher power in the cladding larger MFD
1999 S.O. Kasap, Optoelectronics (Prentice Hall) Higher the Wavelength More the Evanescent Field y Cladding y λ 1 > λ c λ 2 > λ 1 v g1 Core v g2 > v g1 ω 1 < ω cut-off ω 2 < ω 1 E(y) Cladding The electric field of TE 0 mode extends more into the cladding as the wavelength increases. As more of the field is carried by the cladding, the group velocity increases.
Light Intensity (a) The electric field of the fundamental mode (b) The intensity in the fundamental mode LP 01 (c) The intensity in LP 11 (d) The intensity in LP 21 Core Cladding E E 01 r The electric field distribution of the fundamental mode in the transverse plane to the fiber axis z. The light intensity is greatest at the center of the fiber. Intensity patterns in LP 01, LP 11 and LP 21 modes. 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Fiber Key Parameters
Fiber Key Parameters
Effects of Dispersion and Attenuation
Dispersion for Digital Signals Fiber Information Digital signal Emitter t Input Photodetector Information Output Input Intensity Output Intensity ² τ 1/2 Very short light pulses 0 T t 0 t ~2² τ 1/2 An optical fiber link for transmitting digital information and the effect of dispersion in the fiber on the output pulses. 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Modal Dispersion High order mode Low order mode Light pulse Cladding Broadened light pulse Intensity Core Intensity Axial Spread, τ 0 t t Schematic illustration of light propagation in a slab dielectric waveguide. Light pulse entering the waveguide breaks up into various modes which then propagate at different group velocities down the guide. At the end of the guide, the modes combine to constitute the output light pulse which is broader than the input light pulse. 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Major Dispersions in Fiber Modal Dispersion: Different modes travel at different velocities, exist only in multimode fibers This was the major problem in first generation systems Modal dispersion was alleviated with single mode fiber Still the problem was not fully solved
Dispersion in SMF Material Dispersion: Due to the fact different wavelength travels at different velocities because refractive index n is a function of wavelength, exists in all fibers function of the source line width Waveguide Dispersion: Signal in the cladding travels with a different velocity than the signal in the core, significant in single mode conditions
Emitter Input Very short light pulse v g (λ 1 ) v g (λ 2 ) Cladding Core Output Intensity Intensity Intensity Spectrum, ² λ Spread, ² τ λ λ λ 1 o 2 λ 0 t τ t All excitation sources are inherently non-monochromatic and emit within a spectrum, ² 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. 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Group Velocity Dispersion
Modifying GVD GVD = Material disp. + Waveguide dispersion Material dispersion depends on the material properties and difficult to alter Waveguide dispersion can be altered by changing the fiber refractive index profile 1300 nm optimized Dispersion Shifting (to 1550 nm) Dispersion Flattening (from 1300 to 1550 nm) GVD is also called Chromatic Dispersion
GVD = CHD = MD + WGD Dispersion coefficient (ps km -1 nm -1 ) 30 20 10 Dm Dm + Dw 0-10 -20 λ 0 D w Zero Dispersion Wavelength -30 1.1 1.2 1.3 1.4 1.5 1.6 λ (µm) Material dispersion coefficient (D m ) for the core material (taken as SiO 2 ), waveguide dispersion coefficient (D w ) (a = 4.2 µm) and the total or chromatic dispersion coefficient D ch (= D m + D w ) as a function of free space wavelength, λ.
Modifying the WGD to shift the zero dispersion wavelength Dispersion Shifted Fiber Dispersion coefficient (ps km -1 nm -1 ) 20 D m 10 SiO 2-13.5%GeO 2 0 10 D w a (µm) 4.0 3.5 3.0 2.5 20 1.2 1.3 1.4 1.5 1.6 λ (µm) Material and waveguide dispersion coefficients in an optical fiber with a core SiO 2-13.5%GeO 2 for a = 2.5 to 4 µm.
Modifying the WGD to flatten GVD Dispersion Flattened Fiber Dispersion coefficient (ps km -1 nm -1 ) 30 n 20 10 D m r 0-10 λ 1 λ 2 D ch = D m + D w -20-30 D w 1.1 1.2 1.3 1.4 1.5 1.6 1.7 λ (µm) Thin layer of cladding with a depressed index 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 2.
Different Index Profiles 1300 nm optimized Dispersion Shifted
Different Index Profiles Dispersion Flattened Large area dispersion shifted Large area dispersion flattened
Different waveguide dispersion profiles
Dispersion Shifting/Flattening
Polarization Mode Dispersion Due to differently polarized light traveling at slightly different velocity Usually small Significant if all other dispersion mechanisms are small
Polarizations of fundamental mode Two polarization states exist in the fundamental mode in a single mode fiber
Polarization Mode Dispersion (PMD) Each polarization state has a different velocity PMD
Total Dispersion For Multi Mode Fibers: For Single Mode Fibers: Group Velocity Dispersion If PMD is negligible
Mode-field diameter Vs wavelength Note dispersion modified fibers have low MFD (modified WGD)
Disp. & Attenuation Summary
Electrical signal (photocurrent) Fiber 1 0.707 Sinusoidal signal Emitter t f = Modulation frequency Optical Input Optical Output Photodetector 1 khz 1 MHz 1 GHz f el Sinusoidal electrical signal f P i = Input light power 0 t P o = Output light power 0 t P o / P i 0.1 0.05 1 khz 1 MHz 1 GHz f f op An optical fiber link for transmitting analog signals and the effect of dispersion in the fiber on the bandwidth, f op. 1999 S.O. Kasap, Optoelectronics (Prentice Hall) Fiber Optic Link is a Low Pass Filter for Analog Signals
Attenuation Vs Frequency
Attenuation in Fiber Attenuation Coefficient α = P(0)dB P( z)db z db/km Silica has lowest attenuation at 1550 nm Water molecules resonate and give high attenuation around 1400 nm in standard fibers Attenuation happens because: Absorption (extrinsic and intrinsic) Scattering losses (Rayleigh, Raman and Brillouin ) Bending losses (macro and micro bending)
All Wave Fiber for DWDM Lowest attenuation occurs at 1550 nm for Silica
Attenuation characteristics
Bending Loss Field distribution θ θ Cladding Core θ θ > θ c θ Microbending θ < θ Escaping wave R Sharp bends change the local waveguide geometry that can lead to waves escaping. The zigzagging ray suddenly finds itself with an incidence angle θ that gives rise to either a transmitted wave, or to a greater cladding penetration; the field reaches the outside medium and some light energy is lost.
Bending-induced attenuation
Bending effects on loss Vs MFD
Micro-bending losses
1999 S.O. Kasap, Optoelectronics (Prentice Hall) Fiber Production Preform feed Thickness monitoring gauge Furnace 2000 C Polymer coater Ultraviolet light or furnace for curing Take-up drum Capstan Schematic illustration of a fiber drawing tower.