Guided Propagation Along the Optical Fiber Xavier Fernando Ryerson University
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)
Refraction and reflection Snell s Law: n 1 Sin Φ 1 = n 2 Sin Φ 2 Critical Angle: Sin Φc=n 2 /n 1
Step Index Fiber n 1 n 2 n 1 >n 2 Core and Cladding are glass with appropriate optical properties while buffer is plastic for mechanical protection
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 refractiv index than the outer region, the cladding. The fiber has cylindrical symmetry 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)
Meridian Ray Representation = n 2 n 2 1 2 1 n 2 1 n 2 n 2 1
Total Internal Reflection α < α max A B α > α max n 2 n 0 n 1 Lost B θ < θ c θ > θ c Fiber axis Cladding Propagates A Core Maximum acceptance angle α max is that which just gives total internal reflection at the core-cladding interface, i.e. when α = α max then θ = θ c. Rays with α > α max (e.g. ray B) become refracted and penetrate the cladding and ar eventually lost. 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 inde fiber by imagining a stratified medium with the layers of refr indices n a > n b > n c... Consider tw close rays 1 and 2 launched Ofro at the same time but with sligh different launching angles. Ray just suffers total internal reflec Ray 2 becomes refracted B and at reflected at B'. 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 The cross section of a typical single-mode fiber with a tight buffer tube. (d = diameter) 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Fiber Key Parameters
Comparison of fiber structures
Fiber Key Parameters
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)
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)
Skew Rays Along the fiber 1 Meridional 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. 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Skew rays Skew rays circulate around the core and increase the dispersion
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
Major Dispersions in Fiber Modal Dispersion: Different modes travel at different velocities, exist only in multimodal conditions Waveguide Dispersion: Signal in the cladding travel with a different velocity than the signal in the core, significant in single mode conditions Material Dispersion: Refractive index n is a function of wavelength, exists in all fibers, function of the source line width
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)
Field Distribution in the Fiber 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)
Higher order modes Larger MFD y n 2 Cladding E(y) m = 0 m = 1 m = 2 Core 2a n 1 n 2 Cladding The electric field patterns of the first three modes m = ( 0, 1, 2) traveling wave along the guide. Notice different extents of fie penetration into the cladding. 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Mode-field Diameter (2W 0 ) In a Single Mode Fiber, E( r) = 2 E0 exp( r / w 2 0 ) At r = w o, E(W o )=E o /e Typically W o > a
Power in the cladding Lower order modes have higher power in the cladding.
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. 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Mode-field diameter Vs wavelength
(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 mod 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)
Cladding Power Vs Normalized Frequency
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 [d2(vb)/dv2] 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)
Input Emitter 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) Material Dispersion
Material Dispersion Zero Dispersion Wavelength
Modifying Chromatic Dispersion Chromatic Dispersion = Material dispersion + 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)
Different Index Profiles 1300 nm optimized Dispersion Shifted
Different Index Profiles Dispersion Flattened Large area dispersion shifted Large area dispersion flattened
Different dispersion profiles
Dispersion Shifting/Flattening
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.
Zero Dispersion Wavelength Dispersion coefficient (ps km -1 nm -1 ) 30 20 10 Dm Dm + D w 0-10 -20 λ 0 D w -30 1.1 1.2 1.3 1.4 1.5 1.6 λ (µ m) Material dispersion coefficient (D m ) for the core material (taken as SiO 2 ), waveguide dispersion coefficient (D w ) (a = 4.2 µ m) and the total or chromatic dispersion coefficient D ch (= D m + D w ) as a function of free space wavelength, λ.
Dispersion coefficient (ps km -1 nm -1 ) 20 D m 10 SiO 2-13.5%GeO 2 10 0 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.
Total Dispersion For Single Mode Fibers: For Multi Mode Fibers: Group Velocity Dispersion If PMD is negligible
Dispersion & 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.
Power loss in a curved fiber Power in the evanescent field evaporates first
Bending-induced attenuation
Bending effects on loss Vs MFD
Micro-bending losses
Fiber Preform feed Production 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. 1999 S.O. Kasap, Optoelectronics (Prentice Hall)