Guided Propagation Along the Optical Fiber 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 the refracti ve index (n) of a material is : adimensionless number that describes how light propagates through that mediu m. It is defined as c/v https://www.youtube.com/watch?v=dwmf9f65wws https://www.youtube.com/watch?v=yfawfjcrdse&t=28s
Classification based on Refractive index 1. Step-index Optical Fiber 2. Graded-index Optical Fiber Step Index Fiber n 1 n2 n 1 >n 2 Core and Cladding are glass with appropriate optical properties while buffer is plastic for mechanical protection
Step Index Fiber Single Mode Step Index Fiber r Buffer tube: d = 1mm n n 1 n 2 Protective polymerinc coating Cladding: d = 125-150 m Core: d = 8-10 m The cross section of a typical single-mode fiber with a tight buffer tube. (d = diameter) 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Meridian Ray Representation n n n 2 n 2 2 1 2 1 2 n1 2 1 Total Internal Reflection m ax A B m ax n 2 n 0 n 1 Lost B < c > c Fiber axis Cladding Propagates A Core Maximum acceptance angle max is that which just gives total internal reflection at the core-cladding interface, i.e. when = max then = c. Rays with > max (e.g. ray B) become refracted and penetrate the cladding and ar eventually lost. 1999 S.O. Kasap, Optoelectronics (Prentice Hall)
Comparison of fiber structures Graded Index Fiber O 2 1 B B B' c/n a c/n b B' B' Ray 2 A A Ray 1 M B'' n c n b n a a c b 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)
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
Fiber Key Parameters Fiber Key Parameters
Major Issues in fiber-optic Effects of Dispersion and Attenuation
1. Attenuation https://www.youtube.com/watch?v=yzhhgdrw2gk Attenuation in fiber-optic: is the gradual loss in intensity of any kind of flux through a medium. Sinusoidal signal Emitter t f = Modulation frequency P i = Input light power 0 t Optical Input Fiber 0 Optical Output Photodetector P o = Output light power t Electrical signal (photocurrent) 1 0.707 1 khz 1 MHz 1 GHz f el Sinusoidal electrical signal P o / P i 0.1 0.05 1 khz 1 MHz 1 GHz 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 f f
Attenuation Vs Frequency Attenuation in Fiber Attenuation Coefficient 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)
Attenuation characteristics All Wave Fiber for DWDM Lowest attenuation occurs at 1550 nm for Silica
Bending Loss Field distribution Microbending Cladding Core c 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 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 Micro-bending losses
2. Dispersion https://www.youtube.com/watch?v=saeqnd4nyom Dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency. Media having this common property may be termed dispersive media. Sometimes the term chromatic dispersion is used for specificity. Dispersion for Digital Signals Fiber Information Digital signal Emitter t Input Photodetector Information Output Input Intensity Output Intensity ² Very short light pulses 0 T t 0 t ~2² 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)
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 Modal Dispersion High order mode Low order mode Intensity Light pulse Cladding Core Broadened light pulse Intensity Axial Spread, 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)
Polarization Mode Dispersion (PMD) Each polarization state has a different velocity PMD PM dispersion https://www.youtube.com/watch?v=dkchyuxxyxo
Material Dispersion Emitter Input Very short light pulse Cladding v g ( 1 ) Core v g ( 2 ) Output Intensity Intensity Intensity Spectrum, ² Spread, ² 1 o 2 0 t t All excitation sources are inherently non-monochromatic and emit within a spectrum, ², 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 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) Zero Dispersion Wavelength Dispersion coefficient (ps km -1 nm -1 ) 30 20 10 Dm Dm + Dw 0-10 -20 0 D w -30 1.1 1.2 1.3 1.4 1.5 1.6 ( m) Material dispersion coefficient (D m ) for the core material (taken as SiO 2 ), waveguide dispersion coefficient (D w ) (a = 4.2 m) and the total or chromatic dispersion coefficient D ch (= D m + D w ) as a function of free space wavelength,
Total Dispersion For Single Mode Fibers: For Multi Mode Fibers: Group Velocity Dispersion If PMD is negligible Dispersion & Attenuation Summary
Fiber Production, Installation, Maintains tools Left to group of students (25 minutes) next time. Who?