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1、Fiber Optics Lecture 7 Why Nonlinear Effects Important? Nonlinear: Power/intensity-dependent Several recent events: Small cross section of SM increasing power density In-line optical amplifiers increase in the absolute value of power Multiwavelength systems created new nonlinear effects: four-wave m
2、ixing & cross-phase modulation Two major classes: Nonlinear refractive effects: Dependence of n (dispersion) Dependence of attenuation: Polarization Molecules and their dipole moments Distortion of an electron cloud in response to an E-field Non-linear Polarization Nonlinear Refractive Effects In ma
3、terials, In optical fiber: A medium refractive index(pp.196): For a standard silica fiber: Linear n dispersion nonlinear effects 5.8109 Index of Refraction Index of Refraction vs Wavelength Refractive Index for various materials Wave slowing in a medium of higher Index Refractive index vs Frequency
4、for silica Nonlinear Propagation Coefficient The propagation constant Conclusions: The longer the fiber the more the light interacts w/ materials the greater the nonlinear effects power decreases nonlinearity diminish Leff, Aeff :Nonlinear propagation coefficient 2.35103(1/mW)10-6 Effective Length &
5、 effective area Typically, Similar, If multiple electric fields are applied, every possible cross term is generated. At sufficiently high values of E, quadratic or higher terms become important and nonlinear effects are induced in the fiber. Propagation in SM Fiber Understanding Fiber Optics-Hecht G
6、eometrical optics is not useful for SMF, must be handled by full E & M treatment Think of guiding as diffraction constrained by refraction Fields are evanescently damped in the cladding Single Mode Gaussian Approximation Fundamentals of Photonics - Saleh and Teich Fiber Optic Communiocation Systems
7、- Agrawal Gaussian Pulse Mode Field Diameter Fiber Optics Communication Technology- Mynbaev & Scheiner Mitigation If P is high in a fiber application, the nonlinear component of the index is minimized increasing Aeff. Fiber designed for this purpose “ LEAF ” fiber (Large Effective Area) Nonlinear Ef
8、fects Stimulated Raman scattering Stimulated Brillioun scattering Self-phase Modulation Cross-phase Modulation Four-wave Mixing Nonlinear scattering WDM byproducts Nonlinear scattering Signal photon scatters off oscillation that is present in the material, gains or loses frequency equivalent to that
9、 of the material oscillation At high powers, beating of signal frequency and scattered frequency generates frequency component at the difference that drives the material oscillations Stimulated Brillouin Scattering Sound waves represent alternating regions of compressed material and expanded materia
10、l Index of refraction increases with density of polarizable electrons and thus with compression Scattering is induced by index discontinuities SBS, contd Transfer of energy into acoustic wave results in backwards scattering in fiber Brillouin frequency shift: =, where n is the mode index and v is th
11、e speed of sound in the material For fiber, scattered light is 11 GHz (at 1300nm) lower in frequency than signal wavelength (speed of sound is 5.96 km/s) Stimulated Raman scattering Oscillations are Si-O bonds in the glass, frequency 3.3x1013 Hz Scattered photon can come off decreased by that amount
12、 (Stokes) or increased by that amount (anti-Stokes) Stokes shift scatters 1550 nm light up to 1870 nm light Raman shift in silica Spectrum shows major peaks at 1100, 800, and 450 cm-1 Those vibrated oscillations occur at 33, 24, and 13.5 THz Raman gain spectrum shows maximum at 12- 14, 18, 24, and 3
13、3 THz Phase Modulation Self-modulation: Cross-modulation: Effect of these phase changes is a frequency chirp (frequency changes during pulse), broadening pulse and reducing bit rate-length product Self Phase Modulation Pulse Spreading due to Self Phase Modulation Typically, A=0.2 dB/km, i.e., =0.004
14、6 1/km, and = n=2.3510-3 1/mW Then, input power should be 19.6mW Gaussian Pulse in a Kerr Medium Phase change of Gaussian pulse Instantaneous frequency shift Instantaneous Frequency chirp Solitons Working principle Problems arise Up-to-date 40Gbit/s over 70,000km N10Gbit/s WDM system Specific fiber
15、is about to become ready for mass fab.not now! Cross-phase Modulation (XPM) Only occurs in WDM systems When several optical pulses propagate within a fiber simultaneously, Hinder system performance throughchriping f & chromatic dispersion Could be reduced by keeping chromatic dispersion low Very ser
16、ious limitation coherent systems # of channels Compensating technique both linear & nonlinear dispersion Four-wave Mixing Taylor Series expansion of () Through the cubic term: where Importance of Taylor Series terms Group velocity Vg, dispersion D, and dispersion slope S Four-Wave Mixing Phase Matching Requirement Phase mismatch M needs to be small for FWM to occur significantly FWM in a WD
