Non Linear Effects in Fiber
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Transcript of Non Linear Effects in Fiber
Polarization• In molecules, P=μ+αE+βE2+γE3+…• In materials, P=X(o)+X(1)E+X(2)E2+X(3)E3+…
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.
Polarization
Molecules and their dipole moments
Distortion of an electron cloud in response to an E-field
Nonlinear Effects
• Stimulated Raman scattering• Stimulated Brillouin scattering• Four-wave Mixing• Self-phase Modulation• Cross-phase Modulation
Imaginary part of index: absorption
For a sample of absorbance A and thickness d, the imaginary part of the refractive index is equal to
dA
4
10lnmax
Index of Refraction vs Wavelength
Refractive index vs Frequency for silica
Refractive Index for various materials
Wave slowing in a medium of higher Index
Nonlinear index of refraction
Real part of index is best described as a power series
n=n1+n2(P/Aeff)
Term in parentheses is the intensity. For silica fiber, n22.6x10-11 μm2/mW
Interaction Length
where α (in cm-1) is the loss coefficient of the fiber. 0.1 dB/km=2.3x10-7 cm-1.
L
effeL
1
Propagation in Single Mode Fiber
Understanding Fiber Optics-Hecht
Geometrical optics is not useful for single mode fiber, 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 - Agrawal
Gaussian Pulse Mode Field Diameter
Fiber Optics Communication Technology-Mynbaev & Scheiner
w0/a=0.65+1.619V-3/2+2.879V-6 forV between 1.2 and 2.4. Otherwise,use w0/a=(ln V)-1/2
Mitigation
If P is high in a fiber application, the nonlinear component of the index is minimized by increasing the effective area of the fiber. Fiber designed for this purpose is called LEAF fiber (Large Effective Area).
Phase modulation
• Self-modulation: φNL= γPLeff
• Cross-modulation: φNL= 2γPotherLeff
Effect of these phase changes is a frequency chirp (frequency changes during pulse), broadening pulse and reducing bit rate-length product
Gaussian Pulse in a Kerr Medium
Phase change of gaussian pulse
Instantaneous frequency shift
Instantaneous Frequency chirp
Nonlinear scattering• Signal photon scatters off oscillation that is
present in the material, gains or loses frequency equivalent to that 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 material
• Index of refraction increases with density of polarizable electrons and thus with compression
• Scattering is induced by index discontinuities
SBS, continued
• Transfer of energy into acoustic wave results in backwards scattering in fiber
• Brillouin frequency shift equal to 2nv/λ, where n is the mode index and v is the speed of sound in the material
• For fiber, scattered light is 11 GHz 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 (Stokes) or increased by that amount (anti-Stokes)
• Stokes shift scatters 1550 nm light up to 1870 nm light