EE 230: Optical Fiber Communication Lecture 6. Nonlinear Processes in Optical Fibers. From the movie Warriors of the Net. Polarization. In molecules, P= μ + α E+ β E 2 + γ E 3 +… In materials, P=X (o) +X (1) E+X (2) E 2 +X (3) E 3 +…
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Nonlinear Processes in Optical Fibers
From the movie
Warriors of the Net
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.
Distortion of an electron cloud in response to an E-field
Molecules and their dipole moments
For a sample of absorbance A and thickness d, the imaginary part of the refractive index is equal to
Refractive Index for various materials
Refractive index vs Frequency for silica
Wave slowing in a medium
of higher Index
Real part of index is best described as a power series
Term in parentheses is the intensity. For silica fiber, n22.6x10-11μm2/mW
where α (in cm-1) is the loss coefficient of the fiber. 0.1 dB/km=2.3x10-7 cm-1.
Propagation constant is power-dependent
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
Understanding Fiber Optics-Hecht
Fundamentals of Photonics - Saleh and Teich
Fiber Optic Communiocation Systems - Agrawal
Fiber Optics Communication Technology-Mynbaev & Scheiner
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).
Effect of these phase changes is a frequency chirp (frequency changes during pulse), broadening pulse and reducing bit rate-length product
Phase change of gaussian pulse
Instantaneous frequency shift
Instantaneous Frequency chirp
Through the cubic term:
Group velocity Vg, dispersion D, and dispersion slope S
Phase mismatch M needs to be small for FWM to occur significantly
ω1=ω2=ω (power lost from one signal wavelength)
ω3=ω+Χ where Χ is the difference in frequency between adjacent channels
Substitute in phase mismatch expression to get M=β2Χ2
Want β2 to be big to minimize FWM!