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EE 230: Optical Fiber Communication Lecture 6

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Nonlinear Processes in Optical Fibers

From the movie

Warriors of the Net

- 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.

Distortion of an electron cloud in response to an E-field

Molecules and their dipole moments

- Stimulated Raman scattering
- Stimulated Brillouin scattering
- Four-wave Mixing
- Self-phase Modulation
- Cross-phase Modulation

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

n=n1+n2(P/Aeff)

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).

- 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

Phase change of gaussian pulse

Instantaneous frequency shift

Instantaneous Frequency chirp

- 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

- 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

- 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)

- 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

- Spectrum shows major peaks at 1100, 800, and 450 cm-1
- Those vibrational oscillations occur at 33, 24, and 13.5 THz
- Raman gain spectrum shows maximum at 12-14, 18, 24, and 33 THz

Through the cubic term:

where

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

ω4=ω-Χ

Substitute in phase mismatch expression to get M=β2Χ2

Want β2 to be big to minimize FWM!