Optical Solitons Apr. 28, 2014

+ Temporal and spatial solitons (Sec. 19.8 1st Ed, Sec 22.5 2nd Ed):
Self focusing [equation] induced lens cancels diffraction [equation] self trapping beam
Self phase modulation [equation] induced freq chirp cancel dispersion [equation] optical soliton

+ Condition for soliton formation: [equation]
Dispersion [equation] ([equation]) [equation] high freq travels faster than low freq.
Nonlinearity [equation] (SPM, [equation]) [equation] freq chirp [equation], i.e. red shift at leading edge and blue shift at trailing edge.

+ Nonlinear Schrodinger Eqn:
[equation] where [equation], [equation], [equation], [equation] and [equation]

+ Soliton: [equation]
fundamental soliton, [equation] [equation]
[equation] high order soliton changes its shape periodically over a soliton period [equation].

+ Ultrafast optics: A study of very short pulse (with width of order of tens of femtoseconds or less) propagation.
The use of soliton allows compression of pulses with nonlinearity.
Pulse can also be compressed with linear optical elements, e.g. chirped gratings.
Chirped Gaussian pulse (Sec. 22.1 2nd Ed) [equation] where [equation] is the chirp parameter, i.e. [equation] high freq with larger delay and [equation] high freq with smaller delay..

+ Photonic switching and computing (Chapter 20 1st Ed):
goals -- speed, power and size, e.g. opto-mechanic, electro-optic, acoustic-optic and magnetic-optic.

+ All-optical switch (Sec. 23.4 2nd Ed):
Direct method -- Kerr effect and saturable absorption
Indirect method -- photorefractive media, LC
Limitations -- small nonlinearity and heat dissipation.

+ Bistable systems:
Electronics -- Flip-flop, schmidt trigger.
Req. feedback and nonlinear to generate bistability
[equation] where [equation] is a nonlinear function.
The transfer characteristic has a S shape, i.e. hysteresis.

+ Dispersive element:
Interferometer with a Kerr nonlinear medium [equation]

+ Dissipative elements:
Resonator with saturable absorber, i.e. absorption coef. [equation] where [equation] is linear absorption coef. and [equation] is the saturation intensity.
Recall [equation] where [equation]

+ Hybrid devices:
Electronics to provide optical feedback, e.g. EO crystal with feedback from a detector inside a cavity.
SEED -- self-electro-optic effect device with nonlinear absorption depending on voltage induced by light.

+ Optical computing:
Interconnections -- lens, holograms, dark solitons
Use 2nd order nonlinearity to make optical correlator.

Last Modified: April 28, 2014
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