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Robert:•Motivation•Principles of Optics•Applications •Optimization
Andy:Materials
Loss vs. amplification
Theoretical problems
Overview
2 + 2 = 4WM
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Motivation
1. Internet relies on fiber optics.
2. Amplification needed.
Current technology inadequate:
Limited amplification bandwidth
Limited internet speed
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Linear OpticsLow intensity light in transparent media.
•Refraction
•Dispersion
Light slows down in transparent media.
Refractive index is function of frequency.
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Propagation constantBeta (propagation constant) very useful.
Expressible as power series.
Coefficient critical to optimizing FWM.
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Limitations1. Photons do not interact.
2. No new frequencies are created.
3. Too simple for our purposes.
But nonlinear optics provides uswith great possibilities…
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Nonlinear Optics•Kerr effect: refractive index depends on
intensity of light.
•Nonlinearity causes complex behavior.
•Nonlinear Schrödinger Equation
Photons can mix and change their frequencies!
Nonlinear Term
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Four-wave Mixing
Signal
Pump Lasers Photons added to signal
Photons added to idler
Idler(createdto conserve energy)
(Amplified through FWM)2 + 2=4WM
Frequency (ω)/100THz
Log
(In
tensi
ty)
Pump photons mix to form signal and idler photons.
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Elastic Collision Analogy
Energy Conservation:
MomentumConservation:
Pump energies
Energies of signal and idler
Pump momenta
Momenta of signal and idler
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ApplicationsWhat can we use it for?
•Amplification and Frequency conversion.
•Solves world hunger (for internet speed)
Optimization:•How do we turn ideas into high performance technology?
mathematical analysis and approximation.
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Amplification Optimization•Amplification depends on only one number.
•Must be close to –γP for maximum gain.
•Complexity of β solved by quartic approximation.
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Conditions for Maximum Flat Gain
1. Average pump frequency at zero dispersion point ω00.
Where:
2. β4 4 must be positive.
3. And lastly, regarding the pumps:
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Before and After Optimization
Signal Frequency Offset
Gain
Inferior bandwidth
Optimized bandwidth
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Frequency Conversion OptimizationIdler photons used as new signal:
Useful since different frequencies needed in fiber.
Problem: pumps: same average frequency as “a” and “b.”
Stuck with bandwidth we’re given…
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Dispersion Engineering•Optical fibers:
Total internal reflection
•Light strays into cladding.
•Samples 2 refractive indices.
•We can engineer β22, , β3, 3, β4 etc.4 etc.
n22n11
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Frequency Conversion OptimizationIdler photons used as new signal:
Useful since different frequencies needed.
Problem: pumps: same average frequency as “a” and “b.”
Stuck with bandwidth we’re given…
Solution: dispersion engineering: minimize β44 Make β3 3 and β4 4 into “magic ratio.”
Creates greater bandwidth.
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Summary
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Optical Fiber
Nonlinear effect ∝ γPL
Silica Low loss Low nonlinearity γ
High P and L needed for FWM
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Silica V.S. Chalcogenide
Silica Chalcogenide
Made of
SiO2 S, Se, Te+others
γ Low High
Used in Optical Fiber Optical Chip
Loss Low High
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Nonlinear Schrodinger Equation (NLS)
uiuut
u
z
ui
2
2
2
)(2
1
Linear loss coefficient
Numerically solve NLS with loss(Split step Fourier method)
How loss affects gains
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1 pump case
Signal GainIdler Gain
γ+γ- INPUTOUTPUT
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1 pump case
INPUTOUTPUT
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Gain curve – 1 pump
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Gain curve – 1 pump
α = (dB/m) 0 20 40 60 80 100
Chalcogenide
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Peak Gain– 1 pump
loss ∝ e-αL
(dB/m)
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2 pump case INPUTOUTPUT
Signal Gain
Idler Gain
2 pump case
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Gain curve - 2 pump case
Signal Gain Idler Gain
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Asymmetry Problem
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Conclusion FWM : nonlinear optical effect
Parametric amplifications
Conditions for greater bandwidth
How loss affects gain curves— unexpected!!
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Future Work
Asymmetry Problem
Coping with loss
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References
• C. J. McKinstrie, S. Radic and A. R. Chraplyvy. Parametric Amplifiers Driven by Two Pump Waves. IEEE J. Quantum Electron., vol.QE-8, pp. 538–547, 2002.
• G. P. Agrawal (2001). Nonlinear Fiber Optics. Orlando: Academic Press.
• M. R. Lamont, T. T. Kuhlmey and C. M. de Sterke. Multi-order dispersion engineering for optimal four-wave mixing. Optics Express, vol.16, pp. 7551–7563, 2008.
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Thanks for listening