Slow and Fast Nonlinearities in Microfiber Resonators A. Coillet(1) , Ph. Grelu(1) , G. Vienne(2) , L. Tong(2) (1) Institut
Carnot de Bourgogne, UMR 5209 CNRS, Universit´ e de Bourgogne, 21078 Dijon Cedex, France (2) Nanophotonics Group, State Key Laboratory of Modern Optical Instrumentation, Department of Optical Engineering, Zhejiang University, Hangzhou 310027, China
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A. Coillet (ICB)
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Outline
1
Introduction
2
Thermally induced non-linearity
3
Fast non-linearities
4
Conclusion and Perspectives
A. Coillet (ICB)
Slow/Fast N-L in microfiber resonators
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1
Introduction
2
Thermally induced non-linearity
3
Fast non-linearities
4
Conclusion and Perspectives
A. Coillet (ICB)
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Introduction Microfibers Fabrication flexibility, High fraction of evanescent field, Tight optical confinement
1
Sumetsky et al., Microfiber loop resonator, JLW06
2
Jiang et al., Microfiber knot resonator, APL06 A. Coillet (ICB)
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Introduction Microfibers
Resonators
Fabrication flexibility,
Microfiber loop1 or knot2 ,
High fraction of evanescent field,
High field enhancement
Tight optical confinement
1
Sumetsky et al., Microfiber loop resonator, JLW06
2
Jiang et al., Microfiber knot resonator, APL06 A. Coillet (ICB)
Slow/Fast N-L in microfiber resonators
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Introduction Non-linearity + resonator ⇒ bistability
A. Coillet (ICB)
Slow/Fast N-L in microfiber resonators
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Introduction Non-linearity + resonator ⇒ bistability
Thermally-induced non-linearity Low-threshold bistability Silica microwires Simple model predicts experiments Slow response
A. Coillet (ICB)
Slow/Fast N-L in microfiber resonators
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Introduction Non-linearity + resonator ⇒ bistability
Thermally-induced non-linearity Low-threshold bistability Silica microwires Simple model predicts experiments Slow response
Kerr non-linearity Quasi instantaneous effect ∆ ! High input power I I
New highly non-linear glasses Pulse regime with high peak power
A. Coillet (ICB)
Slow/Fast N-L in microfiber resonators
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1
Introduction
2
Thermally induced non-linearity
3
Fast non-linearities
4
Conclusion and Perspectives
A. Coillet (ICB)
Slow/Fast N-L in microfiber resonators
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Microfiber knot resonator Microfiber knot resonator
microfiber diameter: 2.4 µm knot diameter: 1.55 mm λ ∼ 1.55 µm
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Resonance spectra Resonance
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Resonance spectra Resonance
Power increase Power increase ⇓ frequency shift + asymmetry = NL phase shift
A. Coillet (ICB)
Slow/Fast N-L in microfiber resonators
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Resonance spectra Resonance
Power increase Power increase ⇓ frequency shift + asymmetry = NL phase shift
Model dT (t) dt
=−
T (t)−Ta τ
+ c1 P(t) “ ” 1 φ(t) = φ0 +2πna La λ(t) − λ1 +c2 (T (t)−Ta ) 0
a2 (1−K ) √ P(t) = Pin (t) 1+σ 2 K −2σ K cos φ(t) √ K +σ 2 −2σ K cos φ(t) √ Pout = a2 Pin (t) 2 1+σ K −2σ K cos φ(t) Vienne et al., nonlinear microfiber resonator, OL08
A. Coillet (ICB)
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Intensity transfer function Experiment
A. Coillet (ICB)
Transfer function
Slow/Fast N-L in microfiber resonators
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Intensity transfer function Experiment
Transfer function
Comments Low threshold bistability Slow response: τ ' 1 ms Good agreement exp./model ⇒ Thermally-induced NL ∼ slow, intense, optical Kerr effect A. Coillet (ICB)
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1
Introduction
2
Thermally induced non-linearity
3
Fast non-linearities
4
Conclusion and Perspectives
A. Coillet (ICB)
Slow/Fast N-L in microfiber resonators
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Slow/Fast non-linearities Thermal vs. Kerr NL Thermal NL: large magnitude, slow response Kerr NL: small magnitude, quasi-instantaneous response
A. Coillet (ICB)
Slow/Fast N-L in microfiber resonators
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Slow/Fast non-linearities Thermal vs. Kerr NL Thermal NL: large magnitude, slow response Kerr NL: small magnitude, quasi-instantaneous response ⇒ Pulse regime can be dominated by Kerr NL
A. Coillet (ICB)
Slow/Fast N-L in microfiber resonators
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Slow/Fast non-linearities Thermal vs. Kerr NL Thermal NL: large magnitude, slow response Kerr NL: small magnitude, quasi-instantaneous response ⇒ Pulse regime can be dominated by Kerr NL
Requirements Large peak power Low average power
(. 10 mW)
Repetition rate greater than
1 τ
(> 10 kHz)
Pulse duration > resonator round trip time × the finesse
A. Coillet (ICB)
Slow/Fast N-L in microfiber resonators
(> 100 ps)
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Bistability Silica Kerr NL Numerical solutions for different detunings (φ)
Pulse shaping A. Coillet (ICB)
Strong pulse shaping Slow/Fast N-L in microfiber resonators
Bistability AOE’08 01/11/2008
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Highly non-linear glasses Glass with high non-linearities High power requirements for silica non-linear resonator.
(γeff ' 0.09
W−1 m−1 )
Use of highly non-linear glasses, such as tellurite chalcogenide (γeff ' 40 W−1 m−1 )
A. Coillet (ICB)
Slow/Fast N-L in microfiber resonators
(γeff ' 5.2 W−1 m−1 )
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or
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Highly non-linear glasses Glass with high non-linearities High power requirements for silica non-linear resonator.
(γeff ' 0.09
W−1 m−1 )
Use of highly non-linear glasses, such as tellurite chalcogenide (γeff ' 40 W−1 m−1 )
(γeff ' 5.2 W−1 m−1 )
or
Chalcogenide NL resonator: Simulation
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Slow/Fast N-L in microfiber resonators
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1
Introduction
2
Thermally induced non-linearity
3
Fast non-linearities
4
Conclusion and Perspectives
A. Coillet (ICB)
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Conclusion and Perspectives Thermal NL Thermally-induced NL with slow response ⇒ allows bistable operation at low power
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Conclusion and Perspectives Thermal NL Thermally-induced NL with slow response ⇒ allows bistable operation at low power
Kerr NL In picosecond pulse regime, quasi-instantaneous Kerr NL can be dominant Applications in optical switching and processing in the telecom domain. Highly non-linear glasses such as tellurite and chalcogenide drastically reduce the required peak power ⇒ future experiments. A. Coillet (ICB)
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