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Plenary 2: S Coen
Citation preview
Temporal 1D Kerr cavity solitons
a new passive optical buffer technology
Stéphane Coen
Physics Department, The University of Auckland,Auckland, New Zealand
Work performed while onResearch & Study Leave at
The Université Librede Bruxelles (ULB),
Brussels, Belgium
1. What are cavity solitons? 4. Experimental setup
3. Theory & Historical background
2. Temporal cavity solitons 5. Results
6. Conclusion
Pascal KockaertSimon-Pierre GorzaPhilippe EmplitMarc Haelterman
François LeoSpecial thanks to
and to
1. What are cavity solitons?
Traditionally described in passive planar cavities
Planarcavity
filled with anonlinear
material
External plane wavecoherently driving thecavity(driving/holding beam)
1. What are cavity solitons?
Traditionally described in passive planar cavities
Intracavity solitonsuperimposed ona low levelbackground
Planarcavity
filled with anonlinear
material
External plane wavecoherently driving thecavity(driving/holding beam)
1. What are cavity solitons?
Traditionally described in passive planar cavities
Intracavity solitonsuperimposed ona low levelbackground
Planarcavity
filled with anonlinear
material
They exist for a wide range of nonlinearities
The cavity solitons are independentfrom each other and from the boundaries
They can be manipulated by external beams
External plane wavecoherently driving thecavity(driving/holding beam)
L. A. Lugiato, IEEE J. Quantum Elec. 39, 193 (2003)W. J. Firth and C. O. Weiss, Opt. & Phot. News 13, 54 (Feb. 2002)
1. What are cavity solitons?
Traditionally described in passive planar cavities
Intracavity solitonsuperimposed ona low levelbackground
Planarcavity
filled with anonlinear
material
They exist for a wide range of nonlinearities
They can be manipulated by external beams
The cavity solitons are independentfrom each other and from the boundaries
S. Barland et alNature 419, 699 (2002)
L. A. Lugiato, IEEE J. Quantum Elec. 39, 193 (2003)W. J. Firth and C. O. Weiss, Opt. & Phot. News 13, 54 (Feb. 2002)
In semiconductor µ-cavities
External plane wavecoherently driving thecavity(driving/holding beam)
1. What are cavity solitons?
Traditionally described in passive planar cavities
External plane wavecoherently driving thecavity(driving/holding beam)
Intracavity solitonsuperimposed ona low levelbackground
Planarcavity
filled with anonlinear
material
Diffraction Nonlinearity
Cavity solitons are solitons
1. What are cavity solitons?
Traditionally described in passive planar cavities
External plane wavecoherently driving thecavity(driving/holding beam)
Intracavity solitonsuperimposed ona low levelbackground
Planarcavity
filled with anonlinear
material
Diffraction Nonlinearity
Losses
Coherent driving
Cavity solitons are solitons
... but also solitonscavity
1. What are cavity solitons?
Traditionally described in passive planar cavities
External plane wavecoherently driving thecavity(driving/holding beam)
Intracavity solitonsuperimposed ona low levelbackground
Planarcavity
filled with anonlinear
material
Diffraction Nonlinearity
Losses
Coherent driving
Cavity solitons are solitons
... but also solitonscavity
They are solitons in a boxnot W. J. Firth and C. O. Weiss,Opt. & Phot. News 13, 54 (Feb. 2002)
2D Kerr cavity solitons are while 2D Kerr nonlinear
Schrödinger solitons stable
collapse
1. What are cavity solitons?
Traditionally described in passive planar cavities
External plane wavecoherently driving thecavity(driving/holding beam)
Intracavity solitonsuperimposed ona low levelbackground
Planarcavity
filled with anonlinear
material
Diffraction Nonlinearity
Losses
Coherent driving
Cavity solitons are solitons
... but also solitonscavity
They are solitons in a boxnot W. J. Firth and C. O. Weiss,Opt. & Phot. News 13, 54 (Feb. 2002)
2D Kerr cavity solitons are while 2D Kerr nonlinear
Schrödinger solitons stable
collapse
Cavity solitons form
a subset of dissipative solitons
for coherently-driven
optical cavities
Spatial versus Temporal cavity solitons
External plane wavecoherently driving thecavity(driving/holding beam)
Intracavity solitonsuperimposed ona low levelbackground
Planarcavity
filled with anonlinear
material
DispersionNonlinearity
Losses
Coherent driving
We extend the terminologyto the temporal case
Diffraction
Input
Output
Input couplercw driving
beam
Temporal cavity solitons are
along the cavity length
naturallyimmune to longitudinal variations orimperfections
2. Temporal cavity solitons
2. Temporal cavity solitons
Temporal cavity solitons applied to an optical buffer technology
Dispersion Nonlinearity
Losses
Coherent driving
Input
Output
cw drivingbeam
Several temporal CSs can be stored in a cavity like bits in an optical buffer
2. Temporal cavity solitons
Temporal cavity solitons applied to an optical buffer technology
Dispersion Nonlinearity
Losses
Coherent driving
Input
Output
cw drivingbeam
Several temporal CSs can be stored in a cavity like bits in an optical buffer
No intracavity amplifier: The stored CSs as they circulate repeatedly
do notaccumulate noise
2. Temporal cavity solitons
Temporal cavity solitons applied to an optical buffer technology
Dispersion Nonlinearity
Losses
Coherent driving
Input
Output
cw drivingbeam
Several temporal CSs can be stored in a cavity like bits in an optical buffer
No intracavity amplifier: The stored CSs as they circulate repeatedly
do notaccumulate noise
The driving power is independent of thenumber of bits stored
ALL-OPTICAL STORAGE
2. Temporal cavity solitons
Temporal cavity solitons applied to an optical buffer technology
Dispersion Nonlinearity
Losses
Coherent driving
Input
Output
cw drivingbeam
Several temporal CSs can be stored in a cavity like bits in an optical buffer
The double balance makes temporalCSs unique attractive states
No intracavity amplifier: The stored CSs as they circulate repeatedly
do notaccumulate noise
The driving power is independent of thenumber of bits stored
ALL-OPTICAL STORAGE
2. Temporal cavity solitons
Temporal cavity solitons applied to an optical buffer technology
Dispersion Nonlinearity
Losses
Coherent driving
Input
Output
cw drivingbeam
address pulses
Several temporal CSs can be stored in a cavity like bits in an optical buffer
The double balance makes temporalCSs unique attractive states
ALL-OPTICAL RESHAPING
They can be withaddress pulses
excited incoherentlyat a different wavelength
WAVELENGTH CONVERTER
No intracavity amplifier: The stored CSs as they circulate repeatedly
do notaccumulate noise
The driving power is independent of thenumber of bits stored
ALL-OPTICAL STORAGE
2. Temporal cavity solitons
Temporal cavity solitons applied to an optical buffer technology
Dispersion Nonlinearity
Losses
Coherent driving
Input
Output
cw drivingbeam
address pulses
Several temporal CSs can be stored in a cavity like bits in an optical buffer
The double balance makes temporalCSs unique attractive states
ALL-OPTICAL RESHAPING
The driving power is independent of thenumber of bits stored
ALL-OPTICAL STORAGE
They can be withaddress pulses
excited incoherentlyat a different wavelength
WAVELENGTH CONVERTER
No intracavity amplifier: The stored CSs as they circulate repeatedly
do notaccumulate noise
ALL-OPTICAL RETIMING
A periodic modulation of the driving beamcan trap the CSs in specific timeslots
2. Temporal cavity solitons
Temporal cavity solitons applied to an optical buffer technology
Dispersion Nonlinearity
Losses
Coherent driving
Input
Output
cw drivingbeam
address pulses
Several temporal CSs can be stored in a cavity like bits in an optical buffer
The double balance makes temporalCSs unique attractive states
The driving power is independent of thenumber of bits stored
They can be withaddress pulses
excited incoherentlyat a different wavelength
A periodic modulation of the driving beamcan trap the CSs in specific timeslots
No intracavity amplifier: The stored CSsas they circulate repeatedly
do notaccumulate noise
ALL-OPTICAL RESHAPING
WAVELENGTH CONVERTER
ALL-OPTICAL RETIMING
An optical bufferbased on
temporal cavity solitonswould seamlessly combine
all these importanttelecommunications
functions
ALL-OPTICAL STORAGE
Here we report,with a Kerr fiber cavity,the first experimental
observationof these objects
The Kerr cavity
Input
Output
Interferences
Input coupler
Feedback
& DispersionNonlinearity
Combination of a simplenonlinearity with feedback anddispersion in a 1D geometry
“Hydrogen atom” of nonlinear cavity
3. Theory & Historical background
The Kerr cavity
Input
Output
Interferences
Input coupler
Feedback
& DispersionNonlinearity
0f
Destructiveinterferences
Constructiveinterferences
2mp2(m–1)p 2(m+1)p
Linear regime: Fabry-Perot type response
in
P
P0 0
2n L
pff
l==
“Hydrogen atom” of nonlinear cavity
Combination of a simplenonlinearity with feedback anddispersion in a 1D geometry
3. Theory & Historical background
Nonlinear resonances and Bistability
0 f2mp2(m–1)p 2(m+1)p
in
P
P
When approaching the resonance ...... the intracavity power P increases ...
... the nonlinear phase-shift increases ...... the cavity round-trip phase shift increases ...
0 LPffg=+
The Kerr cavity: Nonlinear regime
NL LPfg=
Instantaneous pure Kerrnonlinearity
3. Theory & Historical background
Nonlinear resonances and Bistability
0 f2mp2(m–1)p 2(m+1)p
in
P
P
When approaching the resonance ...... the intracavity power P increases ...
... the nonlinear phase-shift increases ...... the cavity round-trip phase shift increases ...
The Kerr cavity: Nonlinear regime
NL LPfg=
Instantaneous pure Kerrnonlinearity
Positivefeedback
Accelerated approachof the resonance
0 LPffg=+
3. Theory & Historical background
Nonlinear resonances and Bistability
0 f2mp2(m–1)p 2(m+1)p
in
P
P
When approaching the resonance ...... the intracavity power P increases ...
... the nonlinear phase-shift increases ...... the cavity round-trip phase shift increases ...
The Kerr cavity: Nonlinear regime
NL LPfg=
Instantaneous pure Kerrnonlinearity
Positivefeedback
Accelerated approachof the resonance
in
P
P
Incident power
02mp
Tilting of the cavityresonance and bistability0f
0 LPffg=+
3. Theory & Historical background
Nonlinear resonances and Bistability
3. Theory & Historical background
The Kerr cavity: Nonlinear regime
Bistability for variousconstant driving powers
in
P
P
Incident power
02mp
Tilting of the cavityresonance and bistability0f
0 in
P
P
D = 0
D = 4
Onset of bistability: 3D =
0d
aD =
Linear cavity detuningparameter (normalizedwith respect to the losses)
0 02mdpf=-
Bistability for variousconstant detunings
3. Theory & Historical background
Diffractive autosolitonsConnecting the upper and lower bistable states with locked switching waves
N. N. Rosanov and G. V. Khodova,J. Opt. Soc. Am. B 7, 1057 (1990)
0
PP
tinP
The intracavity field can be . The two parts can co-exist and be connected.
in the lower state in one part of the cavity andin the upper state in another part
3. Theory & Historical background
Diffractive autosolitonsConnecting the upper and lower bistable states with locked switching waves
N. N. Rosanov and G. V. Khodova,J. Opt. Soc. Am. B 7, 1057 (1990)
0
PP
tinP
The intracavity field can be . The two parts can co-exist and be connected.
in the lower state in one part of the cavity andin the upper state in another part
The
as the switching wavescannot always lockand
domain ofexistence is limited
the upper statemay be unstable
Not the type of localized structures we are concerned with in this work
3. Theory & Historical background
Intracavity modulation instability
L. A. Lugiato and R. LefeverPhys. Rev. Lett. 58,
2209 (1987)
M. Haelterman, S. Trillo,and S. Wabnitz
Opt. Lett. 17, 745 (1992)
Studied through a linear stability analysis
t
P
P
0
Frequency domain
The upper state isunstable in favor ofa solution
homogeneous
modulated
Anomalous dispersion
0 4 8 12
D = 1
D = 2.5
D = 4
0
1
2
3
4
5
X P?in
Y
P?
t
P Localized dissipative structure
3. Theory & Historical background
Intracavity modulation instabilityStudied through a linear stability analysis
It can indifferent parts ofthe cavity
coexist
with thehomogeneous lowerstate
The upper state isunstable in favor ofa solution
homogeneous
modulated
L. A. Lugiato and R. LefeverPhys. Rev. Lett. 58,
2209 (1987)
M. Haelterman, S. Trillo,and S. Wabnitz
Opt. Lett. 17, 745 (1992)
Anomalous dispersion
0 4 8 12
D = 1
D = 2.5
D = 4
0
1
2
3
4
5
X P?in
Y
P?
t
P Cavity soliton
3. Theory & Historical background
Intracavity modulation instabilityStudied through a linear stability analysis
G. S. McDonald and W. J. Firth,J. Opt. Soc. Am. B 7, 1328 (1990)
S. Wabnitz,Opt. Lett. 18, 601 (1993)
M. Tlidi, P. Mandel, and R. Lefever,Phys. Rev. Lett. 73, 640 (1994)
W. J. Firth and A. J. Scroggie,Phys. Rev. Lett. 76, 1623 (1996)
The upper state isunstable in favor ofa solution
homogeneous
modulated
It can indifferent parts ofthe cavity
coexist
with thehomogeneous lowerstate
L. A. Lugiato and R. LefeverPhys. Rev. Lett. 58,
2209 (1987)
M. Haelterman, S. Trillo,and S. Wabnitz
Opt. Lett. 17, 745 (1992)
Anomalous dispersion
0 4 8 12
D = 1
D = 2.5
D = 4
0
1
2
3
4
5
X P?in
Y
P?
3. Theory & Historical background
0 2 4 6 8 100
2
4
6
8
10
X
Y? = 3.3
0 50 100 150 200 250 300
3456789
Driving power (mW)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.81.9
0
P [W]
Time [ps]
1.6
20-20
1.2
0.8
0.4
4.4 ps
Cavity solitons arise through a sub-criticalTuring bifurcation
3. Theory & Historical background
0 2 4 6 8 100
2
4
6
8
10
X
Y? = 3.3
0 50 100 150 200 250 300
3456789
Driving power (mW)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.81.9
0
P [W]
Time [ps]
1.6
20-20
1.2
0.8
0.4
4.4 ps
Cavity solitons arise through a sub-criticalTuring bifurcation
3. Theory & Historical background
0 2 4 6 8 100
2
4
6
8
10
X
Y? = 3.3
? = 3.8
0 50 100 150 200 250 300
3456789
Driving power (mW)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.81.9
0
Time [ps]
1.6
20-20
1.2
4.4 ps0.8
0.4
P [W]
Cavity solitons arise through a sub-criticalTuring bifurcation
3. Theory & Historical background
0 2 4 6 8 100
2
4
6
8
10
X
Y? = 3.3
? = 3.8
0 50 100 150 200 250 300
3456789
Driving power (mW)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.81.9
0
Time [ps]
1.6
20-20
1.2
4.4 ps0.8
0.4
P [W]
()2
2
21 ( ) ,
Ei E i E t S
th tt
é ù¶ ¶=-+-D- +ê ú¶ ¶ë û
()2signhb=
Cavity solitons arise through a sub-criticalTuring bifurcation
L. A. Lugiato and R. LefeverPhys. Rev. Lett. 58, 2209 (1987)
3. Theory & Historical background
0 2 4 6 8 100
2
4
6
8
10
X
Y? = 3.3
? = 3.8
0 50 100 150 200 250 300
3456789
Driving power (mW)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.81.9
0
Time [ps]
1.6
20-20
1.2
4.4 ps0.8
0.4
P [W]
()2
2
21 ( ) ,
Ei E i E t S
th tt
é ù¶ ¶=-+-D- +ê ú¶ ¶ë û
()2signhb=
Cavity solitons arise through a sub-criticalTuring bifurcation
L. A. Lugiato and R. LefeverPhys. Rev. Lett. 58, 2209 (1987)
Similar to reactiondiffusion systems
Cavity solitonsare localizeddissipativestructures “à la” Prigogine
3. Theory & Historical background
0 2 4 6 8 100
2
4
6
8
10
X
Y? = 3.3
? = 3.8
0 50 100 150 200 250 300
3456789
Driving power (mW)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.81.9
0
Time [ps]
1.6
20-20
1.2
4.4 ps0.8
0.4
P [W]
()2
2
21 ( ) ,
Ei E i E t S
th tt
é ù¶ ¶=-+-D- +ê ú¶ ¶ë û
()2signhb=
Cavity solitons arise through a sub-criticalTuring bifurcation
L. A. Lugiato and R. LefeverPhys. Rev. Lett. 58, 2209 (1987)
Similar to reactiondiffusion systems
Cavity solitonsare localizeddissipativestructures “à la” Prigogine
Fundamentalexample of
self-organizationphenomena in
nonlinear optics
Experimental demonstration of temporal Kerr cavity solitons
4. Experimental setup
PolarizationController
Fiber Coupler90/10
FiberIsolator
90m
290m
To avoid Brillouinscattering
Resonances: 22 kHz
1.85
24Rt s
F
m=
=
Input
Output
Experimental demonstration of temporal Kerr cavity solitons
DFB
EDFA
1 kHz linewidth1551 nm CW pump
DRIVING BEAM
PolarizationController
Fiber Coupler90/10
FiberIsolator
90m
To avoid Brillouinscattering
Output
Resonances: 22 kHz
1.85
24Rt s
F
m=
=
4. Experimental setup
290m
Experimental demonstration of temporal Kerr cavity solitons
DFB
EDFA
1 kHz linewidth1551 nm CW pump
DRIVING BEAM
PolarizationController
Fiber Coupler90/10
FiberIsolator
90m
To avoid Brillouinscattering
Controller
PiezoelectricFiber Stretcher
OutputFiber Coupler95/5
Resonances: 22 kHz
1.85
24Rt s
F
m=
=
4. Experimental setup
290m
Experimental demonstration of temporal Kerr cavity solitons
WDM
PolarizationController
Fiber Coupler90/10
Fiber Coupler95/5
PiezoelectricFiber Stretcher
Controller
FiberIsolator
PRITEL
DFB
EDFA
EDFA
AOM
To avoid Brillouinscattering
1 kHz linewidth1551 nm CW pump
1535 nm, 4 ps, 10 MHzmodelocked fiber laser
DRIVING BEAM
ADDRESSINGBEAM
90m
Output
Resonances: 22 kHz
1.85
24Rt s
F
m=
=
4. Experimental setup
290m
Experimental demonstration of temporal Kerr cavity solitons
WDM
PolarizationController
Fiber Coupler90/10
Fiber Coupler95/5
PiezoelectricFiber Stretcher
Controller
FiberIsolator
PRITEL
DFB
EDFA
EDFA
AOM
To avoid Brillouinscattering
Excitedvia XPM
1 kHz linewidth1551 nm CW pump
1535 nm, 4 ps, 10 MHzmodelocked fiber laser
DRIVING BEAM
ADDRESSINGBEAM
90m
Output
Resonances: 22 kHz
1.85
24Rt s
F
m=
=
4. Experimental setup
290m
Experimental demonstration of temporal Kerr cavity solitons
WDM
PolarizationController
Fiber Coupler90/10
Fiber Coupler95/5
PiezoelectricFiber Stretcher
Controller
FiberIsolator
WDM
PRITEL
DFB
WDM
EDFA
EDFA
AOM
To avoid Brillouinscattering
1 kHz linewidth1551 nm CW pump
1535 nm, 4 ps, 10 MHzmodelocked fiber laser
DRIVING BEAM
ADDRESSINGBEAM
90m
Output
Excitedvia XPM Resonances: 22 kHz
1.85
24Rt s
F
m=
=
4. Experimental setup
290m
Experimental demonstration of temporal Kerr cavity solitons
WDM
PolarizationController
Fiber Coupler90/10
Fiber Coupler95/5
PiezoelectricFiber Stretcher
Controller
FiberIsolator
WDM
PRITEL
DFB
WDM
EDFA
EDFA
AOM
To avoid Brillouinscattering
1 kHz linewidth1551 nm CW pump
1535 nm, 4 ps, 10 MHzmodelocked fiber laser
DRIVING BEAM
ADDRESSINGBEAM
90m
Output
Excitedvia XPM Resonances: 22 kHz
1.85
24Rt s
F
m=
=
4. Experimental setup
290m
Experimental demonstration of temporal Kerr cavity solitons
WDM
PolarizationController
Fiber Coupler90/10
Fiber Coupler95/5
PiezoelectricFiber Stretcher
Controller
FiberIsolator
WDM
BPF
PRITEL
DFB
Fiber Coupler50/50
EDFA1 nm BPF
EDFA
AOM
5 GSa/soscilloscope
Opticalspectrumanalyzer
To avoid Brillouinscattering
Remove ASE
Remove driving beam
1 kHz linewidth1551 nm CW pump
1535 nm, 4 ps, 10 MHzmodelocked fiber laser
DRIVING BEAM
ADDRESSINGBEAM
90mExcited
via XPM
WDM
Resonances: 22 kHz
1.85
24Rt s
F
m=
=
4. Experimental setup
290m
A single soliton in the cavity
5. Results
The intracavity pulse persists in the cavityfor more than 1 s (> 550,000 round-trips)
Losses
Coherent driving
Addressing pulse: Off - CS only sustained by the cw driving beam
A single soliton in the cavity
The intracavity pulse persists in the cavityfor more than 1 s (> 550,000 round-trips)
Autocorrelation reveals it is ,matching simulations
4 ps long Dispersionlength: 230 m
ExperimentSimulations
Dispersion Nonlinearity
Losses
Coherent driving
Addressing pulse: Off - CS only sustained by the cw driving beam
5. Results
A single soliton in the cavity
The intracavity pulse persists in the cavityfor more than 1 s (> 550,000 round-trips)
Addressing pulse: Off - CS only sustained by the cw driving beam
Autocorrelation reveals it is ,matching simulations
4 ps long Dispersionlength: 230 m
ExperimentSimulations
Dispersion Nonlinearity
Losses
Coherent driving
5. Results
Storing data as binary patterns with cavity solitons
5. Results
Interactions of temporal cavity solitons
5. Results
Sending two close addressing pulses andobserving the CSs within the next 1 s
Addressing pulses closer than 25 ps
Only one CS present atthe output
Interactions of temporal cavity solitons
5. Results
Sending two close addressing pulses andobserving the CSs within the next 1 s
Addressing pulses closer than 25 ps
Only one CS present atthe output
With a larger separation betweenthe addressing pulses ...
The two excited CSs repel
Interactions of temporal cavity solitons
5. Results
Sending two close addressing pulses andobserving the CSs within the next 1 s
Addressing pulses closer than 25 ps
Only one CS present atthe output
With a larger separation betweenthe addressing pulses ...
The two excited CSs repel
... but repulsion getsprogressively weaker
Interactions of temporal cavity solitons
5. Results
Sending two close addressing pulses andobserving the CSs within the next 1 s
Addressing pulses closer than 25 ps
Only one CS present atthe output
With a larger separation betweenthe addressing pulses ...
The two excited CSs repel
... but repulsion getsprogressively weaker
Potential buffer capacity:
45 kbit @ 25 Gbit/s
The CSs could be easilytrapped by modulating thedriving power
5. Results5. Results
Writing dynamics of temporal cavity solitons
Time (100 µs/div)
Experiment
Simulation
Writing dynamics of temporal cavity solitons
Time (100 µs/div)
Experiment
Simulation
Output with off-center filter
Inside the cavity
Time (100 µs/div)
5. Results5. Results
5. Results
Erasing of temporalcavity solitons
Complete erasing of thecavity can be obtained
for about4 round-trips
by switching off thedriving beam
5. Results
Erasing of temporalcavity solitons
Complete erasing of thecavity can be obtained
for about4 round-trips
by switching off thedriving beam
Driving beam switchedback on after4 round-trips
5. Results
Erasing of temporalcavity solitons
Complete erasing of thecavity can be obtained
for about4 round-trips
by switching off thedriving beam
From there on, new CSscan be written withoutaffecting the erasureof neighboring CSs
Driving beam switchedback on after4 round-trips
5. Results
Erasing of temporalcavity solitons
Selective erasing ofone CS can be obtainedby overwriting it withan addressing pulseabout 50% morepowerful
This realizes anall-optical XORlogic gate
5. Results
Breathing temporal cavity solitons
Above a certain driving power,the cavity solitons become breathers
0 2 4 6 8 100
2
4
6
8
10
X
Y? = 3.3
? = 3.8
0 50 100 150 200 250 300
3456789
Driving power (mW)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.81.9
Hopfbifurcation
0 2 4 6 8 100
2
4
6
8
10
X
Y? = 3.3
? = 3.8
0 50 100 150 200 250 300
3456789
Driving power (mW)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.81.9
Hopfbifurcation
5. Results
Breathing temporal cavity solitons
Time (50 µs/div)
Above a certain driving power,the cavity solitons become breathers
6. Conclusion
We have reported as well as
the first direct experimental observation oftemporal cavity solitons Kerr cavity solitons
Temporal cavity solitons could be used as bits in an all-optical buffer,combining all-optical storage with wavelength conversion,all-optical reshaping, and re-timing
Our experiments have been performed in a purely 1-dimensional systemwith an instantaneous Kerr nonlinearity
Due to this simplicity, our experiments may constitute themost fundamental example of self-organization in nonlinear optics
P. Del’Haye et al,Nature 450, 1214 (2007)
Kerr frequency combs generated in microresonators may bethe spectral signature of a temporal cavity soliton
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