11.15 k6 s coen

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)



Intracavity solitonsuperimposed ona low levelbackground

Planarcavity


material





Planarcavity


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


L. A. Lugiato, IEEE J. Quantum Elec. 39, 193 (2003)W. J. Firth and C. O. Weiss, Opt. & Phot. News 13, 54 (Feb. 2002)




Planarcavity


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






Planarcavity


material

Diffraction Nonlinearity

Cavity solitons are solitons





Planarcavity


material


Losses

Coherent driving


... but also solitonscavity





Planarcavity


material


Losses

Coherent driving



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





Planarcavity


material


Losses

Coherent driving



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



Planarcavity


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


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




Losses

Coherent driving

Input

Output

cw drivingbeam


No intracavity amplifier: The stored CSs as they circulate repeatedly

do notaccumulate noise




Losses

Coherent driving

Input

Output

cw drivingbeam




The driving power is independent of thenumber of bits stored

ALL-OPTICAL STORAGE




Losses

Coherent driving

Input

Output

cw drivingbeam


The double balance makes temporalCSs unique attractive states




ALL-OPTICAL STORAGE




Losses

Coherent driving

Input

Output

cw drivingbeam

address pulses



ALL-OPTICAL RESHAPING

They can be withaddress pulses

excited incoherentlyat a different wavelength

WAVELENGTH CONVERTER




ALL-OPTICAL STORAGE




Losses

Coherent driving

Input

Output

cw drivingbeam

address pulses





ALL-OPTICAL STORAGE






ALL-OPTICAL RETIMING

A periodic modulation of the driving beamcan trap the CSs in specific timeslots




Losses

Coherent driving

Input

Output

cw drivingbeam

address pulses






A periodic modulation of the driving beamcan trap the CSs in specific timeslots

No intracavity amplifier: The stored CSsas they circulate repeatedly




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


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


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



0 f2mp2(m–1)p 2(m+1)p

in

P

P




NL LPfg=


Positivefeedback

Accelerated approachof the resonance

0 LPffg=+



0 f2mp2(m–1)p 2(m+1)p

in

P

P




NL LPfg=


Positivefeedback

Accelerated approachof the resonance

in

P

P

Incident power

02mp

Tilting of the cavityresonance and bistability0f

0 LPffg=+





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


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


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


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


Intracavity modulation instabilityStudied through a linear stability analysis

It can indifferent parts ofthe cavity

coexist

with thehomogeneous lowerstate


homogeneous

modulated


2209 (1987)


Opt. Lett. 17, 745 (1992)


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


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)


homogeneous

modulated

It can indifferent parts ofthe cavity

coexist

with thehomogeneous lowerstate


2209 (1987)


Opt. Lett. 17, 745 (1992)


0 4 8 12

D = 1

D = 2.5

D = 4

0

1

2

3

4

5

X P?in

Y

P?


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


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]



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=


L. A. Lugiato and R. LefeverPhys. Rev. Lett. 58, 2209 (1987)


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=



Similar to reactiondiffusion systems

Cavity solitonsare localizeddissipativestructures “à la” Prigogine


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=



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


DFB

EDFA

1 kHz linewidth1551 nm CW pump

DRIVING BEAM


Fiber Coupler90/10

FiberIsolator

90m


Output

Resonances: 22 kHz

1.85

24Rt s

F

m=

=


290m


DFB

EDFA


DRIVING BEAM


Fiber Coupler90/10

FiberIsolator

90m


Controller

PiezoelectricFiber Stretcher

OutputFiber Coupler95/5

Resonances: 22 kHz

1.85

24Rt s

F

m=

=


290m


WDM


Fiber Coupler90/10

Fiber Coupler95/5


Controller

FiberIsolator

PRITEL

DFB

EDFA

EDFA

AOM



1535 nm, 4 ps, 10 MHzmodelocked fiber laser

DRIVING BEAM

ADDRESSINGBEAM

90m

Output

Resonances: 22 kHz

1.85

24Rt s

F

m=

=


290m


WDM


Fiber Coupler90/10

Fiber Coupler95/5


Controller

FiberIsolator

PRITEL

DFB

EDFA

EDFA

AOM


Excitedvia XPM



DRIVING BEAM

ADDRESSINGBEAM

90m

Output

Resonances: 22 kHz

1.85

24Rt s

F

m=

=


290m


WDM


Fiber Coupler90/10

Fiber Coupler95/5


Controller

FiberIsolator

WDM

PRITEL

DFB

WDM

EDFA

EDFA

AOM




DRIVING BEAM

ADDRESSINGBEAM

90m

Output

Excitedvia XPM Resonances: 22 kHz

1.85

24Rt s

F

m=

=


290m


WDM


Fiber Coupler90/10

Fiber Coupler95/5


Controller

FiberIsolator

WDM

BPF

PRITEL

DFB

Fiber Coupler50/50

EDFA1 nm BPF

EDFA

AOM

5 GSa/soscilloscope

Opticalspectrumanalyzer


Remove ASE

Remove driving beam



DRIVING BEAM

ADDRESSINGBEAM

90mExcited

via XPM

WDM

Resonances: 22 kHz

1.85

24Rt s

F

m=

=


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



Autocorrelation reveals it is ,matching simulations

4 ps long Dispersionlength: 230 m

ExperimentSimulations


Losses

Coherent driving


5. Results




Autocorrelation reveals it is ,matching simulations

4 ps long Dispersionlength: 230 m

ExperimentSimulations


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


5. Results




With a larger separation betweenthe addressing pulses ...

The two excited CSs repel


5. Results






... but repulsion getsprogressively weaker


5. Results






... 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





Driving beam switchedback on after4 round-trips

5. Results





From there on, new CSscan be written withoutaffecting the erasureof neighboring CSs

Driving beam switchedback on after4 round-trips

5. Results


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

11.15 k6 s coen

Technology

cavity solitonsthey

cavity lengthoutput

cavity li

temporal css

temporal case

external beams

nonlinear material

low levelbackground