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11.15 k6 s coen
1. 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 on
Research & Study Leave at Special thanks to François Leo
and to Pascal Kockaert
The Université Libre Simon-Pierre Gorza
de Bruxelles (ULB), Philippe Emplit
Brussels, Belgium Marc Haelterman
1. What are cavity solitons? 4. Experimental setup
2. Temporal cavity solitons 5. Results
3. Theory & Historical background 6. Conclusion
2. 1. What are cavity solitons?
Traditionally described in passive planar cavities
External plane wave
coherently driving the
cavity
(driving/holding beam)
Planar
cavity
filled with a
nonlinear
material
3. 1. What are cavity solitons?
Traditionally described in passive planar cavities
External plane wave
coherently driving the
cavity
(driving/holding beam)
Planar
cavity
filled with a Intracavity soliton
nonlinear superimposed on
material a low level
background
4. 1. What are cavity solitons?
Traditionally described in passive planar cavities
External plane wave
coherently driving the
cavity
(driving/holding beam)
Planar
cavity
filled with a Intracavity soliton
nonlinear superimposed on
material a low level
background
The cavity solitons are independent
from each other and from the boundaries
They can be manipulated by external beams
They exist for a wide range of nonlinearities
L. A. Lugiato, IEEE J. Quantum Elec. 39, 193 (2003)
W. J. Firth and C. O. Weiss, Opt. & Phot. News 13, 54 (Feb. 2002)
5. 1. What are cavity solitons?
Traditionally described in passive planar cavities In semiconductor µ-cavities
External plane wave
coherently driving the
cavity
(driving/holding beam)
Planar
cavity
filled with a Intracavity soliton
nonlinear superimposed on
material a low level
background
The cavity solitons are independent
from each other and from the boundaries
They can be manipulated by external beams
They exist for a wide range of nonlinearities
L. A. Lugiato, IEEE J. Quantum Elec. 39, 193 (2003) S. Barland et al
W. J. Firth and C. O. Weiss, Opt. & Phot. News 13, 54 (Feb. 2002) Nature 419, 699 (2002)
6. 1. What are cavity solitons?
Traditionally described in passive planar cavities
External plane wave Cavity solitons are solitons
coherently driving the
cavity
(driving/holding beam)
Planar
cavity Diffraction Nonlinearity
filled with a Intracavity soliton
nonlinear superimposed on
material a low level
background
7. 1. What are cavity solitons?
Traditionally described in passive planar cavities
External plane wave Cavity solitons are solitons
coherently driving the
cavity
(driving/holding beam) Coherent driving
Planar
cavity Diffraction Nonlinearity
filled with a Intracavity soliton
nonlinear superimposed on Losses
material a low level
background
... but also cavity solitons
8. 1. What are cavity solitons?
Traditionally described in passive planar cavities
External plane wave Cavity solitons are solitons
coherently driving the
cavity
(driving/holding beam) Coherent driving
Planar
cavity Diffraction Nonlinearity
filled with a Intracavity soliton
nonlinear superimposed on Losses
material a low level
background
... but also cavity solitons
They are not solitons in a box
W. J. Firth and C. O. Weiss,
Opt. & Phot. News 13, 54 (Feb. 2002)
2D Kerr cavity solitons are
stable while 2D Kerr nonlinear
Schrödinger solitons collapse
9. 1. What are cavity solitons?
Traditionally described in passive planar cavities
External plane wave Cavity solitons are solitons
coherently driving the
cavity
(driving/holding beam) Coherent driving
Planar
cavity Diffraction Nonlinearity
filled with a Intracavity soliton
nonlinear superimposed on Losses
material a low level
background
... but also cavity solitons
They are not solitons in a box
W. J. Firth and C. O. Weiss,
Opt. & Phot. News 13, 54 (Feb. 2002)
Cavity solitons form
a subset of dissipative solitons 2D Kerr cavity solitons are
stable while 2D Kerr nonlinear
for coherently-driven Schrödinger solitons collapse
optical cavities
10. 2. Temporal cavity solitons
Spatial versus Temporal cavity solitons
We extend the terminology
External plane wave to the temporal case
coherently driving the
cavity
(driving/holding beam) Coherent driving
Planar
cavity Diffraction Nonlinearity
filled with a Intracavity soliton Dispersion
nonlinear superimposed on Losses
material a low level
background
cw driving
beam Input coupler
Input
Temporal cavity solitons are naturally
immune to longitudinal variations or
imperfections along the cavity length
Output
11. 2. Temporal cavity solitons
Temporal cavity solitons applied to an optical buffer technology
Several temporal CSs can be stored in a cavity like bits in an optical buffer
Coherent driving
Dispersion Nonlinearity
Losses
cw driving
beam
Input
Output
12. 2. Temporal cavity solitons
Temporal cavity solitons applied to an optical buffer technology
Several temporal CSs can be stored in a cavity like bits in an optical buffer
No intracavity amplifier: The stored CSs do not
accumulate noise as they circulate repeatedly Coherent driving
Dispersion Nonlinearity
Losses
cw driving
beam
Input
Output
13. 2. Temporal cavity solitons
Temporal cavity solitons applied to an optical buffer technology
Several temporal CSs can be stored in a cavity like bits in an optical buffer
No intracavity amplifier: The stored CSs do not
accumulate noise as they circulate repeatedly Coherent driving
The driving power is independent of the Dispersion Nonlinearity
number of bits stored
Losses
ALL-OPTICAL STORAGE
cw driving
beam
Input
Output
14. 2. Temporal cavity solitons
Temporal cavity solitons applied to an optical buffer technology
Several temporal CSs can be stored in a cavity like bits in an optical buffer
No intracavity amplifier: The stored CSs do not
accumulate noise as they circulate repeatedly Coherent driving
The driving power is independent of the Dispersion Nonlinearity
number of bits stored
Losses
ALL-OPTICAL STORAGE
The double balance makes temporal cw driving
CSs unique attractive states beam
Input
Output
15. 2. Temporal cavity solitons
Temporal cavity solitons applied to an optical buffer technology
Several temporal CSs can be stored in a cavity like bits in an optical buffer
No intracavity amplifier: The stored CSs do not
accumulate noise as they circulate repeatedly Coherent driving
The driving power is independent of the Dispersion Nonlinearity
number of bits stored
Losses
ALL-OPTICAL STORAGE
The double balance makes temporal address pulses
cw driving
CSs unique attractive states beam
ALL-OPTICAL RESHAPING
Input
They can be excited incoherently with
address pulses at a different wavelength
WAVELENGTH CONVERTER
Output
16. 2. Temporal cavity solitons
Temporal cavity solitons applied to an optical buffer technology
Several temporal CSs can be stored in a cavity like bits in an optical buffer
No intracavity amplifier: The stored CSs do not
accumulate noise as they circulate repeatedly Coherent driving
The driving power is independent of the Dispersion Nonlinearity
number of bits stored
Losses
ALL-OPTICAL STORAGE
The double balance makes temporal address pulses
cw driving
CSs unique attractive states beam
ALL-OPTICAL RESHAPING
Input
They can be excited incoherently with
address pulses at a different wavelength
WAVELENGTH CONVERTER
A periodic modulation of the driving beam
can trap the CSs in specific timeslots
ALL-OPTICAL RETIMING
Output
17. 2. Temporal cavity solitons
Temporal cavity solitons applied to an optical buffer technology
Several temporal CSs can be stored in a cavity like bits in an optical buffer
No intracavity amplifier: The stored CSs do not
accumulate noise as they circulate repeatedly An optical buffer
Coherent driving
The driving power is independent of the based on Nonlinearity
Dispersion
number of bits stored temporal cavity solitons
Losses
would seamlessly combine
ALL-OPTICAL STORAGE
all these important
address pulses
The double balance makes temporal cw driving
CSs unique attractive states
telecommunications
beam
functions
ALL-OPTICAL RESHAPING
Input
They can be excited incoherently with Here we report,
address pulses at a different wavelength with a Kerr fiber cavity,
WAVELENGTH CONVERTER the first experimental
A periodic modulation of the driving beam
observation
can trap the CSs in specific timeslots of these objects
ALL-OPTICAL RETIMING
Output
18. 3. Theory & Historical background
The Kerr cavity
“Hydrogen atom” of nonlinear cavity
Input coupler
Input Interferences
Feedback
Nonlinearity
& Dispersion
Output
Combination of a simple
nonlinearity with feedback and
dispersion in a 1D geometry
19. 3. Theory & Historical background
The Kerr cavity Linear regime: Fabry-Perot type response
“Hydrogen atom” of nonlinear cavity
Constructive
Input coupler interferences
Input Interferences
P
Feedback
2p
Nonlinearity Pin = n0L
f
f0 =
& Dispersion l
0
2(m–1)p 2mp 2(m +1)p
f
Output Destructive
interferences
Combination of a simple
nonlinearity with feedback and
dispersion in a 1D geometry
20. 3. Theory & Historical background
The Kerr cavity: Nonlinear regime
Nonlinear resonances and Bistability Instantaneous pure Kerr
nonlinearity
When approaching the resonance ...
... the intracavity power P increases ...
fLP
NL =g
... the nonlinear phase-shift increases ...
... the cavity round-trip phase shift increases ...
P
Pin
0 f
2(m–1)p 2mp 2(m +1)p
fg
=
f LP
0+
21. 3. Theory & Historical background
The Kerr cavity: Nonlinear regime
Nonlinear resonances and Bistability Instantaneous pure Kerr
nonlinearity
When approaching the resonance ...
... the intracavity power P increases ...
fLP
NL =g
Positive ... the nonlinear phase-shift increases ...
feedback ... the cavity round-trip phase shift increases ...
Accelerated approach
of the resonance
P
Pin
0 f
2(m–1)p 2mp 2(m +1)p
fg
=
f LP
0+
22. 3. Theory & Historical background
The Kerr cavity: Nonlinear regime
Nonlinear resonances and Bistability Instantaneous pure Kerr
nonlinearity
When approaching the resonance ...
... the intracavity power P increases ...
fLP
NL =g
Positive ... the nonlinear phase-shift increases ...
feedback ... the cavity round-trip phase shift increases ...
Incident power
Accelerated approach
of the resonance
P
P Pin
Pin
0 f
2(m–1)p 2mp 2(m +1)p
Tilting of the cavity fg
=
f LP
0+
0 f
0 resonance and bistability
2mp
23. 3. Theory & Historical background
The Kerr cavity: Nonlinear regime
Nonlinear resonances and Bistability
Bistability for various
d0
Linear cavity detuning constant detunings
D parameter (normalized
=
a respect to the losses)
with
P D
=4
Bistability for various
Incident power
constant driving powers
D
=0
P
Pin Pin
0
Onset of bistability: D
=3
dp
0
=f
2m -
0 Tilting of the cavity
0 f
0 resonance and bistability
2mp
24. 3. Theory & Historical background
The intracavity field can be in the lower state in one part of the cavity and
in the upper state in another part. The two parts can co-exist and be connected.
Diffractive autosolitons
Connecting 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)
P
P
0 Pin
t
25. 3. Theory & Historical background
The intracavity field can be in the lower state in one part of the cavity and
in the upper state in another part. The two parts can co-exist and be connected.
Diffractive autosolitons
Connecting 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)
P
P
The domain of
existence is limited
as the switching waves
cannot always lock
and the upper state
may be unstable
0 Pin
t
Not the type of localized structures we are concerned with in this work
26. 3. Theory & Historical background
Intracavity modulation instability
Studied through a linear stability analysis Anomalous dispersion
5
The homogeneous D
=
4
L. A. Lugiato and R. Lefever 4
upper state is
Y?
Phys. Rev. Lett. 58, D
=
2.5
unstable in favor of 3
P
2209 (1987)
a modulated solution 2 D
=
1
M. Haelterman, S. Trillo,
and S. Wabnitz 1
Opt. Lett. 17, 745 (1992)
0
0 4 8 12
X?
Pin
P
Frequency domain
P
t
0
27. 3. Theory & Historical background
Intracavity modulation instability
Studied through a linear stability analysis Anomalous dispersion
5
The homogeneous D
=
4
L. A. Lugiato and R. Lefever 4
upper state is
Y?
Phys. Rev. Lett. 58, D
=
2.5
unstable in favor of 3
P
2209 (1987)
a modulated solution 2 D
=
1
M. Haelterman, S. Trillo,
and S. Wabnitz 1
It can coexist in Opt. Lett. 17, 745 (1992)
different parts of 0
0 4 8 12
the cavity with the X?
Pin
homogeneous lower
state
P Localized dissipative structure
t
28. 3. Theory & Historical background
Intracavity modulation instability
Studied through a linear stability analysis Anomalous dispersion
5
The homogeneous D
=
4
L. A. Lugiato and R. Lefever 4
upper state is
Y?
Phys. Rev. Lett. 58, D
=
2.5
unstable in favor of 3
P
2209 (1987)
a modulated solution 2 D
=
1
M. Haelterman, S. Trillo,
and S. Wabnitz 1
It can coexist in Opt. Lett. 17, 745 (1992)
different parts of 0
0 4 8 12
the cavity with the X?
Pin
homogeneous lower
state
P Cavity soliton 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)
tW. J. Firth and A. J. 1623 (1996)
Phys. Rev. Lett. 76,
Scroggie,
29. 3. Theory & Historical background
Driving power (mW)
Cavity solitons arise through a sub-critical
0 50 100 150 200 250 300
Turing bifurcation
9
8
7
6
5
4
3
10 1.9
P [W] 1.8
1.6 1.6
8
1.4
1.2 1.2
6
1
Y
0.8 4.4 ps 4 0.8
0.6
0.4 ? = 3.3 0.4
2
0.2
0 0
20
- 0 20 0 2 4 6 8 10
Time [ps] X
30. 3. Theory & Historical background
Driving power (mW)
Cavity solitons arise through a sub-critical
0 50 100 150 200 250 300
Turing bifurcation
9
8
7
6
5
4
3
10 1.9
P [W] 1.8
1.6 1.6
8
1.4
1.2 1.2
6
1
Y
0.8 4.4 ps 4 0.8
0.6
0.4 ? = 3.3 0.4
2
0.2
0 0
20
- 0 20 0 2 4 6 8 10
Time [ps] X
31. 3. Theory & Historical background
Driving power (mW)
Cavity solitons arise through a sub-critical
0 50 100 150 200 250 300
Turing bifurcation
9
8
7
6
5
4
3
10 1.9
P [W] 1.8
1.6 1.6
8
1.4
1.2 1.2
6
? = 3.8 1
Y
0.8 4.4 ps 4 0.8
0.6
0.4 ? = 3.3 0.4
2
0.2
0 0
20
- 0 20 0 2 4 6 8 10
Time [ps] X
32. 3. Theory & Historical background
Driving power (mW)
Cavity solitons arise through a sub-critical
0 50 100 150 200 250 300
Turing bifurcation
9
2 8
E é
¶ 2 ¶ ù 7
=( E
êi
- D E (S
ih t )
1 +- 2 ú,t
)- +
t ë
¶ ¶
t 6
û 5
L. A. Lugiato and R. Lefever 4
h(
= 2)
sign b Phys. Rev. Lett. 58, 2209 (1987) 3
10 1.9
P [W] 1.8
1.6 1.6
8
1.4
1.2 1.2
6
? = 3.8 1
Y
0.8 4.4 ps 4 0.8
0.6
0.4 ? = 3.3 0.4
2
0.2
0 0
20
- 0 20 0 2 4 6 8 10
Time [ps] X
33. 3. Theory & Historical background
Driving power (mW)
Cavity solitons arise through a sub-critical
0 50 100 150 200 250 300
Turing bifurcation
9
2 8
E é
¶ 2 ¶ ù 7
=( E
êi
- D E (S
ih t )
1 +- 2 ú,t
)- +
t ë
¶ ¶
t 6
û 5
L. A. Lugiato and R. Lefever 4
h(
= 2)
sign b Phys. Rev. Lett. 58, 2209 (1987) 3
10 1.9
Similar to reaction P [W] 1.8
diffusion systems 1.6 1.6
8
1.4
Cavity solitons
1.2 1.2
are localized 6
dissipative ? = 3.8 1
Y
structures 0.8 4.4 ps 0.8
4
“à la” Prigogine
0.6
0.4 ? = 3.3 0.4
2
0.2
0 0
20
- 0 20 0 2 4 6 8 10
Time [ps] X
34. 3. Theory & Historical background
Driving power (mW)
Cavity solitons arise through a sub-critical
0 50 100 150 200 250 300
Turing bifurcation
9
2 8
E é
¶ 2 ¶ ù 7
=( E
êi
- D E (S
ih t )
1 +- 2 ú,t
)- +
t ë
¶ ¶
t 6
û 5
L. A. Lugiato and R. Lefever 4
h(
= 2)
sign b Phys. Rev. Lett. 58, 2209 (1987) 3
10 1.9
Similar to reaction P [W] 1.8
diffusion systems 1.6 1.6
8
1.4
Cavity solitons
1.2 1.2
are localized 6
dissipative ? = 3.8 1
Y
structures 0.8 4.4 ps 0.8
4
“à la” Prigogine
0.6
0.4 ? = 3.3 0.4
Fundamental 2
example of 0.2
self-organization
phenomena in 0 0
nonlinear optics 20
- 0 20 0 2 4 6 8 10
Time [ps] X
35. 4. Experimental setup
Experimental demonstration of temporal Kerr cavity solitons
Input
Fiber Coupler Output
90/10
Polarization
Controller
t R =s
1.85 m
90m
F =
24
Resonances: 22 kHz
290m
Fiber
Isolator
To avoid Brillouin
scattering
36. 4. Experimental setup
Experimental demonstration of temporal Kerr cavity solitons
DRIVING BEAM EDFA
1 kHz linewidth
DFB
1551 nm CW pump
Fiber Coupler Output
90/10
Polarization
Controller
t R =s
1.85 m
90m
F =
24
Resonances: 22 kHz
290m
Fiber
Isolator
To avoid Brillouin
scattering
37. 4. Experimental setup
Experimental demonstration of temporal Kerr cavity solitons
DRIVING BEAM EDFA
1 kHz linewidth
DFB
1551 nm CW pump
Fiber Coupler Fiber Coupler Output
90/10 95/5
Polarization
Controller
t R =s
1.85 m
90m
F =
24
Resonances: 22 kHz
290m
Fiber
Isolator Piezoelectric
Fiber Stretcher
To avoid Brillouin Controller
scattering
43. 5. Results
A single soliton in the cavity
Addressing pulse: Off - CS only sustained by the cw driving beam
The intracavity pulse persists in the cavity
for more than 1 s (> 550,000 round-trips)
Coherent driving
Losses
44. 5. Results
A single soliton in the cavity
Addressing pulse: Off - CS only sustained by the cw driving beam Experiment
Simulations
The intracavity pulse persists in the cavity
for more than 1 s (> 550,000 round-trips)
Coherent driving
Dispersion Nonlinearity
Losses
Autocorrelation reveals it is 4 ps long, Dispersion
matching simulations length: 230 m
45. 5. Results
A single soliton in the cavity
Addressing pulse: Off - CS only sustained by the cw driving beam Experiment
Simulations
The intracavity pulse persists in the cavity
for more than 1 s (> 550,000 round-trips)
Coherent driving
Dispersion Nonlinearity
Losses
Autocorrelation reveals it is 4 ps long, Dispersion
matching simulations length: 230 m
47. 5. Results
Interactions of temporal cavity solitons
Sending two close addressing pulses and
observing the CSs within the next 1 s
Addressing pulses closer than 25 ps
Only one CS present at
the output
48. 5. Results
Interactions of temporal cavity solitons
Sending two close addressing pulses and
observing the CSs within the next 1 s
Addressing pulses closer than 25 ps
Only one CS present at
the output
With a larger separation between
the addressing pulses ...
The two excited CSs repel
49. 5. Results
Interactions of temporal cavity solitons
Sending two close addressing pulses and
observing the CSs within the next 1 s
Addressing pulses closer than 25 ps
Only one CS present at
the output
With a larger separation between
the addressing pulses ...
The two excited CSs repel
... but repulsion gets
progressively weaker
50. 5. Results
Interactions of temporal cavity solitons
Sending two close addressing pulses and
observing the CSs within the next 1 s
Addressing pulses closer than 25 ps
Only one CS present at
the output
With a larger separation between
the addressing pulses ...
The two excited CSs repel
... but repulsion gets
progressively weaker
The CSs could be easily
trapped by modulating the
driving power
Potential buffer capacity:
45 kbit @ 25 Gbit/s
52. 5. Results
Writing dynamics of temporal cavity solitons
Output with off-center filter
Experiment Inside the cavity
Simulation
Time (100 µs/div)
Time (100 µs/div)
53. 5. Results
Erasing of temporal
cavity solitons
Complete erasing of the
cavity can be obtained
by switching off the
driving beam for about
4 round-trips
54. 5. Results
Erasing of temporal
cavity solitons
Complete erasing of the
cavity can be obtained
by switching off the
driving beam for about
4 round-trips
Driving beam switched
back on after
4 round-trips
55. 5. Results
Erasing of temporal
cavity solitons
Complete erasing of the
cavity can be obtained
by switching off the
driving beam for about
4 round-trips
Driving beam switched
back on after
4 round-trips
From there on, new CSs
can be written without
affecting the erasure
of neighboring CSs
56. 5. Results
Erasing of temporal
cavity solitons
Selective erasing of
one CS can be obtained
by overwriting it with
an addressing pulse
about 50% more
powerful
This realizes an
all-optical XOR
logic gate
57. 5. Results
Driving power (mW)
Breathing temporal cavity solitons
0 50 100 150 200 250 300
Above a certain driving power, 9
the cavity solitons become breathers 8
7
6
5
4
Hopf 3
10 bifurcation
1.9
1.8
1.6
8
1.4
1.2
6
? = 3.8 1
Y
4 0.8
0.6
? = 3.3 0.4
2
0.2
0 0
0 2 4 6 8 10
X
58. 5. Results
Driving power (mW)
Breathing temporal cavity solitons
0 50 100 150 200 250 300
Above a certain driving power, 9
the cavity solitons become breathers 8
7
6
5
4
Hopf 3
10 bifurcation
1.9
1.8
1.6
8
1.4
1.2
6
? = 3.8 1
Y
4 0.8
0.6
? = 3.3 0.4
2
0.2
0 0
Time (50 µs/div) 0 2 4 6 8 10
X
59. 6. Conclusion
We have reported the first direct experimental observation of
temporal cavity solitons as well as 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 system
with an instantaneous Kerr nonlinearity
Due to this simplicity, our experiments may constitute the
most fundamental example of self-organization in nonlinear optics
Kerr frequency combs generated in microresonators may be
the spectral signature of a temporal cavity soliton
P. Del’Haye et al,
Nature 450, 1214 (2007)