Transcript Zakharov 70 final - SOLITONS, COLLAPSES AND TURBULENCE

Solitons, Collapses and Turbulence
ULTRALONG FIBRE LASERS
Sergei K. Turitsyn
Photonics Research Group
Aston University, UK
Chernogolovka, 5 August, 2009
Acknowledgements
In collaboration with:
J. D. Ania-Castañón
S. Babin
G.E. Falkovich
V. Mezentsev
E. Podivilov
E.G. Turitsyna
T. J. Ellingham
D. Churkin
P. Harper
S. Kablukov
V. Karalekas
Supported by:
EPSRC, Information Technology
EPSRC, Physics and Engineering
HEFCE (UK)
The Royal Society
The Leverhulme Trust
Ericsson (UK)
XTera Communications (UK)
Russian Ministry of Science
British Council
Advantage West Midlands
European Research and
Development Fund
Chernogolovka, 5 August, 2009
Back in the USSR
There are places to remember …
It was twenty years ago today,
that Sgt. Pepper taught the band to play…
Solitons, wave collapse, self-focusing, wave turbulence, NLSE…
Chernogolovka, 5 August, 2009
Starting from conclusions
Message of the talk:
Ultra-long Raman fibre laser is a new photonic device that
brings together soliton theory (important for applications of
lossless fibre spans - transmission, signal processing) and
wave turbulence theory (responsible for the spectral
broadening of laser radiation in the cavity) that are both
important for the operation and applications of such lasers.
Chernogolovka, 5 August, 2009
Ultra-long Raman fibre lasers
Raman amplification – practical example of nonlinear photonic technology
Amplified
Spontaneous
Emissions
Transmission Fibre
Amplified
Spontaneous
Emissions
Amplified
Signal
Weak
Signal
1550 nm
pump wave output
pump wave input
e.g. 1450 nm
 Distributed Raman fibre amplifiers provide a gain medium for signal in optical
fibres over distances on the scale of 100 km and more.
 Fibre Raman lasers with cavities of 1 km scale exploit Raman effect to create
radiation at shifted Stokes wavelengths in optical fibre waveguide.
 A combination of the techniques of a distributed amplification developed for
signal transmission in long fibre spans and a laser cavity formation using fibre
Bragg grating (FBG) => Ultra-long fibre laser.
Chernogolovka, 5 August, 2009
Ultra-long fibre laser
Some people see things and say "Why?", others dream things that never were and
say "Why not?" George Bernard Shaw
Lasers are typically considered in the context of their
applications as coherent sources of light.
New concept: to use ultra-long Raman fibre laser as a quite
unique, very specific type of transmission medium.
Chernogolovka, 5 August, 2009
Ultra-long Raman fibre laser
System design is based on symmetry:
- Use of two bi-directional primary pumps around 1365 nm.
- Fibre Bragg gratings  cavity for 1455 nm radiation.
- High enough pump power  whole link becomes an ultra-long laser
operating at 1455 nm .
Schematic depiction of the ultra-long Raman fibre laser
Chernogolovka, 5 August, 2009
Operation principle (symmetry is the key)
Primary pumps at 1365 nm
generate radiation at 1455 nm.
Secondary pumps at 1455 nm
are stabilized when the energy
transfer from the primary pump
balances attenuation and energy
loss to the signal.
 Due to symmetry, spatial
distribution of the radiation
at 1455 nm is even.
Signal at 1550 nm is amplified
by the evenly distributed power
at 1455 nm leading to quasi-lossless
amplification.
a)
b)
Pumps, signal and noise evolution inside the cell for a 60 km span length.
Pumps, signal and noise evolution inside the cell for a 100 km span length.
Chernogolovka, 5 August, 2009
270 km ultra-long fibre laser
Low loss both for pumping waves and generated radiation => record length
Chernogolovka, 5 August, 2009
Ultra-long fibre laser:
Solitons
Previous applications of the nonlinear Schrödinger equation (NLSE):
A  2 A
2
i
 2  A A  iG ( Z ) A  i   gain ( z )A
z t
A U e
0 G ( z  )dz 
z
;
z

c( z )  exp  2 G ( z )dz 
 0

U 0  2U 0
U  2U
2
2
averaging=>
i



c
(
z
)

U
i
 2  c( z ) U U  0
0 U0  0
2
z
t
z
t
True NLSE, but on average
Chernogolovka, 5 August, 2009
True soliton generation
First experimental transmission of true NLSE soliton. P. Harper et al, 2008
Normalised
intensity
Frequency Resolved Optical Gating (FROG)
0
-10
-5
0
5
10
Time (ps)
Normalised
intensity
Normalised
intensity
0
0
-10
-5
0
5
-10
10
-5
0
5
10
Time (ps)
Time (ps)
Normalised
intensity
0
FROG picture for soliton
-10
-5
0
5
10
Time (ps)
Chernogolovka, 5 August, 2009
Experimental observation of true soliton
Amazingly, this is the first experimental demonstration of true soliton
propagation in the integrable system (without loss!) implemented in optical fibre.
0 km
3 km
5 km
7 km
10 km
12 km
14 km
17 km
22 km
Wavelength
Time
2
Top row: experimental results
1.5
T/T0
Bottom: numerical simulations
Pulse width vs Distance
1
0.5
0
0
5
10
15
20
25
Chernogolovka,
5 August, 2009
Distance Z/L
D
Ultra-long fibre laser:
From solitons to wave turbulence
Science never solves a problem
without creating ten more."
George Bernard Shaw
Telecommunication applications => quasi - lossless fibre span => true solitons
Laser properties of such ultra-long resonator => ?
Chernogolovka, 5 August, 2009
Resonator modes are observed in cavities up to 270 km
Inter-mode beating
peaks correspond to the
fundamental relation
for the laser modes
c
 
2nL
Insets: radio frequency
spectra of ultra-long fibre
laser for different cavity
lengths
Chernogolovka, 5 August, 2009
Random temporal behaviour of radiation
Typical random temporal behavior of the generated radiation
Nonlinear dynamics of modes is not deterministic
Chernogolovka, 5 August, 2009
Spectral broadening of the radiation
Intra-cavity power
Connection with wave turbulence:
S. Babin, E. Podivilov et al, JOSA B, 2007
 Number of the longitudinal modes:
 B /   B2nL / c  L
 Interaction of 1 000 000 (L=1 km) or
even 100 000 000 (L=100 km) laser modes!
 Large (huge) number of small amplitude
modes, but nonlinear effects are important.
• Broadening can be observed at high enough powers (P > 10 mW)
• Level of broadening is growing with increase of the power =>
nonlinear nature of the spectral broadening.
Chernogolovka, 5 August, 2009
Ultra-long fibre laser => optical wave turbulence
Motivation: nonlinear spectral broadening of radiation
Side lobs due to grating
reflection function
System forgets about
the boundary conditions
when power is increased
Spectral broadening with increase of the cavity power
Chernogolovka, 5 August, 2009
Mathematical model for short fibre lasers
S. Babin, E. Podivilov et al, JOSA B, 2007 – model for short fibre lasers
Randomly seeded modes are nonlinear coupled
dEk
1
*
 rt
 ( g   k  i k ) Ek  iL El Em El  m  k
dt
2
l ,m
Gain/loss
 rt  2nL / c – cavity round trip time
– integral round trip gain
Dispersion
Four-wave-mixing
 k   ln( R1k R2 k ) - effective grating losses
Gain is saturated with power.
Limitation of the model: spatial distribution of power is neglected
Chernogolovka, 5 August, 2009
Ultra-long Raman fibre laser => optical wave turbulence
• The key interaction mechanism – four wave mixing between
longitudinal cavity modes enhanced by the long interaction length.
• Huge number of weakly interacting waves => fast randomisation
of the phases => statistical description =>
Mathematical tools of a weak wave turbulence. 1d problem.
• V.E. Zakharov, V.S. L'vov, and G. Falkovich, Kolmogorov spectra of turbulence I:
Wave turbulence (Springer-Verlag, Berlin, 1992).
• A. Dyachenko, A.C. Newell, A. Pushkarev, V.E. Zakharov, Optical turbulence: weak
turbulence, condensates and collapsing fragments in the nonlinear Schrodinger
equation, Physica D 57 (1-2) 96 (1992) .
• V.E. Zakharov, F. Dias, A. Pushkarev, One-dimensional wave turbulence, Physics
Reports, 398, 1, 1-65 (2004).
Chernogolovka, 5 August, 2009
Terminology: Optical turbulence
The term optical turbulence is used in the literature in rather
different research contexts:
• An atmospheric effect caused by fluctuations of the refractive index
in air that affects the propagation of light beams.
• Optical turbulence in experiments with a ring resonator
synchronously driven by a train of picosecond light pulses with
feedback (F. Mitschke, G. Steinmeyer and A. Schwache).
• Turbulent-like behaviour of optical waves can be found in
semiconductor lasers with delayed feedback - generalized complex
Swift-Hohenberg equation (Hochheiser, Moloney, Lega, Newell).
• Theoretical studies of wave turbulence in the context of 2D
nonlinear Schrödinger equation are often called optical turbulence
because of its relevance to the propagation of high-frequency light
beams (Zakharov, Newell, Pushkarev, Nazarenko, Dyachenko el al).
Chernogolovka, 5 August, 2009
Kinetic equation model for short fibre laser
Nonlinear attenuation
Spectrum of generated modes
[ (W)  a 2 L   NL ]I (W) 
 2 g R PLI (W) 
 NL 
Nonlinear gain
 NL
I
2
 I (W1 ) I (W 2 ) I (W1  W 2  W)dW1dW 2
2
IL
3 1  (4 L / 3 2 )2
Valid when
 I  4 W2
S. Babin, E. Podivilov et al, JOSA B, 2007
Analytical solution for the formed spectrum in shorter (~ 1 km) laser
(under assumption of the Gaussian shape of the fibre gratings response)
2I0
I (W ) 
p G cosh(2 W G )
G ~ 2I 0 L  2
Chernogolovka, 5 August, 2009
Weak wave turbulence approach
1 km laser cavity - 1000000 longitudinal modes; order of 1 W power is
shared sharing between them finite generated power
Babin et al 2007 - weak wave turbulence: assuming weak Four Wave
Mixing (FWM) interactions, wide spectrum and the random phases.
Weak turbulence: effective nonlinearity / dispersion ratio
<<1
Prediction of weak turbulence theory: sign of the dispersion has no impact.
Motivation:
- FWM + modulation instability
- FWM
Turitsyna, Falkovich, Turitsyn, Mezentsev, 2009
Chernogolovka, 5 August, 2009
Testing of modelling: power generation
Modelling gives a good approximation of key measured laser characteristics
Points – experiment
Solid lines - numerics
Power threshold of laser generation is increasing
with length due to additional losses
Chernogolovka, 5 August, 2009
Impact of the dispersion sign
on the total generated power
Considered
 2 L from -300 to 300 ps²
Anomalous dispersion
(with modulation instability)
Chernogolovka, 5 August, 2009
Impact of the dispersion sign on the
total generated power
Dramatic difference in the case of normal dispersion (no MI)
Chernogolovka, 5 August, 2009
Histograms of the total generated power
Intermediate narrow
spectrum - less
fluctuation, asymmetric
State after narrow
spectrum is destroyed wider fluctuation range,
more symmetric
distribution
Modulation instability
suppresses power
fluctuations compared
to pure FWM
interactions in case of
normal dispersion
Chernogolovka, 5 August, 2009
Degrees of freedom. Mode cross-correlations
1
K nm ( )   an (t )a (t   )  lim
T  T
*
m
t 0 T
*
a
(
t
)
a
 n m (t   )dt
t0
Scale of mode cross-correlations – many degrees of freedom
Chernogolovka, 5 August, 2009
Nonlinearity versus dispersion
in the developed asymptotic states
Nonlinear effects vs dispersive:
 Nonlinearity / dispersion ratio
does not depend on
and the total pump power.
 Since 
 1, the developed
state can not be treated within
weak turbulence approximation.
Strong optical wave turbulence
Chernogolovka, 5 August, 2009
Another twist: Ultra-long random Rayleigh lasers
1550 nm
Raman gain
Laser power
Loss level
LRS
0
Random distributed
feedback
Lost scattered photons
incident
photons
Amplified
backscattered
photons
Raman pump
LRS
z
Laser
output
2 pump lasers
1455 nm
Backscattered
photons
Lasing in random amplifying medium (proposed by Letokhov in 1968)
Chernogolovka, 5 August, 2009
Lasing supported by randomness
Typical laser threshold
Stochastic behaviour
near the threshold
and stabilisation
5
160
140
Amplitude (a.u.)
Output power (mW)
4
120
100
80
60
40
2
1
20
0
0,0
3
0,5
1,0
1,5
2,0
Total pump power (W)
2,5
0
0,0
0,5
1,0
1,5
2,0
2,5
Time (ms)
 New type of laser – ultra-long random laser
 A new, high-precision photonic tool to study wave
transport and localization in 1d disordered medium
Chernogolovka, 5 August, 2009
Conclusions
 Experimental demonstration of the longest laser with the
resolvable mode structure with a cavity of 270 km. New
paradigm – use of laser as a transmission mdeium.
 In the short (< 25 km) fibre spans the signal attenuation
is effectively zero, opening ways for applications of
integrable nonlinear systems in optical data processing.
New practical frame for soliton applications.
 Spectral broadening – four-wave-mixing induced
8
10
stochastic interaction of up to ~
cavity modes
generated in ultra-long fibre laser resonator
Chernogolovka, 5 August, 2009
Conclusions
The sign of cavity dispersion has dramatic impact on
optical turbulence that determines the spectral and
temporal properties of generated radiation.
Normal dispersion: intermediate state (condensate)
with an extremely narrow spectrum that experiences
an instability and a sharp transition to a strongly
fluctuating regime.
Anomalous dispersion: triangular spectra and more
coherent temporal behaviour of generated radiation.
Chernogolovka, 5 August, 2009
Conclusions
An example of one-dimensional wave turbulence in optical
fibre system. Wave turbulence of radiation at 1455 nm in ultralong fibre laser supports implementation of the integrable
nonlinear system for signal at 1550 nm.
The ultra-long Raman fibre laser brings together research and
engineering areas such as laser physics and optical
communications and mathematical theories of solitons
(applications of lossless fibre spans – transmission, signal
processing), wave turbulence (responsible for the spectral
broadening of laser radiation in the cavity) and disordered
systems (ultra-long random laser).
Chernogolovka, 5 August, 2009
Ultra-long fibre laser: Dreams
 Quantum key distribution systems use entanglement - a quantum mechanical
phenomenon, in which the quantum states of two or more objects are linked together.
 In the ultra-long laser two edges of the fibre cavity (that can be separated by
hundreds of km) are connected through laser modes.
Chernogolovka, 5 August, 2009
Then you can start to make it better…
 “Normal lasers” - in 1960s – “a solution looking for a
problem”
 Present time - markets: communication, life sciences &
health care, manufacturing, mobility & transport, military &
security, illumination & energy, pollution control,
entertainment, food industry, basic science.
 Ultra-long fibre lasers – now – high-speed optical
communications, possible applications for secure
communications, but mostly blue sky research.
Chernogolovka, 5 August, 2009
Solitons, Collapses and Turbulence
Jojo was a man who thought he was a loner,
But he knew it couldn't last.
Jojo left his home in Tucson, Arizona
…
Get back, get back.
“There are no such things as applied
Get back to where you once belonged
sciences,
only applications of science.”
Get back, get
back.
Get back to where you once belonged...
Louis Pasteur
Beatles, Get back, 1970
After 20 years of work on applied things we get back to where we started:
solitons (in lasers), self-focusing (fs inscription), wave turbulence (fibre
lasers), NLSE, …
Chernogolovka, 5 August, 2009