Supercontinuum Generation
in Photonic Crystal Fibers
John M. Dudley
Laboratoire d’Optique P-M Duffieux,
Institut FEMTO-ST CNRS UMR 6174
Université de Franche-Comté
BESANÇON, France.
POWAG 2004 Bath July 12-16
With thanks to …
Université Libre de Bruxelles
& University of Auckland
Stéphane Coen
Université de Franche-Comté
Laurent Provino, Hervé Maillotte, Pierre Lacourt, Bertrand Kibler,
Cyril Billet
Université de Bourgogne
Guy Millot
Georgia Institute of Technology
Rick Trebino, Xun Gu, Qiang Cao
National Institute of Standards
& Technology
Kristan Corwin, Nate Newbury, Brian Washburn, Scott Diddams
+
Ole Bang (COM), Ben Eggleton (OFS & Sydney), Alex Gaeta (Cornell),
John Harvey (Auckland), Rüdiger Paschotta (ETH Zurich),
Stephen Ralph (Georgia Tech), Philip Russell (Bath), Bob Windeler (OFS)
+
ACI photonique
What exactly are we trying to understand?
Ranka et al. Optics Letters 25, 25 2000
Femtosecond Ti:sapphire laser
Anomalous GVD pumping
grating
PCF
• Output spectrum
What exactly are we trying to understand?
Birks et al. Optics Letters 25, 1415 2000
Femtosecond Ti:sapphire laser
Anomalous GVD pumping
grating
TAPER
• Output spectrum
What exactly are we trying to understand?
Ranka et al. Optics Letters 25, 25 2000
Femtosecond Ti:sapphire laser
Anomalous GVD pumping
PCF
• Broadening mechanisms
•
•
•
•
Spectral structure
Evolution of spectrum along the fiber
• Output spectrum
Stability
Flatness
…etc…
Understand, control, exploit…
grating
Objectives
● Develop a detailed understanding of ultrashort pulse propagation
and supercontinuum (SC) generation in solid-core PCF
Concentrate on femtosecond pulse pumping regime
– soliton generation dynamics
– noise and stability issues
● Appreciate the utility of time-frequency spectrograms for
interpreting nonlinear fiber pulse propagation
● Briefly (if time) address mechanisms using longer pulses
Introduction (I)
● It has been known since 1970 that ultrashort light pulses injected in
a nonlinear medium yield extreme spectral broadening or
supercontinuum (SC) generation.
● Multiple physical processes involved – Self- & cross-phase modulation
–
–
Multi-wave mixing
Raman scattering
…etc…
Introduction (II)
● Many previous studies of spectral broadening carried out with
conventional fibers since 1971.
● Higher nonlinearity and novel dispersion of PCF has meant that
much old physics has been poorly recognised as such.
● There are, however, new features associated with SC generation in
PCF based on pumping close to near-IR zero dispersion points.
Wavelength (nm)
300
1300
Dn = 770 THz
Dn/n0 ~ 2
2000
Dn = 81 THz
Dn/n0 ~ 0.5
Pulse propagation in single mode fibers
Analysis of single-mode fiber propagation equations yield:
scalar approach
transverse
profile
field
envelope
propagation
constant
Frequency dependence of b – chromatic dispersion
(group velocity)-1
group velocity dispersion (GVD)
[ps2/km]
[ps / nm·km]
Propagation equation (I)
Nonlinear Envelope Equation (NEE)
 co-moving frame
dispersion
co-moving frame
Kerr nonlinearity
Raman response
self-steepening
SPM, FWM, Raman
Propagation equation (II)
Nonlinear Envelope Equation (NEE)
 co-moving frame
dispersion
self-steepening
SPM, FWM, Raman
Validity to the few-cycle regime has been established
Blow & Wood
Brabec & Krausz
Ranka & Gaeta
Karasawa et al.
IEEE JQE 25 2665 (1989)
Phys. Rev. Lett. 78 3283 (1997)
Opt. Lett. 23 534 (1998)
IEEE JQE 37 398 (2001)
Application to PCF pulse propagation
Gaeta
Dudley & Coen
Opt. Lett. 27 924 (2002)
Opt. Lett. 27 1180 (2002)
Simulations of SC generation in PCF
• We first consider propagation in highly nonlinear PCF with a high
air-fill fraction, and a small central “core” diameter  2.5 mm
• Treat anomalous dispersion regime pumping l > 780 nm
Simulations of SC generation in PCF
• We first consider propagation in highly nonlinear PCF with a high
air-fill fraction, and a small central “core” diameter  2.5 mm
By the way…
FREE SOFTWARE for PCF dispersion
calculation (multipole method) now
available from University of Sydney
cudosMOF
• Treat anomalous dispersion regime pumping l > 780 nm
So…what does a simulation look like?
Evolution with propagation distance
Complex spectral and temporal evolution in 15 cm of PCF
Pulse parameters: 30 fs FWHM, 10 kW peak power, l = 800 nm
Temporal evolution
Distance (m)
Distance (m)
Spectral evolution
Wavelength (nm)
Time (ps)
Understanding the details…
Solitons
Perturbed solitons
Raman self-frequency shift
Dispersive waves
Simplify things : Nonlinear Schrödinger Equation
Nonlinear Schrödinger Equation (NLSE):
co-moving frame
Kerr nonlinearity
instantaneous power (W)
The NLSE has a number of analytic solutions and scaling rules.
Higher-order effects can (sometimes) be treated as perturbations,
making the physics clear.
Nonlinear Schrödinger Equation
Nonlinear Schrödinger Equation (NLSE)
co-moving frame
Kerr nonlinearity
instantaneous power (W)
Consider propagation in highly
nonlinear PCF: ZDW at 780 nm
l = 850 nm
b2 = -13 ps2 km-1
g = 100 W-1km-1
T0 = 28 fs (FWHM 50 fs)
Fundamental solitons
Initial condition
= 165 W
N=1
Invariant evolution
soliton
wavenumber
Higher-order solitons
Initial condition
N=3
Periodic evolution
= 10 cm
Higher-order solitons
Initial condition
Periodic evolution
= 10 cm
Soliton decay – soliton fission
In the presence of perturbations, a higher order N-soliton is unstable,
and will break up into N constituent fundamental 1-solitons
…quite a bit of work yields…
Soliton decay – soliton fission
In the presence of perturbations, a higher order N-soliton is unstable,
and will break up into N constituent fundamental 1-solitons
Initial condition
Raman
Higher-order
dispersion
NLSE + PERTURBATION
Selfsteepening
Soliton decay – soliton fission
In the presence of perturbations, a higher order N-soliton is unstable,
and will break up into N constituent fundamental 1-solitons
Soliton decay – soliton fission
In the presence of perturbations, a higher order N-soliton is unstable,
and will break up into N constituent fundamental 1-solitons
Physics of the self-frequency shift
Dt’
Dt
Dl’
Dl
FT
NN==11
-13
-13
THz
THz
l
t
sees
seesgain
gain
25 fs FWHM  14 THz bandwidth
pump
pump
Soliton decay – soliton fission
Illustration : Raman perturbation only
ZDW
Distance (z/zsol)
Distance (z/zsol)
Pulse parameters: N = 3, FWHM = 50 fs, P0 = 14.85 kW, zsol = 10 cm
Time (ps)
Wavelength (nm)
Soliton decay – soliton fission
Illustration : Raman perturbation only
Distance (z/zsol)
Pulse parameters: N = 3, FWHM = 50 fs, P0 = 14.85 kW, zsol = 10 cm
Time (ps)
The spectrogram
● The spectrogram shows a pulse in both domains simultaneously
gate
pulse
pulse variable delay gate
Soliton fission in the time-frequency domain
ZDW
projected axis spectrogram
Dispersive wave radiation
A propagating 1-soliton in the presence of higher-order dispersion
can shed energy in the form of a low amplitude dispersive wave.
Phasematching between the propagating soliton and a linear wave.
DW
b3 > 0  DW > 0
BLUE SHIFT
l
Wai et al.
Opt. Lett. 11 464 (1986)
Akhmediev & Karlsson
Phys. Rev. A 51 2602 (1995)
Dispersive wave radiation
A propagating 1-soliton in the presence of higher-order dispersion
can shed energy in the form of a low amplitude dispersive wave.
Distance (m)
Distance (m)
Pulse parameters: N = 1 soliton at 850 nm, b3 > 0, no Raman
Wavelength (nm)
Time (ps)
Does that remind you of anything?
SC generation – anomalous dispersion pump
Signatures of soliton fission and dispersive wave generation
in SC generation are now apparent…
Temporal evolution
Distance (m)
Distance (m)
Spectral evolution
Wavelength (nm)
Time (ps)
SC generation – anomalous dispersion pump
Signatures of soliton fission and dispersive wave generation
in SC generation are now apparent…
Temporal evolution
Distance (m)
Distance (m)
Spectral evolution
Wavelength (nm)
Time (ps)
SC generation – anomalous dispersion pump
DW
115 THz
S3
S2
ZDW
fine
structure
S1
Intuitive correlation of
time and frequency domains
What about the experiments ?
Spectrum (20 dB / div.)
Experimental Measurements – spectra
Experiment
Simulation
Wavelength (nm)
Experimental Measurements – Raman solitons
Good comparison between simulations and experiments
Simulation
Washburn et al. Electron. Lett. 37 1510 (2001)
Experiment
Experimental Measurements – XFROG
XFROG measures the spectrally resolved cross-correlation
between a reference field ERef(t) (fs pump pulse at 800 nm) and
the field to be characterized E(t) (the SC from 500-1200 nm).
The cross-correlation is measured using sum-frequency
generation (SFG) by mixing the reference pump pulse with
the SC.
Experimental Measurements – XFROG
Interpretation of experimental XFROG data is facilitated by the
numerical results above.
Distinct anomalous
dispersion regime
Raman solitons
Low amplitude
ultrafast oscillations
Gu et al.
Dudley et al.
Opt. Lett. 27 1174 (2002)
Opt. Exp. 10 1251 (2002)
Experimental Measurements – XFROG
Interpretation of experimental XFROG data is facilitated by the
numerical results above.
Distinct anomalous
dispersion regime
Raman solitons
Low amplitude
ultrafast oscillations
Gu et al.
Dudley et al.
Opt. Lett. 27 1174 (2002)
Opt. Exp. 10 1251 (2002)
SC generation – normal dispersion pump
Four wave mixing
ws
wp wi
w
Dudley et al. JOSA B 19, 765-771 (2002)
SC generation – anomalous vs normal dispersion pumps
Each case would yield visually similar supercontinua but they are
clearly very different
 the difference is in the dynamics
ZDW
ZDW
Propagation with negative dispersion slope
For a PCF with a second zero dispersion point, the negative
dispersion slope completely changes the propagation dynamics
reduced core diameter ~ 1.2 mm
Modeled GVD
old regime
b3 > 0
Harbold et al. Opt. Lett. 27, 1558 (2002)
Skyrabin et al. Science 301 1705 (2003)
Hillisgøe et al. Opt. Exp. 12, 1045 (2004)
Efimov et al. CLEO Paper IML7 (2004)
new regime
b3 < 0
Propagation with negative dispersion slope
For a PCF with a second zero dispersion point, the negative
dispersion slope completely changes the propagation dynamics
reduced core diameter ~ 1.2 mm
Modeled GVD
old regime
b3 > 0
Harbold et al. Opt. Lett. 27, 1558 (2002)
Skyrabin et al. Science 301 1705 (2003)
Hillisgøe et al. Opt. Exp. 12, 1045 (2004)
Efimov et al. CLEO Paper IML7 (2004)
new regime
b3 < 0
Suppressing the Raman self-frequency shift
Suppressing the Raman self-frequency shift
Initial Raman shifting is arrested by dispersive wave generation
ZDW
Distance (m)
Distance (m)
Pulse parameters: 50 fs FWHM, 2 kW peak power, l = 1200 nm, N ~ 1.7
Wavelength (nm)
Time (ps)
Suppressing the Raman self-frequency shift
A detailed treatment shows that dispersive wave generation is
associated with spectral recoil of the generating soliton.
Recoil
RED SHIFT
ZDW
b3 > 0
BLUE SHIFT
DW
l
In the “conventional regime” the Raman shift and spectral recoil are
in the same direction and reinforce.
Suppressing the Raman self-frequency shift
A detailed treatment shows that dispersive wave generation is
associated with spectral recoil of the generating soliton.
DW
b3 < 0
RED SHIFT
ZDW
Recoil
BLUE SHIFT
l
Around the second ZDW, the Raman shift and spectral recoil are in
opposite directions and can thus compensate.
Suppressing the Raman self-frequency shift
Biancalana et al.
Theory of the self frequency shift compensation by the resonant
radiation in photonic crystal fibers
To appear in Phys Rev E August 2004.
SC generation with nanosecond pulses
1 ns input pulses from mchip laser at 1064 nm, 4 m of PCF
P = 26 W
P = 43 W
P = 98 W
P = 72 W
SC generation with nanosecond pulses
Simulations reproduce experiments over a 50 dB dynamic range
P = 43 W
P = 26 W
P = 98 W
exp
exp
exp
sim
sim
sim
Supercontinuum stability
As early as 2001, experiments reported that supercontinuum
generation in PCF could be very unstable.
Hollberg et al. IEEE J. Quant. Electron. 37 1502 (2001)
Nonlinear spectral broadening processes are very sensitive to
technical or quantum noise sources.
Nakazawa et al. Phys. Rev. A 39 5768 (1989)
The NEE model, extended to include quantum noise sources, can
be used to clarify physical origin of instabilities and determine
useful parameter regimes for quiet continuum generation.
Drummond & Corney J. Opt. Soc. Am. B 18, 139 (2001)
Quantifying the supercontinuum coherence
150 fs input pulses, 1 nJ energy at 850 nm, 10 cm of PCF
● We quantify the phase stability in
terms of the degree of coherence:
 Dudley and Coen, Opt. Lett. 27, 1180 (2002)
Experimentally accessible
 Gu et al. Opt. Exp. 11, 2697 (2003).
 Lu & Knox Opt. Exp. 12, 347 (2004).
 Giessen et al. Talk today at 15:15
Quantifying the supercontinuum coherence
150 fs input pulses, 1 nJ energy at 850 nm, 10 cm of PCF
● We quantify the phase stability in
terms of the degree of coherence:
 Dudley and Coen, Opt. Lett. 27, 1180 (2002)
Experimentally accessible
 Gu et al. Opt. Exp. 11, 2697 (2003).
 Lu & Knox Opt. Exp. 12, 347 (2004).
 Giessen et al. Talk today at 15:15
Conclusions
Physics of femtosecond pulse pumped SC generation in PCF with
a single ZDW can be understood in terms of well-known physics.
More novel effects (higher order dispersion, negative dispersion
slope) may have been anticipated theoretically but PCF allows
them to be studied through clean experiments.
Technological applications require that the physics is understood.
Still a lot to do … noise, new SC regimes, more XFROG experiments,
polarization-dependent effects…