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Supercontinuum Generation in Photonic Crystal F ibers. 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 Li bre de Bruxelles - PowerPoint PPT Presentation
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Supercontinuum Generation in Photonic Crystal Fibers
John M. Dudley
Laboratoire d’Optique P-M Duffieux,Institut FEMTO-ST CNRS UMR 6174Université de Franche-Comté BESANÇON, France.
POWAG 2004 Bath July 12-16
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
With thanks to …
What exactly are we trying to understand?
Femtosecond Ti:sapphire laserAnomalous GVD pumping PCF grating
• Output spectrum
Ranka et al. Optics Letters 25, 25 2000
• Output spectrum
What exactly are we trying to understand?
Femtosecond Ti:sapphire laserAnomalous GVD pumping TAPER grating
Birks et al. Optics Letters 25, 1415 2000
What exactly are we trying to understand?
Femtosecond Ti:sapphire laserAnomalous GVD pumping PCF grating
• Output spectrum
Ranka et al. Optics Letters 25, 25 2000
• Broadening mechanisms• Spectral structure• Evolution of spectrum along the fiber• Stability• Flatness …etc…
Understand, control, exploit…
Objectives
● Develop a detailed understanding of ultrashort pulse propagation and supercontinuum (SC) generation in solid-core PCF
● Appreciate the utility of time-frequency spectrograms for interpreting nonlinear fiber pulse propagation
● Briefly (if time) address mechanisms using longer pulses
Concentrate on femtosecond pulse pumping regime
– soliton generation dynamics
– noise and stability issues
● It has been known since 1970 that ultrashort light pulses injected in a nonlinear medium yield extreme spectral broadening or supercontinuum (SC) generation.
Introduction (I)
● Multiple physical processes involved – Self- & cross-phase modulation– Multi-wave mixing– Raman scattering
…etc…
● 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.
Introduction (II)
300 1300 2000
~ 2 ~ 0.5
770 THz 81 THz
Wavelength (nm)
scalar approach
fieldenvelope
propagation constant
Pulse propagation in single mode fibers
Analysis of single-mode fiber propagation equations yield:
transverse profile
Frequency dependence of – chromatic dispersion
group velocity dispersion (GVD)(group velocity)-1
[ps2/km] [ps / nm·km]
Propagation equation (I)
Nonlinear Envelope Equation (NEE)
co-moving frame
dispersion self-steepening SPM, FWM, Raman
co-moving frame
Kerr nonlinearity
Raman response
Propagation equation (II)
Nonlinear Envelope Equation (NEE)
co-moving frame
dispersion self-steepening SPM, FWM, Raman
Blow & Wood IEEE JQE 25 2665 (1989)Brabec & Krausz Phys. Rev. Lett. 78 3283 (1997)Ranka & Gaeta Opt. Lett. 23 534 (1998)Karasawa et al. IEEE JQE 37 398 (2001)
Validity to the few-cycle regime has been established
Application to PCF pulse propagation
Gaeta Opt. Lett. 27 924 (2002)Dudley & Coen Opt. Lett. 27 1180 (2002)
• We first consider propagation in highly nonlinear PCF with a high air-fill fraction, and a small central “core” diameter 2.5 m
Simulations of SC generation in PCF
• Treat anomalous dispersion regime pumping > 780 nm
• We first consider propagation in highly nonlinear PCF with a high air-fill fraction, and a small central “core” diameter 2.5 m
Simulations of SC generation in PCF
• Treat anomalous dispersion regime pumping > 780 nm
By the way…
FREE SOFTWARE for PCF dispersion calculation (multipole method) now available
from University of Sydney
cudosMOF
So…what does a simulation look like?
Evolution with propagation distance
Time (ps)
Dis
tanc
e (m
)
Complex spectral and temporal evolution in 15 cm of PCF
Dis
tanc
e (m
)
Wavelength (nm)
Spectral evolution Temporal evolution
Pulse parameters: 30 fs FWHM, 10 kW peak power, = 800 nm
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
= 850 nm2 = -13 ps2 km-1
= 100 W-1km-1
0 = 28 fs (FWHM 50 fs)
Fundamental solitons
Initial condition
= 165 W
Invariant evolution
solitonwavenumber
N = 1
Higher-order solitons
Initial condition
Periodic evolution
= 10 cm
N = 3
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
NLSE + PERTURBATION
Raman
Self-steepening
Higher-order dispersion
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
t
FT
pump
sees gain
-13THz
N = 1
25 fs FWHM 14 THz bandwidth
t
’FT
’
pump
sees gain
-13THz
N = 1
Soliton decay – soliton fission
Illustration : Raman perturbation onlyD
ista
nce
(z/z
sol)
Time (ps)
Pulse parameters: N = 3, FWHM = 50 fs, P0 = 14.85 kW, zsol = 10 cm
Dis
tanc
e (z
/zso
l)
Wavelength (nm)
ZD
W
Soliton decay – soliton fission D
ista
nce
(z/z
sol)
Time (ps)
Illustration : Raman perturbation only
Pulse parameters: N = 3, FWHM = 50 fs, P0 = 14.85 kW, zsol = 10 cm
The spectrogram
● The spectrogram shows a pulse in both domains simultaneously
pulse
gate
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.
> 0 > 0 BLUE SHIFT
Phasematching between the propagating soliton and a linear wave.
Wai et al. Opt. Lett. 11 464 (1986)
Akhmediev & KarlssonPhys. Rev. A 51 2602 (1995)
Dispersive wave radiation
Time (ps)
Dis
tanc
e (m
)
Dis
tanc
e (m
)
Wavelength (nm)
Pulse parameters: N = 1 soliton at 850 nm, > 0, no Raman
A propagating 1-soliton in the presence of higher-order dispersion can shed energy in the form of a low amplitude dispersive wave.
Does that remind you of anything?
SC generation – anomalous dispersion pump
Time (ps)
Dis
tanc
e (m
)
Signatures of soliton fission and dispersive wave generationin SC generation are now apparent…
Dis
tanc
e (m
)
Wavelength (nm)
Spectral evolution Temporal evolution
SC generation – anomalous dispersion pump
Time (ps)
Dis
tanc
e (m
)
Signatures of soliton fission and dispersive wave generationin SC generation are now apparent…
Dis
tanc
e (m
)
Wavelength (nm)
Spectral evolution Temporal evolution
SC generation – anomalous dispersion pump
ZDW
Intuitive correlation of time and frequency domains
DW
S1
S2
S3
115 THzfine
structure
What about the experiments ?
Experimental Measurements – spectra
Wavelength (nm)
Sp
ectr
um (
20 d
B /
div.
)
Simulation
Experiment
Experimental Measurements – Raman solitons
Good comparison between simulations and experiments
Washburn et al. Electron. Lett. 37 1510 (2001)
Simulation 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 amplitudeultrafast oscillations
Gu et al. Opt. Lett. 27 1174 (2002)Dudley et al. 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 amplitudeultrafast oscillations
Gu et al. Opt. Lett. 27 1174 (2002)Dudley et al. Opt. Exp. 10 1251 (2002)
SC generation – normal dispersion pump
Four wave mixing
is p
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 m
old regime new regime
3 > 0 3 < 0
Modeled GVD
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)
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 m
old regime new regime
3 > 0 3 < 0
Modeled GVD
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)
Suppressing the Raman self-frequency shift
Suppressing the Raman self-frequency shift
Time (ps)
Dis
tanc
e (m
)
Dis
tanc
e (m
)
Wavelength (nm)
Initial Raman shifting is arrested by dispersive wave generation
Pulse parameters: 50 fs FWHM, 2 kW peak power, = 1200 nm, N ~ 1.7
ZD
W
Suppressing the Raman self-frequency shift
A detailed treatment shows that dispersive wave generation is associated with spectral recoil of the generating soliton.
ZD
W
> 0
BLUE SHIFT
Recoil RED SHIFT
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.
ZD
W
Around the second ZDW, the Raman shift and spectral recoil are in opposite directions and can thus compensate.
Recoil BLUE SHIFT
< 0 RED SHIFT
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
P = 26 W P = 43 W
P = 98 W P = 72 W
1 ns input pulses from chip laser at 1064 nm, 4 m of PCF
P = 26 W P = 43 W P = 98 W
exp exp exp
sim simsim
Simulations reproduce experiments over a 50 dB dynamic range
SC generation with nanosecond pulses
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.
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.
Nakazawa et al. Phys. Rev. A 39 5768 (1989)
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:
Gu et al. Opt. Exp. 11, 2697 (2003).
Lu & Knox Opt. Exp. 12, 347 (2004).
Giessen et al. Talk today at 15:15
Experimentally accessible
Dudley and Coen, Opt. Lett. 27, 1180 (2002)
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:
Gu et al. Opt. Exp. 11, 2697 (2003).
Lu & Knox Opt. Exp. 12, 347 (2004).
Giessen et al. Talk today at 15:15
Experimentally accessible
Dudley and Coen, Opt. Lett. 27, 1180 (2002)
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…
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