Supercontinuum Generation in Photonic Crystal Fibers

1
Supercontinuum Generation in Photonic Crystal
Fibers

• John M. Dudley

Laboratoire dOptique P-M Duffieux, Institut
FEMTO-ST CNRS UMR 6174 Université de
Franche-Comté BESANÇON, France.
POWAG 2004 Bath July 12-16
2
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
3
What exactly are we trying to understand?
Ranka et al. Optics Letters 25, 25 2000
Femtosecond Tisapphire laser Anomalous GVD
pumping
grating
PCF

• Output spectrum

4
What exactly are we trying to understand?
Birks et al. Optics Letters 25, 1415 2000
Femtosecond Tisapphire laser Anomalous GVD
pumping
grating
TAPER

• Output spectrum

5
What exactly are we trying to understand?
Ranka et al. Optics Letters 25, 25 2000
Femtosecond Tisapphire laser Anomalous GVD
pumping
grating
PCF

• Broadening mechanisms
• Spectral structure
• Evolution of spectrum along the fiber
• Stability
• Flatness
• etc
• Understand, control, exploit

• Output spectrum

6
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
7
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

8
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
2000
Dn 770 THz Dn 81 THz
Dn/n0 2 Dn/n0
0.5
9
Pulse propagation in single mode fibers
Analysis of single-mode fiber propagation
equations yield
scalar approach
propagation constant
transverse profile
fieldenvelope
Frequency dependence of b chromatic dispersion
group velocity dispersion (GVD)
(group velocity)-1
ps2/km ps / nmkm
10
Propagation equation (I)
Nonlinear Envelope Equation (NEE)
? co-moving frame
self-steepening
dispersion
SPM, FWM, Raman
co-moving frame
Kerr nonlinearity
Raman response
11
Propagation equation (II)
Nonlinear Envelope Equation (NEE)
? co-moving frame
self-steepening
dispersion
SPM, FWM, Raman
Validity to the few-cycle regime has been
established
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)
Application to PCF pulse propagation
Gaeta Opt. Lett. 27 924 (2002)Dudley
Coen Opt. Lett. 27 1180 (2002)
12
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 gt
  780 nm

13
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 gt
  780 nm

14
Sowhat does a simulation look like?
15
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
Spectral evolution
Temporal evolution
Distance (m)
Distance (m)
Wavelength (nm)
Time (ps)
16
Understanding the details

• Solitons
• Perturbed solitons
• Raman self-frequency shift
• Dispersive waves

17
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.
18
Nonlinear Schrödinger Equation
Nonlinear Schrödinger Equation (NLSE)
co-moving frame
Kerr nonlinearity
instantaneous power (W)
l 850 nmb2 -13 ps2 km-1g 100 W-1km-1
Consider propagation in highly nonlinear PCF ZDW
at 780 nm
T0 28 fs (FWHM 50 fs)
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Fundamental solitons
Initial condition

165 W
N 1
Invariant evolution
solitonwavenumber
20
Higher-order solitons
Initial condition
N 3
Periodic evolution
10 cm
21
Higher-order solitons
Initial condition
Periodic evolution
10 cm
22
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
23
quite a bit of work yields
24
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
Self-steepening
25
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
26
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
27
Physics of the self-frequency shift
25 fs FWHM ? 14 THz bandwidth
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Soliton decay soliton fission
Illustration Raman perturbation only
Pulse parameters N 3, FWHM 50 fs, P0 14.85
kW, zsol 10 cm
Distance (z/zsol)
Distance (z/zsol)
ZDW
Time (ps)
Wavelength (nm)
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Soliton decay soliton fission
Illustration Raman perturbation only
Pulse parameters N 3, FWHM 50 fs, P0 14.85
kW, zsol 10 cm
Distance (z/zsol)
Time (ps)
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The spectrogram

• The spectrogram shows a pulse in both domains
  simultaneously

pulse variable delay gate
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Soliton fission in the time-frequency domain
ZDW
projected axis spectrogram
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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.
b3 gt 0 ? DW gt 0 BLUE SHIFT
Wai et al. Opt. Lett. 11 464 (1986)
Akhmediev KarlssonPhys. Rev. A 51 2602 (1995)

33
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.
Pulse parameters N 1 soliton at 850 nm, b3 gt
0, no Raman
Distance (m)
Distance (m)
Time (ps)
Wavelength (nm)
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Does that remind you of anything?
35
SC generation anomalous dispersion pump
Signatures of soliton fission and dispersive wave
generationin SC generation are now apparent

Spectral evolution
Temporal evolution
Distance (m)
Distance (m)
Wavelength (nm)
Time (ps)
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SC generation anomalous dispersion pump
Signatures of soliton fission and dispersive wave
generationin SC generation are now apparent

Spectral evolution
Temporal evolution
Distance (m)
Distance (m)
Wavelength (nm)
Time (ps)
37
SC generation anomalous dispersion pump

DW
ZDW
115 THz
fine structure
S3
S2
S1
Intuitive correlation of time and frequency
domains
38
What about the experiments ?
39
Experimental Measurements spectra
Experiment
Spectrum (20 dB / div.)
Simulation
Wavelength (nm)
40
Experimental Measurements Raman solitons
Good comparison between simulations and
experiments

Simulation
Experiment

Washburn et al. Electron. Lett. 37 1510 (2001)
41
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.

42
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)
43
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)
44
SC generation normal dispersion pump
Four wave mixing

w
ws
wi
wp
Dudley et al. JOSA B 19, 765-771 (2002)
45
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
46
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 new regime
b3 gt 0 b3 lt 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)
47
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 new regime

b3 gt 0 b3 lt 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)
48
Suppressing the Raman self-frequency shift

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Suppressing the Raman self-frequency shift
Initial Raman shifting is arrested by dispersive
wave generation

Pulse parameters 50 fs FWHM, 2 kW peak power, l
1200 nm, N 1.7
Distance (m)
Distance (m)
ZDW
Time (ps)
Wavelength (nm)
50
Suppressing the Raman self-frequency shift
A detailed treatment shows that dispersive wave
generation is associated with spectral recoil of
the generating soliton.

DW
Recoil RED SHIFT
b3 gt 0 BLUE SHIFT
ZDW
l
In the conventional regime the Raman shift and
spectral recoil are in the same direction and
reinforce.

51
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 lt 0 RED SHIFT
Recoil BLUE SHIFT
ZDW
l
Around the second ZDW, the Raman shift and
spectral recoil are in opposite directions and
can thus compensate.

52
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.
53
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
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SC generation with nanosecond pulses
Simulations reproduce experiments over a 50 dB
dynamic range

P 43 W
P 98 W
P 26 W
exp
exp
exp
sim
sim
sim
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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)
56
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 1515

57
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 1515

58
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