1. 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

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,
Femtosecond Ti:sapphire laser
Anomalous GVD pumping
grating
PCF
Output spectrum

4. What exactly are we trying to understand?
Birks et al. Optics Letters 25,
Femtosecond Ti:sapphire laser
Anomalous GVD pumping
grating
TAPER
Output spectrum

5. What exactly are we trying to understand?
Ranka et al. Optics Letters 25,
Femtosecond Ti:sapphire 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. Concentrate on femtosecond pulse pumping regime
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) 300 1300 2000 Dn = 770 THz Dn = 81 THz
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)
Dn = 770 THz Dn = 81 THz
Dn/n0 ~ Dn/n0 ~ 0.5

9. Pulse propagation in single mode fibers
Analysis of single-mode fiber propagation equations yield:
scalar approach
transverse profile
propagation constant
field envelope
Frequency dependence of b – chromatic dispersion
(group velocity)-1
group velocity dispersion (GVD)
[ps2/km] [ps / nm·km]

10. Propagation equation (I)
Nonlinear Envelope Equation (NEE)
 co-moving frame
dispersion
self-steepening
SPM, FWM, Raman
co-moving frame
Kerr nonlinearity
Raman response

11. 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 IEEE JQE (1989) Brabec & Krausz Phys. Rev. Lett (1997) Ranka & Gaeta Opt. Lett (1998) Karasawa et al. IEEE JQE (2001)
Application to PCF pulse propagation
Gaeta Opt. Lett (2002) Dudley & Coen Opt. Lett (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 > 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 > 780 nm

14. So…what 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 nm b2 = -13 ps2 km-1 g = 100 W-1km-1
Consider propagation in highly nonlinear PCF: ZDW at 780 nm
T0 = 28 fs (FWHM 50 fs)

19. Fundamental solitons Initial condition = 165 W Invariant evolution
soliton wavenumber

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
Dt’ FT
Dl’
pump
sees gain
-13 THz
N = 1 t Dt FT Dl
pump
sees gain
-13 THz
N = 1 l
25 fs FWHM  14 THz bandwidth

28. Soliton decay – soliton fission
Illustration : Raman perturbation only
Pulse parameters: N = 3, FWHM = 50 fs, P0 = kW, zsol = 10 cm
Distance (z/zsol)
Distance (z/zsol)
ZDW
Time (ps)
Wavelength (nm)

29. Soliton decay – soliton fission
Illustration : Raman perturbation only
Pulse parameters: N = 3, FWHM = 50 fs, P0 = kW, zsol = 10 cm
Distance (z/zsol)
Time (ps)

30. The spectrogram
The spectrogram shows a pulse in both domains simultaneously
pulse
gate
pulse variable delay gate

31. Soliton fission in the time-frequency domain
ZDW
projected axis spectrogram

32. 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. l DW
b3 > 0  DW > BLUE SHIFT
Wai et al Opt. Lett (1986)
Akhmediev & Karlsson Phys. Rev. A (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 > 0, no Raman
Distance (m)
Distance (m)
Wavelength (nm)
Time (ps)

34. Does that remind you of anything?

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

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

37. SC generation – anomalous dispersion pumpDW
ZDW
115 THz S3
fine structure S2 S1
Intuitive correlation of time and frequency domains

38. What about the experiments ?

39. Experimental Measurements – spectra
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 (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 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 amplitude ultrafast oscillations
Gu et al. Opt. Lett (2002) Dudley et al. Opt. Exp (2002)

43. 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. Opt. Lett (2002) Dudley et al. Opt. Exp (2002)

44. SC generation – normal dispersion pump
Four wave mixing w ws wp wi
Dudley et al. JOSA B 19, (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 > b3 < 0
Harbold et al. Opt. Lett. 27, 1558 (2002) Skyrabin et al. Science (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 > b3 < 0
Harbold et al. Opt. Lett. 27, 1558 (2002) Skyrabin et al. Science (2003) Hillisgøe et al. Opt. Exp. 12, 1045 (2004) Efimov et al. CLEO Paper IML7 (2004)

48. Suppressing the Raman self-frequency shift

49. 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
Wavelength (nm)
Time (ps)

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
b3 > 0 BLUE SHIFT
Recoil RED 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
Recoil BLUE SHIFT
b3 < 0 RED 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

54. SC generation with nanosecond pulses
Simulations reproduce experiments over a 50 dB dynamic range
P = 26 W
P = 43 W
P = 98 W
exp
exp
exp
sim
sim
sim

55. Supercontinuum stability
As early as 2001, experiments reported that supercontinuum generation in PCF could be very unstable.
Hollberg et al. IEEE J. Quant. Electron (2001)
Nonlinear spectral broadening processes are very sensitive to technical or quantum noise sources.
Nakazawa et al. Phys. Rev. A (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 15:15

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 15:15

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…