supercontinuum generation in photonic crystal f ibers

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…