Dispersion/Stretcher/Compressor Ecole …web.luli.polytechnique.fr/IT_ELLI/14 Thursday N...

TrainingCourseC2:Dispersion/Stretcher/Compressor

Characterisa7onforUltra-IntenseLasers28May-June1-2018

EcolePolytechnique,Palaiseau,FRANCE

Outline

•  Pulsemeasurementtechniquesforshortpulses

•  Self-referencedspectralinterferometry

•  Pulseop7miza7oninaCPA

Introduc)on:temporalmetrics

3

•  Whataretheessen7alcharacteris7csofapulsedlaser?•  Repe77onrate•  Pulsedura7on,pulseshapeI(t),temporalphaseφ(t)•  Stabilityoftheseparameters

ISO11554(2006)or(2008)

Inprac7ceweneedtoknowalotmore:•  Pulse“contrast”•  Forfew-cyclepulses:carrier-

envelopephase(CEP)

Direct detection of light

4

Allfastdetectorsarebasedonthephoto-electriceffect.Theabsorp7onofaphotonisfollowedbyeither:

•  Theemissionofanelectron(photocathodeforexample)•  Thegenera7onofanelectron-hole(semi-conductorforexample)

Inphotocathodes,thejunc7on’scapacitanceandthetransportofchargeslimitsthe7meresponseto~10ps

Photoconductorscandoaliclebecer(~1ps,limitedbychargerecombina7on)

Butinallcases,theelectricsignalmustbesampled(oscilloscope)anditisdifficiletosamplefastermuchfasterthan1pointevery10ps(connectors).

𝜏=𝑅𝐶 R=50ΩC=1pFτ=50ps

Currently,thefastestdetectors(noelectronic,noconnector)arestreakcamerasPrinciple:cathoderaytube(i.eformerTVscreens)


Typical1950sUnitedStatesmonochrometelevisionset(source:Wikipedia)

A14-inchcathoderaytubeshowingitsdeflec7oncoilsandelectronguns(source:Wikipedia)

fenetre d’entree

photocathode

electrode d’accelerationeventuellement dynodes pour amplifier le signal

optique electronique

anode

plaques de deflection

ecran a phosphore

fenetre de sortie

fenêtre d’entrée

photocathode

système d’otique électronique

plaques de déflexion

écran àphosphore

fenêtre de sortieanode

électroded’accélération

dimensiontemporelle

dimension au choix

dimensionénergétique

Currently,thefastestdetectors(noelectronic,noconnector)arestreakcamerasPrinciple:cathoderaytube(i.eformerTVscreens)Temporalresolu7on:0.2-0.5ps,butinprinciplecouldbeasshortas~100fs.


Inputwindow

Photocathode

Electrosta7clenses

Deflec7onplates

Phosphorscreen

OutputwindowAnode

Accelera7ngelectrode(cathode)

Timedirec7on

Inputslitdirec7on

Laserpulse!

Direct detection of lightFemto-Photography:VisualizingPhotonsinMo7onataTrillionFramesPerSecondhcp://web.media.mit.edu/~raskar/trillionfps/

•  Directdetec7oninthetemporaldomainisnotfastenoughforps-fspulses.Whatismore,temporalphasecannotbemeasured.

•  Solu7on:

•  Switchfromthetemporaltothespectraldomain•  Replaceoftemporalintensityandphasebyspectralintensityandphase

Spectral approach: principle

Construc7veinterférences

Destruc7veinterferences

Destruc7veinterférences Whyisitsimpler?

1.  Thespectralintensityofshort(broadband)pulsescanbemeasuredveryeasilywithaspectrometer!

2.  Allwhatremainstodoistomeasurethephaserela2onshipbetweenthespectralcomponents.Thisisexactlythesameissueasinthespa7aldomain.Itiseasytotakeanimage.Thechallengeistomeasurethespa7alphase.

3.  Actuallythetechniquesdevelopedforthespa7aldomaincanbetransposedtothespectraldomain.

Fourier optics Exemple 1 : linear spatial phase (prism)

Exemple 2: quadratic spatialphase (lens)

Reference Shift (change of direction)

Defocus

Time-spaceanalogy

Example1:linearspectralphase(prismequivalent)

Example2:quadra7cspectralphase(lensequivalent)

Referencepulse Timedelay Stretching/compression

t

I(t)

t

I(t)

t

I(t)

𝜑(𝜔)=𝛼+𝛽(𝜔− 𝜔↓0 ) 𝜑(𝜔)=𝛾(𝜔− 𝜔↓0 )↑2 

•  Pulsa7onω↔wavevectorkxorky-morepreciselyE(ω)↔E(kx)orE(kx)•  Moregenerally:chroma7cdispersion↔longitudinalpropaga7on(diffrac7on)•  Linearspectralphase↔op7caldelay•  Quadra7cspectralphase↔temporalbroadening

Time-spaceanalogy

Time-spaceanalogy

Manyapproaches:

1.  BydirectcomparisonwithaknownpulseSpectralinterferometrySelf-referencedspectralinterferometry(SRSI)

2.  Byusingaprismeffect(measurementofthelocalgradientofthespectralphase)Frequency-resolvedop2calga2ng(FROGanditsnumerousvariants,GRENOUILLE…)

3.  Byusingalenseffect(measurementofthelocalcurvatureofthespectralphase)Dispersion-scan(d-scan)

4.  Bycombiningaprismeffectandcomparison(globalgradientofthespectralphase)Spectralshearinterferometry(SPIDER)

SRSI:self-referencedspectralinterferometrySPIDER:SpectralPhaseInterferometryforDirectElectric-fieldReconstruc7onFROG:Frequency-ResolvedOp7calGa7ngGRENOUILLE:trytofindout!

Pulsemeasurementtechniques

AnalogueoftheHartmann-Shackwavefrontsensor•  Spa7aldomain:measurementofthelocal(kx,ky)distribu7on

ateach(x,y)posi7onviaanarrayofmicrolenses•  Spectraldomain:spectrumoftemporalslicesviaasetof

7megates

τ

Spectrometer

Nonlinearop7csprovidesaconvenientwayto“gate”pulses:sum-frequencywiththepulseitself!Butthisisnotvery“clean”(precise)…ablindreconstruc7onalgorithmisrequired

R. Trebino, K. W. DeLong, D. N. Fittinghoff, J. N. Sweetser, M. A. Krumbügel, and D. J. Kane, "Measuring Ultrashort Laser Pulses in the Time-Frequency Domain Using Frequency-Resolved Optical Gating," Review of Scientific Instruments 68,

3277-3295 (1997)

SFG

Filtre

50/50

FROG

Delay (fs)S

pect

rum

(nm

)-200 -150 -100 -50 0 50 100 150 200

375

380

385

390

395

400

405

410

415

420

425

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Experimental

Delay (fs)

Spe

ctru

m (n

m)

-200 -150 -100 -50 0 50 100 150 200375

380

385

390

395

400

405

410

415

420

425

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Retrieved

Analogtoshearinterferometryinthespa7aldomain•  Spa7aldomain:beamreplicas,7ltedindifferentdirec7ons

(kx,ky),interfereinthespace.Spa7alphaseisextractedfromthispacernviaFourierfiltering

•  Spectraldomain:pulsereplicas,spectrallyshiued,interfereinthespectraldomain.SpectralphaseisextractedfromthispacernviaFourierfiltering.

Iaconis,C;Walmsley,I.A.(1998),"SpectralPhaseInterferometryforDirectElectric-FieldReconstrucNonofUltrashortOpNcalPulses",Opt.LeQ.,23(10):792–794

t

Spectrometer

50%

Howdowedospectralshearing?Withsum-frequency!

Compresseur

Impulsionàdérivedefréquence

SFG Filtre

SPIDER

365 370 375 380 385 390 395 4000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Wavelength (nm)

Spec

tral in

tens

ity

Experimental

Thisistheanalogofawavefrontcurvaturesensor•  Space:letthebeampropagate,measurethebeamprofilein

different planes and analyzewhere each part of the beamfocuses.

•  Spectraldomain:adddispersion,measurethe7meintensity

asafunc7onofaddeddispersion,watchwheretheintensityismaximum.

•  Issue:wehavenowaytomeasurethetemporalintensity.

Technicalsolu7on:measuresomethingwhichisafunc7onofI(t)→Second-ordernonlineareffects(secondharmonictyp.)giveaccesstoI(t)2→Asecondharmonic+aspectrometer:auto-convolu2onofI(ω)

Dispersionscan

Visu

Visu

Visu

Visu

Chinesemirror

Prismrwedgepair

SHG Spectrometer

Measured Retrieved

Whichtechniqueisthebest?

•  Noanswertothisques7on…

•  Eachtechniquehasstrengthsandweaknesses:

•  FROG:•  Rathersimpletobuild,intui7vetraces,canmeasureverycomplexpulse,

calibra7oniseasy•  Timedirec7onambiguity,blindalgorithm,notveryprecise,lowdynamic

•  SPIDER:•  Simplealgorithm,precise,noaddeddispersion(few-cyclepulses)•  Notintui7ve,heavycalibra7onprocedure,cannotmeasureverycomplex

pulses•  D-scan:

•  Supersimpletobuild,intui7vetraces,canbepartofthesource,canmeasuredcomplexpulses

•  Blindalgorithm,scanningtechnique,op7mizedforagivenbandwidth

Outline




SRSI is a self-referenced pulse measurement technique with unique properties:

•  Single-shot (spectrum and phase are measured)

•  High dynamic range (coherent contrast measurement)

•  Easy to align (no beam splitting, totally collinear)

•  Compact footprint (A5)

•  Accurate: no calibration step, no blind iterative algorithm

“Self-referenced spectral interferometry”, T.Oksenhendler et al., APB 99, p1-6 (2010),

Self-ReferencedSpectralInterferometry

Anyweakness?SRSIcannotmeasuredpulseslongerthan2xtheFTLdura7on…ActuallythistechniquewasinventedforpulsecompressioninCPAsystems.

Spectralinterferometry

Two delayed pulses: I(t)

Pulse 1

Pulse 2

t

ω

I(ω)

Spectral interference pattern:

Spectralinterferometry

DC term AC term

Quadratic equation

Both pulses are completely characterized if one spectral phase is known. A reference pulse is needed, with: -  flat phase -  broader spectrum

() ()ωωω 21~~ EE≠∀if

CrossPolarizedWavegenera7on(XPW)

•  Whenanintensewavegoesthroughamediawithananisotropicχ(3)(suchasBaF2orLiF),anorthogonallypolarizedwaveisgenerated:

•  Undertheslowlyvaryingenvelope,theundepletedregimeandthincrystalapproxima7ons:

•  Thepulseisfilteredbyitsowntemporalintensity

XPW pulse Input pulse

N. Minkovski, G. I. Petrov, S. M. Saltiel, O. Albert, and J. Etchepare, "Nonlinear polarization rotation and orthogonal polarization generation experienced in a single-beam configuration," J. Opt. Soc. Am. B 21, 1659-1664 (2004) L. Canova, O. Albert, N. Forget, B. Mercier, S. Kourtev, N. Minkovski, S. M. Saltiel, R. Lopez Martens, “Influence of spectral phase on cross-polarized wave generation with short femtosecond pulses,” APB 93, 443-453 (2008)

Genera7onofareferencepulse?Spectral domain

before XPW Time domain

Spectral domain

after XPW

I(t)

t

Broader spectrum

Flatter phase

ω

I(ω) φ(ω)

Broader spectrum

Flatter phase

ω

I(ω) φ(ω)

Modulated spectrum

Spectral phase I(t)

t

XPW

Genera7onofareferencepulse?Spectral domain

before XPW Time domain

Spectral domain

After XPW

I(t)

t ω

I(ω) φ(ω)

ω

I(ω) φ(ω)

I1(x,y) φ1(x,y)

Space domain

I2(x,y) φ2(x,y)

Space domain

f f

Fourier domain

XPW pulse Input pulse

XPW active media

BaF2

XPW filtering

Spectrometer

Birefringent plate

Polarizer

Replica generation Main pulse extinction

Polarizer

XPW generates a reference pulse that is used for spectral interferometry

SRSIexperimentalsetup

BaF2,1mm

SRSIsetup(for>20fspulses)

Spectrum

Phase&amplituderetrieval

Interferogram

Spectral complex amplitude

Time complex amplitude

XPW phase

Phase difference +

FT

Spectral phase approximation

First approximation:

Hope:

300 350 400 4500

0.2

0.4

0.6

0.8

1

SRSI

Spe

ctrum

(u.a)

Frequency (THz)

340 360 380 400 4200

0.2

0.4

0.6

0.8

1

Frequency (THz)

Spec

tral in

tensit

y (u.a

)

340 360 380 400 420-3

-2

-1

0

1

2

3

Spec

tral p

hase

(rad

)

Input spectral amplitude and phase reconstruction

-1500 -1000 -500 0 500 1000 1500

10-4

10-3

10-2

10-1

100

Time (fs)

Temp

oral In

tensit

y (u.a

.)

FFT-1

Consistency check with the XPW spectrum enlargement and cleaning

300 350 400 4500

0.2

0.4

0.6

0.8

1

Frequency (THz)

Spec

tral in

tensit

y (u.a

)

Input spectrumXPW spectrum

Exp. Data : CEA laser and hollow core fiber: 810nm, 160nm, 10µJ, 1kHz

ComparisonwithSPIDER

-50 -25 0 25 500.00.10.20.30.40.50.60.70.80.91.0

Time (fs)

Tem

pora

l Int

ensi

ty (u

.a.)

SRSISPIDER

340 360 380 400 4200

0.2

0.4

0.6

0.8

1

Frequency (THz)

Spec

tral i

nten

sity

(u.a

)

340 360 380 400 420-3

-2

-1

0

1

2

3Sp

ectra

l pha

se (r

ad)

SRSI PhaseSPIDER Phase

≈12 fs

Hollow-core fiber (Ar, 2 bar)

Amplified Ti:Sa laser Dazzler SRSI

SPIDER

Feedback

-210fs2 were added by Dazzler to compensate for the dispersion of the optics of the SRSI device

300 320 340 360 380 400 420 440 4600

2

4

6

8

10

12

Frequency (THz)

Nor

mal

ized

spe

ctra

l int

ensi

ty XPW

Input

Input and XPW spectra extracted from a single-shot interferogram:

FWHM bandwidths: 66nm (input) and 83nm (XPW)

66nm

83nm

Dynamicrange–spectraldomain

300 320 340 360 380 400 420 440 460-80

-70

-60

-50

-40

-30

-20

-10

0

10

Frequency (THz)

Nor

mal

ized

spe

ctra

l int

ensi

ty

Dynamic range of spectrometer

~25dB

Dynamic range of the measurement

>50dB

XPW

Input

Spectral range of validity of the measurement (~200nm)

Dynamicrange–spectraldomainThe SNR varies like , for the amplitude and the phase!


-400 -200 0 200 400-60

-50

-40

-30

-20

-10

0

Time (fs)

Nor

mal

ized

tim

e in

tens

ity

FWHM=14.51fsFWHM=14.59fs

Spectral domain Time domain

Measured I(t)

FTL I(t) Spectrum

Phase

Artifacts ?

Pulse duration FWHM = 14.5fs

FTL FWHM = 14.6fs

-400 -200 0 200 400-60

-50

-40

-30

-20

-10

0

Time (fs)

Nor

mal

ized

tim

e in

tens

ity

FWHM=14.51fsFWHM=14.59fs

Number of illuminated pixels (~512)

SNR of the CCD detector (~25dB)

For a measurement limited by shot-noise, the expected time dynamic range is:

=52dB

Expected dynamic range

Effect of residual spectral phase

Measured I(t)

FTL I(t)


•  To quantify the loss of coherent contrast, we used standard deviation over the measured temporal range (T=400fs):

•  To check the validity of the phase measurement and assess the dynamic time range: feedback residual phase to pulse shaper

Dynamicrange–7medomain

Expected dynamic range

Before feedback

After feedback

σ=34.6fs

σ=19.3fs

σFTL=18.6fs

Post-pulseat10-2

-500 0 5000

0.2

0.4

0.6

0.8

1

Time (fs)

Tim

e in

tens

ity

MeasuredΔt=24fs σ=10.5fsFTLΔt=24fs σ=10.5fs

700 750 800 850 9000

0.2

0.4

0.6

0.8

1

Wavelength (nm)

Spec

tral i

nten

sity

700 750 800 850 900-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Spec

tral p

hase

(rad

)

Withoutpulsereplica

10-2

700 750 800 850 9000

0.2

0.4

0.6

0.8

1

Wavelength (nm)

Spec

tral i

nten

sity

700 750 800 850 900-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Spec

tral p

hase

(rad

)

Withpulsereplica

MeasuredI(t)

MeasuredI(ω

)and

φ(ω

)

Post-pulseat10-3

10-2

-500 0 5000

0.2

0.4

0.6

0.8

1

Time (fs)

Tim

e in

tens

ity


700 750 800 850 9000

0.2

0.4

0.6

0.8

1

Wavelength (nm)

Spec

tral i

nten

sity

700 750 800 850 900-0.3

-0.2

-0.1

0

0.1

0.2

0.3Sp

ectra

l pha

se (r

ad)

700 750 800 850 9000

0.2

0.4

0.6

0.8

1

Wavelength (nm)

Spec

tral i

nten

sity

700 750 800 850 900-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Spec

tral p

hase

(rad

)

Withoutpulsereplica Withpulsereplica

MeasuredI(t)

MeasuredI(ω

)and

φ(ω

)

10-3

Post-pulseat10-4

-500 0 5000

0.2

0.4

0.6

0.8

1

Time (fs)

Tim

e in

tens

ity


700 750 800 850 9000

0.2

0.4

0.6

0.8

1

Wavelength (nm)

Spec

tral i

nten

sity

700 750 800 850 900-0.3

-0.2

-0.1

0

0.1

0.2

0.3Sp

ectra

l pha

se (r

ad)

700 750 800 850 9000

0.2

0.4

0.6

0.8

1

Wavelength (nm)

Spec

tral i

nten

sity

700 750 800 850 900-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Spec

tral p

hase

(rad

)


MeasuredI(t)

MeasuredI(ω

)and

φ(ω

)

10-4

Post-pulseat5.10-5

-500 0 5000

0.2

0.4

0.6

0.8

1

Time (fs)

Tim

e in

tens

ity


700 750 800 850 9000

0.2

0.4

0.6

0.8

1

Wavelength (nm)

Spec

tral i

nten

sity

700 750 800 850 900-0.3

-0.2

-0.1

0

0.1

0.2

0.3Sp

ectra

l pha

se (r

ad)

700 750 800 850 9000

0.2

0.4

0.6

0.8

1

Wavelength (nm)

Spec

tral i

nten

sity

700 750 800 850 900-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Spec

tral p

hase

(rad

)


MeasuredI(t)

MeasuredI(ω

)and

φ(ω

)

5. 10-5

Pre/postpulses

-500 -400 -300 -200 -100 0 100 200 300 400 50010-6

10-5

10-4

10-3

10-2

10-1

100

Time (fs)

Tim

e in

tens

ity

-100 fs-150 fs-200 fs-250 fs-300 fs-350 fs-400 fs-50 fs100 fs150 fs200 fs250 fs300 fs350 fs400 fs50 fs

• Inthiscase:the7me-dependantdynamicrangeis>43dBovera7mewindowof+/-500fsat800nm

Outline




Pulseop7miza7oninaCPA

Pulse measurement

Gain

Observable

Pulse shaper

Amplifier Adjustment

Actuator

Comparison to optimal pulse

Target

Correction

« Filter»

Pulseshapers

Temporalshapingatfemtosecond7mescales?Someexo7cnonlineareffectsareactuallyreallyfastS7ll,thefastestmodulatorshavea7meresolu7onofafewps

Direct temporal shaping ? IMPOSSIBLE in most case (99.99%)

Pulse shaper

fs

Top-Hat?

Pulseshapers•  Solu7on:spectraldomain!Controlthespectralamplitudeandspectralphase

•  Twoapproaches:

•  Transfertheissueinthespa7aldomainandusespa7almodulators(SLM,deformablemirrorsetc) «transverseshaping» 4f-lines spectro-spaNalencoding

•  Usepropaga7oneffects

«longitudinalshaping» AOPDFs

Pulseop7miza7oninaCPA

Pulse measurement

Gain

Observable

Pulse shaper

Amplifier Adjustment

Actuator

Comparison to optimal pulse

Target

Correction

« Filter»

Pulseop7miza7onü Ok,it’ssimple:calibratedpulseshapersarequan7ta7ve

ü  directprogrammingoftheoppositeofthemeasuredphaseü  directprogrammingofthedesiredamplitudemodula7on

Amplitude control

Phase control

Text file

amp.txt

Text file

phase.txt

Diffraction efficiency

ViewoftheDazzler(AOPDF)souware:

Calibra7on

The shaper and the pulse measurement device must be calibrated

( )[ ]τωωωϕ 1cos)( −−=Dazzler

( )[ ]τωωωϕ 0cos)( −=meas

( )[ ]τωωδωτωϕωϕ 0sin)()( −×≈+ Dazzlermeas

+

=

10 ωωδω −=

Fast modulations are amplified

•  Measurementbandwidthisgenerally<pulsebandwidth

Spectralsupportofthemeasurement

340 360 380 400 4200

0.2

0.4

0.6

0.8

1

Frequency (THz)

Spec

tral in

tens

ity (u

.a)

340 360 380 400 420-3

-2

-1

0

1

2

3

Spec

tral p

hase

(rad

)

•  Measurementbandwidthisgenerally<pulsebandwidth

•  …butthebandwidthmustouenbedefinedonalargersupport=>mathema7calextrapola2onofthespectralphaseonthesides

Spectralbandwidth

340 360 380 400 4200

0.2

0.4

0.6

0.8

1

Frequency (THz)

Spec

tral in

tens

ity (u

.a)

340 360 380 400 420-3

-2

-1

0

1

2

3

Spec

tral p

hase

(rad

)

Spectralresolu7on•  Theresolu7onoftheshapersvariestyp.from0.15nmto0.6nmat800nm.

•  Itmakesnosensetousepointsmuchcloserthan0.15-0.6nm

•  but…amplitude/phasevaria7onscannotbeinfinitelysteep

ν0ν ν

ν0

Ι(ν) φ(ν)100%

ΔνΔν Δφ ?

Groupdelayconstraint

z(ω)

LcngΔ

=maxτ

νν0

φ(ν)

derivative

νν0

τ(ν)

<|τmax|

2maxτ

νφ<

Δ

Δ

Spectralresolu7onofpulsemeasurements

•  Spectralresolu7on≠numberofacquisi7onpointsex:foraSPIDERmeasurement,theeffec7veresolu7onisrelatedtothespectralshear,nottheresolu7onofthespectrometerex:foraFROGmeasurement,theeffec7veresolu7onis~1/maxdelay

•  Inmostcases,thespectralresolu7onis>2nm@800nmorequivalently,I(t)ismeasuredovera7mewindowofabout~1ps.

•  Conclusion:complexamplitude/phasefeaturesaremostouenundersampled

Resolu7on/maximumgroupdelayconstraint:conclusions

Before feeding back some spectral phase function:

•  The measured spectral phase must be extrapolated

•  Noise has to be removed to avoid sharp phase jumps exceeding the spectral resolution of the Dazzler (group delay constraint)

•  The effective spectral resolution of the pulse measurement must be assessed

νν0

τ(ν)

<|τmax|

νν0

τ(ν)

<|τmax|

340 360 380 400 4200

0.2

0.4

0.6

0.8

1

Frequency (THz)

Spec

tral in

tens

ity (u

.a)

340 360 380 400 420-3

-2

-1

0

1

2

3

Spec

tral p

hase

(rad

)

340 360 380 400 4200

0.2

0.4

0.6

0.8

1

Frequency (THz)

Spec

tral in

tens

ity (u

.a)

340 360 380 400 420-3

-2

-1

0

1

2

3

Spec

tral p

hase

(rad

)

0

0.2

0.4

0.6

0.8

1

1.2

740 760 780 800 820 840 860

lambda (nm)

spec

trum

(a.u

.)

Amplifier output Amplifier input

Satura7oneffectsinCPAs

AM-FMcoupling

•  Amplitudetophasemodula7oncoupling

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

770 780 790 800 810 820 830

lambda (nm)

Phas

e (ra

d)

-1-0.8-0.6-0.4-0.200.20.40.60.81

spec

trum

(a.u

.)

Amplitude modulation only

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

770 780 790 800 810 820 830

lambda (nm)

Phas

e (ra

d)

-1-0.8-0.6-0.4-0.200.20.40.60.81

spec

trum

(a.u

.)

AM-FMcoupling

Amplitude modulation only => Phase modulation

Amplitude to phase modulation coupling

EffectsofB-integralinaCPAlaser

ShaperOscillator Stretcher Amplifiers Compressor

ω tω tt

Chirp

Phasemodula7on

Amplitudemodula7on

Ex:SPM

SPM

FM-AM

AM-FM

Thankyouforyouracen7on&

Timeforques7ons

Annexe

Une difficulté majeure…on peut prouver que l’on peut pas mesurer la phase spectrale sans référence externe en utilisant uniquement des dispositifs optiques linéaires et stationnaires :

AOPDFprincipe

P. Tournois Opt. Comm 140 245-249 (1997)

• Principle=controlofthegroupdelayτ(ω)

• How?Throughbirefringence

Principe


Acous7cwaveissta7cwithrespecttothespeedoflight



Principe




Principe


z(ω)



•  Principle=controlofthegroupdelayτ(ω)

•  How?Throughbirefringence

Principle

z(ω)

Principe


z(ω)



Principe

( ))()(),( ωωωτ zLcnzc

nz egog −+=

Lcn

T gΔ=max


z(ω)



Dispersion/Stretcher/Compressor Ecole …web.luli.polytechnique.fr/IT_ELLI/14 Thursday N...

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