Intense lasers: high peak power Part 2:...

pageBrunoLeGarrec 1

Intense lasers: high peak powerPart 2: PropagationBrunoLeGarrec

DirecteurdesTechnologiesLasersduLULILULI/EcolePolytechnique,routedeSaclay

91128Palaiseaucedex,France

[email protected]

31/08/2016

LPA school Capri 2017

pageBrunoLeGarrec 2LPA school Capri 2017

Outline:

• Weneedhighpowerlasers:highenergyandhighrepetitionrate=highaveragepower

=>ButthekWlevellookslikeabarrier• Weneedhighqualitybeamsforfrequency

conversion,forpumpingTi-SapphireorforOPCPA

• Itissaidthatdiodepumplasersarehighlyefficientwhileflashlamppumpedlasersarenot.

• WhatdoweknowaboutkWclassdiode-pumpedsolidstatelasers(DPSSL)?

• Isthereany“oftheshelf”technology?


Technicalspecification

Createalaserbeamthatcanbepropagatedandfocussed:• Lowdivergence(<<0.1mrad)• Highintensity(Power/beamarea>>GW/cm2)• Focusability tofewwavelengths• Monochromatic(Δλ/λ <<10-6)• Largebandwidth(Δλ/λ =¼)

Butgettingthesethreeparametersatthesametimeishighlychallenging:• Highestpossibleefficiency• Highbeamquality(closetoM2=1)• Highenergy/highpower(+highrepetitionrate=highaveragepower

/kilowattormultikilowattrange)

pageBrunoLeGarrec 4

Some data about high average power lasers

5

10

15

20

25

0 100 200 300 400 500 600 700 800

Wal

l-plu

g ef

ficie

ncy

(%)

Power (W)

QCW

QCW

• Diode pumped lasers can be very efficient

• Examples can be found in Quantum Electronics39 (1) 1-17 (2009) when power > 100 W and optical to electrical efficiency can reach 23-24% (cooling is not taken into account)

• Most of these examples concerns CW lasers

• Two examples are high rep-rate QCW lasers (rep-rate > kHz), efficiency looks very good too (17-24%)


Lookingatbothefficiencyandbeamquality

0

20

40

60

80

100

0 5 10 15 20 25

M2_xM2_y

Wall-plug efficiency (%)

M"s

quar

ed"

valu

e

QCW QCW

• None of these highly efficient lasers are suitable for frequency conversion because M2 > 10

• As soon as M2 > 4, it is quite impossible to have a good frequency conversion efficiency unless having intra-cavity frequency conversion


Why ?

Ifwediscussthepossibilityofextendingsolid-statelasertechnologytohigh-average-powerandofimprovingtheefficiencyofsuchlasers,thecriticalelementsofthelaserdesignare:• thethermalmanagement(removingheatfromthecenterofthesolid

withacoolingsystemattheendsurfaces),• thethermalgradientcontrol(minimizingopticalwavefrontdistortions),• thepumpenergyutilization(overallefficiencyincludingabsorption,

storedenergy,gainetc),• theefficientextraction(fillingmostofthepumpedvolumewithextracting

radiationandmatchingpumpdurationtotheexcited-statelifetime).Doesitmakesensetooptimizealltheseparameters?Wecanwinaworldrecordinlaserextractionefficiencybutcanweachieveefficientsecond-harmonic-generationorhowmanytimesdiffractionlimitedisthelaserbeam?

Wavefront and light rays

Flat intensity and phase beam: • diffraction limited beam focused to

the diffraction limit according to the Airy disk pattern.

• The larger the size of the beam “a”, the smaller the focal spot.

• The shape of the focal spot is the square of the 1st order Bessel function: J1(z)/z.

If the beam is suffering distortions, then the wavefront is no longer a plane. Rays are perpendicular to the wavefront. A “ray” has a direction given by its “k” vector

Wavefront

« k » vectors


Backtobasics=wavefrontdistortion

• AflatwavefrontbeamshouldgiveaperfectAirydiskpatternwhenfocused

• Adistortedwavefrontbeamcannotbefocusedtothatminimumsize

• InotherwordstheencircledenergyislowortheM2 ishigh

• M2 meansthatthebeamisM2 xDiffractionLimit

aλ

θ 22.1

=

a

Tache d ’AiryAiry disk

M2 x Airy disk

A real beam propagates like a perfect beamwhose intensity would be divided by M4 !


Beam transportObject plane Image plane

Beam transport is possible withafocal optical systems

A pinhole is located at the focal plane

Spatial frequencies can be seenat the focal plane


Beam transportObject plane Image plane

Image relay planes

Pinholes are relay imaged too


Spatial Filter

f1 f2

L

( ) ⎥⎦

⎤⎢⎣

⎡

−−+−

−=⎥

⎦

⎤⎢⎣

⎡

−⎥⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡

−=

22121

1

12 11

1101

101

1101

fLffLffLfL

fL

fM

Optical system is afocal when C=0 21 ffL +=

Beam size magnification=G 12 fGf =

⎥⎦

⎤⎢⎣

⎡

−

−=

GLG

M10


Relay imaging

Stage 1 input Stage 2 output

f1 f2

L L1 L2

⎥⎦

⎤⎢⎣

⎡

−

−−=⎥

⎦

⎤⎢⎣

⎡

−

−⎥⎦

⎤⎢⎣

⎡

GGLLG

GLGL

10/10101 22

GLL 2=

⎥⎦

⎤⎢⎣

⎡

−

−−=⎥

⎦

⎤⎢⎣

⎡⎥⎦

⎤⎢⎣

⎡

−

−

GLGLGL

GLG

10101

/1011

1LGL =


Filtering is possible in the Fourier planeThe electromagnetic field in the focal plane of a lens can be

calculated in the framework of Fresnel diffraction.

Reduced variables are optical frequencies (X, Y) = (x, y)/λfPinhole size = half-angle of the pinhole as seen from the lens =

optical frequency θ = λ/pÀλ =1µm,θ =1mrad ó p=1mm

0000000 ),(2),()(2),( 22 dydxYyXxifExpyxAyxkikExpf

iYXA πλ ∫∫+=

A(x0,y0)

50 10

Spatial frequency

10020µrads

mm150

High frequenciesremoved by pinholes

Low frequenciesremoved by DFM

Frequencies that can growwith non linear Kerr effect (B)

= distance between actuators


The Functions of Spatial Filtering

• Suppressing high spatial frequency modulations with a single pinhole

• Reducing ASE solid angle• Magnifying beam size• Imaging relay planes

pageBrunoLeGarrec 15

Energy balance in an optically pumped SSL*

Lamp input Power supply and circuit losses

Heat dissipated by lamp Power irradiated

Power absorbed bypumping cavity

Power absorbed byLaser rod

Power absorbed byCoolant and flowtubes

Reabsorptionby lamp

Heat dissipated by rod Stimulated emission Fluorescence output

Laser output Optical losses

External Power

100%

50% 50%

2% 0.6%

30% 8% 7% 5%

0.6%5% 2.6%

Lamp input 100%Heat dissipated by lamp 50%Power radiated (0,3 to 1,5 µm) 50%

Power absorbed byPump cavity 30 %Coolant and flowtubes 7%Lamp 5 %Laser rod 8%

Heat dissipated by rod 5%Fluorescence 0.4%Stimulated emission 2.6 %

Optical losses 0,6 %Laser output 2%

*From W. Koechner “Solid state laser engineering”NIF/LMJ are in the range 0.5 to 1 %


Amplifying solid-state medium: Rod or slab

Optical resonator or cavity

Output laser beam

Pump(flash lamps, laser diodes )

Back to basics = laser physics

• During pumping, all that is not “in” the beam must be removed as heat otherwise it will induce wave front distortions of the output laser beam


Thermalgradient:thermallensing

• Assumption:uniforminternalheatgenerationandcoolingalongthecylindricalsurfaceofaninfinitelylongrodleadstoaquadraticvariationoftherefractiveindexwithradiusr :n=n0-½n2r2

• Thisperturbationisequivalenttoasphericallensf’=2πr2K/(Padn/dT)withK thethermalconductivity,dn/dT thethermo-opticcoefficientand Pa theabsorbedpower.

• Temperature- andstress-dependantvariationoftherefractiveindex+thedistortionoftheend-facecurvaturemodifiesthefocallengthabout25%

Probe beam Focal point


Thermalmanagement• Thermo-opticaldistortions

• K isthethermalconductivityanddn/dtthethermo-opticcoefficientandα thethermalexpansioncoefficient

• Figureofmerit=K/(dn/dt)• +Thermallyinducedbirefringence• Stressfracturerelatedtoshockparameter

• Figureofmerit=K/α• Wecancomparethebehaviourofdifferentlasermaterials

RS

ETpoisson therm cond T

therm ex young

=−( ) .

.

1 ν κ

α

wtdddP

Tcondtherm

cmw ,, with .

2/ 3

=∝Δκ


Thermal management

How much power ? At 20% stress fracture : rod slab

b=0.2 RT

(W/cm)Pl

(W/cm)PV

(W/cm3)P (W)

for 100 cm3

glassLG750

0.43 2.2 1 100

SFAPSr5(PO4)3F

0.8 4 2.2 220

YLFLiYF4

1.8 9 4.3 430

YAG 8 40.2 19.2 1920

Al2O3 100 500 240 24000

P R b

P R bt

l rod T

V diskT

,

,

=

=

8

12 2

π


Working at cryogenic temperature

5

10

15

20

25

30

35

40

100 150 200 250 300

Optical efficiency of diode-pumped 10% Yb-doped sesquioxides ceramics. Efficiency = laser output/diode output

Y2O3Lu2O3Sc2O3

Optic

al to

opt

ical e

fficien

cy (%

)

Temperature (K)

• G. Slack, D. Oliver, “Thermal conductivity of garnets and phonon scattering by rare-earth ions”, Phys. Rev. B, 4(2), p.592-609, 1971


Thermalmanagement

IknowwhatIwanttodo:

Removeheatfromthe(centerofthe)solidwithacoolingsystem(attheendsurfaces)=>bettercooling

Minimizeopticaldistortions(wavefrontdistortion)=getaflatthermalgradient=>better“uniform”pumping

Increasethepumpingefficiency(absorption,storedenergy,gainetc)=>diodepumping

Increasetheextractionefficiency,fillingmostofthepumpedvolumewithextractingradiationandmatchingpumpdurationtotheexcited-statelifetime=>diodepumping

Doesitmakesensetooptimizealltheseelements?CanIachievesecondharmonicgenerationorhowmanytimes

diffractionlimitedismylaserbeam?


Thermalgradientcontrol• Ifthegainprofileisflat(pump

uniformity)thenthethermalgradientwillbeflattoo

• InfactIonlycareofthetransversegradientbecausethebeamdon’t“see”theaxialone

• Manythinslabs(atBrewsteranglecanbeassociatedtodesignanamplifier)


Cryogenic gas cooled multi-slab amplifier

Optica Vol. 4, Issue 4, pp. 438-439 (2017) https://doi.org/10.1364/OPTICA.4.000438

Intense lasers: high peak power Part 2:...

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