TrainingCourseC2:Dispersion/Stretcher/Compressor

Characterisa7onforUltra-IntenseLasers28May-June1-2018

EcolePolytechnique,Palaiseau,FRANCE

Marseille

CLARTÉteam:Controloflightandradia7onanalysis:Electromagne7ctreatment

DeputyEditor

Contents

•  Diffraction gratings: history, principles, models •  Classification

–  Metal gratings

–  Multilayer dielectric grating

–  Hybrid metallo-dielectric gratings

–  Gratings exhibiting wide spectral tolerance

Whatisadiffrac7ongra7ng?

z

ε (x) : modulated area

x

y

M ε : superstrate

ε 0 : substrate

Periodicmodula7onofamedium: i.e.periodicmodula7onoftherefrac7veindex

That’sall?

Yes…butthat’salot!!

6

Reflection of a Plane wave on a flat interface

θrθi

θt

x

y

1

2

Hk

E

θrθi

θt

x

y

1

2

Ek

H

.0

xy

z

α

β

γ

=

=

k r

In TE polarization In TM polarization

αi=2πnisinθi/λαr=2πnisinθr/λ

αr=αi

Reflec7onoflightbyadiffrac7ongra7ng

Gra7ng’slaw

αm=αi+2πm/dαi=2πnisinθi/λαm=2πnmsinθi/λ

Firstdiffrac7ongra7ngobserva7on:withabirdfeather

JamesGregory:«Letinthesun’slightbyasmallholetoadarkenedhouse,andattheholeplaceafeather,(themoredelicateandwhitethebe;erforthispurpose,)anditshalldirecttoawhitewallorpaperoppositetoitanumberofsmallcirclesandovals,(ifImistakethemnot,)whereofoneissomewhatwhite,(towit,themiddle,whichisoppositetothesun,)andalltherestseverallycoloured.Iwouldgladlyhearhisthoughtsofit.»

13May1673

Observa7ons

•  Strangeandveryinteres7ngeffect:producingsepara7onofcolorsinsunlight.

•  JustayearbeforeNewtonmadethesameobserva7onwithaprism.

•  Whatisthemain≠gra7ngs&prisms?->Gregoryproducedmul7plespectraandunseparated/undeviatedspotinplaceofNewton’ssinglespectrum.

D.Rieenhouse

•  1785:observa7onofdiffrac7oneffectthroughasilkhandkerchiefbyF.Hopkinson

•  CorrespondencewithD.Rieenhouse•  In1785Rieenhousemadeperhapsthefirstdiffrac7ongra7ngusing50hairsbetweentwofinelythreadedscrews,withanapproximatespacingofabout100linesperinch

Discoveryofthediffrac7ongra7ngeffect:F.Hopkinson,1786.

Firstman-madediffrac7ongra7ng?

Diffrac7ongra7ngs:perfecttooltotunetheop7calproper7esof

materials

BirthofMETAMATERIALS

Howtomakegold(goodlightreflector)black?

Metallicgra7ngsTheWood’sanomalies(1902)

•  Periodicand//groovesetchedinametallicsubstrate

•  Illumina7onbyawhitelampinTMpolariza7on

Au

Robert W. Wood

R. W. Wood, Philos. Mag. 4, 396-402 (1902)

Metallicgra7ngs:theWood’sanomalies(1902)

Robert W. Wood

R. W. Wood, Philos. Mag. 4, 396-402 (1902)

Only in TM polarization:

The scalar theory of gratings fails:

Firstaccuratenumericalmethods(1970’s)

M. C. Hutley, D. Maystre., Opt. Commun. 19 (1976)

Experimental data: d=555.5 nm, For h=37 nm and θ=6.6°, R

Demonstra7onofthegra7ng’slaw

z

ε (x) : modulated area

x

y

M ε : superstrate

ε 0 : substrate

Periodicmodula7on:

Gra7ngoperatorR(x):Linear Periodic

ε(x,y)=ε(x+d,y)

Ei(x,y)=Ei(y)exp(iαix)

Ed(x+d,y)=R(x+d)Ei(x+d,y)=R(x)Ei(x+d,y)

Incidentplanewave:

Ed(x,y)=R(x)Ei(x,y)R(x)=R(x+d)

Ed(x+d,y)=R(x)Ei(x,y)exp(iαid)=Ed(x,y)exp(iαid)

Let us define the function:

Demonstra7onofthegra7ng’slaw

v(x,y)=Ed(x,y)/exp(iαix)

Let us calculate v(x+d,y): v(x+d,y)=Ed(x+d,y)/[exp(iaix) exp(iaid]) v(x+d,y)=R(x+d,y)Ei(x+d,y)/[exp(iαix)exp(iαid]) v(x+d,y)=R(x,y)/exp(iαix)=v(x,y)

Function v(x,y) is periodic, it can expanded onto Fourier series

αm=αi+2πm/d

Pseudo-periodic field:

Periodicallymodulatedinterface:gra7ng’slaw

θrθi

x

y

1

2

k

Planeinterface:Descartes’slaw

αm=αi+2πm/dαm=αi

Periodicallymodulatedinterface:gra7ng’slaw

θrθi

x

y

1

2

k

Planeinterface:Descartes’slaw

αm=αi+2πm/dαm=αi

Howtopredictthereflectedefficiency?

Howtopredictthereflectedefficiency?

θrθi

x

y

1

2

k

αm=αi+2πm/dαm=αi

1 2

1 2

1 2

1 2

r

β βµ µβ βµ µ

−=

+

1 2

1 2

1 2

1 2

r

β βε εβ βε ε

−=

+

Fresnelcoefficients,dependonthepolariza7on

InTE InTM

Nosimpleruleforgra7ng.Theefficiencydepndsonahighnumberofparameters:h,d,op7calcontrast,shapeofgrooves,lambda,…

Electromagnetic model

Reduction of the Maxwell equations into a set of first order differential equations. Integration of this set of equation from the substrate to the superstrate along the y coordinate. Boundary conditions: calculation of the electromagnetic field in the homogeneous media. A second integration permits the calculation of the EM field inside the grating.

z

ε (x) : modulated area

x

y

M ε : superstrate

ε 0 : substrate

Analytic resolution of Maxwell equations

Analytic resolution of Maxwell equations

Numerical resolution of Maxwell equations

M.NevièreandE.Popov,LightPropagaBoninPeriodicMedia:DiffracBonTheoryandDesign(MarcelDekker,NewYork,2003)

Electric field distribution inside metallic gratings

0 1 2 3 4 50

1

2

3

4

5

0.100.140.200.250.400.500.771.21.42.02.73.75.27.210142027375272100

x (µm)

y (µ

m)

0 100 200 300 400 500 6000

100

200

300

400

500

600

H

Normal incidence

Au

Air

SiO2

Au

0.10000.13410.18000.24140.32390.43440.58280.78181.0491.4071.8872.5323.3974.5576.1128.20011.00

X in nm

Y in

nm

N.Bonodetal.,Opt.Express15,11427-11432(2007)N.Bonod,E.Popov,Opt.Lee.33,2398-2400(2008)N.Bonodetal.,Opt.Express16,15431-15438(2008)

Diffrac7ongra7ngsinpulsecompressorsystems

Classifica7onofdiffrac7ongra7ngsinpulsecompressorsystems

N.Bonod,J.Néauport,Adv.Opt.Photonics8,156-199(2016)

Howtodesignhigheffiencyreflec?ongra?ng?

1ststep:designingahighreflec7vecomponent.Metals,totalinternalreflec7on,mul7layermirror.2ndstep:etchingaperiodicstructureQues?on:Onlythe0-thorderpropagatesinreflec7onwhenillumina7ngthegra7nginnormalincidence.When7l7ngtheincidenceandincreasingtheangleofincidence,whatorderwillfirstappear?

Howtodesignhigheffiencyreflec?ongra?ng?

3rdstep:op7mizingtheshapeofthemodula7ontoachieveahighefficiency.Thissteprequirescomputa7onalmethods.•  InmostCPAapplica7ons,diffrac7ongra7ngsfeature2propaga7ngorders(−1stand0thorder),alltheotherordersbeingevanescent

Metalgra7ngs

Goldisusuallypreferredformetallicreflec7vegra7ngsduetoitshighreflec7vityoverthespectralrangeofinterest(from700to1200nm)Noblemetal:doesnotrequireaprotec7vetransparentoxidelayerlikesilveroraluminumSincethepioneeringworksofWood,ithasbeenwellknownthatmetallicgra7ngsarehighlysensi7vetoincidentpolariza7on.So-calledWood’sanomaliesareobservedonlyinTMpolariza7on

Metalgra7ngs

R.Boydetal.,Appl.Opt.34,1697-1706(1995)

1stmaximumachievedinthecaseofTMpolariza7onTEpolariza7on:highdiffractedefficienciesbutfordeepergrooves:metallicgra7ngswillbeeasiertomanufactureinTMpolariza7on:metallicgra7ngsusedinCPAsystemsoperateinTMpolariza7onBothpolariza7onsofferdiffractedlargerthanthereflectedefficiencyoflightinthebarecorrespondingmetal

Metalgra7ngs

Largespectraltoleranceoftheirreflectedefficiency:crucialimportancetorecompressshortpulsesthatfeatureabroadspectrum.Typicaldiffrac7onefficienciesof92%inTMandbroadbandwidth

J.Brieenetal.,Opt.Lee.21,540-542(1996)

MultiLayer Dielectric gratings

TwoadvantagesforCPAapplica7onscomparedwithnoblemetals:(i)  theycanfeaturenegligiblelosses,whichcanbeofhigh

importancetoachievingalmostperfectop7calperformance,nearly100%ofdiffrac7onefficiency

(ii)theyfeaturemuchhigherLIDTsthanmetals(iii)Proposedin1995asanalterna7vetometallicgra7ngs

M.D.Perry,R.D.Boyd,J.A.Brieen,D.Decker,B.W.Shore,C.Shannon,andE.Shults,“High-efficiencymul7layerdielectricdiffrac7ongra7ngs,”Opt.Lee.20,940–942(1995).

MultiLayer Dielectric gratings

Multilayer dielectric gratings (1995)

M.D.Perryetal.,Opt.Lee.20,940-942(1995)

MLDgra7ngs: -operateinTEpolariza7on -almostperfectreflec7on

Role of electric field on LIDT

Bri;enSPIE52732003Bri;enSPIE27141996

Increasing the angle of incidence permits to decrease the electric field inside the pillars

Gratings should be illuminated with high angles of incidence !

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.01.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

Max

imum

of E

nhan

cem

ent |

E|2

Reflected efficiency -1 order

MLD 1780 l/mm, 77.2° MLD 1740 l/mm, 62°

0.0 0.2 0.4 0.6 0.8 1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Max

imum

of e

nhan

cmee

nt o

f |E

|2

Reflected effiicency in -1 order

Influence of the grating profile on LIDT

Identical period and reflected eficiencies but different near field enhancement N. Bonod et al., Opt. Commun. 260, 649-655 (2006)

α

h

e

c

Dielectric multilayers

H

d

HoribaJobin-Yvon

CEACESTAIns7tutFresnel

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

2,0 2,5 3,0 3,5 4,0 4,5 5,0 5,5 6,0 6,5 7,0 7,5 8,0

Fluence (J/cm²)Pr

obab

ility

PW01PW04PW08PW10

Influenceofthegra?ngprofileonLIDT

J.Neauportetal.,Opt.Express15,12508-12522(2007).

R=96%

LIDT vs max |E|2

LIDT>4.5 J/cm2

S/1 mode 1.057µm

Gaussian beam 200µm @ 1/e² ∼ 200 sites, 100 shots per site

10 Hz, 500 fs RH

Localisation of the damage at a sub-micrometer scale

S.Hocquet,J.Néauport,N.Bonod,Appl.Phys.Lee.99,061101(2011)

Damagesini7ateattheoppositetoincomingwaveGoodconcordancewithEfieldcomputa7ons.SEMmeasurementsshowthatripplesreducedamagethresholdofMLDgra7ngs.

Metal-MultiLayer Dielectric gratings

Hybrid metal-dielectric grating

‘A metal layer is inserted between the substrate and the dielectric stack to reduce the number of dielectric bilayers and thus the mechanical stress within the

stack’

Reduced numbers of dielectric layers

3 to 4 pairs are sufficient

Gold layer

Grating

HfO2

SiO2 h c

HfO2 SiO2

Substrate

Au SiO2

HfO2

HfO2 SiO2

SiO2

First proposed to decrease the number of dielectric layers for decresing the stress indside the stack

N.Bonodetal.,Opt.Commun.260,649-655(2006)

2010: First hybrid metal-dielectric grating

HfO2

SiO2 h c

HfO2

SiO2

Substrate

Au SiO2

HfO2

HfO2 SiO2

SiO2

Sensitivity to crazings: Two samples of MLD and MMLD stacks (EBPVD) 120×140 mm2 have been exposed to a few air/vacuum cycles. Samples were observed using an intense fiber lamp: a few fractures were observed on the MLD stack only.

J.Neauportetal.,Opt.Express18,23776-23783(2010)

Hybrid metal-dielectric gratings

α e (nm) h (nm) DC (-1) reflected order diffraction efficiency, measured / calculated |E/E0|²

80° 164 394 0.346 96.7% / 99.2% 1.71

81° 180 400 0.365 96.3% / 95.5% 1.97

78° 124 456 0.357 96.9% / 97.2% 1.59

Hybrid metal-dielectric gratings: high efficiency

J.Neauportetal.,Opt.Express18,23776-23783(2010)

Hybridmetallo-dielectricgra7ng:LIDT

Hybrid metal-dielectric grating: LIDT>3 J/cm2 (500 fs)

J.Neauportetal.,Opt.Express18,23776-23783(2010)

Wide spectral tolerance

Wide spectral tolerance High reflectivity over a wide spectral range centered around 800 nm

1740lines/mm

Full dielectric grating

Etching in low and high refractive index

H.Guanetal.,Opt.Lee.39,170-173(2014)

D.H.Martzetal.,Opt.Express17,23809-23816(2009)

Etching in the low refractive index, TE polarization

2op?miza?onsteps:Op7miza7onofthereflec7vityofthedielectricstackbymodula7ngthethicknessofthelayersOp7miza7onofthereflectedefficiency(-1storder)bymodula7ngthegrooveprofile

Thereflectedefficiencymustbeop7mizedwithrespecttothegra7ngprofileandthedielectricstacksimultaneously.

HfO2

SiO2 hc

HfO2 SiO2

Substrate Au SiO2 HfO2

HfO2 SiO2

SiO2

NOSOLUTION!!!

Solutions can be found

Thereflectedefficiencyaveragedoverthespectrumishigherthan95%

7 dielectric layers (HfO2/SiO2) are needed

The grating is etched in the silica layer, the groove depth= 700 nm

700 720 740 760 780 800 820 840 860 880 9000.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Ref

lect

ed e

ffici

ency

Wavelength in nm

ordre -1 totale

HfO2

SiO2 h c

HfO2 SiO2

Substrate

Au SiO2

HfO2

HfO2 SiO2

SiO2

FirstorderMeasurementat785nm,55.5°:95%

120x140

*HORIBAJobinYvonSASmanufacturesMMLDgra7ngsunderaworldwideexclusivelicenseofthepatent,Op7mizeddielectricreflec7vediffrac7ongra7ng-PCT/FR2010/052684-US20120300302”.

FirstwidespectralMMLDmanufactured(2014)

Conclusions

1780s:discoveryofdiffrac7ongra7ngs1960s:discoveryoflasers60s-70s:discoveryofop7callithographythankstolasers.Op7callithographyrevolu7onizedthefabrica7onofgra7ngs1980s:Diffrac7ongra7ngsrevolu7onizedhighenergylasersHighpowerlaserspushdiffrac7ongra7ngstowardstheirextremelimits:highdiffrac7onefficiency,largesize(hugesizecomparedtothewavelength),highLIDT,widespectraltolerance,wavefrontquality,…

N.Bonod,J.Néauport,“Diffrac7ongra7ngs:fromprinciplestoapplica7onsinhighintensitylasers,”Adv.Opt.Photonics8,156-199(2016)