Efficient nonlinear generation of high power, higher order, ultrafast "perfect" vortices in green

6.7 MB·

by  N. Apurv Chaitanya

January12,2016
AbstractWereportonefficientnonlineargenerationofultrafast,
higherorder“perfect”vorticesatthegreenwavelength.Based
on Fourier transformation of the higher order Bessel-Gauss
beamgeneratedthroughthecombinationofspiralphaseplate
andaxiconwehavetransformedtheGaussianbeamoftheultra-
fastYb-fiberlaserat1060nmintoperfectvorticesofpower4.4
Wandorderupto6.Usingsingle-passsecondharmonicgener-
ation(SHG)ofsuchvorticesin5-mmlongchirpedMgO-doped,
periodicallypoledcongruentLiNbO3crystalwehavegenerated
perfectvorticesatgreenwavelengthwithoutputpowerof1.2W
andvortexorderupto12atsingle-passconversionefficiency
6
of27%independentofitsorder.Thisisthehighestsingle-pass
1
SHGefficiencyofanyopticalbeamsotherthanGaussianbeams.
0
Unlikethedisintegrationofhigherordervorticesinbirefringent
2
crystals,here,theuseofquasi-phasematchingprocessenables

n generationofhighqualityvorticesevenathigherorders.The
a greenperfectvorticesofallordershavetemporalandspectral
J
width of 507 fs and 1.9 nm, respectively corresponding to a

1 time-bandwidthproductof1.02.
1

]
s
c
i Efficient nonlinear generation of high power, higher order,
t
p
o ultrafast “perfect” vortices in green
.
s
c
i N. Apurv Chaitanya1,2,*, M. V. Jabir1, G. K. Samanta1
s
y
h
p
[ Opticalvortices,havingphasesingularities(phasedis- differentwavelengthsacrosstheelectromagneticspectrum

locations)inthewavefront,carryvanishingintensityatthe inaccessibletolasers.Assuch,frequencyup-conversionof
1
singularpoint.Duetothescrew-like(helical)phasestruc- highpower,ultrafast,opticalvorticesat1.064µmhasgiven
v
4 turearoundthepointofsingularity,suchbeamscarryorbital accesstohigherorderopticalvortices(l=12)inthegreenat
7 angularmomentum(OAM).Thephasedistributionofthe 0.532µm[6].Similarly,frequencydown-conversioninopti-
3 opticalvorticescanberepresentedas∼exp(ilθ),withθ as calparametricoscillatorshasproducedopticalvortexbeam
2 azimuthalangleandtheintegerl,astopologicalcharge(or- of order, l =1, with spectral tunability across 1 µm [7]
0 der).EachphotonofthebeamcarriesOAMofl(cid:125).Sincethe and 2 µm [8]. So far, the nonlinear generation of vortex
.
1 discoveryofOAMassociatedwithopticalvortices[1],these beams with high power/energy has been restricted to the
0 beams have drawn a great deal of attention from various vorticesoflowerorders[6].Incaseofopticalvortices,the
6 fieldsofscienceandtechnologyincludinghighresolution beam area and divergence [9] increases linearly with the
1 microscopy[2],quantuminformation[3],materialprocess- orderofthevortices.Asaresult,thenonlinearparametric
v: ing[4]andparticlemicro-manipulationandlithography[5]. gain,whichdependsontheintensityofthedrivingfields
i However,themajorchallengethroughtheseapplicationsis andtheoverlappingintegraloftheinteractingbeams,and
X
theneedforsourcesofcoherentradiationinvortexspatial thus the conversion efficiency of the nonlinear processes
r profilesatdifferenttopologicalchargesandwavelengths. decreaseswiththeorderofthevortices.Therefore,nonlin-
a
Theopticalvorticesaretypicallygeneratedbyspatial ear generation of higher order optical vortices especially
phasemodulationofGaussianbeamsusingdifferenttypes withhighpower/energyrequiresopticalvorticeswithbeam
of modulators including spatial light modulators (SLMs) areaandbeamdivergenceindependenttotheirorders.For-
andspiralphaseplates(SPP).However,allofthosemodula- tunately,recentdevelopmentinthefieldofstructuredbeams
torshaveitsownadvantagesanddisadvantagesintermsof providedanewclassofopticalvortexbeamsknownas“per-
wavelengthcoverage,modeconversionefficiency,damage fect”vortex[10,11].Unlikevortices,theperfectvortices
thresholdandpowerhandlingcapabilitiesandcost[6].On haveannularringradiusindependentofitsorders.
theotherhand,nonlinearfrequencyconversiontechniques Typically,FouriertransformationoftheBessel-Gauss
canbeusedtoaccesshighpower/energyopticalvorticesat (BG)beamofdifferentordersisusedtogenerateperfect
1Photonic Sciences Lab., Physical Research Laboratory, Navarangpura, Ahmedabad 380009, Gujarat, India 2Indian Institute of Technology-
Gandhinagar,Ahmedabad382424,Gujarat,India
*Correspondingauthor:e-mail:[email protected]
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2 N.ApurvChaitanyaetal:Nonlineargenerationof“perfect”vortices
vortices [11]. However, the combination of SPP and axi-
conconvertingtheGaussianbeamintoLaguerre-Gaussian
(LG)beamsandBGbeamsofdifferentorders,aspresented
inthecurrentreport,canbeconsideredasoneofthesim-
plest schemes for generating high power perfect vortices
ofdifferentorders.Thecomplexfieldamplitudeoftheex-
perimentallyrealizableperfectvortexoforder,lattheback
focalplane(z=0)oftheFouriertransforminglensmaybe
representedinpolarcoordinatesas[11]
w (cid:18) (ρ−ρ )2(cid:19)
E(ρ,θ)=il−1 gexp − r exp(ilθ) (1)
w w2
o o
Here,w isthewaistradiusoftheGaussianbeamcon-
g
finingthevortexbeam.ρ = fsin(n−1)α istheradiusof
r
theperfectvortexring, f isthefocallengthoftheFourier
transforminglens,andnandα arerespectivelytherefrac- Figure1 Schematicoftheexperimentalsetupfornonlineargen-
tiveindexandbaseangleoftheaxicon.2w (w =2f/kw , erationofultrafastperfectvortices.λ/2;half-waveplate,PBS1,2;
o o g
theGaussianbeamwaistradiusatthefocus)istheannular polarizingbeamsplittercube,SPP1,2;spiralphaseplates,λ/4;
widthoftheperfectvortex.k=2π/λ isthewavevectorof quater-waveplate,L1-3;lens,M;mirrors,C;MgO:CLNcrystalfor
thebeamofwavelengthλ infreespace.UsingEqn.(1),we frequency-doubling,S;Dichroicmirror;PM,Powermeter.(a-d)
canwritetheintensityoftheperfectvortexas, Spatialintensityprofileofthebeamsrecordedatdifferentposi-
tionsalongthepropagationdirection.
(cid:18)w (cid:19)2 (cid:18) (ρ−ρ )2(cid:19)
g r
I(ρ,θ)= exp −2 (2)
w w2 (see Fig. 1(d)) at the centre of the nonlinear crystal to a
o o
measuredbeamradiusof∼166µm.A5-mm-longand2
As evident from the Eqn. (2), the intensity of the perfect x1mm2 inaperture,MgO-doped,periodicallypoledcon-
vortexisindependentofitsorder.Therefore,onecanexpect gruentLiNbO (MgO:CLN)crystal(C)withlinearchirped
3
thenonlinearfrequencyconversionefficiencyofsuchper- gratingperiodof6.61-6.91µmisusedforsecondharmonic
fectvorticestobeindependentoftheirorders[12].Using generation (SHG) of the pump vortex beam. The crystal
such perfect vortices, here, we report, for the best of our hasspectralacceptancebandwidthof15nmtocoverentire
knowledge,thefirstexperimentaldemonstrationofnonlin- pumpspectrumandphase-matchingtemperatureof130◦C
eargenerationofperfectvorticesofpower>1.2Watgreen to avoid any detrimental photorefractive effect. Both the
withconversionefficiencyashighas27%andtopological facesofthecrystalisARcoatedfor530and1060nm.The
charge(order)ashighas12.Wehavealsoexperimentally crystalishousedinanovenwhosetemperaturecanbevar-
verifiedthatathighpowerregime,theconversionefficiency iedupto200◦Cinstepsof0.1◦C.Aλ/2isplacedbefore
ofperfectvorticesisindependenttoitsorder. theaxicontoadjustthepolarizationoftheinputbeamto
Theschematicoftheexperimentalsetupisshownin thenonlinearcrystal.Thedichroicmirror,S,separatesthe
Fig.1. An ultrafast Yb-fiber laser at 1060 nm similar to fundamentalfromthesecondharmonic.
Ref.[6]producingoutputinGaussian(Fig.1(a))intensity We have recorded the spatial intensity distribution of
distribution (M2 <1.1) is used as the pump source. The thepumpbeamandfrequency-doubledgreenbeamusinga
laseroutputhastemporalandspectralwidthof260fsand CCD-basedbeamprofiler(SP-620U,Ophir)atdifferentpo-
15nmrespectivelyatarepetitionrateof78MHz.Thein- sitionalongthepropagationdirectionwiththeresultsshown
putpowertothenonlinearcrystaliscontrolledusingahalf inFig.2.Firstcolumn,(a)-(c)ofFig.2showstheintensity
waveplate(λ/2)andpolarizingbeamsplittercube(PBS1). profileofthepumpvorticesoforder,l =1,3and6respec-
p
Usingonlytwospiralphaseplates,SPP1andSPP2,ofwind- tivelymeasuredbeforetheaxicon.Asexpected,theannular
ingnumbers1and2respectivelyandavortex doubler[6] ringradiusofthevorticesinthefirstcolumnincreaseswith
comprisingofPBS2,quarterwaveplate(λ/4)andaplane theorder.Theaxiconconvertsthevortices(LGbeams)into
mirror(M)withhighreflectancefor1060nm,wehavegen- BGbeamsofsameorder,however,theBGbeamsmaintain
erated optical vortices of order l =1−6. The intensity itsstructureoveradistance,z =w /(n−1)α,where
p max LG
profileofthegeneratedvortexbeam(l =2)isgiveninFig. w isthebeamradiusoftheLGbeambeforetheaxicon
p LG
1(b).Theantireflection(AR)coatedaxiconofapexangle andnandα aretherefractiveindexandbaseangleofthe
∼178◦, converts vortex beam (LG beam) into BG beam axicon respectively. In our experiment, the z for input
max
(seeFig.1(c))ofsameorder.Aplano-convexlens,L1,of vortexorderl =1ismeasuredtobe16cm.Thesizeofthe
p
focallength, f =25mmFouriertransformstheBGbeam BGbeamoforder1,3and6asshowninsecondcolumn
1
intoperfectvortices.Theimagingsystemcomprisingtwo ofFig.2(d)-(f)respectively,measuredatadistancez /2
max
plano-convexlensesL2andL3withfocallengths f =200 fromtheaxicon,increaseswiththeorderofinputLGbeam.
2
mmand f =50mmrespectively,imagestheperfectvortex Dependingupontheorderoftheinputvortices,theFourier
3
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3
Figure2 Spatialintensitydistributionofthebeamsrecordedat
differentpositionsalongbeampropagation.(a-c)normalvortex
pumpbeamsoforders1,3and6recordedbeforetheaxicon,
corresponding(d-f)Bessel-Gaussbeamrecordedat13cmafter
Figure3 Variationinringradiusoftheannularintensitydistri-
theaxicon,and(g-i)perfectvorticesattheFourierplaneoflens
butionofperfectvorticeswithitsorderat(a)pumpand(b)SH
L1.(j-l)characteristiclobestructureofthepumpperfectvortices.
wavelengths.Thesolidlinesarelinearfittotheexperimentaldata.
(m-o)farfieldintensitydistributionoftheSHperfectvorticesof
orders2,6and12and(p-r)correspondinglobestructures.
icalconstraininaccessingtheseperfectvorticesandalso
transforminglensL1isplacedatadistanceof∼15.5cm to tighly focus the perfect vortices for efficient nonlinear
from the axicon produces perfect vortices at the Fourier interaction,wehaveimagedthepumpperfectvorticesusing
plane.Thethirdcolumn,(g)-(i)ofFig.2,showstheannular lensesL2andL3in2f2−2f3configuration(magnification
intensitydistributionoftheperfectvorticesofordersl =1, factorof0.25)atthecrystalplanesituatedatadistance500
p
3and6respectivelymeasuredatthecrystalplane.Fromthe mm away from the Fourier plane of lens L1. As evident
intensityprofilesofthirdcolumn,itisevidentthattheannu- from the Fig. 3 (a), the pump perfect vortices have annu-
larringradiusoftheperfectvorticesareindependenttotheir larringradiusofρrp=166±6 µmfororders,lp=1−6.
order.Giventheintensitydistributionoftheperfectvortices, Theerrorintheringradiusiscomparabletothepixelsize
itisdifficulttouseinterferometrictechniquetodetermine (4.46µm)oftheCCDcamerausedtorecordthevortices.
itstopologicalcharge(order).Therefore,weusedtilted-lens Pumpingthenonlinearcrystalwiththeperfectvortices,the
technique [13] where, the perfect vortex of order l while generatedSHbeamisimagedatthefarfield(>2maway
passingthroughthetitledplano-convexlens(tiltedabout fromthecrystal)usingalensoffocallength f =750mm.
y axis at an angle ∼6◦) splits into n=|l|+1 number of ThevariationofannularringradiusoftheSHvorticeswith
brightlobesatthefocalplaneofthelens.Fromthenumber itsorderisshowninFig.3(b).AsevidentfromFig.3(b),
ofbrightlobesasshowninfourthcolumn,(j)-(l)ofFig.2,it theSHvorticeshaveannularringradiusρsh=420±12µm
r
isevidentthatthepumpperfectvorticeshaveorderslp=1, fortheorders,lsh=2−12confirmingnonlineargeneration
3and6respectively.Fifthcolumn,(m)-(o)ofFig.2,rep- ofperfectvorticesatgreenwavelength.Thesmallvariation
resentstheintensitydistributionofthefrequency-doubled intheradiusoftheSHvorticescanbeattributedmainlyto
perfect vortices recorded at the far field (distance >2 m theexactpositioningoftheCCDcameraintheimageplane.
awayfromthecrystal).Usingtilted-lenstechniquewehave FromEqn.(2)itisevidentthattheintensityoftheper-
confirmedtheordersoftheSHvorticesasshowninthesixth fect vortexis independent of its order. Therefore, theSH
column,(p)-(r)ofFig.2,tobe2,6and12respectively,twice efficiencywhichisproportionaltotheintensityoftheinput
theorderofthepumpvortices.Suchobservationvalidates beamshouldbeconstantwiththeorderoftheinputvortcies.
theangularmomentumconservationinfrequency-doubling ToverifytheorderindependentSHefficiencyoftheultra-
process of perfect vortices. The independence of annular fast,highpowerperfectvortices,wepumpedthenonlinear
ring radius of the second-harmonic (SH) vortices shown crystalwithperfectvorticesofpower∼2.8Wandmeasured
infifthcolumn,ontheordersofthepumpvortices,proves the SH power for different vortex orders with the results
nonlineargenerationofperfectvorticesatgreenwavelength. showninFig.4.Althoughthefiberlasercanproduceoutput
Unlikedisintegrationofhigherordervorticesinbirefringent powerupto5W,duetolossesinthevortexdoublersetup,
crystal[6],useofquasi-phase-matchingenablesgeneration thehigherordervortices(l >3)havemaximumpowerof
p
ofhighqualityperfectvortices(seefifthcolumnofFig.2) ∼2.8W.AsevidentfromFig.4,theperfectvorticeshave
evenathigherorders. single-passSHefficiencyof∼25%forallordersl =1to
p
Wehavemeasuredtheannularringradiusofthepump 6.WehavealsomeasuredthevariationofSHpowerwith
and SH vortices for all orders with the results shown in pumppoweroftheperfectvorticesoforders,l =1and3
p
Fig.3.Theperfectvorticesatfundamentalwavelengthis withtheresultsshownintheinsetofFig.4.Forbothorders,
producedattheFourierplaneofthelensL1withmeasured asevidentfromtheinsetofFig.4,theSHpowerincreases
annualringradiusof∼650µm.However,toavoidmechan- linearlywiththepumppoweratsameslopeefficiencyof
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4 N.ApurvChaitanyaetal:Nonlineargenerationof“perfect”vortices
Figure5 VariationofSHvortexpowerandefficiencyasfunction
ofpumpvortexpower.(Inset)DependenceofSHpowerwiththe
Figure4 DependenceofvortexSHefficiencywiththeorderof
squareofthepumppower.Linesareguidetoeyes.
thepumpvortex.(Inset)variationofSHvortexpowerwiththe
pumpvortexpowerfortwodifferentorders,lp=1and3.Lines
arelinearfittotheexperimentaldata.
η ∼29.7%.TheSHperfectvorticeshavemaximumoutput
powerof1.2Wforthepumppowerof4.4Wresultinga
maximumsingle-passvortexfrequency-doublingefficiency
of∼27%.Thiscanbeconsideredasthehighestsingle-pass
SHGefficiencyofopticalbeamotherthanGaussianbeam.
UnlikequadraticdependenceofSHpowertothepump
powers, the linear increase of SH vortex power with the
pump vortex power (see inset of Fig. 4), clearly indicate
thesaturationeffectinthesingle-passSHefficiency.Toget
furtherinsightofthesaturationeffect,wehaveinvestigated
thepowerscalingcharacteristicsofthegreenperfectvortex
source.Usingthepumpvortexoforderl =3withannular
p
ringradiusof∼166µm,wehavemeasuredtheSHpower
asafunctionofpumppower.TheresultsareshowninFig.
5.AsevidentfromFig.5,atlowerpumppower(<2.8W),
the SH power and efficiency show respectively quadratic Figure6 DependenceofSHpoweroncrystaltemperaturewhile
andlinearlydependencetothepumppower.However,at pumpedwithperfectvortexoforderlp=1.
pumppower>2.8W,theSHpowerincreaseslinearlywith
thepumppowerandtheSHconversionefficiencyremains
almostconstantintherangeof25-27%clearlyindicating crystalwithperfectvortex(l =3)ofpower1Wandmea-
p
thesaturationeffectinthevortexSHprocess.Thedeviation suredtheSHpowerwhileadjustingthecrystaltemperature
ofSHpowerfromitslineardependencewiththesquareof withtheresultsshowninFig.6.AsevidentfromFig.6,the
thepumppowerasshownintheinsetofFig.5,confirmsthe SHpowerincreaseswiththeincreaseofcrystaltemperature
saturationeffectinthevortexSHGprocess.Suchsaturation from 50 to 200◦C with highest SH power at T =142◦C
effectcanbeattributedtothehighnonlinearparametricgain and a measured temperature acceptance bandwidth (full-
arisingfromhighnonlinearcoefficientandlonginteraction widthathalf-maxima,FWHM)of∆T =110◦C.Asaresult,
of the MgO:CLN crystal, and also due to the high peak the power of the SH vortices is insensitive to the fluctua-
poweroftheultrafastpumppulses.Whileonecanexpect tiontotheambienttemperatureandalsotheinstabilityof
higher SH vortex power (>1.2 W) for pump vortices of thetemperatureovenusedtomaintainthecrystaltemper-
smallerannularringradiusandorhigherpumppower>4.4 ature. Using a CCD based spectrometer and an intensity
W, however, due to low damage threshold of the PPLN auto-correlatorwehavemeasuredthespectralandtemporal
crystal[14]especiallyatthegreenwavelengths,wehave width (FWHM) of the SH vortex of all orders to be 1.9
observedcrystaldamageforpumppowerbeyond4.4Wand nm centered at 530 nm and 507 fs respectively resulting
pumpvortexradiusbelow166µm. atime-bandwidthproductof1.02.SimilartotheRef.[6],
To study the temperature dependent phase-matching here we did not observe any variation in the spectral and
characteristics of the MgO:CLN crystal, we pumped the temporalwidthoftheSHvorticeswiththeorder.
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5
Inconclusion,wehaveexperimentallydemonstratedthe
efficientnonlineargenerationofhighpower,higherorder,
ultrafast perfect vortices at the green with output power
>1.2 W and vortex order up to l =12 at single-pass
sh
conversionefficiencyof27%.Thisisthehighestefficiency
in the single-pass SHG of any structured beam. Similar
schemecanbeusedtogeneratehigherorderhighefficient
vorticesatotherwavelengths.
Keywords: Secondharmonicgeneration,Perfectvortex,Orbital
angularmomentum,Ultrafastlaser,Visiblewavelength
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