Twisted Photons: Applications of Light with Orbital Angular Momentum, First Edition

280 Pages·2011·12.4 MB·English

Editedby
JuanP.TorresandLluisTorner
TwistedPhotons
Related Titles
Clarke,D. Meschede,D.
StellarPolarimetry Optics, LightandLasers
ThePracticalApproachtoModernAspects
2010 ofPhotonicsandLaserPhysics
ISBN:978-3-527-40895-5
2007
Ro¨mer,H. ISBN:978-3-527-40628-9
Theoretical Optics
Busch,K.,Lo¨lkes,S.,Wehrspohn,R.B.,
AnIntroduction Fo¨ll,H.(eds.)
2009 PhotonicCrystals
ISBN:978-3-527-40776-7 AdvancesinDesign,Fabrication,and
Characterization
Wang,L.V.,Wu,H.-i
2004
BiomedicalOptics ISBN:978-3-527-40432-2
PrinciplesandImaging
2007
ISBN:978-0-471-74304-0
Edited by Juan P. Torres and Lluis Torner
Twisted Photons
Applications of Light with
Orbital Angular Momentum
TheEditors AllbookspublishedbyWiley-VCHare
carefullyproduced.Nevertheless,authors,
Prof.JuanP.Torres editors,andpublisherdonotwarrantthe
UniversitatPolitecnicadeCatalunya informationcontainedinthesebooks,
ICFO-TheInstituteofPhotonicSciences includingthisbook,tobefreeoferrors.
MediterraneanTechnologyPark Readersareadvisedtokeepinmindthat
AvCanalOlimpics/n statements,data,illustrations,procedural
08860Castelldefels(Barcelona) detailsorotheritemsmayinadvertentlybe
Spain inaccurate.
[email protected]
LibraryofCongressCardNo.:appliedfor
Prof.LluisTorner
UniversitatPolitecnicadeCatalunya BritishLibraryCataloguing-in-Publication
ICFO-TheInstituteofPhotonicSciences Data
MediterraneanTechnologyPark Acataloguerecordforthisbookisavailable
AvCanalOlimpics/n fromtheBritishLibrary.
08860Castelldefels(Barcelona)
Spain
Bibliographicinformationpublishedbythe
[email protected]
DeutscheNationalbibliothek
TheDeutscheNationalbibliothek
liststhispublicationintheDeutsche
Nationalbibliografie;detailedbibliographic
dataareavailableontheInternetat
<http://dnb.d-nb.de>.
2011WILEY-VCHVerlag&Co.KGaA,
Boschstr.12,69469Weinheim,Germany
Allrightsreserved(includingthoseof
translationintootherlanguages).Nopart
ofthisbookmaybereproducedinany
form–byphotoprinting,microfilm,orany
othermeans–nortransmittedortranslated
intoamachinelanguagewithoutwritten
permissionfromthepublishers.Registered
names,trademarks,etc.usedinthisbook,
evenwhennotspecificallymarkedassuch,
arenottobeconsideredunprotectedbylaw.
Typesetting LaserwordsPrivateLtd.,
Chennai,India
PrintingandBinding FabulousPrintersPteLtd.,
Singapore
CoverDesign Grafik-DesignSchulz,
Fußgo¨nheim
PrintedinSingapore
Printedonacid-freepaper
ISBN:978-3-527-40907-5
V
Contents
Preface XI
ListofContributors XV
ColorPlates XIX
1 TheOrbitalAngularMomentumofLight:AnIntroduction 1
LesAllenandMilesPadgett
1.1 Introduction 1
1.2 ThePhenomenologyofOrbitalAngularMomentum 4
References 9
2 VortexFlowofLight:‘‘Spin’’and‘‘Orbital’’FlowsinaCircularly
PolarizedParaxialBeam 13
AleksandrBekshaevandMikhailVasnetsov
2.1 Introduction 13
2.2 SpinandOrbitalFlows:GeneralConcepts 14
2.3 TransverseEnergyFlowsinCircularlyPolarizedParaxialBeams 15
2.4 OrbitalRotationwithoutOrbitalAngularMomentum 21
2.5 Conclusion 22
References 23
3 HelicallyPhasedBeams,andAnalogieswithPolarization 25
MilesPadgett
3.1 Introduction 25
3.2 RepresentationofHelicallyPhasedBeams 26
3.3 ExploitingtheAnalogousRepresentationsofSpinandOrbitalAngular
Momentum 27
3.3.1 RotationalDopplerShiftsandGeometricalPhase 27
3.3.2 ModeSortingusingGeometricPhase 29
3.3.3 EntanglementofSpatialModes 30
3.3.4 PhotonDragandtheMechanicalFaradayEffect 32
3.4 Conclusions 33
References 34
TwistedPhotons:ApplicationsofLightwithOrbitalAngularMomentum.
EditedbyJuanP.TorresandLluisTorner
Copyright2011WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
ISBN:978-3-527-40907-5
VI Contents
4 TrappingandRotationofParticlesinLightFieldswithEmbedded
OpticalVortices 37
MichaelMaziluandKishanDholakia
4.1 Introduction 37
4.2 Laguerre–GaussianLightBeams 38
4.3 OriginofOpticalTorquesandForces 41
4.3.1 IntuitivePictureofOpticalForces 41
4.3.2 AngularMomentumwithinGeometricOptics 43
4.3.3 ParaxialBeams 44
4.3.4 Maxwell’sStressTensor 45
4.3.5 LinearMomentumTransfer 49
4.3.6 AngularMomentumTransfer 50
4.3.7 PolarizationSpinMomentum 50
4.4 OpticalVortexFieldsfortheRotationofTrappedParticles 51
4.4.1 StudiesofRotationofTrappedObjectsusingOptical
VortexFields 51
4.5 OpticalVortexFieldsforAdvancedOpticalManipulation 57
4.6 Conclusions 61
Acknowledgments 62
References 62
5 OpticalTorquesinLiquidCrystals 67
EnricoSantamatoandBrunoPiccirillo
5.1 TheOpticalReorientationandthePhoton
AngularMomentumFlux 70
5.1.1 DynamicalEquationsofLiquidCrystals 71
5.1.2 AngularMomentumFluxes 73
5.2 DynamicalEffectsInducedinLiquidCrystalsbyPhotonSAM
andOAMTransfer 78
5.2.1 ExperimentsonOAMTransferinLiquidCrystals 81
5.2.1.1 OrbitalPhotonAngularMomentumTransferwithUnpolarized
Light 83
5.2.1.2 InvestigationoftheCombinedEffectoftheSpinandOrbitalPhoton
AngularMomentumTransferwithLinearlyPolarizedLight 83
5.2.1.3 InvestigationoftheCombinedEffectoftheSpinandOrbitalPhoton
AngularMomentumTransferwithCircularlyPolarizedLight 85
5.3 Conclusions 89
References 90
6 DrivingOpticalMicromachineswithOrbitalAngularMomentum 93
VincentL.Y.Loke,TheodorAsavei,SimonParkin,NormanR.Heckenberg,
HalinaRubinsztein-Dunlop,andTimoA.Nieminen
6.1 Introduction 93
6.2 Symmetry,Scattering,andOpticallyDrivenMicromachines 93
6.3 ExperimentalDemonstration 96
Contents VII
6.3.1 APreliminaryDesign 96
6.3.2 Fabrication 97
6.3.3 OpticalTrappingandRotation 97
6.3.4 OpticalMeasurementofTorque 98
6.3.5 Discussion 100
6.4 ComputationalOptimizationofDesign 102
6.4.1 ComputationalModelingofMicrorotors 102
6.4.2 PerformanceofaFour-ArmedRotor 105
6.4.3 Discussion 111
6.5 Conclusion 113
References 113
7 RotationalOpticalMicromanipulationwithSpecificShapesBuiltby
Photopolymerization 117
Pe´terGalaja,Lo´ra´ndKelemen,La´szlo´Oroszi,andPa´lOrmos
7.1 Introduction 117
7.2 MicrofabricationbyPhotopolymerization 118
7.2.1 FabricationbyScanningaSingleFocusedLaserBeam 118
7.2.2 ParallelPhotopolymerizationusingDiffractiveOptics 120
7.3 Light-DrivenRotors,Micromachines 121
7.3.1 Propeller 121
7.3.2 PropellerwithReversedDirectionofRotation 124
7.3.3 ComplexMicromachines 126
7.4 IntegratedOpticalMotor 128
7.5 AngularTrappingofFlatObjectsinOpticalTweezersFormedby
LinearlyPolarizedLight 131
7.6 TorsionalManipulationofDNA 134
7.6.1 DirectMeasurementofTorque 135
7.7 Conclusion 138
Acknowledgment 139
References 139
8 SpiralPhaseContrastMicroscopy 143
ChristianMaurer,StefanBernet,andMonikaRitsch-Marte
8.1 PhaseContrastMethodsinLightMicroscopy 143
8.2 FourierFilteringinOpticalImaging 144
8.3 SpiralPhaseFourierFiltering 146
8.3.1 IsotropicEdgeEnhancement 148
8.3.2 PseudoreliefImages 149
8.3.3 SpiralFringeMetrologywithSPC 150
8.4 ImplementationandPerformance 151
8.5 Conclusions 152
References 152
VIII Contents
9 ApplicationsofElectromagneticOAMinAstrophysicsandSpace
PhysicsStudies 155
BoThide´,NicholasM.EliasII,FabrizioTamburini,SiavoushM.
Mohammadi,andJose´T.Mendon¸ca
9.1 Introduction 155
9.2 UbiquitousAstronomicalPOAM 156
9.3 ApplicationsofPOAMinAstronomy 158
9.3.1 Sub-RayleighResolution 159
9.3.2 OpticalVorticeswithStarlight 162
9.4 ApplicationsofPOAMinSpacePhysics 165
9.A. Appendix:TheoreticalFoundations 169
9.A.1 ClassicalFieldPicture 169
9.A.2 PhotonPicture 170
References 175
10 OpticalVortexCatStatesandtheirUtilityforCreatingMacroscopic
SuperpositionsofPersistentFlows 179
EwanM.Wright
10.1 Introduction 179
10.2 OpticalVortexCatStates 181
10.2.1 LinearFiberPropagation 181
10.2.2 QuantumFiberPropagation 182
10.2.3 OpticalVortexCatStateviaSelf-PhaseModulation 184
10.2.4 Photonic-CrystalFibers 186
10.2.5 OtherSchemes 188
10.3 MacroscopicSuperpositionofPersistentFlows 189
10.3.1 OpticalLight-ShiftPotential 189
10.3.2 RingTrapandQuantumStirring 190
10.3.3 MatterWavesonaRing 191
10.3.4 MacroscopicSuperpositionofPersistentFlows 192
10.3.5 Discussion 194
10.4 SummaryandConclusions 195
References 195
11 ExperimentalControloftheOrbitalAngularMomentumofSingle
andEntangledPhotons 199
GabrielMolina-TerrizaandAntonZeilinger
11.1 IntroductiontothePhotonOAM 199
11.2 ControloftheOAMStateofaSinglePhoton 201
11.3 ControloftheOAMStateofMultiplePhotons 203
11.4 ApplicationsinQuantumInformation 207
11.5 Discussion 209
11.6 Conclusion 211
References 211
Contents IX
12 RotatingAtomswithLight 213
KristianHelmersonandWilliamD.Phillips
12.1 Introduction 213
12.2 OrbitalAngularMomentumofLight 213
12.3 TheMechanicalEffectsofLight 214
12.4 RotatingBose–EinsteinCondensates 215
12.4.1 ExperimenttoTransferOrbitalAngularMomentumtoaBEC
((cid:1)=0) 216
12.4.2 EfficiencyoftheOAMTransferProcess 218
12.5 MeasuringtheRotationalMotionoftheAtoms 220
12.5.1 InterferenceoftheRotatingStatewithaNonrotatingState 220
12.5.2 InterferenceoftheRotatingStatewithaCounterrotatingState 222
12.5.3 ObservationofFork-LikeInterferenceStructure 223
12.5.4 MeasurementoftheDopplerShiftoftheRotatingAtoms 223
12.6 GeneratingOtherRotationalStatesofAtoms 224
12.6.1 VorticesofHigherCharge 224
12.6.2 RotationalStatesofMultilevelAtomicCondensates 227
12.6.3 MatterwaveAmplificationofaVortexState 228
12.7 Supercurrents 230
12.7.1 GenerationofaSupercurrentinaBEC 230
12.8 Conclusion 231
Acknowledgments 232
References 232
Index 237
XI
Preface
The book Twisted Photons: Applications of the Orbital Angular Momentum of Light
that we are honored to edit contains 12 salient contributions that focus on new
applicationsthatuseoneofthepropertiesthatcharacterizeselectromagneticwaves
in general, and light beams, in particular: the topology of their spatial shape.
Thisisanimportantdegreeoffreedomthataddsuptothetoolkitconstitutedby
the other propertiesthat characterize a light beam, namely, polarization, energy,
and spectrum, thus putting forward a powerful enabling tool with widespread
applications in several areas of science and technology where its use allows the
exploration of unchartered territories, both in the realm of the very small and
delicate(e.g.,singleatoms,invivocells,andmicromachines)andintherealmof
theverybig(e.g.,astronomy).
Thetopichasbeenextensivelystudiedduringthelasttwodecadesandmanyof
the corresponding techniques are well understood, and conceptually and experi-
mentallymastered.Thegoalofthisbookistopresentthetopictoabroadaudience,
andtoillustrateitspotentialbyexaminingexamplesofitsuseindifferentareasof
application.
WhatistheOrbitalAngularMomentumofLight?
Light carries energy and both, linear and angular momenta. The total angular
momentumcan containa spincontributionassociated with polarization,and an
orbital contribution associated with the spatial profile of the light intensity and
phase. By and large, a beam of light with a single intensity peak and smooth
wave front, that is, a Gaussian-like shape that propagates in free space, shows
no azimuthal phase variations, and the propagation of the energy flow follows a
straightpathalongthedirectionofpropagationofthebeam.
Lightwithorbitalangularmomentumexhibitsdrasticdifferences,asillustrated
in the images that appear in the cover of this book (see also L. Allen and M.
J. Padgett, The orbital angular momentum of light: an introduction). The picture
showsthesimplestkindoflightbeamsthatcarryorbitalangularmomentum.The
intensity of the light beam, as depicted in the two figures on the left, presents
a central dark area (the beam axis) with no intensity. Such light beams exhibit a
corkscrew-likespiralingofthephasearoundthebeamaxiswithnoenergy(topand
TwistedPhotons:ApplicationsofLightwithOrbitalAngularMomentum.
EditedbyJuanP.TorresandLluisTorner
Copyright2011WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim
ISBN:978-3-527-40907-5