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Twisted Photons: Applications of Light with Orbital Angular Momentum

Juan P. Torres (Editor), Lluis Torner (Editor)
ISBN: 978-3-527-40907-5
288 pages
March 2011
Twisted Photons: Applications of Light with Orbital Angular Momentum (3527409076) cover image
This book deals with applications in several areas of science and technology that make use of light which carries orbital angular momentum. In most practical scenarios, the angular momentum can be decomposed into two independent contributions: the spin angular momentum and the orbital angular momentum. The orbital contribution affords a fundamentally new degree of freedom, with fascinating and wide-spread applications. Unlike spin angular momentum, which is associated with the polarization of light, the orbital angular momentum arises as a consequence of the spatial distribution of the intensity and phase of an optical field, even down to the single photon limit. Researchers have begun to appreciate its implications for our understanding of the ways in which light and matter can interact, and its practical potential in different areas of science and technology.
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Preface XI

List of Contributors XV

Color Plates XIX

1 The Orbital Angular Momentum of Light: An Introduction 1
Les Allen and Miles Padgett

1.1 Introduction 1

1.2 The Phenomenology of Orbital Angular Momentum 4

References 9

2 Vortex Flow of Light: ‘‘Spin’’ and ‘‘Orbital’’ Flows in a Circularly Polarized Paraxial Beam 13
Aleksandr Bekshaev and Mikhail Vasnetsov

2.1 Introduction 13

2.2 Spin and Orbital Flows: General Concepts 14

2.3 Transverse Energy Flows in Circularly Polarized Paraxial Beams 15

2.4 Orbital Rotation without Orbital Angular Momentum 21

2.5 Conclusion 22

References 23

3 Helically Phased Beams, and Analogies with Polarization 25
Miles Padgett

3.1 Introduction 25

3.2 Representation of Helically Phased Beams 26

3.3 Exploiting the Analogous Representations of Spin and Orbital Angular Momentum 27

3.3.1 Rotational Doppler Shifts and Geometrical Phase 27

3.3.2 Mode Sorting using Geometric Phase 29

3.3.3 Entanglement of Spatial Modes 30

3.3.4 Photon Drag and the Mechanical Faraday Effect 32

3.4 Conclusions 33

References 34

4 Trapping and Rotation of Particles in Light Fields with Embedded Optical Vortices 37
Michael Mazilu and Kishan Dholakia

4.1 Introduction 37

4.2 Laguerre–Gaussian Light Beams 38

4.3 Origin of Optical Torques and Forces 41

4.3.1 Intuitive Picture of Optical Forces 41

4.3.2 Angular Momentum within Geometric Optics 43

4.3.3 Paraxial Beams 44

4.3.4 Maxwell’s Stress Tensor 45

4.3.5 Linear Momentum Transfer 49

4.3.6 Angular Momentum Transfer 50

4.3.7 Polarization Spin Momentum 50

4.4 Optical Vortex Fields for the Rotation of Trapped Particles 51

4.4.1 Studies of Rotation of Trapped Objects using Optical Vortex Fields 51

4.5 Optical Vortex Fields for Advanced Optical Manipulation 57

4.6 Conclusions 61

Acknowledgments 62

References 62

5 Optical Torques in Liquid Crystals 67
Enrico Santamato and Bruno Piccirillo

5.1 The Optical Reorientation and the Photon Angular Momentum Flux 70

5.1.1 Dynamical Equations of Liquid Crystals 71

5.1.2 Angular Momentum Fluxes 73

5.2 Dynamical Effects Induced in Liquid Crystals by Photon SAM and OAM Transfer 78

5.2.1 Experiments on OAM Transfer in Liquid Crystals 81

5.2.1.1 Orbital Photon Angular Momentum Transfer with Unpolarized Light 83

5.2.1.2 Investigation of the Combined Effect of the Spin and Orbital Photon Angular Momentum Transfer with Linearly Polarized Light 83

5.2.1.3 Investigation of the Combined Effect of the Spin and Orbital Photon Angular Momentum Transfer with Circularly Polarized Light 85

5.3 Conclusions 89

References 90

6 Driving Optical Micromachines with Orbital Angular Momentum 93
Vincent L.Y. Loke, Theodor Asavei, Simon Parkin, Norman R. Heckenberg, Halina Rubinsztein-Dunlop, and Timo A. Nieminen

6.1 Introduction 93

6.2 Symmetry, Scattering, and Optically Driven Micromachines 93

6.3 Experimental Demonstration 96

6.3.1 A Preliminary Design 96

6.3.2 Fabrication 97

6.3.3 Optical Trapping and Rotation 97

6.3.4 Optical Measurement of Torque 98

6.3.5 Discussion 100

6.4 Computational Optimization of Design 102

6.4.1 Computational Modeling of Microrotors 102

6.4.2 Performance of a Four-Armed Rotor 105

6.4.3 Discussion 111

6.5 Conclusion 113

References 113

7 Rotational Optical Micromanipulation with Specific Shapes Built by Photopolymerization 117
Péter Galaja, Lóránd Kelemen, László Oroszi, and Pál Ormos

7.1 Introduction 117

7.2 Microfabrication by Photopolymerization 118

7.2.1 Fabrication by Scanning a Single Focused Laser Beam 118

7.2.2 Parallel Photopolymerization using Diffractive Optics 120

7.3 Light-Driven Rotors, Micromachines 121

7.3.1 Propeller 121

7.3.2 Propeller with Reversed Direction of Rotation 124

7.3.3 Complex Micromachines 126

7.4 Integrated Optical Motor 128

7.5 Angular Trapping of Flat Objects in Optical Tweezers Formed by Linearly Polarized Light 131

7.6 Torsional Manipulation of DNA 134

7.6.1 Direct Measurement of Torque 135

7.7 Conclusion 138

Acknowledgment 139

References 139

8 Spiral Phase Contrast Microscopy 143
Christian Maurer, Stefan Bernet, and Monika Ritsch-Marte

8.1 Phase Contrast Methods in Light Microscopy 143

8.2 Fourier Filtering in Optical Imaging 144

8.3 Spiral Phase Fourier Filtering 146

8.3.1 Isotropic Edge Enhancement 148

8.3.2 Pseudorelief Images 149

8.3.3 Spiral Fringe Metrology with SPC 150

8.4 Implementation and Performance 151

8.5 Conclusions 152

References 152

9 Applications of Electromagnetic OAM in Astrophysics and Space Physics Studies 155
Bo Thidé, Nicholas M. Elias II, Fabrizio Tamburini, Siavoush M. Mohammadi, and José T.Mendon¸ca

9.1 Introduction 155

9.2 Ubiquitous Astronomical POAM 156

9.3 Applications of POAM in Astronomy 158

9.3.1 Sub-Rayleigh Resolution 159

9.3.2 Optical Vortices with Starlight 162

9.4 Applications of POAM in Space Physics 165

9.A. Appendix: Theoretical Foundations 169

9.A.1 Classical Field Picture 169

9.A.2 Photon Picture 170

References 175

10 Optical Vortex Cat States and their Utility for Creating Macroscopic Superpositions of Persistent Flows 179
Ewan M. Wright

10.1 Introduction 179

10.2 Optical Vortex Cat States 181

10.2.1 Linear Fiber Propagation 181

10.2.2 Quantum Fiber Propagation 182

10.2.3 Optical Vortex Cat State via Self-Phase Modulation 184

10.2.4 Photonic-Crystal Fibers 186

10.2.5 Other Schemes 188

10.3 Macroscopic Superposition of Persistent Flows 189

10.3.1 Optical Light-Shift Potential 189

10.3.2 Ring Trap and Quantum Stirring 190

10.3.3 Matter Waves on a Ring 191

10.3.4 Macroscopic Superposition of Persistent Flows 192

10.3.5 Discussion 194

10.4 Summary and Conclusions 195

References 195

11 Experimental Control of the Orbital Angular Momentum of Single and Entangled Photons 199
Gabriel Molina-Terriza and Anton Zeilinger

11.1 Introduction to the Photon OAM 199

11.2 Control of the OAM State of a Single Photon 201

11.3 Control of the OAM State of Multiple Photons 203

11.4 Applications in Quantum Information 207

11.5 Discussion 209

11.6 Conclusion 211

References 211

12 Rotating Atoms with Light 213
Kristian Helmerson and William D. Phillips

12.1 Introduction 213

12.2 Orbital Angular Momentum of Light 213

12.3 The Mechanical Effects of Light 214

12.4 Rotating Bose–Einstein Condensates 215

12.4.1 Experiment to Transfer Orbital Angular Momentum to a BEC (_ = 0) 216

12.4.2 Efficiency of the OAM Transfer Process 218

12.5 Measuring the Rotational Motion of the Atoms 220

12.5.1 Interference of the Rotating State with a Nonrotating State 220

12.5.2 Interference of the Rotating State with a Counterrotating State 222

12.5.3 Observation of Fork-Like Interference Structure 223

12.5.4 Measurement of the Doppler Shift of the Rotating Atoms 223

12.6 Generating Other Rotational States of Atoms 224

12.6.1 Vortices of Higher Charge 224

12.6.2 Rotational States of Multilevel Atomic Condensates 227

12.6.3 Matter wave Amplification of a Vortex State 228

12.7 Supercurrents 230

12.7.1 Generation of a Supercurrent in a BEC 230

12.8 Conclusion 231

Acknowledgments 232

References 232

Index 237

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Juan P. Torres is one of the group leaders of ICFO-The Institute of Photonic Sciences in Barcelona, Spain, where he conducts research in nonlinear and quantum optics. He also holds a position as associate professor at the Technical University of Catalonia where he teaches in photonics and electrical engineering. Professor Torres obtained his PhD in Science from the Technical University of Catalonia and afterwards held a post-doctoral position at the University of California at Berkeley. He has authored about 100 articles and received an award for young investigators from the Government of Catalonia in 2002.

Lluis Torner is the founding Director of ICFO-The Institute of Photonic Sciences in Barcelona, Spain, and professor of photonics at the Technical University of Catalonia. He conducts research and innovation in photonics, with emphasis on fundamentals and applications of nonlinear optics, optical vortices and optical solitons. He has co-authored more than 300 articles in scienti¿ c journals. He is a Fellow of the Optical Society of America, the European Optical Society and the European Physical Society, and he currently serves as President of the Association of Research Institutions of Catalonia.
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"Overall, this volume provides a convenient entry into a field which has achieved much but which also
has considerable scope for further growth. If one wishes to play a role in the future of orbital angular
momentum then this is an excellent place to start." (Contemporary Physics Book Reviews, 25 August 2011)

 

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