Author Affiliations ............................................ xi
Preface ...................................................... xiii
1. Introduction to Phase-Structured Electromagnetic Waves ....... 1
Les Allen and Miles Padgett
1.1. Introduction ............................................ 1
1.2. Laguerre-Gaussian Beams and Orbital Angular Momentum .... 2
1.3. Bessel and Mathieu Beams ................................ 7
1.4. General Solution of the Wave Equation ................... 8
1.5. Classical or Quantum? ................................... 8
1.6. Creating Laguerre-Gaussian Beams with Lenses and
Holograms ............................................... 9
1.7. Coherence: Spatial and Temporal ........................ 11
1.8. Transformations Between Basis Sets ..................... 12
1.9. Conclusion ............................................. 14
References .................................................. 15
2. Angular Momentum and Vortices in Optics ..................... 19
Gerard Nienhuis
2.1. Introduction ........................................... 19
2.2. Classical Angular Momentum of Fields and Particles ..... 22
2.2.1. Angular Momentum of Particles and Radiation ..... 22
2.2.2. Rate of Change of Contributions to Angular
Momentum ........................................ 24
2.3. Separation of Radiative Angular Momentum in L and S .... 24
2.3.1. Classical Description ........................... 24
2.3.2. Quantum Operators ............................... 25
2.4. Multipole Fields and Their Vortex Structure ............ 27
2.4.1. Spherical Multipole Fields ...................... 27
2.4.2. Cylindrical Multipole Fields .................... 30
2.5. Angular Momentum of Monochromatic Paraxial Beams ....... 33
2.5.1. Paraxial Approximation .......................... 33
2.5.2. Angular Momentum of a Monochromatic Beam ........ 34
2.5.3. Uniform Orbital and Spin Angular Momentum ....... 36
2.5.4. Nonuniform Polarization ......................... 38
2.6. Quantum Description of Paraxial Beams .................. 40
2.6.1. Quantum Operators for Paraxial Fields ........... 40
2.6.2. Quantum Operators for Spin and Orbital
Angular Momentum ................................ 41
2.7. Nonmonochromatic Paraxial Beam ......................... 42
2.7.1. Angular Momentum of Nonmonochromatic Beam ....... 42
2.7.2. Spin of Rotating Polarization ................... 43
2.7.3. Orbital Angular Momentum of Rotating Mode
Pattern ......................................... 44
2.7.4. Angular Momentum of Rotating Nonuniform
Polarization .................................... 46
2.8. Operator Description of Classical Paraxial Beams ....... 48
2.8.1. Dirac Notation of Paraxial Beams ................ 48
2.8.2. Paraxial Beams and Quantum Harmonic
Oscillators ..................................... 49
2.8.3. Raising and Lowering Operators for Modes ........ 51
2.8.4. Orbital Angular Momentum and the Hermite-
Laguerre Sphere ................................. 53
2.9. Dynamics of Optical Vortices ........................... 55
2.9.1. Invariant Mode Patterns ......................... 55
2.9.2. Rotating Patterns of Vortices with Same
Orientation ..................................... 57
2.9.3. Vortex Creation and Annihilation ................ 57
2.10.Conclusion ............................................. 59
References .................................................. 60
3. Singular Optics and Phase Properties ........................ 63
Enrique J. Galvez
3.1. Fundamental Phase Singularities ........................ 64
3.2. Beams with Composite Vortices .......................... 69
3.3. Noninteger Vortex Beams ................................ 72
3.4. Propagation Dynamics ................................... 74
3.5. Conclusions ............................................ 74
Acknowledgments ............................................. 75
References .................................................. 75
4. Nanoscale Optics: Interparticle Forces ...................... 79
Luciana C. Davila Romero and David L. Andrews
4.1. Introduction ........................................... 79
4.2. QED Description of Optically Induced Pair Forces ....... 82
4.2.1. Quantum Foundations ............................. 82
4.2.2. Defining the Geometry ........................... 85
4.2.3. Tumbling Cylindrical Pair ....................... 87
4.2.4. Collinear Pair .................................. 90
4.2.5. Cylindrical Parallel Pair ....................... 92
4.2.6. Spherical Particles ............................. 94
4.2.7. Spherical Particles in a Laguerre-Gaussian
Beam ............................................ 96
4.3. Overview of Applications ............................... 98
4.4. Discussion ............................................ 101
Acknowledgments ............................................ 102
References ................................................. 102
5. Near-Field Optical Micromanipulation ....................... 107
Kishan Dholakia and Peter J. Reece
5.1. Introduction .......................................... 107
5.1.1. What Is the Near Field? ........................ 108
5.1.2. Optical Geometries for the Near Field and
Initial Guiding Studies ........................ 109
5.2. Theoretical Considerations for Near-Field Trapping .... 111
5.3. Experimental Guiding and Trapping of Particles in
the Near Field ........................................ 114
5.3.1. Near-Field Surface Guiding and Trapping ........ 114
5.3.2. Trapping Using TIR Objectives .................. 122
5.3.3. Micromanipulation Using Optical Waveguides ..... 126
5.4. Emergent Themes in the Near Field ..................... 129
5.4.1. Optical Force Induced Self-Organization of
Particles in the Near Field .................... 129
5.4.2. Near-Field Trapping with Advanced Photonic
Architectures .................................. 132
5.5. Conclusions ........................................... 134
Acknowledgments ............................................ 134
References ................................................. 134
6. Holographic Optical Tweezers ............................... 139
Gabriel C. Spalding, Johannes Courtial, and
Roberto Di Leonardo
6.1. Background ............................................ 139
6.2. Example Rationale for Constructing Extended Arrays
of Traps .............................................. 140
6.3. Experimental Details .................................. 142
6.3.1. The Standard Optical Train ..................... 142
6.4. Algorithms for Holographic Optical Traps .............. 149
6.4.1. Random Mask Encoding ........................... 151
6.4.2. Superposition Algorithms ....................... 152
6.4.3. Gerchberg-S ax ton Algorithms .................. 153
6.4.4. Direct-Search Algorithm and Simulated
Annealing ...................................... 156
6.4.5. Summary ........................................ 156
6.4.6. Alternative Means of Creating Extended
Optical Potential Energy Landscapes ............ 157
6.5. The Future of Holographic Optical Tweezers ............ 162
Acknowledgments ............................................ 162
References ................................................. 162
7. Atomic and Molecular Manipulation Using Structured Light ... 169
Mohamed Babiker and David L. Andrews
7.1. Introduction .......................................... 169
7.2. A Brief Overview ...................................... 170
7.3. Transfer of OAM to Atoms and Molecules ................ 171
7.4. Doppler Forces and Torques ............................ 172
7.4.1. Essential Formalism ............................ 173
7.4.2. Transient Dynamics ............................. 175
7.4.3. Steady State Dynamics .......................... 178
7.4.4. Dipole Potential ............................... 179
7.5. The Doppler Shift ..................................... 180
7.5.1. Trajectories ................................... 181
7.5.2. Multiple Beams ................................. 181
7.5.3. Two- and Three-Dimensional Molasses ............ 184
7.6. Rotational Effects on Liquid Crystals ................. 185
7.7. Comments and Conclusions .............................. 187
Acknowledgments ............................................ 191
References ................................................. 191
8. Optical Vortex Trapping and the Dynamics of Particle
Rotation ................................................... 195
Timo A. Nieminen, Simon Parkin, Theodor Asavei,
Vincent L. Y. Loke, Norman R. Heckenberg, and
Halina Rubinsztein-Dunlop
8.1. Introduction .......................................... 195
8.2. Computational Electromagnetic Modeling of Optical
Trapping .............................................. 196
8.3. Electromagnetic Angular Momentum ...................... 199
8.4. Electromagnetic Angular Momentum of Paraxial and
Nonparaxial Optical Vortices .......................... 202
8.5. Nonparaxial Optical Vortices .......................... 205
8.6. Trapping in Vortex Beams .............................. 211
8.7. Symmetry and Optical Torque ........................... 218
8.8. Zero Angular Momentum Optical Vortices ................ 226
8.9. Gaussian "Longitudinal" Optical Vortex ................ 228
8.10.Conclusion ............................................ 231
References ................................................. 231
9. Rotation of Particles in Optical Tweezers .................. 237
Miles Padgett and Jonathan Leach
9.1. Introduction .......................................... 237
9.2. Using Intensity Shaped Beams to Orient and Rotate
Trapped Objects ....................................... 238
9.3. Angular Momentum Transfer to Particles Held in
Optical Tweezers ...................................... 240
9.4. Out of Plane Rotation in Optical Tweezers ............. 242
9.5. Rotation of Helically Shaped Particles in Optical
Tweezers .............................................. 243
9.6. Applications of Rotational Control in Optical
Tweezers .............................................. 244
References ................................................. 247
10.Rheological and Viscometric Methods ........................ 249
Simon J. W. Parkin, Gregor Knöner, Timo
A. Nieminen, Norman R. Heckenberg, and
Halina Rubinsztein-Dunlop
10.1.Introduction .......................................... 249
10.2.Optical Torque Measurement ............................ 251
10.2.1.Measuring Spin Angular Momentum ................ 251
10.2.2.Measuring Orbital Angular Momentum ............. 253
10.3.A Rotating Optical Tweezers Based Microviscometer ..... 254
10.3.1.Experimental Setup for a Spin Based
Microviscometer ................................ 255
10.3.2.Results and Analysis ........................... 256
10.3.3.Orbital Angular Momentum Used for Microviscometry ... 261
10.4.Applications .......................................... 264
10.4.1.Picolitre Viscometry ........................... 264
10.4.2.Medical Samples ................................ 265
10.4.3.Flow Field Measurements ........................ 266
10.5.Conclusion ............................................ 268
References ................................................. 268
11.Orbital Angular Momentum in Quantum Communication
and Information ............................................ 271
Sonja Franke-Arnold and John Jeffers
11.1.Sending and Receiving Quantum Information ............. 273
11.1.1.Generation of Entangled OAM States ............. 275
11.1.2.Detection of OAM States at the Single Photon
Level .......................................... 277
11.1.3.Intrinsic Security ............................. 279
11.2.Exploring the OAM State Space ......................... 280
11.2.1.Superpositions of OAM States ................... 280
11.2.2.Generating Entangled Superposition States ...... 283
11.2.3. Storing OAM Information ....................... 284
11.3.Quantum Protocols ..................................... 286
11.3.1.Advantages of Higher Dimensions ................ 286
11.3.2.Communication Schemes .......................... 287
11.4.Conclusions and Outlook ............................... 290
Acknowledgments ............................................ 291
References ................................................. 291
12.Optical Manipulation of Ultracold Atoms .................... 295
G.Juzeliunas and P.Öhberg
12.1.Background ............................................ 295
12.2.Optical Forces and Atom Traps ......................... 296
12.3.The Quantum Gas: Bose-Einstein Condensates ............ 299
12.3.1.Bose-Einstein Condensation in a Cloud of
Atoms .......................................... 300
12.3.2.The Condensate and Its Description ............. 301
12.3.3.Phase Imprinting the Quantum Gas ............... 303
12.4.Light-Induced Gauge Potentials for Cold Atoms ......... 308
12.4.1.Background ..................................... 308
12.4.2.General Formalism for the Adiabatic Motion
of Atoms in Light Fields ....................... 309
12.5.Light-Induced Gauge Potentials for the A Scheme ....... 311
12.5.1.General ........................................ 311
12.5.2.Adiabatic Condition ............................ 313
12.5.3.Effective Vector and Trapping Potentials ....... 314
12.5.4.Co-Propagating Beams with Orbital Angular
Momentum ....................................... 315
12.5.5.Counterpropagating Beams with Shifted
Transverse Profiles ............................ 317
12.6.Light-Induced Gauge Fields for a Tripod Scheme ........ 320
12.6.1.General ........................................ 320
12.6.2.The Case where S12 = 0 ......................... 322
12.7.Ultra-Relativistic Behavior of Cold Atoms in Light-
Induced Gauge Potentials .............................. 323
12.7.1.Introduction ................................... 323
12.7.2.Formulation .................................... 324
12.7.3.Quasi-Relativistic Behavior of Cold Atoms ...... 325
12.7.4.Proposed Experiment ............................ 327
12.8.Final Remarks ......................................... 329
References ................................................. 330
Index ......................................................... 335
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