Coherent Laser Beam Combining

Coherent Laser Beam Combining......Page 1
Contents......Page 7
Preface......Page 17
Acronyms......Page 19
List of Contributors......Page 23
Part One: Coherent Combining with Active Phase Control......Page 29
1.1 Introduction......Page 31
1.2 Coherent Beam Combining System Requirements......Page 33
1.3 Active Phase-Locking Controls......Page 36
1.3.1 Optical Heterodyne Detection......Page 39
1.3.2 Synchronous Multidither......Page 41
1.4 Geometric Beam Combining......Page 42
1.4.1 Tiled Aperture Combiners......Page 43
1.4.2 Filled Aperture Combiners Using Diffractive Optical Elements......Page 44
1.4.2.1 Overview of DOE Combiners......Page 45
1.4.2.2 DOE Design and Fabrication......Page 46
1.4.2.3 DOE Thermal and Spectral Sensitivity......Page 48
1.5 High-Power Coherent Beam Combining Demonstrations......Page 49
1.5.1 Coherent Beam Combining of Zigzag Slab Lasers......Page 50
1.5.2.1 Phase Locking of Nonlinear Fiber Amplifiers......Page 54
1.5.2.2 Path Length Matching with Broad Linewidths......Page 58
1.5.2.3 Diffractive CBC of High-Power Fibers......Page 59
1.5.2.4 CBC of Tm Fibers at 2 µm......Page 65
1.6 Conclusion......Page 67
References......Page 68
2.1 Introduction......Page 73
2.1.1 Beam Combination Architectures......Page 74
2.1.2 Active and Passive Coherent Beam Combining......Page 75
2.2 Locking of Optical Coherence by Single-Detector Electronic-Frequency Tagging......Page 76
2.2.1 LOCSET Theory......Page 77
2.2.2.1 Photocurrent Signal......Page 78
2.2.2.2 LOCSET Demodulation......Page 81
2.3.1 LOCSET Beam Combining and Phase Error Analysis......Page 83
2.3.2 In-Phase and Quadrature-Phase Error Analysis......Page 84
2.3.3 Two-Channel Beam Combining......Page 86
2.3.4 16-Channel Beam Combining......Page 88
2.3.5 32-Channel Beam Combining......Page 90
2.4 LOCSET High-Power Beam Combining......Page 91
2.4.1 Kilowatt-Scale Coherent Beam Combining of Silica Fiber Lasers......Page 92
2.4.2 Kilowatt-Scale Coherent Beam Combining of Photonic Crystal Fiber Amplifiers......Page 95
References......Page 99
3.1.1 Brief History of Coherent Beam Combining......Page 103
3.1.2 Coherent Beam Combining: State of the Art......Page 104
3.1.3 Key Technologies for Coherent Beam Combining......Page 105
3.2.1 Theory of Single-Frequency Dithering Technique......Page 106
3.2.2 Kilowatt Coherent Beam Combining of High-Power Fiber Amplifiers Using Single- Frequency Dithering Technique......Page 113
3.2.3 Coherent Polarization Beam Combining of Four High-Power Fiber Amplifiers Using Single-Frequency Dithering Technique......Page 116
3.2.4 Target-in-the-Loop Coherent Beam Combination of Fiber Lasers Based on Single- Frequency Dithering Technique......Page 119
3.3.1 Theory of Sine–Cosine Single-Frequency Dithering Technique......Page 122
3.3.2 Coherent Beam Combining of Nine Beams Using Sine–Cosine Single-Frequency Dithering Technique......Page 125
3.4 Summary......Page 127
References......Page 128
4.1 Introduction to Hill Climbing Control Algorithms for Active Phase Control......Page 131
4.1.1 Conventional SPGD-Based Control Algorithm for Active Phase Control......Page 132
4.1.2 Orthonormal Dither-Based Control Algorithm......Page 134
4.1.3 Multiple Detector-Based Control Algorithm......Page 142
4.2.1 Semiconductor Amplifier Active Coherent Combination......Page 145
4.2.1.1 Introduction to SCOWA Semiconductor Waveguide and Phase Control......Page 146
4.2.1.2 Tiled Array Beam Combination......Page 148
4.2.1.3 Single-Beam Active Coherent Combination Using Diffractive Optical Elements......Page 153
4.2.2.1 Introduction to Fiber Amplifier Active Beam Combination Architectures......Page 156
4.2.2.2 Tiled Array Beam Combination......Page 157
4.2.2.3 Single-Beam Active Coherent Combination Using Diffractive Optical Elements......Page 161
Disclaimer......Page 162
References......Page 163
5.1 Introduction......Page 165
5.2 The Tiled Arrangement......Page 166
5.2.1 Calculation of the Far-Field Intensity Pattern......Page 167
5.2.2.1 Impact of the Near Field Arrangement......Page 169
5.2.2.2 Impact of Collimation System Design and Errors......Page 171
5.2.2.3 Impact of Phase Error......Page 173
5.2.3 Beam Steering......Page 174
5.3 Key Elements for Active Coherent Beam Combining of a Large Number of Fibers......Page 175
5.3.1 Collimated Fiber Array......Page 176
5.3.2 Collective Phase Measurement Technique......Page 179
5.3.2.1 Principle of the Measurement......Page 180
5.3.2.3 Phase Retrieval Techniques......Page 181
5.3.3 Phase Modulators......Page 183
5.4 Beam Combining of 64 Fibers with Active Phase Control......Page 184
5.5 Beam Combining by Digital Holography......Page 186
5.5.1 Principle......Page 187
5.5.2 Experimental Demonstration......Page 189
5.6 Conclusion......Page 191
References......Page 192
6.1 Introduction......Page 195
6.2 Fiber Array Engineering......Page 196
6.3 Turbulence-Induced Phase Aberration Compensation with Fiber Array-Integrated Piston and Tip–Tilt Control......Page 201
6.4.1 Fiber Array Control System Engineering: Issues and Considerations......Page 203
6.4.2 SPGD-Based Coherent Beam Combining: Round-Trip Propagation Time Issue......Page 204
6.4.3 Coherent Beam Combining at an Unresolved Target over 7 km Distance......Page 206
6.5 Target Plane Phase Locking for Resolved Targets......Page 210
6.5.1 Speckle Metric Optimization-Based Phase Locking......Page 211
6.5.2 Speckle Metrics......Page 212
6.5.3 Experimental Evaluation of Speckle Metric-Based Phase Locking......Page 214
6.6 Conclusion......Page 216
References......Page 217
7.1 Introduction......Page 221
7.2.1 Introduction: Thermal and Electronic RIC Mechanisms......Page 222
7.2.3 Description of the Electronic RIC Mechanism......Page 223
7.2.4 Description of the Thermal RIC Mechanism......Page 228
7.2.5 Comparison of Electronic and Thermal Contributions to the Pump-Induced Phase Shift......Page 229
7.2.6 Phase Shifts in the Case of Periodic Pulse Pumping and in the Presence of Amplified Signal......Page 231
7.3.1 Previous Observations of the RIC Effect in Laser Fibers......Page 233
7.3.2 Methodology of Pump/Signal-Induced RIC Measurements......Page 234
7.3.3 Characterization of RIC in Different Fiber Samples......Page 235
7.3.4 Phase Shifts Induced by Signal Pulses......Page 238
7.3.5 Evaluation of the Polarizability Difference......Page 240
7.3.6 Comparison of the RIC Effects in Aluminum and Phosphate Silicate Fibers......Page 241
7.4.1 Coherent Combining of Fiber Lasers: Alternative Techniques......Page 243
7.4.2 Operation Algorithm and Simulated Results......Page 245
7.4.3 Environment Noise in Optical System to be Compensated......Page 250
7.4.4 Combining of Two Er-Doped Amplifiers through the RIC Control in Yb-Doped Fibers......Page 251
7.4.5 Extension Algorithm for Combining of N Amplifiers......Page 252
7.5 Conclusions and Recent Progress......Page 254
References......Page 255
8.1 Introduction......Page 259
8.2 Beam Combining Techniques......Page 262
8.2.1 Filled and Tiled Apertures......Page 263
8.2.2.1 Direct Phase Locking Techniques......Page 264
8.2.2.2 Indirect Phase Locking Techniques......Page 265
8.2.3.1 Indirect Phase Locking Techniques......Page 267
8.2.4 Case of Pulsed Laser......Page 268
8.3.1 Approximations and Validity Domain of the Calculation......Page 271
8.3.2 Pulse Propagation in the Resonant Medium......Page 272
8.3.3 Practical Calculation of the Output Pulse Based on the CW Regime......Page 273
8.3.4 Pulse Shape Distortion......Page 274
8.3.5 Influence of the Amplified Spontaneous Emission......Page 275
8.4.1 Physical Principle of the Stimulated Brillouin Scattering......Page 276
8.4.2 SBS Gain......Page 277
8.4.3 SBS Threshold Input Power......Page 278
8.4.5 Domain of SBS Predominance......Page 279
8.4.6 Physical Principle of the Stimulated Raman Scattering......Page 280
8.5.1 Phase Noise Measurement......Page 281
8.5.2 In-Pulse Phase Shift Measurement......Page 286
8.5.3 In-Pulse Phase Shift Calculation......Page 287
8.5.3.1 Kerr-Induced Phase Shift......Page 288
8.5.3.2 Gain-Induced Phase Shift......Page 290
8.6 Experimental Setup and Results of Coherent Beam Combining of Pulsed Amplifiers Using a Signal Leak between the Pulses......Page 294
8.7 Alternative Techniques for Pulse Energy Scaling......Page 297
8.8 Conclusion......Page 299
References......Page 300
9.1 Introduction......Page 305
9.2.1 Description and Propagation of Femtosecond Pulses......Page 306
9.2.2 Coherent Combining over a Large Bandwidth......Page 308
9.2.3 Influence of Spectral Phase Mismatch on the Combining Efficiency......Page 309
9.2.4 Space–Time Effects......Page 311
9.3.1.1 Experimental Implementations......Page 312
9.3.1.2 Measurement of Spectral Phase Mismatch......Page 315
9.3.2.1 Principle......Page 318
9.3.2.2 Experimental Demonstrations......Page 320
9.4.1 Temporal Multiplexing: Divided Pulse Amplification......Page 323
9.4.2 Passive Enhancement Cavities......Page 324
9.4.3 Coherent Combining with Disjoint Spectra: Ultrafast Pulse Synthesis......Page 326
9.5 Conclusion......Page 327
References......Page 328
Part Two: Passive and Self-Organized Phase Locking......Page 331
10.1 Introduction......Page 333
10.2 Coherent Beam Combining Requirements......Page 334
10.3 General Mathematical Framework of Passive Laser Resonators......Page 335
10.3.1 Coherent Beam Combining by a Simple Beam Splitter......Page 336
10.3.2 Effect of Wavelength Diversity......Page 339
10.4.1 Generalized Michelson Resonators......Page 342
10.4.2 Grating Resonators......Page 346
10.5 Parallel Coupled Cavities Based on Space-Invariant Optical Architectures......Page 349
10.5.1 Space-Invariant Parallel Coupled Resonators with Weakly Coupled Cavities......Page 351
10.5.2 Spatially Filtered Resonators and the Effect of Path Length Phase Errors......Page 353
10.5.3 Talbot Resonators......Page 357
10.6 Parallel Coupled Resonators Based on Space-Variant Optical Architectures: the Self- Fourier Cavity......Page 364
10.7 Conclusion......Page 368
References......Page 369
11.1 Introduction......Page 373
11.2.1 Different Configurations......Page 374
11.2.2 Principles......Page 375
11.3.1 Power Stability......Page 378
11.3.2 Cophasing Building Dynamics......Page 379
11.3.3 Frequency Tunability......Page 381
11.3.4 Effect of Laser Gain Mismatched on Combining Efficiency......Page 382
11.3.5 Pointing Agility......Page 383
11.3.6 Coherence Properties of Multiple Beams Phase Locked by Mutual Injection Process......Page 384
11.4.2 Main Influencing Parameters......Page 388
11.5.1 Q-Switched Regime......Page 390
11.5.2 Mode-Locked Regime......Page 393
11.6 Conclusion......Page 395
References......Page 396
12.1 Introduction......Page 399
12.2.1 Efficient Coherent Combining of Two Fiber Lasers......Page 400
12.2.2 Compact Coherent Combining of Four Fiber Lasers......Page 403
12.2.3 Efficient Coherent Combining of Four Fiber Lasers Operating at 2 µm......Page 404
12.3.1 Effects of Amplitude Dynamics......Page 405
12.3.2 Effects of Quantum Noise......Page 409
12.3.3 Effects of Many Longitudinal Modes......Page 412
12.3.4 Effects of Time-Delayed Coupling......Page 416
12.4.1 Simultaneous Spectral and Coherent Combining......Page 419
12.4.2 Phase Locking 25 Fiber Lasers......Page 421
References......Page 426
13.1 Introduction......Page 429
13.2 External Cavity Passive Coherent Beam Combining......Page 430
13.2.1 Laser Scheme......Page 431
13.2.2.1 The Michelson Cavity......Page 432
13.2.2.2 General Case: The N-Arm Cavity......Page 434
13.2.3.1 Influence of the Number of Arms N......Page 436
13.2.3.2 Influence of the Arm Length Difference ΔL......Page 437
13.3.1 Dammann Gratings......Page 438
13.3.2 Quantum Cascade Lasers......Page 441
13.3.3 The Five-Arm External Cavity......Page 442
13.4.1 Principle......Page 446
13.4.2 Grating Design and Realization......Page 447
13.4.3 Antireflection Coating Design......Page 450
13.5 Conclusion......Page 451
References......Page 452
14.1 Introduction......Page 455
14.2 Phase Conjugation......Page 457
14.2.1 Gain Holography......Page 459
14.2.2 Four-Wave Mixing within a Saturable Gain Media......Page 461
14.2.3 Self-Pumped Phase Conjugation......Page 462
14.2.3.1 Seeded Self-Pumped Phase-Conjugate Module......Page 463
14.2.3.2 Self-Starting Self-Adaptive Gain Grating Lasers......Page 465
14.3 PCSOCBC......Page 466
14.3.1 CW Experimental PCSOCBC......Page 467
14.3.2 Understanding Operation of PCSOCBC: Discussion......Page 470
14.3.3 Power Scaling Potential......Page 472
14.3.3.1 Scaling the Number of Modules......Page 473
14.3.3.2 Higher Power Modules......Page 476
14.3.3.3 Pulsed Operation......Page 477
14.4 Conclusions......Page 478
References......Page 479
15.1 Introduction......Page 483
15.2 Principles of SBS-PCM......Page 484
15.3 Reflectivity of an SBS-PCM......Page 485
15.4 Beam Combining Architectures......Page 489
15.5 Phase Controlling Theory......Page 490
15.6.1 Conventional Phase Fluctuation of SBS-PCM......Page 495
15.6.2 Phase Fluctuation without PZT Controlling......Page 496
15.6.3 Phase Fluctuation with PZT Controlling......Page 499
References......Page 503
Index......Page 507