Passive and Active Fiber Laser Array Beam Combining by Wei-Zung Chang A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Electrical Engineering) in The University of Michigan 2012 Doctoral Committee: Professor Almantas Galvanauskas, Chair Professor Karl M. Krushelnick Professor Duncan G. Steel Professor Herbert G. Winful DEDICATION To my family and friends ii ACKNOWLEDGEMENTS At this moment when I am writing this ACKNOWLEDGEMENTS section, all I feel is full of appreciation to those who give me so much support and love during my Ph.D. study in Ann Arbor. First, I would like to express appreciation to my advisor, Prof. Almantas Galvanauskas, for academic guidance in fiber laser field. Second, I would like to express gratitude to all the committee members: Prof. Karl Krushelnick, Prof. Duncan Steel, and Prof. Herbert Winful for contributing precious time to provide feedback regarding my research and thesis. Third, I would like to thank Prof. Ted Norris' classes: Classical Optics & Ultrafast Optics; Prof. Almantas Galvanauskas' classes: Optical Wave in Crystals & Photonic Crystals; Prof. Duncan Steel's classes: Quantum Mechanics I & II; and Prof. Herbert Winful's class: Nonlinear Optics for strengthening my background of optics. Fourth, I would like to acknowledge Dr. Tsai-Wei Wu's cooperation with passive beam combining project and Dr. Leo Siiman & Tong Zhou's company for pulse coherent combining and pulse synthesis projects. Fifth, I am indebted to Chao Zhang, Dr. Chi-Hung Liu, Cheng Zhu, I-Ning Hu, Dr. Matthew Rever, Dr. Shenghong Huang, Michael Haines, Alex Kaplan, Max Himmel, Dr. iii Kai-Chung Hou, Dr. Michael Swan, Dr. Xiuquan Ma, and Caglar Yavuz for all the help in the lab and effective discussion in research. Sixth, I am obliged to Wayne Gray, George Tsai, Marvin Eisenberg, Warren Manning, Mitsunobu Umeda, Richardo Yi, Kok-Heng Chong, Abhishek Aphale, Jefferson Timacdog, John Coleman, Irwin Salim, Dennis Deng, Drew Pilarski, Stephen Reynolds, and many others for their friendship. Finally, I am thankful for my family's unconditional love and endless support as well as Buddha's enlightenment that gives me the wisdom to pass through the most difficult time. Om Mani Padme Hum! iv TABLE OF CONTENTS DEDICATION................................................................................................................... ii ACKNOWLEDGEMENTS ............................................................................................ iii LIST OF FIGURES ........................................................................................................ vii LIST OF TABLES ........................................................................................................... xi CHAPTER 1 Introduction ............................................................................................... 1 CHAPTER 2 Model for Passive Coherent Beam Combining in Fiber Laser Arrays 7 2.1 Introduction .......................................................................................................... 7 2.2 Model and Benchmark ......................................................................................... 9 2.3 Simulation for Two-Channel Fiber Laser Arrays .............................................. 14 2.4 Simulation for Four-Channel Fiber Laser Arrays .............................................. 20 2.5 Discussion and Conclusion ................................................................................ 21 CHAPTER 3 Dynamical Bidirectional Model for Coherent Beam Combining in Passive Fiber Laser Arrays ............................................................................................ 23 3.1 Introduction ........................................................................................................ 23 3.2 Model ................................................................................................................. 24 3.3 Simulation Results.............................................................................................. 28 3.4 Nonlinearity ........................................................................................................ 32 3.5 Array Lasing Frequencies - The Minimum Loss ............................................... 35 3.6 Conclusion .......................................................................................................... 38 3.7 Appendix: Array Mode Spacing - The Greatest Common Divisor .................... 38 CHAPTER 4 Array Size Scalability of Passively Coherently Phased Fiber Laser Arrays............................................................................................................................... 43 4.1 Introduction ........................................................................................................ 43 v 4.2 Experimental Configuration ............................................................................... 44 4.3 Power Combining Efficiency ............................................................................. 46 4.4 Power Fluctuation .............................................................................................. 49 4.5 Beat Spectra ........................................................................................................ 51 4.6 Discussion and Conclusion ................................................................................ 54 4.7 Appendix ............................................................................................................ 55 CHAPTER 5 Coherent Femtosecond Pulse Combining from Four Parallel Chirped Pulse Fiber Amplifiers .................................................................................................... 56 5.1 Introduction ........................................................................................................ 56 5.2 Experiment ......................................................................................................... 59 5.2.1 Fiber Chirped Pulse Amplifier Array ......................................................... 59 5.2.2 Equalization of Parallel-Channel Optical Paths .......................................... 62 5.2.3 Channel Active-Phasing Control System .................................................... 64 5.3 Results ................................................................................................................ 66 5.3.1 Combined Pulse Temporal Quality ............................................................. 66 5.3.2 Combining Efficiency vs. Time .................................................................. 67 5.3.3 Combining Efficiency vs. Phase Modulation Amplitude ........................... 69 5.4 Discussion on Scalability ................................................................................... 71 5.5 Conclusion .......................................................................................................... 74 5.6 Appendix ............................................................................................................ 74 CHAPTER 6 Femtosecond Pulse Spectral Synthesis in Coherently Combined Multi- Channel Fiber Chirped Pulse Amplifiers ..................................................................... 77 6.1 Introduction ........................................................................................................ 77 6.2 Concept ............................................................................................................... 78 6.2.1 Phase Locking Strategies ............................................................................ 79 6.2.2 Combining Elements ................................................................................... 82 6.3 Experimental Setup ............................................................................................ 84 6.4 Experimental Results.......................................................................................... 87 6.5 Discussion .......................................................................................................... 90 CHAPTER 7 Summary and Future Work ................................................................... 92 7.1 Summary ............................................................................................................ 92 7.2 Future Work ....................................................................................................... 94 BIBLIOGRAPHY ........................................................................................................... 96 vi LIST OF FIGURES Figure 2.1 A two-channel fiber laser array structure. ........................................................ 7 Figure 2.2 A two-channel fiber laser array in the unidirectional configuration. ............. 10 Figure 2.3 Output powers of single Er-doped fiber laser in the time (left) and spectral (right) domains for (a)  = 0.003 m-1W-1 and (b)  = 0 m-1W-1. The power reflectivity is 4% as indicated in the figure. .................................................. 13 Figure 2.4 A unidirectional Er-doped fiber laser array with L = 24.3 and L = 24.0 m in 1 2 Fig. 2.2. The output powers from (a) upper port with partial reflectivity and (b) lower, angle-cleaved, port. The separation between spikes is measured to be 0.667 GHz. ................................................................................................ 15 Figure 2.5 Power spectrum of a two-channel fiber laser array with L = 24.08 m and L = 1 2 24.0 m. P in (a) refers to the output power from the port of 4% reflectivity, 1 and P (b) is from the angle-cleaved one. The spikes are separated by 2.5 2 GHz. The spectrum of the green-circled spike of (a) is further zoomed in for (c) linear and (d) nonlinear arrays. ................................................................ 16 Figure 2.6 Er-doped fiber laser arrays configured in Fig. 2.2 with L = 24.001 and L = 1 2 24.0 m. The computation window in frequency domain covers more than 1 THz. The left plots refer to the output powers from the port with partial reflectivity, while the right ones show the other, angle-cleaved, one. No frequency-dependent losses are applied for (a) and b equals 0.13 ps2m-1 in (b). .................................................................................................................. 18 Figure 2.7 Fig. 7. Beat spectra of amplified spontaneous emission for the higher reflectivity port (red curves) and the zero-reflectivity port (blue curves) an Er-doped fiber laser array with round-trip path length difference of 0.682 m. (a) Simulation result obtained by averaging the spectrum over 500 consecutive roundtrips (b) Experimental beat spectrum measurement from Ref [16], used with permission. (c) Simulation of spectrum above threshold. ....................................................................................................................... 19 vii Figure 2.8 Four-channel fiber laser array (a) spectrum of amplified spontaneous emissions with pattern periods measured to be 6.67 GHz. (b) Major output powers in the temporal (left) and spectral (right) domains. ........................... 21 Figure 3.1 A two-channel fiber laser array ...................................................................... 26 Figure 3.2 The spatial distributions of one of the fiber laser (L1 = 24.3 m) are plotted as an example for (a) both propagating waves and (b) the gain field along the z axis. The three curves consisting of red circles present the self-consistent steady-state solutions obtained from our model, while that of solid black lines are calculated from Matlab with its built-in BVP solver. As for array dynamics, the time evolution of the output power and the averaged gain variable (over z) of each fiber are displayed in (c) and (d). The output power refers to the combined power coming out of the partially-reflected, R1, port as seen in Fig. 3.1. ......................................................................................... 29 Figure 3.3 An Er-doped fiber laser array in Fig. 3.1 with L 24.3 and L 24.0 m. The 1 2 output powers from (a) upper port with partial reflectivity and (b) lower, angle-cleaved, port are plotted for time (left) and frequency (right) domains respectively. The separation between spikes in the frequency domain is 0.333 GHz. ............................................................................................................... 30 Figure 3.4 Evolution diagram of the output power spectrum for (a) the array modes, (b) the zoom-in longitudinal modes and (c) the relative phase difference Δϕ(π) between two incident (backward) waves at z = 0. All of them start from random and noisy spontaneous emissions. The free spectral range in (b) is 4.1MHz. ......................................................................................................... 32 Figure 3.5 A two-channel fiber laser array is simulated with  = 0.9 W-1m-1. The array outputs are plotted in (a) and (b) respectively for both temporal (left) and spectral (right) domains. The relative phase difference of the circled spectral packets (in (a)) is plotted in (c) for nonlinear and in (d) for linear fiber laser arrays. ............................................................................................................. 34 Figure 3.6 The logarithmic plot of the output power ratio in terms of relative phase Δϕ.35 Figure 3.7 A unidirectional two-channel fiber laser array. .............................................. 35 Figure 3.8 Power spectra of a two channel fiber laser array with fiber lengths 24.0005m and 24.0m for (a) b = 0 ps2m-1 and (b) b = 0.13 ps2m-1. ................................ 37 Figure 3.9 The frequency dependent losses (m-1), plotted in the log scale with blue lines, are overlapped with the lasing spectrum of the output fields (red spikes) for (a) zero and (b) nonzero b coefficients respectively. ..................................... 37 Figure 3.10 A four-channel fiber laser array. The figure is taken and modified from Ref. [58]. ................................................................................................................ 39 viii Figure 3.11 Coherent combining of a four-channel fiber laser array with lengths 24.0, 24.3, 23.733 and 24.633 m. The period of the power spectrum pattern indicated by the red arrow is measured to be 66.7 GHz. ............................... 42 Figure 4.1 Experimental setup as an example of 16-channel combining. ....................... 45 Figure 4.2 Configurations of 2- to 16-channel combining with a 2-laser array interval. 45 Figure 4.3 Combined-power efficiency and power fluctuation (error bars for experimental results) versus fiber array size. ................................................ 46 Figure 4.4 Combined-power efficiency versus fiber array size between previous (Shirakawa [60], Kouznetsov [65]) and present works. ................................ 49 Figure 4.5 Peak-to-peak power fluctuation ranges versus array size from experiments, simulation, and N3 fitting. .............................................................................. 51 Figure 4.6 Experimental setup for beat spectrum measurements as an example of 4- channel combining. ........................................................................................ 52 Figure 4.7 Beat spectra of 2-channel (a) and the zoom-in of designated packet (b); and those of 4-channel (c) and the zoom-in of designated packet (d). ................. 53 Figure 4.8 Simulation of beat spectra for 2-channel (a) with 47.82 and 46-m in-fiber lengths; and that of 4-channel (b) with 47.89, 46, 46.42, and 46.21-m in-fiber lengths. ........................................................................................................... 54 Figure 5.1 Experimental setup for four channel monolithic fiber pulse combining. ....... 59 Figure 5.2 Schematic and 3D rendering of the micro-optic delay line. ............................ 63 Figure 5.3 Power noise in the unlocked state for one, two, three, and four channels: (a) time domain, (b) frequency domain. The DET data indicates our detector noise floor. ..................................................................................................... 66 Figure 5.4 Pulse quality results: (a) normalized spectrum of individual channels and all four channels combined, (b) normalized autocorrelation traces of individual channels and all four channels combined – the dashed line shows the calculated (from the spectral measurement) bandwidth limited autocorrelation of the combined pulse. ................................................................................... 67 Figure 5.5 Combining efficiency and power noise: (a) combining efficiency for two, three, and four channel locking over a five minute time period, (b) four channel locked and unlocked noise. .............................................................. 69 Figure 5.6 Four channel combining efficiency with feedback blocks. The momentary decrease in efficiency due to blocking and subsequent overshoot of our detector occurs in less than one second. ........................................................ 69 ix