Preface.Introduction.Chapter 1. Selected Topics in Electromagnetic Wave Propagation.1.1. Maxwell's Equations and the Fundamental Fields.1.2. Electromagnetic Wave Propagation in Sourceless Media.1.3. Power Transmission.1.4. Group Velocity.1.5. Reflection and Transmission of Waves at Plane Interfaces.1.6. Material Resonances and Their Effects on Wave Propagation.Problems.References.Chapter 2. Symmetric Dielectric Slab Waveguides.2.1. Ray Analysis of the Slab Waveguides.2.2. Field Analysis of the Slab Waveguides.2.3. Solutions of the Eigenvalue Equations.2.4. Power Transmission and Confinement.2.5. Leaky Waves.2.6. Radiation Modes.2.7. Wave Propagation in Curved Slab Waveguides.Problems.References.Chapter 3. Weakly-Guiding Fibers with Step Index Profiles.3.1. Rays and Fields in the Step Index Fiber.3.2. Field Analysis of the Weakly-Guiding Fiber.3.3. Eigenvalue Equation for LP Modes.3.4. LP Mode Characteristics.3.5. Single Mode Fiber Parameters.3.6. Derivation of the General Step Index Fiber Modes.Problems.References.Chapter 4. Loss Mechanisms in Silica Fiber.4.1. Basic Loss Effects in Transmission.4.2. Fabrication of Silica Fibers.4.3. Intrinsic Loss.4.4. Extrinsic Loss.4.5. Bending Loss.4.6. Source-to-Fiber Coupling.Problems.References.Chapter 5. Dispersion.5.1. Pulse Propagation in Media Possessing Quadratic Dispersion.5.2. Material Dispersion.5.3. Dispersion in Optical Fiber.5.4. Chromatic Dispersion Compensation.5.5. Polarization Dispersion.5.6. System Considerations and Dispersion Measurement.Problems.References.Chapter 6. Special Purpose Index Profiles.6.1. Multimode Graded Index Fiber.6.2. Special Index Profile Optimization.Problems.References.Chapter 7. Nonlinear Effects in Fibers I: Non-Resonant Processes.7.1. Nonlinear Optics Fundamentals.7.2. Nonlinear Phase Modulation on Pulses.7.3. The Nonlinear Schrodinger Equation.7.4. Additional Non-Resonant Processes.Problems.References.Chapter 8. Nonlinear Effects in Fibers II: Resonant Processes and Amplification.8.1. Raman Scattering.8.2. Stimulated Brillouin Scattering.8.3. Rare-Earth-Doped Fiber Amplifiers.Problems.References.Appendix A: Properties of Bessel Functions.Appendix B: Notation.Index.

Fundamentals of optical fibers

Commercial 0.5 kW Yb-doped fiber amplifiers have been characterized and found to be suitable for coherent beam combining. Eight such fiber amplifiers have been coherently combined in a tiled-aperture configuration with 78% combining efficiency and total output power of 4 kW. The power-in-the-bucket vertical beam quality of the combined output is 1.25 times diffraction limited at full power. The beam-combining performance is independent of output power.

Coherent combining of a 4 kW, eight-element fiber amplifier array.

A compact, low-noise, single-frequency fiber laser by using a newly developed Yb³⁺ heavily doped single-mode phosphate glass fiber has been demonstrated Over 400 mW stable continuous wave single transverse and longitudinal mode laser at 106 μm was achieved from a 08 cm long active fiber The measured slope efficiency and estimated quantum efficiency of laser emission are 727% and 93%, respectively The signal-to-noise ratio is higher than 72 dB, and the linewidth of the fiber laser is less than 7 kHz, while the measured relative intensity noise is less than -130 dB/Hz at frequencies of over 15 MHz

400 mW ultrashort cavity low-noise single-frequency Yb^3+-doped phosphate fiber laser

Taking the improved SRS threshold formula into consideration, the power scaling of tandem-pumped Yb-doped silica fiber lasers and amplifiers is analyzed by new models. The results show that the power scaling of tandem-pumped Yb-doped fiber lasers and amplifiers is primarily limited by optical damage, SRS and thermal lens, while the pump brightness induced limitation is almost removed. It is also found that tandem-pumped Yb-doped fiber lasers and amplifiers, based upon state-of-art fiber technology, have the potential to achieve a power limit of 70.7 kW with a core diameter of 63.4 μm, and in the case of a strict single-mode fiber, the power limit is about 13.3 kW with a core numerical aperture of 0.03.

Power scaling analysis of tandem-pumped Yb-doped fiber lasers and amplifiers.

Coherent polarization beam combining (CPBC) of fiber lasers has the potential to scale the output total power while simultaneously maintaining good beam quality. In this paper, we will present the very recent technical advance in a single-channel coherently combinable linearly polarized narrow-linewidth fiber amplifier and high-power CPBC system. The noise property of a recently developed near 2 kW fiber amplifier and its feasibility in a CPBC system, CPBC of four 500-W-level fiber amplifiers and two kilowatt fiber amplifiers are demonstrated for the first time, which is also the first result for a 2 kW CPBC system. We have also performed numerical analysis on the performance scaling of CPBC, and deduced handy design guidelines for CPBC of a 64-element high-power system.

High-power coherent beam polarization combination of fiber lasers: progress and prospect [Invited]

Coherent beam combination of a 1.08 kW fiber amplifier array has been demonstrated for the first time, to our knowledge. In the experiment, nine fiber amplifiers are tiled into a 3×3 array, and the output power of each amplifier is approximately 120 W. A single frequency dithering algorithm is used to compensate the phase noises between the elements, which runs on a signal processor based on field programmable gate array for phase control on the fiber amplifiers. When the phase control system goes into closed loop, the fringe contrast of the far-field intensity pattern is improved to more than 85%, and the residual phase error is less than λ/15.

Coherent beam combination of 1.08 kW fiber amplifier array using single frequency dithering technique.

We present a theoretical and experimental study of a target-in-the-loop (TIL) high-power adaptive phase-locked fiber laser array. The system configuration of the TIL adaptive phase-locked fiber laser array is introduced, and the fundamental theory for TIL based on the single-dithering technique is deduced for the first time. Two 10-W-level high-power fiber amplifiers are set up and adaptive phase locking of the two fiber amplifiers is accomplished successfully by implementing a single-dithering algorithm on a signal processor. The experimental results demonstrate that the optical phase noise for each beam channel can be effectively compensated by the TIL adaptive optics system under high-power applications and the fringe contrast on a remotely located extended target is advanced from 12% to 74% for the two 10-W-level fiber amplifiers.

Target-in-the-loop high-power adaptive phase-locked fiber laser array using single-frequency dithering technique

We present what we believe to be a new approach of multitone driven amplifier for power scaling and coherent beam combining. A novel multitone seed is generated by a sine wave phase-modulated single-frequency laser and used for stimulated Brillouin scattering suppression of the amplifier. The theory for coherent beam combining of multitone lasers is presented for the first time. We optimize the all-fiber master-oscillator power-amplifier system with high scalability and flexibility based on compact, high efficiency Yb-doped fiber amplifier chain. With this amplifier system, we demonstrated a 275-W high-power output when driven by the phase-modulated single-frequency laser, while the ultimate output power is only 120 W when driven by the single-frequency laser. Scaling this amplifier to a higher power can be expected by adding pumps as the output power is limited by the pumps.

A 275-W Multitone Driven All-Fiber Amplifier Seeded by a Phase-Modulated Single-Frequency Laser for Coherent Beam Combining

We demonstrate a high power all fiber single-frequency MOPA laser. The center wavelength of the single-frequency fiber laser seed is 1064 nm with a linewidth narrower than 20 kHz. A two-stage power amplification configuration is employed. A single-frequency fiber laser with an output power of 29.2 W is obtained, and the optical to optical efficiency is 78%.

29.2 W, 20 kHz linewidth all fiber single-frequency MOPA laser

Multi-tone radiation is a promising technique to suppress stimulated Brillouin scattering (SBS) effects and improve the ultimate output power of the fiber laser/amplifier. Coherent beam combining of fiber lasers/ amplifiers is another feasible way to increase the output laser power from single gain medium while simultaneously maintaining good beam quality. In this paper, we combine the multi-tone driven all-fiber amplifiers and active phase compensation to demonstrate high power phase locking for coherent beam combining. First, we present the theory of coherent beam combining of multi-tone lasers. Second, we optimize the all-fiber power amplifier oscillator power-amplifier (MOPA) system with high scalability and flexibility based on compact, high efficiency Yb-doped fiber amplifier chains. Then, two categories of multi-tone master oscillators are used to driven the amplifier chains. The first category is two coupled single-frequency lasers and the second is a frequency modulated single-frequency laser. The output powers are all boosted to 275W without any distinct SBS. Last, phase locking of the amplifier chains are implemented using stochastic parallel gradient descent (SPGD) algorithm. Scaling this configuration to a higher power involves increasing the power per chain and adding the number of amplifier channels.

Xiaolin Dong

Papers

Coherent beam combination of 1.08 kW fiber amplifier array using single frequency dithering technique.

Target-in-the-loop high-power adaptive phase-locked fiber laser array using single-frequency dithering technique

A 275-W Multitone Driven All-Fiber Amplifier Seeded by a Phase-Modulated Single-Frequency Laser for Coherent Beam Combining

29.2 W, 20 kHz linewidth all fiber single-frequency MOPA laser

Phase locking of a 275W high power all-fiber amplifier seeded by two categories of multi-tone lasers