There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

A chain of four Tm-doped fibers amplified a single-frequency, 2040 nm diode laser to 608 W with M2=1.05±0.03, limited by available pump power. Stimulated Brillouin scattering limits were investigated by splicing different lengths of passive fiber to the output of the final amplifier stage. Integrated rms phase noise above 1 kHz was less than λ/30, suggesting the possibility of further scaling via coherent beam combining. To our knowledge, this is the highest power obtained from any single-frequency, single-mode fiber laser.

Low-phase-noise, single-frequency, single-mode 608 W thulium fiber amplifier

We present theoretical and experimental research on coherent beam combining of fiber amplifiers using stochastic parallel gradient descent (SPGD) algorithm. The feasibility of coherent beam combining using SPGD algorithm is detailed analytically. Numerical simulation is accomplished to explore the scaling potential to higher number of laser beams. Experimental investigation on coherent beam combining of two and three W-level fiber amplifiers is demonstrated. Several application fields, i.e., atmosphere distortion compensating, beam steering, and beam shaping based on coherent beam combining using SPGD algorithm are proposed.

Coherent Beam Combining of Fiber Amplifiers Using Stochastic Parallel Gradient Descent Algorithm and Its Application

A three-stage Yb-fiber amplifier emitted 1.43 kW of single-mode power when seeded with a 25 GHz linewidth master oscillator (MO). The amplified output was polarization stabilized and phase locked using active heterodyne phase control. A low-power sample of the output beam was coherently combined to a second fiber amplifier with 90% visibility. The measured combining efficiency agreed with estimated decoherence effects from fiber nonlinearity, linewidth, and phase-locking accuracy. This is the highest-power fiber laser that has been coherently locked using any method that allows brightness scaling.

Active phase and polarization locking of a 1.4 kW fiber amplifier.

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.

A novel, highly accurate, all electronic technique for phase locking arrays of optical fibers is demonstrated. We report the first demonstration of the only electronic phase locking technique that doesn’t require a reference beam. The measured phase error is λ/20. Excellent phase locking has been demonstrated for fiber amplifier arrays.

First experimental demonstration of self-synchronous phase locking of an optical array

We report high power phase locked fiber amplifier array using the Self-Synchronous Locking of Optical Coherence by
Single-detector Electronic-frequency Tagging technique. We report the first experimental results for a five element
amplifier array with a total locked power of more than 725-W. We will report on experimental measurements of the
phase fluctuations versus time when the control loop is closed. The rms phase error was measured to be λ/60. Recent
results will be reported. To the best of the authors' knowledge this is the highest fiber laser power to be coherently
combined.

High-power phase locking of a fiber amplifier array

We demonstrate coherent beam combining using a two-dimensionally patterned diffractive optic combining element. Fifteen Yb-doped fiber amplifier beams arranged in a 3×5 array were combined into a single 600 W, M2=1.1 output beam with 68% combining efficiency. Combining losses under thermally stable conditions at 485 W were found to be dominated by spatial mode-mismatch between the free space input beams, in quantitative agreement with calculations using the measured amplitude and phase profiles of the input beams.

Two-dimensional diffractive coherent combining of 15 fiber amplifiers into a 600 W beam

Single-frequency coherent beam combination (CBC) of 16 fiber lasers with kW class output power is presented. In addition, kW scale CBC of three Photonic Crystal Fiber (PCF) amplifiers in a filled aperture configuration is reported.

Coherent beam combining of fiber amplifiers in a kW regime

We present an experimental study on active coherent combining of five Yb (Ytterbium)-doped fiber laser amplifiers that
employs multiplexed volume Bragg gratings (MVBGs), reporting a combining efficiency of 82% and near-diffraction
limited beam quality at a combined input power of 380 W, and 70% combining efficiency with equal beam quality at
670 W input power.

Chunte A. Lu

Papers

First experimental demonstration of self-synchronous phase locking of an optical array

High-power phase locking of a fiber amplifier array

Two-dimensional diffractive coherent combining of 15 fiber amplifiers into a 600 W beam

Coherent beam combining of fiber amplifiers in a kW regime

Active coherent superposition of five fiber amplifiers at 670W using multiplexed volume Bragg gratings