Theoretical analysis and quantitative measurements of fiber amplifier coherent combining on a remote surface through turbulence

Coherent beam combining of fiber amplifier arrays is an efficient way to overcome the physical limitations to fiber laser power scaling. Moreover, coherent combining techniques involving active phase control of the laser emitters offer the largest versatility, as they can also be used for complex purposes such as beam steering, wavefront shaping or atmospheric turbulence compensation. We reported last year the first experimental demonstration of coherent combining of fiber amplifiers on a remote scattering surface, after propagation through turbulent atmosphere, using the backscattered signal. These results were achieved with a frequency-tagging technique, and appropriate spatial filtering to lower sensitivity to backward turbulence, and compensate only for onward turbulent propagation. We present now experimental measurements of turbulence strength and resulting residual phase error. With turbulence compensation using the backscattered signal for phase control, this error is lambda/15 rms. We also present the theoretical analysis of this experiment, emphasizing how limiting the aperture and not the field of view of the phase difference measurement subsystem reduces sensitivity to backward turbulence, without decreasing the optical flux on the detector.