Phase control requirements of high intensity laser beam combining

Aiming at getting the general requirements of the beam combine for ignition scale laser facilities, the analytical expressions including the factors affecting the combine results are derived. The physical meanings of every part are illustrated. Based on these expressions, the effects of the factors, including the beam configuration, piston error, and tip/tilt error, are studied analytically and numerically. The results show that the beam configuration cannot affect the Strehl ratio (SR) of the combined beam, but it influences the FWHM of the main peak and the ratio of the main peak and the side peak. The beam separation should be no more than 1.24 times the individual beam width for the multibeam combine, and be close to the individual beam width for the two-beam combine as much as possible. The piston error can change the characteristics of the combine beam focus, including the peak intensity, the focal spot morphology, the fractional energy contained within a certain area, and the center of mass. For the two-beam combine, a piston error less than 2π/5 rad is suitable, and for the multibeam combine, the standard deviation of the piston error should be no more than 2π/10 rad. The tip/tilt error has a great influence on the combined results. It affects the superposition degree of the focal spots of the combined elements directly. A requirement of 0.5~1 μrad for the standard deviation of the tip/tilt error is adequate.