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.

Fractional Fourier transform of flat-topped multi-Gaussian beams.

The fractional Fourier transform (FRFT) of the flat-topped multi-Gaussian beam (FMGB) is investigated based on the three kinds of FRFT optical systems: Lohmann I, Lohmann II, and quadratic graded-index systems. The analytical expressions for the FRFT of the FMGB are derived based on the propagation of the FMGB through the three systems. By introducing a hard-edge aperture function, the analytical expressions for the FRFT of the FMGB carried out by the apertured FRFT optical systems are presented. The FRFT characteristics of the FMGB for the three kinds of FRFT optical systems with and without apertures are discussed in detail. Results show that the three types of FRFT optical systems have the same function when the apertures are ignored but that significantly different characteristics are exhibited when the apertures appear.

Propagation of flat-topped multi-Gaussian beams through an apertured ABCD optical system.

The generalized analytical expression for the propagation of flat-topped multi-Gaussian beams through a misaligned apertured ABCD optical system is derived. Using this analytical expression, the propagation characteristics of flat-topped multi-Gaussian beams through a spatial filter are investigated. The analytical formula of the electric field distribution in the focal plane is also derived for revealing the effects of the misalignment parameters clearly. It is found that different misalignment parameters have different influences on the electric field distributions of the beam focus spot and the output beam characteristics. The intensity distribution of the beam is mainly determined by the misalignment matrix element E, and the phase distribution is affected by the misalignment matrix elements G and E.

Characteristics of beam alignment in a high power four-pass laser amplifier.

Beam alignment is used to control the pointing, rotation, and position of a beam automatically. We give an overview of the beam alignment system for a four-pass amplifier system. The coupling relationships between dependent quantities and deviations thereof for parameters of key optical elements are analyzed using matrix optics techniques. The rotation characteristics of a near field are discussed. The characteristics of the four-pass adjustment in the cavity spatial filter are shown and the output characteristics are provided. Finally, we develop an adjustment procedure.