Beam combination of a radial laser array: Flat-topped beam

An analytical expression of a radial laser array for flat-topped beam is derived based on the generalized Collins formula. The intensity distribution of the resulting beam focused by a lens at the focus plane, for phase-locked and nonphase-locked cases, is studied numerically. The effect of the Fresnel number and normalized radius on intensity distribution for phase-locked and nonphase-locked cases is also presented. It is found that intensity distribution for nonphase-locked case is much less sensible to the Fresnel number and normalized radius than that of phase-locked case.