Tolerance on tilt error for coherent combining of fiber lasers

Limited by the precision of optical machining and assembling,the optical axes of lasers in an array cannot be strictly parallel to each other,which will result in the beam quality degradation of the combined beam. The tolerance on tilt error for coherent combining of fiber lasers is studied in detail.The complex amplitude distribution in the far field for the Gaussian beam with tilt angle is obtained by a novel coordinate transform method.Effect of tilt error on coherent combining is modelled analytically.Beam propagation factor is used to evaluate the effect of coherent combining.Numerical results show that for ring-distributed fiber laser array with central wavelength A and geometry size D,if the root-mean-square(RMS)value of the tilt error is smaller than 0.72λ/D,the energy encircled in the diffraction-limited bucket can be ensured to be more than 50% of the value when there is no tilt error.The results are helpful to the designing and manufacturing of fiber array for coherent combining.