Aimed at the application of multilayer dielectric gratings (MDGs) in spectral beam combining (SBC) technologies, a theoretical model of trapezoidal MDGs has been proposed and a beam propagation model of a SBC system based on trapezoidal MDGs has further been built up. The phase modulation introduced by the MDG involves optical path difference on the top surface of the relief, that in the relief and that of the multilayer dielectric films, which is affected by the relief groove depth, the relief duty cycle, base angles of the trapezoidal relief, the beam incidence angle, and so on. Using the diffraction integral method and the principle of incoherent superposition, the intensity distribution of the combined beam of the SBC system based on the MDG has been numerically calculated and analyzed. On this basis, the beam quality of the combined beam has been calculated by using the intensity second-order moment method, and the effect of both parameters of the MDG and the incidence angle of the central beam on the characteristics of the combined beam has been discussed in detail. The results show that the beam quality of the combined beam after passing through SBC is significantly better than that of the laser array before passing through SBC. Reasonable selection of the parameters of the trapezoidal MDG and the incidence angle of the central beam has no effect on the beam quality of the combined beam but influences the power of the combined beam. However, the fabrication errors of the trapezoidal MDG have significant effect on both the beam quality and the power of the combined beam. (C) 2016 Optical Society of America
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