The unevenly distributed Lorentz-Gaussian beams are difficult to reproduce in practice, because they require modulation in both amplitude and phase terms. Here, a new linearly polarized Lorentz-Gauss beam modulated by a helical axicon (LGB-HA) is calculated, and the two various experimental generation methods of this beam, Fourier transform method (FTM) and complex-amplitude modulation (CAM) method, are depicted. Compared with the FTM, the CAM method can modulate the phase and amplitude simultaneously by only one reflection-type phase-only liquid crystal spatial light modulator. Both of the methods are coincident with the numerical results. Yet CAM is simpler, efficient, and has a higher degree of conformance through data comparison. In addition, considering some barriers exist in shaping and reappearing the complicated Lorentz-Gauss beam with heterogeneous distribution, the evolution regularities of the beams with different parameters (axial parameter, topological charge, and phase factor) were also implemented.
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