  The unwanted zero-order diffraction is still an issue in beam shaping using
pixelated spatial light modulators. In this paper, we report a new approach for
zero-order free beam shaping by designing an asymmetric triangle reflector and
introducing a digital blazed grating and a digital lens to the phase hologram
addressed onto the spatial light modulator. By adding the digital lens phase to
the previously reported complex-amplitude coding algorithms, we realized the
generation of complex beams without the burden of zero-order diffraction. We
comparatively investigated the produced complex light fields using the modified
complex-amplitude coding algorithms to validate the proposed method.
