For the generation of optical propagation modes using a phase-only spatial light modulators, it is essential that both phase and amplitude components of their complex fieldsare encoded. In this paper, we obtain the complete expression of the complex field generated at Fresnel and Fraunhoferdistances when applying a simple technique consisting of the use of checkerboard-type holograms to encode both phase and amplitude information. The obtained expression is verified with a developed simulator that calculates the complex field generated at any propagation distance, corroborating that the desired mode propagates in even diffraction orders, even in near field.
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