  Spatial qudits are D-dimensional ($D\geq 2$) quantum systems carrying
information encoded in the discretized transverse momentum and position of
single photons. We present a proof-of-principle demonstration of a method for
preparing arbitrary pure states of such systems by using a single phase-only
spatial light modulator (SLM). The method relies on the encoding of the complex
transmission function corresponding to a given spatial qudit state onto a
preset diffraction order of a phase-only grating function addressed at the SLM.
Fidelities of preparation above 94% were obtained with this method, which is
simpler, less costly, and more efficient than those that require two SLMs for
the same purpose.
