Encoding complex amplitude information onto phase-only diffractive optical elements using binary phase Nyquist gratings

We reexamine a simple technique for encoding complex amplitude information onto a phase-only spatial light modulator (SLM). The basis for the approach is to spatially vary the diffraction efficiency of a two-dimensional checkerboard binary phase diffraction grating where the period for the Nyquist grating is two pixels. As the phase depth of this 2D grating changes spatially, the amount of light diffracted into the zero order can be controlled. Unwanted information is encoded onto the first diffraction orders and is directed away from the center. This process uses a very simple coding algorithm to generate a complex beam reconstruction on-axis and allows exploiting the full spatial resolution for encoding amplitude. However, its experimental realization with the current liquid-crystal on silicon (LCOS) technology is strongly affected by the limitations imposed by the fringing effect in these devices. We provide experimental evidence of how this effect impacts the efficiency of diffraction gratings displayed on the SLM. We then show how it affects the encoding technique, both in the near field and in the Fourier transform domain, where the limitations imposed by the fringing effect are clearly visible in the form of a focused peak. These results provide evidence of the usefulness of the technique but also about the limitations imposed by the current LCOS technology, which do not allow fully exploiting their high resolution. Finally, we discuss the performance of these newer LCOS devices compared to other SLMs.