Realization of complex amplitude optical diffractive elements with optimized liquid crystal modulators

In this paper we present a revision of our research work dealing with the generation of complex transmittance optical diffractive elements by means of liquid crystal spatial light modulators (LC-SLM). In general these modulators provide a coupled amplitude and phase modulation, and not an arbitrary complex modulation. For this reason we employ an encoding technique to display complex values, based on the phase modulation. The first step is to optimize the response of the display to provide a pure phase-only modulation. This optimization is done by means of the adequate selection of the polarization ellipse used to illuminate the display, and the polarization state of light at the output. Once the pure phase-only modulation is obtained, we use a complex encoding technique based on producing a spatially variant distribution of the maximum phase depth on a certain phase carrier. The paper includes a theoretical revision of these procedures and experimental results that demostrate the possibility of displaying complex difractive elements with this kind of displays, such as correlation filters, apodizers and Fresnel lenses.