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17 February 2020 Analytical modeling of blazed gratings on two-dimensional pixelated liquid crystal on silicon devices
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Phase spatial light modulators and, in particular, parallel-aligned liquid crystal on silicon (PA-LCoS) microdisplays are widely used to display programmable diffractive optical elements (DOEs). These are pixelated elements with inherent different characteristics when compared with DOEs produced with micro-optics fabrication techniques. Specifically, programmable DOEs may be affected by the fill factor, time-flicker, fringing-field and interpixel cross talk effects, and limited and quantized modulation depth of the LCoS device. Among the multilevel DOEs, we focus on the important case of the blazed gratings. We develop the corresponding analytical expressions for the diffracted field where, as novelties of this work, fill factor and flicker are introduced together with phase depth and the number of quantization levels. Different experimental-based normalizations are considered, which may lead to wrong conclusions if the fill factor is not considered in the expressions. We also analyze the differences arising between one- and two-dimensional pixelated devices. When compared with numerical procedures, our approach provides an analytical expression that facilitates the design, prediction, and discussion of experiments. As an application, we prove, for the limiting case of no interpixel cross talk, that multiorder DOEs cannot be more efficient than the equivalent single-order DOE. We also show how the results for DOEs with a unit fill factor can be adapted to DOEs with a fill factor smaller than one with a very efficient procedure.

© 2020 Society of Photo-Optical Instrumentation Engineers (SPIE) 0091-3286/2020/$28.00 © 2020 SPIE
Andrés Márquez, Francisco J. Martínez-Guardiola, Jorge Francés, Cristian Neipp, Manuel G. Ramírez, Eva M. Calzado, Marta Morales-Vidal, Sergi Gallego, Augusto Beléndez, and Inmaculada Pascual "Analytical modeling of blazed gratings on two-dimensional pixelated liquid crystal on silicon devices," Optical Engineering 59(4), 041208 (17 February 2020).
Received: 11 October 2019; Accepted: 4 February 2020; Published: 17 February 2020

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