First-order optical systems in information processing and optronic devices

Résumé

This work involves a theoretical, numerical as well as an experimental study. On the basis of a matrix formalism, we developed a flexible optical system design corresponding to ortho-symplectic transformations; rotator, separable fractional Fourier transform (FRFT), and gyrator operation (GT). These fractional transformations pay a relevant role in optical information processing. Such types of setups are demanded in different applications such as beam characterization, mode conversion, phase-space tomography, etc. This optical system design comprises generalized lenses (assembled set of thin cylindrical lenses) and fixed free-space intervals, where one or two-parametric transformation is reached only by means of lens rotations, or by means of lens power variation. In contrast to previous optical systems, this optical system generates (as a function of the transformation parameter) an output signal without additional scaling, rotation and phase modulation factors. We also demonstrate for first time the main properties and applications of the GT operation, which is little-known by the optical community. In particular, we study the application of the GT operation as an image processing tool (noise reduction, encryption, etc.) as well as an optical mode converter. The experimental implementation of the GT operation is demonstrated for the transformation of Hermite-Gaussian modes into Laguerre-Gaussian ones. Moreover, we also propose and analyze several optronic systems for complex field generation at quasi-real time as well as a Fourier micro-spectrometer based on SOI waveguide array. The numerical and experimental results are in excellent agreement with the theoretical predictions attesting the feasibility of these optical systems.