Dual polarization Fourier transform processor using geometric-phase lenses

Abstract

This work presents a novel optical system for polarization image processing using geometric-phase (Pancharatnam-Berry) lenses. Such lenses are half-wave plates where the orientation of the fast (slow) axis follows a quadratic relation with the radial coordinate, and they present the same focal length but opposite sign for left and right circular polarizations. Therefore, they split an input collimated beam in a converging beam and a diverging beam with opposite circular polarizations. This coaxial polarization selectivity introduces a new degree of freedom in optical processing systems and makes it interesting for imaging and filtering applications that require polarization sensitivity. Here we profit from these properties to build an optical Fourier filter system with polarization sensitivity. A telescopic system is used to have access to two real Fourier transform planes, one for each circular polarization. A second symmetric optical system is used to recombine the two beams onto a single final image. As a result, polarization sensitive optical Fourier filtering can be applied, as demonstrated with simple bandpass filters.

Polarization fourier filtering with a 4f system using geometric phase lenses

“…In Ref. [6] we explained in detail the optical system that we have used to perform 4-f using GPLs based on two telescope systems, that perform unit magnification. The first telescope system images the two foci pair given by GPL to obtain two real (nonvirtual) Fourier planes, one for each circular polarization (right and left), and the second telescopic system provides two images ( and ) with the same magnification of the FT planes at two output planes.…”

“…Another key point is to orient this second GP lens flipped with respect to the first one as we explained in Ref. [6]. The input object is placed before the first GPL.…”

“…In this manuscript we combine the sensitivity of GPL with polarization and the Fourier processors to perform polarization-sensitive optical Fourier processing [6]. The proposed optical system offers a unique and powerful approach to signal analysis and manipulation.…”

“…Polarization-sensitive Fourier processing enables the characterization and manipulation of both spatial and polarization properties of light simultaneously, providing a more comprehensive analysis of the signal's behavior. This capability is particularly valuable in applications such as polarization imaging, polarization-based pattern recognition, and polarization-encoded Fourier processing [6]. By leveraging the combined power of Fourier processing and polarization sensitivity, researchers and engineers can unlock new avenues for advanced signal processing, enabling improved detection, discrimination, and classification of optical signals in various scientific and technological domains.…”