Liquid Crystal Devices for the Reconfigurable Generation of Optical Vortices

We present two liquid crystal devices specifically designed to dynamically generate optical vortices. Two different electrode geometrical shapes have been lithographically patterned into vertical-aligned liquid crystal cells. First, we demonstrate a pie-shape structure with 12 slices, which can be adjusted to produce spiral phase plates (SPP) that generate optical vortices. Moreover, the same device can be used to generate a pseudo-radially polarized beam, by simply adding two quarter-wave plates on each side. A second device has been fabricated with spiral shaped electrodes, which result from the combination of a SPP with the phase of a diffractive lens. This device acts as a spiral diffractive lens (SDL), thus avoiding the requirement of any additional physical external lens to provide focusing of the generated optical vortices. In both devices, the phase modulation can be adjusted by means of the voltage applied to the patterned electrodes, in order to change the properties of the generated optical vortex beams. Experimental demonstrations are provided for different wavelengths.

I. Introduction

Optical VORTICES (OV) have received much attention both for their physical insights as well as for their possible applications, for instance as elements for particle trapping [1], image processing [2], special phase contrast microscopy [3], and free-space communication [4]. The essential characteristic of a field vortex is the spiral phase profile, , where is the topological charge and denotes the azimuth angle. The most suitable way to generate an OV is by passing a fundamental mode laser beam through an external spiral phase element, such as a computer generated hologram (CGH) [5], or spiral phase plates (SPP) [6]–[8], these showing improved efficiency. The ideal SPP has a continuous surface thickness topology that imposes the desired azimuthal phase. However, due to the fabrication limitations, SPPs usually take multilevel quantized phase values. These kinds of multilevel SPP have been fabricated using various methods, e.g., multi-stage vapor deposition process [2] or direct electron-beam writing [9]. They provide in general high efficiency, but they do not allow changing the operating wavelengths and/or topological charges. Alternatively, SPPs can be programmed onto a liquid crystal (LC) spatial light modulator (SLM) [10], [11]. SPPs displayed in such devices can be reprogrammed, but they suffer from a limited light efficiency due to the SLM pixelated structure. Each pixel consists of an active region with width that transmits (or reflects) light, surrounded by opaque areas (dead zones) that contain control electronics and wires. There are two consequences of this structure. First, the fraction of the incident intensity that is transmitted (or reflected) is given by the fill factor , where denotes pixel spacing. Second, the main central diffraction order has an intensity fraction proportional to the square of the fill factor or , while the rest of the intensity is spread onto other higher diffraction orders [12].