Katherine Badham

Analysis of a segmented q-plate tunable retarder for the generation of first-order vector beams.

In this work we study a prototype q-plate segmented tunable liquid crystal retarder device. It shows a large modulation range (5π rad for a wavelength of 633 nm and near 2π for 1550 nm) and a large clear aperture of one inch diameter. We analyze the operation of the q-plate in terms of Jones matrices and provide different matrix decompositions useful for its analysis, including the polarization transformations, the effect of the tunable phase shift, and the effect of quantization levels (the device is segmented in 12 angular sectors). We also show a very simple and robust optical system capable of generating all polarization states on the first-order Poincaré sphere. An optical polarization rotator and a linear retarder are used in a geometry that allows the generation of all states in the zero-order Poincaré sphere simply by tuning two retardance parameters. We then use this system with the q-plate device to directly map an input arbitrary state of polarization to a corresponding first-order vectorial beam. This optical system would be more practical for high speed and programmable generation of vector beams than other systems reported so far. Experimental results are presented.

Nondiffracting Bessel beams with polarization state that varies with propagation distance.

We generate nondiffracting Bessel beams whose polarization state varies with propagation distance. We use a reflective geometry where a single parallel-aligned spatial light modulator device is used to spatially modulate two orthogonal linear polarizations with two axicon phase profiles. Then, by adding an extra phase retardation radial profile between these linear states, we are able to modulate the state of polarization along the line focus of the axicon. We provide experimental results that demonstrate the polarization axial control with zero-order and higher order Bessel beams.

Generation of integer and fractional vector beams with q-plates encoded onto a spatial light modulator.

We generate programmable vector beams with arbitrary q-plates encoded using a spatial light modulator system. Consequently, we can analyze new and exotic q-plate designs without the difficulty of fabricating individual plates. We show experimental results for positive and negative integer and new fractional vector beam values.

Performance of a q-plate tunable retarder in reflection for the switchable generation of both first- and second-order vector beams

We examine the performance of a tunable liquid crystal q-plate in a reflective geometry. When the device is tuned to a half-wave retardance, it operates as a q-plate with twice the value (2q) by adding a quarter-wave retarder between the mirror and the q-plate. However, when the device is tuned to a quarter-wave retardance, it acts as the original q-plate without the retarder. Experimental results are shown. Using an input tunable polarization state generator, the system allows the switchable production of all states on both the first- and second-order Poincaré spheres.

Nondiffracting vector beams where the charge and the polarization state vary with propagation distance.

We generate nondiffracting vector beams where the charge and the polarization state vary with the propagation distance. We use reflective geometry where a parallel-aligned spatial light modulator is used to spatially modulate two orthogonal linear polarizations. We encode spiral phases with equal charge but with opposite signs onto the two polarization directions to encode a vector beam and add two axicon phases. Both the charge and the phase shift between the two axicons can be varied along the focus line. We provide experimental results that demonstrate both features.

Diffraction gratings generating orders with selective states of polarization

We propose specially designed double anisotropic polarization diffraction gratings capable of producing a selective number of diffraction orders and with selective different states of polarization. Different polarization diffraction gratings are demonstrated, including linear polarization with horizontal, vertical and ± 45° orientations, and circular R and L polarization outputs. When illuminated with an arbitrary state of polarization, the system acts as a complete polarimeter where the intensities of the diffraction orders allow measurement of the Stokes parameters with a single shot. Experimental proof-of-concept is presented using a parallel-aligned liquid crystal display operating in a double pass architecture.

Generation of vector beams at 1550 nm telecommunications wavelength using a segmented q-plate

We present the use of a q -plate device operating at the 1550 nm telecommunications wavelength. A prototype liquid-crystal device from Citizen Holdings Co. is demonstrated to be useful for the generation of vector beams and orbital angular momentum transfer at this important wavelength.

Parallel generation of multiple first-order vector beams with a polarization grating and a q-plate device

Vector beams, usually generated using q-plates, are of interest because their polarization state varies spatially. In general, the q-plate performance is examined by illuminating the device and detecting the output beam with polarization states on the 6 cardinal points on the zero-order Poincare sphere, requiring a total of 36 separate measurements. In this work we present a powerful technique to generate arbitrary vector beams in parallel, thus reducing the number of measurements required. We begin with a programmable polarization diffraction grating capable to generate an arbitrary number of diffraction orders with defined polarization states selected at will. Then we combine this grating with a segmented q-plate device with q = 1/2 value. Using this combination, the parallel generation of six arbitrary first-order vector beams is achieved in a single shot. Therefore, the analysis of these beams can be greatly reduced.

Polarization state vector beam spectrum analyzer using q-plates encoded onto a spatial light modulator

Vector beams where the polarization state is spatially dependent are being examined as new optical communication channels. We demonstrate a vector beam spectrum analyzer capable of simultaneously determining the topological charge and the state of polarization of an input vector beam. We encode a two-dimensional polarization diffraction grating that generates six different q-plate channels from -3 to +3 in the horizontal direction, and each is split in the vertical direction into the six polarization channels at the cardinal points of the corresponding higher-order Poincaré sphere. The horizontal q-plate grating is a optimized phase-only grating that produces harmonics of a given input q-plate having a charge of +1 all of which have equal strengths. The vertical polarization grating is specially designed to produce 6 orders where the amplitude and phase of each order can be independently controlled. Different gratings are required for the horizontal and vertical polarizations to create the desired polarization states in each diffracted order. Consequently, we generate 36 different channels in parallel. We demonstrate this polarization diffraction element using a single phase-only liquid-crystal spatial light modulator in a reflective optical architecture. Details are given regarding experimental details on this process. Finally, we demonstrate that this system can act as a vector beam polarization state spectrum analyzer allowing both the topological charge and the polarization state of the input vector beam to be simultaneously determined in a single experiment.

Physical and encoded Q-plates for the generation of switchable vector beams

In this work we report on our achievements in generating switchable and arbitrary vector beams by means of q-plates. Two kind of q-plates are considered: i) a physical prototype from Citizen Co. and ii) a virtual device that is encoded onto a spatial light modulator (SLM). In both cases experimental and analytical results within the Jones formalism are shown. The performance of a segmented and tunable liquid crystal q-plate prototype is characterized at visible and telecommunications wavelengths, and the generation of first-order vector beams is probed. By using a reflective geometry and tuning the q-plate at half-wave or at quarter-wave retardance, it is shown how the device can operate either as a q-plate with double order. Finally, we show the generation of arbitrary programmable integer and fractional vector beams by encoding a q-plate onto a SLM based system. The system is based on a double-pass configuration that consecutively modulates the vertical and the horizontal polarization components of light using a transmissive LCoS display. Therefore, new and exotic q-plate designs can be analyzed prior to their fabrication.