All-digital wavefront sensing for structured light beams

Optimization of DMD-based independent amplitude and phase modulation by analysis of target complex wavefront

The paper presents the results of a comprehensive study on the optimization of independent amplitude and phase wavefront manipulation which is implemented using a binary digital micromirror device. The study aims to investigate the spatial resolution and quantization achievable using this approach and its optimization based on the parameters of the target complex wave and the modulation error estimation. Based on a statistical analysis of the data, an algorithm for selecting parameters (carrier frequency of binary pattern and aperture for the first diffraction order filtering) that ensures the optimal quality of the modulated wavefront was developed. The algorithm takes into account the type of modulation, that is, amplitude, phase, or amplitude-phase, the size of the encoded distribution, and its requirements for spatial resolution and quantization. The results of the study will greatly contribute to the improvement of modulated wavefront quality in various applications with different requirements for spatial resolution and quantization.

Phase front retrieval and correction of Bessel beams

Bessel beams generated with non-ideal axicons are affected by aberrations. We introduce a method to retrieve the complex amplitude of a Bessel beam from intensity measurements alone, and then use this information to correct the wavefront and intensity profile using a deformable mirror.

Caustics of Non-Paraxial Perfect Optical Vortices Generated by Toroidal Vortex Lenses

In this paper, we consider the comparative formation of perfect optical vortices in the non-paraxial mode using various optical elements: non-paraxial and parabolic toroidal vortex lenses, as well as a vortex axicon in combination with a parabolic lens. The theoretical analysis of the action of these optical elements, as well as the calculation of caustic surfaces, is carried out using a hybrid geometrical-optical and wave approach. Numerical analysis performed on the basis of the expansion in conical waves qualitatively confirms the results obtained and makes it possible to reveal more details associated with diffraction effects. Equations of 3D-caustic surfaces are obtained and the conditions of the ring radius dependence on the order of the vortex phase singularity are analyzed. In the non-paraxial mode, when small light rings (several tens of wavelengths) are formed, a linear dependence of the ring radius on the vortex order is shown. The revealed features should be taken into account when using the considered optical elements forming the POV in various applications.

Digital Stokes polarimetry and its application to structured light: tutorial

Stokes polarimetry is a mature topic in optics, most commonly performed to extract the polarization structure of optical fields for a range of diverse applications. For historical reasons, most Stokes polarimetry approaches are based on static optical polarization components that must be manually adjusted, prohibiting automated, real-time analysis of fast changing fields. Here we provide a tutorial on performing Stokes polarimetry in an all-digital approach, exploiting a modern optical toolkit based on liquid-crystal-on-silicon spatial light modulators and digital micromirror devices. We explain in a tutorial fashion how to implement two digital approaches, based on these two devices, for extracting Stokes parameters in a fast, cheap, and dynamic manner. After outlining the core concepts, we demonstrate their applicability to the modern topic of structured light, and highlight some common experimental issues. In particular, we illustrate how digital Stokes polarimetry can be used to measure key optical parameters such as the state of polarization, degree of vectorness, and intra-modal phase of complex light fields.

High dynamic range spatial mode decomposition

An accurate readout of low-power optical higher-order spatial modes is of increasing importance to the precision metrology community. Mode sensors are used to prevent mode mismatches from degrading quantum and thermal noise mitigation strategies. Direct mode analysis sensors (MODAN) are a promising technology for real-time monitoring of arbitrary higher-order modes. We demonstrate MODAN with photo-diode readout to mitigate the typically low dynamic range of CCDs. We look for asymmetries in the response of our sensor to break degeneracies in the relative alignment of the MODAN and photo-diode and consequently improve the dynamic range of the mode sensor. We provide a tolerance analysis and show methodology that can be applied for sensors beyond first order spatial modes.

Real-time Stokes polarimetry using a digital micromirror device

Stokes polarimetry (SP) is a powerful technique that enables spatial reconstruction of the state of polarization (SoP) of a light beam using only intensity measurements. A given SoP is reconstructed from a set of four Stokes parameters, which are computed through four intensity measurements. Since all intensities must be performed on the same beam, it is common to record each intensity individually, one after the other, limiting its performance to light beams with static SoP. Here, we put forward a novel technique to extend SP to a broader set of light beams with dynamic SoP. This technique relies on the superposition principle, which enables the splitting of the input beam into identical copies, allowing the simultaneous measurement of all intensities. For this, the input beam is passed through a multiplexed digital hologram displayed on a polarization-insensitive Digital Micromirror Device (DMD) that grants independent and rapid (20 kHz) manipulation of each beam. We are able to reliably reconstruct the SoP with high fidelity and at speeds of up to 27 Hz, paving the way for real-time polarimetry of structured light.

Beyond the display: phase-only liquid crystal on Silicon devices and their applications in photonics [Invited]

Existing for almost four decades, liquid crystal on Silicon (LCOS) technology is rapidly growing into photonic applications. We review the basics of the technology, from the wafer to the driving solutions, the progress over the last decade and the future outlook. Furthermore we review the most exciting industrial and scientific applications of the LCOS technology.

Combining average molecular tilt and flicker for management of depolarized light in parallel-aligned liquid crystal devices for broadband and wide-angle illumination

We demonstrate a complete semiphysical and analytical model describing the angular and wavelength dependencies not only of retardance, but also its flicker, in parallel aligned liquid crystal (PA-LC) devices. It relies on the fitting of the molecules' equivalent tilt angle as a function of applied voltage. The wide range of calculations it offers without requiring extensive characterization makes the model unique. We focus on PA-LCoS application as a polarization state generator across the visible spectrum and for a wide range of incidence angles. This approach offers novel capabilities for managing arbitrary states of both full and partial polarization. To highlight the richness of situations with PA-LCoS devices, we provide results for two different digital addressing sequences producing different levels of flicker.

Using a complex optical orbital-angular-momentum spectrum to measure object parameters

Light beams can be characterized by their complex spatial profiles in both intensity and phase. Analogous to time signals, which can be decomposed into multiple orthogonal frequency functions, a light beam can also be decomposed into a set of spatial modes that are taken from an orthogonal basis. Such decomposition can potentially provide a tool for spatial spectrum analysis, which may enable stable, accurate, and robust extraction of physical object information that may not be readily achievable using traditional approaches. As a proof-of-concept example, we measure an object's opening angle using orbital-angular-momentum (OAM) -based complex spectrum, achieving a >15  dB signal-to-noise ratio. Moreover, the dip (i.e., notch) positions of the OAM intensity spectrum are dependent on an object's opening angle but independent of the opening's angular orientation, whereas the slope of the OAM phase spectrum is dependent on the opening's orientation but independent of the opening angle.

Mode crosstalk matrix measurement of a 1 km elliptical core few-mode optical fiber

The spatial modes of a 1 km elliptical core few-mode optical fiber (6 spatial modes) are analyzed by using liquid crystal on silicon spatial light modulators to measure the fiber's mode crosstalk matrix in Hermite-Gaussian, Laguerre-Gaussian, and linearly polarized spatial mode bases. It is shown that the fiber's spatial modes can be described by Hermite-Gaussian modes, which can propagate 1 km over the optical fiber with <-20  dB (1%) average mode crosstalk even when the fiber has multiple 1 cm diameter bends. The use of elliptical core few-mode optical fibers for space division multiplexing in data centers is discussed.

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.

Using the nonseparability of vector beams to encode information for optical communication

In this work, it is experimentally demonstrated that the nonseparability of vector beams (e.g., radial and azimuthal polarization) can be used to encode information for optical communication. By exploiting the nonseparability of a vector beam's space and polarization degrees of freedom using conventional wave plates, it is shown that 2 bits of information can be encoded when applying the identity and three Pauli operators to its polarization degree of freedom. It is also shown that vector beams can be efficiently decoded with as low as 2.7% cross talk using a Mach-Zehnder interferometer that exploits a higher-order Pancharatnam-Berry phase and liquid crystal q-plates.

Real-time phase measurement of optical vortices based on pixelated micropolarizer array

The special spiral phase structure of an optical vortex leads to an intriguing study in modern singular optics. This paper proposes a real-time phase measurement method of vortex beam based on pixelated micropolarizer array (PMA). Four phase-shifting fringe images can be obtained from a single interference image, thus the vortex beam phase can be obtained in real-time. The proposed method can achieve full-field phase measurement of the vortex beam with the advantages of lower computation and vibration resistance. In the experiments, the typical phases of vortex with different topological charges are loaded on a spatial light modulator (SLM) to generate diffraction vortex beam, and the phase distribution of vortex beam is obtained in real-time, which confirm the robustness of this method. This method is of great significance in promoting the study of optical vortices.

Interferometric characterization of the structured polarized light beam produced by the conical refraction phenomenon

The interest on the conical refraction (CR) phenomenon in biaxial crystals has revived in the last years due to its prospective for generating structured polarized light beams, i.e. vector beams. While the intensity and the polarization structure of the CR beams are well known, an accurate experimental study of their phase structure has not been yet carried out. We investigate the phase structure of the CR rings by means of a Mach-Zehnder interferometer while applying the phase-shifting interferometric technique to measure the phase at the focal plane. In general the two beams interfering correspond to different states of polarization (SOP) which locally vary. To distinguish if there is an additional phase added to the geometrical one we have derived the appropriate theoretical expressions using the Jones matrix formalism. We demonstrate that the phase of the CR rings is equivalent to that one introduced by an azimuthally segmented polarizer with CR-like polarization distribution. Additionally, we obtain direct evidence that the Poggendorff dark ring is an annular singularity, with a π phase change between the inner and outer bright rings.

Identifying Orbital Angular Momentum of Vectorial Vortices with Pancharatnam Phase and Stokes Parameters

In this work, an explicit formula is deduced for identifying the orbital angular moment (OAM) of vectorial vortex with space-variant state of polarization (SOP). Different to scalar vortex, the OAM of vectorial vortex can be attributed to two parts: 1. the azimuthal gradient of Pancharatnam phase; 2. the product between the azimuthal gradient of orientation angle of SOP and relevant solid angle on the Poincaré sphere. With our formula, a geometrical description for OAM of light beams can be achieved under the framework of the traditional Poincaré sphere. Numerical simulations for two types of vectorial vortices have been carried on to confirm our presented formula as well as demonstrate the geometrical description of OAM. Furthermore, this work would pave the way for precise characterization of OAM charge of vectorial vortices.

4 × 20 Gbit/s mode division multiplexing over free space using vector modes and a q-plate mode (de)multiplexer

Vector modes are spatial modes that have spatially inhomogeneous states of polarization, such as, radial and azimuthal polarization. In this work, the spatially inhomogeneous states of polarization of vector modes are used to increase the transmission data rate of free-space optical communication via mode division multiplexing. A mode (de)multiplexer for vector modes based on a liquid crystal q-plate is introduced. As a proof of principle, four vector modes each carrying a 20-Gbit/s quadrature phase shift keying signal (aggregate 80 Gbit/s) on a single wavelength channel (λ∼1550  nm) were transmitted ∼1  m over the lab table with <-16.4  dB mode crosstalk. Bit error rates for all vector modes were measured at the 7% forward error correction threshold with power penalties <3.41  dB.

Predictive capability of average Stokes polarimetry for simulation of phase multilevel elements onto LCoS devices

Parallel-aligned (PA) liquid-crystal on silicon (LCoS) microdisplays are especially appealing in a wide range of spatial light modulation applications since they enable phase-only operation. Recently we proposed a novel polarimetric method, based on Stokes polarimetry, enabling the characterization of their linear retardance and the magnitude of their associated phase fluctuations or flicker, exhibited by many LCoS devices. In this work we apply the calibrated values obtained with this technique to show their capability to predict the performance of spatially varying phase multilevel elements displayed onto the PA-LCoS device. Specifically we address a series of multilevel phase blazed gratings. We analyze both their average diffraction efficiency ("static" analysis) and its associated time fluctuation ("dynamic" analysis). Two different electrical configuration files with different degrees of flicker are applied in order to evaluate the actual influence of flicker on the expected performance of the diffractive optical elements addressed. We obtain a good agreement between simulation and experiment, thus demonstrating the predictive capability of the calibration provided by the average Stokes polarimetric technique. Additionally, it is obtained that for electrical configurations with less than 30° amplitude for the flicker retardance, they may not influence the performance of the blazed gratings. In general, we demonstrate that the influence of flicker greatly diminishes when the number of quantization levels in the optical element increases.