Phase measurement using an optical vortex lattice produced with a three-beam interferometer

Generation of optical vortex lattices by in-line phase modulation with partially coherent light

Of late, generation of different kinds of optical vortex lattices has been gaining much attention due to various applications. Several methods have been reported for the generation of optical vortex lattices using a coherent light source involving interferometric, diffractive, and pinhole phase plate methods. Owing to cost effectiveness and ease in optical implementation, these days use of incoherent or partially coherent light beams is becoming popular. In this study, we demonstrate generation of different kinds of optical vortex lattices through in-line modulation of phase distributions employing the phase concatenation approach and a light-emitting diode as a light source. It is a non-interferometric and flexible technique for the selection of the parameters that characterize the optical vortices and their arrays. The proposed method allows generation of an array of optical vortices of different topological charges with zero and non-zero radial indices having different symmetries.

Vortex beam as a positioning tool

Remote positioning by precise measurements of lateral displacements of laser beams at large distances is inevitably disturbed by the influence of atmospheric turbulences. Here we propose the use of optical vortices, which exhibit lower transversal variations at an experimentally validated range of 100 meters. We show the higher precision of the localization of vortex points as compared with standard centroid-based assessment of Gaussian beams. Numerical simulations and experimental measurements show further improvements by averaging of the positions of up to four secondary vortices forming a stable constellation when higher values of the topological charges are used.

Goal-driven method for decoding the configuration of coherent wave groups required for the generation of arbitrary-order vortex lattices

Together, the number of waves, wave vectors, amplitudes, and additional phases constitute the coherent wave group configuration and determine the pattern of the interference field. Identifying an appropriate wave group configuration is key to generating vortex lattices via interferometry. Previous studies have approached this task by first assigning the four elements, then calibrating the vortex state of the interference field. However, this method has failed to progress beyond generating third-order vortex lattices, which are insufficient for some practical applications. Therefore, this study proposes a method for determining the proper wave group configurations corresponding to arbitrary-order vortex lattices. We adopt a goal-driven approach: First, we set a vortex lattice as the target field and model it, before decomposing the target field into a sum of multiple harmonics using Fourier transforms. These harmonics constitute the wave group required to generate the target vortex lattice. As vortex lattices of any order can be set as the target field, the proposed method is compatible with any mode order. Simulations and experiments were conducted for fourth- and fifth-order vortex lattices, thus demonstrating the effectiveness of the proposed method.

Control of plasmon-polariton vortices on the surface of a metal layer

Surface plasmon polaritons (SPPs) can be excited at the interface of a metal layer and a dielectric layer by various methods. If an inhomogeneity of permittivity with a curvilinear boundary is created in the metal layer by the external electric field, the incident SPPs and the reflected ones from this inhomogeneity interfere with one another. A nonrectangular vortex lattice appears when such SPP interference occurs, and the lattice configuration can be controlled by varying the external electric field. Based on control of the SPP vortex lattice and reading out of the vortex localization, the plasmon logic gates "AND," "OR," and "NOT" can be realized. These logic gates represent a functionally complete basis for logical operations in processors operating at optical frequencies.

Chip-scale optical vortex lattice generator on a silicon platform

An optical vortex (OV) with an isolated field singularity has been extensively studied in a variety of fields. An OV lattice with a network of optical vortices may find more advanced applications in widespread areas such as optical metrology, optical manipulation, and quantum processing. An OV lattice generated by traditional approaches relies on a number of bulky diffractive optical elements with large volumes and long working distances. Here we present a simple and compact on-chip OV lattice emitter on silicon photonics platforms. The principle relies on three-plane-wave interference. We design, fabricate, and demonstrate an on-chip OV lattice emitter consisting of three parallel waveguides with etched tilt gratings. The tilt gratings facilitate flexible light emission in a wide range of directions, enabling the generation of an OV lattice above the silicon chip. The demonstrated on-chip OV lattice emitter may open a door to generate, manipulate, and detect an OV lattice using photonic integrated circuits.

Vortex topographic microscopy for full-field reference-free imaging and testing

Light vortices carry orbital angular momentum and have a variety of applications in optical manipulation, high-capacity communications or microscopy. Here we propose a new concept of full-field vortex topographic microscopy enabling a reference-free displacement and shape measurement of reflective samples. The sample surface is mapped by an array of light spots enabling quantitative reconstruction of the local depths from defocused wavefronts. Light from the spots is converted to a lattice of mutually uncorrelated double-helix point spread functions (PSFs) whose angular rotation enables depth estimation. The PSFs are created by self-interference of optical vortices that originate from the same wavefront and are shaped by a spiral phase mask (SPM). The method benefits from the isoplanatic PSFs whose shape and size remain unchanged under defocusing, ensuring high precision in a wide range of measured depths. The technique was tested using a microscope Nikon Eclipse E600 working with a micro-hole plate providing structured illumination and the SPM placed in the imaging path. The depth measurement was demonstrated in the range of 11 µm exceeding the depth of field of the microscope objective up to 19 times. Throughout this range, the surface depth was mapped with the precision better than 30 nm at the lateral positions given with the precision better than 10 nm. Application potential of the method was demonstrated by profiling the top surface of a bearing ball and reconstructing the three-dimensional relief of a reflection phase grating.

Capturing and visualizing transient X-ray wavefront topological features by single-grid phase imaging

The detection, localisation and characterisation of stationary and singular points in the phase of an X-ray wavefield is a challenge, particularly given a time-evolving field. In this paper, the associated difficulties are met by the single-grid, single-exposure X-ray phase contrast imaging technique, enabling direct measurement of phase maxima, minima, saddle points and vortices, in both slowly varying fields and as a means to visualise weakly-attenuating samples that introduce detailed phase variations to the X-ray wavefield. We examine how these high-resolution vector measurements can be visualised, using branch cuts in the phase gradient angle to characterise phase features. The phase gradient angle is proposed as a useful modality for the localisation and tracking of sample features and the magnitude of the phase gradient for improved visualization of samples in projection, capturing edges and bulk structure while avoiding a directional bias. In addition, we describe an advanced two-stage approach to single-grid phase retrieval.

Singularimetry of local phase gradients using vortex lattices and in-line holography

We have developed a differential form of singularimetry, which utilizes phase vortices or intensity gradient singularities as topological fiducial markers in a structured illumination context. This approach analytically measures phase gradients imparted by refracting specimens, yielding quantitative information that is both local and deterministic. We have quantified our phase gradient experiments to demonstrate that lattices of wave field singularities can be used to detect subtle phase gradients imparted by a spherical specimen and fiber optic cylinders.