Phase singularities in microscopic imaging

In the optical vortex microscopy the focused Gaussian beam with optical vortex scans a sample. An optical vortex can be introduced into a laser beam with the use of a special optical element--a vortex lens. When moving the vortex lens, the optical vortex changes its position inside the spot formed by a focused laser beam. This effect can be used as a new precise scanning technique. In this paper, we study the optical vortex behavior at the sample plane. We also estimate if the new scanning technique results in observable effects that could be used for a phase object detection.

This work presents an investigation of tight focusing of optical vortices, which produce regions where the Poynting vector is directed opposite to the beam's propagation direction-known as areas of reverse energy flow. We study both phase optical vortices and polarization optical vortices (cylindrical vector beams). For phase optical vortices, it is shown that the emergence of reverse energy flow as well as splitting of the initial optical vortex depends on the handedness of the circular polarization and the phase of the initial optical vortex. An optical vortex with an initial topological charge of $m\; \le \; - {3}$ splits into three optical vortices with topological charges $m + {2}$, ${-}{1}$, and ${-}{1}$ when the polarization is right circular. In contrast, under left-hand circular polarization, a vortex with the topological charge $m$ is preserved at the focus. The reverse-flow regions are located between the centers of phase singularities (screw dislocation points). As the topological charge of the phase vortex increases, the region of reverse flow along the radial coordinate widens, and the distance from the vortex center to the optical axis also increases. In the focusing of cylindrical vector beams (polarization optical vortices), the reverse energy flow region is also observed, but screw dislocations are absent.

A full comparative analysis of the chain of phase singularities generated when a quasi-plane wave and a Gaussian beam pass a double-phase-ramp (DPR) converter is presented based on the theoretical and experimental data. The overall output beam structure includes a system of interrelated optical vortices (OVs) whose linear trajectories form a threedimensional singular skeleton which can be applied for the trapping and guiding of microparticles. An internal structure of each individual phase singularity is characterized by the OV topological charge and by the morphology parameters of the equal intensity ellipses in the OV-core area. The rectilinear equidistant OV trajectories form a chain in the transverse cross section, and their identical morphology parameters can be useful for the applications to metrology and micromanipulation. As a separate result, we consider the DPR-induced transformations of the incident Laguerre-Gaussian beams of the lowest orders and show that the incident multicharged OVs are transformed into small sub-chains of the OVs located in the near-axial region.

Nonlinear propagation effects on high-power optical-vortex pulses in anisotropic crystals is reported. Nonlinear effects on optical-vortex pulse generation through the spin-orbit interaction and its propagation in an anisotropic crystal is investigated.The beam of the left-circularly-polarized optical vortex pulse is focused on one of the surfaces of a LiNbO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> or rutile crystal (NC) by a convex lens L1. After propagating along the optic axis of the crystal, the beam is collimated by another convex lens L2.

This paper outlines a new research project (CREST) for structure health monitoring. The purpose is to develop a networked sensor for static, full-axis deformation of large and long structures such as bridges, roads, and railways. We propose a novel technique based on the combined use of an optical vortex (OV) beam and correlation image sensors (CIS). Since the beam profile of OV involves definitive features known as zeros or phase singularities and they are invariant through propagation, we can encode and transmit information to determine geometrical relations between the sender and receiver nodes. By demodulating an amplitude and phase profile of OV using the CIS, all (three lateral and three rotational) displacement components can be determined. The basic optical setup is presented and the results of the fundamental experiments are shown.

Conventional correlation-based tracking methods are limited by the correlation window size and a lack in ability to track individual speckles or particles. Wang et al.[1] in their definition of Optical Vortex Metrology (OVM) propose that phase singularities are optimal encoders for position marking and can be localized with accuracy. OVM is widely used to process real-life and pseudo optical vortices [1, 2, 3], but so far the accuracy of the method has not been determined. Optical Vortex Metrology (OVM) uses phase singularities, produced in the complex signal generated by a Laguerre-Gauss filter operation applied to an image, for displacement measurements. Each phase singularity is essentially a pseudo-phase vortex, which can be uniquely identified from its structure, enabling it to be tracked between images. OVM is of interest here as not only the technique has potential to provide accurate position tracking but also pointwise rotation measurement.

An adjustable optical vortex array (OVA) based on decentered annular beam pumping has been demonstrated in an end-pumped Nd:YVO4 laser. This method allows for not only the transverse mode locking of different modes, but also the ability to adjust the mode weight and phase by manipulating the position of the focusing lens and axicon lens. To explain this phenomenon, we propose a threshold model for each mode. Using this approach, we were able to generate optical vortex arrays with 2-7 phase singularities, achieving a maximum conversion efficiency of 25.8%. Our work represents an innovative advancement in the development of solid-state lasers capable of generating adjustable vortex points.

Optical vortices, having doughnut-shaped spatial profile with zero intensity around the phase singularity, are of great interest due to its wide range of applications in variety of fields in science and technology. Two spatially separated entwined vortices with opposite topological charge forms a vortex dipoles. Due to their entwining nature, the vortex dipoles are created and annihilated in pairs of opposite charge, and carry a very stable topological structures. In recent times, vortex dipoles have created a lot of interest in studying in propagation dynamics [1] and optical vortex metrology [2]. Typically, optical vortex dipoles are created using holographic techniques. Recently, a new technique has been demonstrated to generate vortex dipole through coupling between the amplitude and phase differences of the superposing beams [3]. Here we report, for the first time to the best of our knowledge, on the generation of tunable vortex dipole directly from an optical parametric oscillator (OPO). Pumping a continuous wave (cw), doubly resonant OPO with Gaussian beam and carefully adjustment of the cavity mirrors, we have generated vortex dipole of power as much as 84 mW tunable across 968 nm-1181 nm. The generic scheme can used to generate vortex dipole at any wavelength and at all time scales.

When a phase singularity is suddenly imprinted on the axis of an ordinary Gaussian beam, an optical vortex appears and starts to grow radially, by effect of diffraction. This radial growth and the subsequent evolution of the optical vortex under focusing or imaging can be well described in general within the recently introduced theory of circular beams, which generalize the hypergeometric-Gaussian beams and which obey novel kinds of ABCD rules. Here, we investigate experimentally these vortex propagation phenomena and test the validity of circular-beam theory. Moreover, we analyze the difference in radial structure between the newly generated optical vortex and the vortex obtained in the image plane, where perfect imaging would lead to complete closure of the vortex core.

Chapter 4 Singular optics

The number of zero lines of the real and imaginary parts of the optical vortex (OV), both are the same as the topological charge (TC), and all of these lines intersect at one point where the phase singularity is. Furthermore, zero crossings distribute regularly on the transverse plane of the OV lattice. Zero lines of the real and imaginary parts of the non-diffracting fields without OV that generated by multi-waves interference are periodic but coincident. We stack two groups of these kind of zero lines which can be regarded as a set of zero lines of the real part and a set of zero lines of the imaginary part respectively, to satisfy the cross state of zero lines of an OV lattice. Then two groups of multi-waves corresponding to the two fields can be obtained. The expected OV lattice that generated by the two groups of engineered waves interference together is validated through both numerical simulations and experiments.

Topological reactions of optical correlation vortices

The etching processes of Si [1 0 0] wafer have been studied using two different methods; namely the wet chemical etching method, using HNO3-HF-CH3COOH solution, and the Ultra Low Frequency Plasma (ULFP) method at (1KHz). Ion etching using inert gas only (e.g., argon gas), and ion chemical etching using an active gas (beside the inert gas) such as oxygen techniques were used. Calculations of the different parameters produced by chemical etching and plasma etching for silicon wafer (sample) such as ( hole depth, hole width and etching rate) were investigated using the images of Optical Scanning microscope (OSM) and Joel Scanning microscope (JSM). The formed hole width (ω) increases by increasing the exposure time of the sample in the different types of etching. Values of the hole width were in the range of 2- 7 µm during exposure times of (30 to 100 min). The sample growth exponent constant was about ( 0.0707 and 0.0537 µm/min ) .Hole has depths in the range of( 0.5 to 3 µm) in time of (30 to 100 min).The average distances between the holes were decreased by increasing the exposure time from (14 to 4 µm) in the time range of (30 – 100 min). The rates of etching were ranged from (0.0226 to 0.0448 µm/ min) either for dry or wet etching. Normal 0 21 false false false MS X-NONE X-NONE The etching processes of Si [1 0 0] wafer have been studied using two different methods; namely wet chemical etching method, using HNO3-HF-CH3COOH solution, and Ultra Low Frequency Plasma (ULFP) method at (1KHz). Ion etching used inert gas only (e.g., argon gas) while ion chemical etching used an active gas (beside the inert gas) such as oxygen techniques were used. Calculations of the different parameters produced by chemical etching and plasma etching for silicon wafer (sample) such as ( hole depth, hole width and etching rate) were investigated using the images of Optical Scanning Microscope (OSM) and Joel Scanning Microscope (JSM). The formed hole width (ω) increased by increasing the exposure time of the sample in the different types of etching. Values of the hole width were in the range of 2- 7 µm during exposure times of (30 to 100 min). The sample growth exponent constant was about (0.0707 and 0.0537 µm/ min). Hole has depths in the range of( 0.5 to 3 µm) in time of (30 to 100 min).The average distances between the holes were decreased by increasing the exposure time from (14 to 4 µm) in the time range of (30 – 100 min). The rates of etching were ranged from (0.0226 to 0.0448 µm/ min) either for dry or wet etching. /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;}

Summary form only given. An optical vortex is a spiral dislocation of the phase front that has a helical phase ramp around a phase singularity. The order of the singularity multiplied by its sign is referred to as the topological charge of the vortex. The propagation of the singular light beams in nonlinear media exhibits a large variety of phenomena. In this report the results of the theoretical and experimental investigations of the noncollinear interaction (degenerate four-wave mixing) of two singular beams in Kerr nonlinear medium are presented.

Phase singularities are loci of darkness surrounded by monochromatic light in a scalar field, with applications in optical trapping, super-resolution imaging, and structured light-matter interactions. Although 1D singular structures, like optical vortices, are common due to their robust topological properties, uncommon 0D (point) and 2D (sheet) singularities can be generated by wavefront-shaping devices like metasurfaces. With the design flexibility of metasurfaces, we deterministically position ten identical point singularities using a single illumination source. The phasefront is inverse-designed using phase-gradient maximization with an automatically-differentiable propagator and produces tight longitudinal intensity confinement. The array is experimentally realized with a TiO2 metasurface. One possible application is blue-detuned neutral atom trap arrays, for which this field would enforce 3D confinement and a potential depth around 0.22 mK per watt of incident laser power. We show that metasurface-enabled point singularity engineering may significantly simplify and miniaturize the optical architecture for super-resolution microscopes and dark traps.