Tunable, vortex dipole doubly resonant optical parametric oscillator

We report on direct generation of optical vortices from a continuous-wave (cw), Gaussian beam pumped doubly resonating optical parametric oscillator (DRO). Using a 30-mm long MgO doped periodically poled lithium tantalate (MgO:sPPLT) crystal based DRO, pumped in the green by a frequency-doubled Yb-fiber laser in Gaussian spatial profile we have generated signal and idler beams in vortex mode of order, l = 1, tunable across 970-1178 nm. Controlling the overlap between the Gaussian pump beam with the fundamental cavity mode of the resonant signal and idler beams of the DRO through the tilt of the pump beam and/or the cavity mirror in transverse plane, we have generated both signal and idler beams in vortex and vortex dipole spatial profiles. Using the theoretical formalism for the vortex beam generation through the superposition of two Gaussian beams we have numerically calculated the spatial profile of the generated beam in close agreement with our experiment results. The generic experimental scheme can be used to generate optical vortex across the electromagnetic spectrum and in all time scales (cw to ultrafast) using suitable OPO.

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.

The spatial dynamics of vortex dipole nested in a Gaussian opti cal beam is analyzed with scal ar diffraction theory. It is shown that the generation and annihilation of vortices are accompanied by extrem e wave front distortions. Process of nucleation and annihilation of vortex dipole is considered to confirm the vortex aftereffect in the process of transformation of an aberration wave front into a singular one. After the vortex dipole annihilation the absolute values of the average and Gaussian curvatures increase greatly in the local areas of wave front. The phase reconstruction error increases in these areas in the process of wave front sensing. To investigate the features of the vortex aftereffect for simple field the light rays which take part in the combined translational and rotary motion of energy around the field zero-lines are constructed. The phase is computed as a potential of the optical field using the light rays. Integration of the phase gradient along the ray or energy-stream line allows a uniq ue value of the phase to be connected with a point of the ray. Wave front of the beam is constructed from the computed phase. As in the vicinity of the vortex core the energy-stream line takes a spiral shape the phase incursion along th e line increases. After the vortex annihilation and vanishing of the spiral shape the incursion remains and creates the vortex aftereffect in the form of the extreme wave front distortions. The revealed effect should be taken into accoun t when constructing the systems of adaptive optics aimed at functioning in strong turbulence conditions. Keywords: Singular phase, optical vortex, strong turbulence, phase reconstruction

We propose a distinct concept on the generation of optical vortex through coupling between the amplitude and phase differences of the superposing beams. For the proof-of-concept demonstration, we propose a simple free-space optics recipe for the controlled synthesis of an optical beam with a vortex dipole by superposing two transversely scaled Gaussian beams. The experimental demonstration using a Sagnac interferometer introduces the desired amount of radial shear and linear phase difference between the two out-of-phase Gaussian beams to create a vortex pair of opposite topological charge in the superposed beam. Flexibility to tune their location and separation using the choice of direction of the linear phase difference and the amount of amplitude difference between the superposing beams has potential applications in optical tweezers and traps utilizing the local variation in angular momentum across the beam cross section.

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.

The use of vortex laser beams has increased in various areas of optics and photonics, necessitating enhanced beam quality for wide usage. In the field of high-power lasers, a range of methods to implement vortex laser beams has been proposed. Nonetheless, enhancing beam quality becomes more challenging as the laser power increases. This study presents the successful implementation of a high-quality, high-intensity vortex laser beam exceeding 1020W/cm2—an essential advancement for enhancing the performance and applicability of high-power lasers. We achieved this by integrating a spiral phase mirror (SPM) with an orbital angular momentum of l=1, specially designed for the vortex beam, along with an adaptive optical system, into a 150-TW femtosecond Ti:sapphire laser. Importantly, SPM, featuring a modulation structure to correct for a 45° incidence angle, was utilized to produce the vortex beam. The adaptive optical system, comprising a Shack–Hartmann wavefront sensor and a deformable mirror, employed a feedback loop to correct wavefront aberrations distorting the vortex beam. Notably, the negligible difference between the Hartmanngrams of the Gaussian and vortex beams (l=1) allowed the Gaussian beam’s Hartmanngram to serve effectively as the input reference for wavefront correction, resulting in a successfully corrected vortex beam wavefront. Experimental results, both pre- and post-wavefront correction, were compared with simulation results obtained via field-tracing. The peak intensity of the focused high-quality vortex laser beam ultimately reached 1.8×1020W/cm2, exceeding previously reported experimental results. The results of this study could significantly contribute to the exploration of high-intensity angular momentum transfer in relativistic laser-plasma interactions.

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.

A new technique for displacement measurement is proposed that makes use of phase singularities in the complex signal generated by a Laguerre-Gauss filter operation applied to a speckle pattern. The core structures of phase singularities are used as unique fingerprints attached to the object surface, and the displacement is determined by tracing the movement of registered phase singularities with their correspondence being identified by the fingerprints. Experimental results for translational and rotational displacement measurements are presented that demonstrate large dynamic range and high spatial resolution of the proposed optical vortex metrology.

A full theoretical and experimental analysis of the chain of phase singularities generated when a Gaussian beam passes a double-phase-ramp converter is presented. The overall output beam structure includes a system of interrelated optical vortices (OVs) whose trajectories form a three-dimensional singular skeleton that can be applied for the trapping and guiding of microparticles. The internal structure of each individual phase singularity is characterized by the OV topological charge and by the morphology parameters of equal intensity ellipses in the OV-core area: ellipticity (minor-to-major axes ratio) and the inclination angle. The morphology parameters’ evolution is shown to be valuable for the metrology applications.

Laser trapping and micro-manipulation using optical vortices

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.

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.

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.

In this paper the concept of optical vortex scanning microscope (OVSM) is presented. In the OVSM a sample is scanned by the focused laser beam with optical vortex. The beam possessing an optical vortex contains a line along which the phase is undetermined. At image plane this line is seen as the single point. The position of such special singular point (vortex points) changes when the beam is diffracted by a sample. The vortex point sensitivity is higher than the sensitivity of the whole focused beam. In the OVSM the position of vortex point is traced while scanning the sample. In this paper the behavior of focused vortex beam, when scanning the phase step is studied. This simple example illustrates both the OVSM idea and the method for data analysis.

Chapter 4 Singular optics