Formation of optical vortices through superposition of two Gaussian beams

Ultrafast vortex arrays generated from a mode-locked oscillator with dispersion management

Herein, we demonstrate the generation of optical vortex arrays pulses using a Sagnac common-path interferometric vortex generator. Hermite-Gaussian (HG) modes with different orders are initially obtained from a SESAM mode-locked laser in the positive dispersion regime. Then, in the interferometric vortex generator, by controlling the phase difference and sheering displacement between two HG modes, optical vortex pulses with different numbers of phase singularities are generated through superposition. The generated HG10 mode has a pulse width of 2 ps and maximum energy of 0.75 nJ. One-dimensional vortex arrays and triangular vortex arrays are also generated, which are formed by HGm0 and HG0n modes, respectively. This work has potential applications in the massive manipulation of microparticles, optical communication, and so on.

Spin Hall Effect in Paraxial Vectorial Light Beams with an Infinite Number of Polarization Singularities

Elements of micromachines can be driven by light, including structured light with phase and/or polarization singularities. We investigate here a paraxial vector Gaussian beam with an infinite number of polarization singularities residing evenly on a straight line. The intensity distribution is derived analytically and the polarization singularities are shown to exist only in the initial plane and in the far field. The azimuthal angle of the polarization singularities is shown to increase in the far field by π/2. We obtain the longitudinal component of the spin angular momentum (SAM) density and show that it is independent of the azimuthal angle of the polarization singularities. Upon propagation in free space, an infinite number of C-points is generated, where polarization is circular. We show that the SAM density distribution has a shape of four spots, two with left and two with right elliptic polarization. The distance to the transverse plane with the maximal SAM density decreases with decreasing distance between the polarization singularities in the initial plane. Generating such alternating areas with positive and negative SAM density, despite linear polarization in the initial plane, manifests the optical spin Hall effect. Application areas of the obtained results include designing micromachines with optically driven elements.

Red, orange, and dual wavelength vortex emission from Pr:WPFGF fiber laser using a microscope slide output coupler

Visible vortex beams have a large array of applications; however, the sources are often large or complex. Here, we present a compact vortex source with red, orange, and dual wavelength emission. This Pr:Waterproof Fluoro-Aluminate Glass fiber laser uses a standard microscope slide as an interferometric output coupler, yielding high quality first order vortex modes in a compact setup. We further demonstrate the broad (∼5 nm) emission bands in the orange (610 nm), red (637 nm) and near-infrared regions (698 nm), with the potential for green (530 nm) and cyan (485 nm) emission. This is a low-cost, compact and accessible device giving high quality modes for visible vortex applications.

Unidirectional ring vortex laser using a wedge-plate shearing interferometer

In response to growing demand from optical vortex (OV) beam applications, numerous generation techniques have been developed competing in power scalability, purity, and wavelength flexibility. Direct vortex emission from lasers typically grants access to efficient, high power, and pure mode generation. In this work we demonstrate a compact, unidirectional Nd:YVO₄ ring laser with an intracavity wedge-plate shearing interferometer (WPSI) as an output coupler, which converted the internal Gaussian mode to LG₀₁ (Laguerre-Gaussian OV) output. It directly generated a watt-level LG₀₁ OV with high mode purity (98%) in a single longitudinal mode. The monolithic WPSI has advantages in stability and simplicity compared to other designs. The system is compact and cheap, using off-the-shelf components, and can be readily adapted to any gain media, widening the scope for OV generation at wavelengths currently unobtainable using competing methods.

>30 W vortex LG01 or HG10 laser using a mode transforming output coupler

High-power vortex light generated directly from lasers will help drive their applications in material processing, optical manipulation, levitation, particle acceleration, and communications, but limited power has been achieved to date. In this work, we demonstrate record vortex average power of 31.3 W directly from a laser, to the best of our knowledge, using an interferometric mode transforming output coupler to convert a fundamental mode Nd:YVO₄ laser into a LG₀₁ vortex output. The vortex laser was Q-switched with up to 600 kHz pulse rate with a high slope efficiency of 62.5% and an excellent LG₀₁ modal purity of 95.2%. We further demonstrate > 30W laser power in a high quality HG₁₀ mode by simple adjustment of the output coupler. Experimental investigations of varying output coupling transmission are compared with theory. This successful implementation of the interferometric output coupler in a high power system demonstrates the suitability of the mode transforming method for robust turn-key vortex lasers with high efficiency and high modal purity, with scalable power and pulse rate.

Tunable vortex beam generation using an optical parametric oscillator with an antiresonant-ring interferometer

We report a high-average-power picosecond optical vortex source tunable in the near-infrared, using an antiresonant-ring (ARR) interferometer internal to an optical parametric oscillator (OPO) in combination with an external cylindrical lens for astigmatic mode conversion. The ARR OPO is tunable in the signal across 1457-1647 nm with a vortex intensity profile and up to 1 W of average power at 1602 nm. The corresponding idler is tunable over 3006-3945 nm in a Gaussian intensity profile with as much as 1.6 W at 3168 nm. The vortex signal and the Gaussian idler exhibit passive power stability better than 1.7% rms and 1.3% rms, respectively, over >1h. The signal pulses have a Gaussian duration of <19ps with a time-bandwidth product of ΔτΔν<3.6 across the tuning range.

Converting an array of edge dislocations into a multi-vortex beam

We theoretically show how, using a cylindrical lens, a Gaussian beam with a finite number of parallel zero-intensity lines (edge dislocations) is transformed into a vortex beam that carries orbital angular momentum (OAM) and topological charge (TC). Remarkably, while the original beam is assumed to carry a non-zero OAM and have no TC, the latter is shown to appear during free-space propagation. Considering two parallel center-symmetric zero-intensity lines located as an example, we look into the dynamics of generating two intensity nulls at the double focal length: with increasing distance between the vertical zero-intensity lines, two optical vortices are first generated on the horizontal axis before converging at the origin and then diverging along the vertical axis. Irrespective of the between-line distance, such an optical vortex has ${\rm TC} = - {2}$ at any distance from the optical axis, except for the original plane. With changing distance between the zero-intensity lines, the OAM that the beam carries is changing, taking positive and negative values, or a zero value at a certain between-line distance. We also show that if the number of zero-intensity lines is infinite, a vortex beam with finite OAM and infinite TC is generated.

Sampling a vortex from a Gaussian beam using a wedge-plate shearing interferometer

Many vortex-generation techniques have been developed to address a range of potential applications, exploiting their unique amplitude and phase profiles and their possession of orbital angular momentum. In this work, we present what may be the simplest method of vortex beam generation, requiring only a wedged optic: the wedge-plate shearing interferometer (WPSI). We show that the WPSI can reflect a first order Laguerre-Gaussian vortex beam (LG₀₁) with a theoretical purity of >99% from an input fundamental Gaussian beam, with 98% LG₀₁ purity experimentally demonstrated. We demonstrate 1% power conversion with a route to 14%. The monolithic WPSI is a simple, compact, and highly stable device, which can operate at any wavelength that the material is transparent to. We anticipate that it will be useful where sampling a robust, high-purity vortex beam from a Gaussian laser beam is required, including low-cost vortex generation for metrology or education.

Anomalous ring-connected optical vortex array

In this study, an anomalous ring-connected optical vortex array (ARC-OVA) via the superposition of two grafted optical vortices (GOVs) with different topological charges (TCs) has been proposed. Compared with conventional OVAs, the signs and distribution of the OVs can be individually modulated, while the number of OVs remains unchanged. In particular, the positive and negative OVs simultaneously appear in the same intensity ring. Additionally, the size of the dark core occupied by the OV can be modulated, and the specific dark core is shared by a pair of plus-minus OVs. This work deepens our knowledge about connected OVAs and facilitates new potential applications, especially in particle manipulation and optical measurement.

Theory of diffraction of vortex beams from 2D orthogonal periodic structures and Talbot self-healing under vortex beam illumination

This work presents a detailed analytic approach to the diffraction of vortex beams from 2D orthogonal periodic structures. Using the presented formulation, the diffraction of vortex beams from 2D sinusoidal and Ronchi gratings is investigated. For these gratings, the Talbot self-healing effect under vortex beam illumination is examined. In the illumination of a 2D grating with a vortex beam, we refer the Talbot self-healing effect to the filling of the null area of the incident beam under propagation. We show that, for an incident vortex beam having odd value of topological charge, the generated Talbot self-images over the self-healing area are a 2D array of optical vortices, in which each of the individual self-images gets the form of an optical vortex with a topological charge of l=1 regardless of the topological charge of the incident beam. Both the Talbot self-healing effect and generation of the 2D array of optical vortices occur optimally between a definite interval of propagation distance. Using an intuitive approach based on the interference of the diffracted orders of the grating, we determine the self-healing interval. We show that a 2D array of optical vortices can be generated directly in the interference of eight copies of a vortex beam having proper lateral shifts and relative tilts. Easy tuning and energy preservation are two main advantages that the interference-based method has over the above-mentioned diffraction-based method for generating a 2D array of optical vortices. However, setup and implementation of the diffraction-based method are very simple. We believe that both the diffraction-based and interference-based methods for creating vortex beam arrays might find applications in optical tweezers, micromanipulations, and microfluidics.

Vortex laser by transforming Gaussian mode with an interferometric output coupler

Generation of vortex beams directly from the laser source can be limited in power and efficiency, or to specific pump sources and gain media. Here, we propose a new high power and high efficiency vortex laser methodology with interferometric mode transformation as output coupling, which uses high power handling and low loss optics that have wavelength versatility. Experimental demonstration is made in a diode-pumped Nd:YVO₄ laser using an imbalanced Sagnac interferometer as output coupler producing high quality vortex output beams (M² = 2.07) with fully selectable control of handedness whilst the intracavity mode is maintained as a fundamental Gaussian. Vortex output power >3W is produced with only small reduction in efficiency compared to the equivalent TEM₀₀ laser. Continuous variation of vortex output coupling transmission and the quality of the vortex is investigated experimentally showing good agreement with theory. This work reveals a new approach to high power structured laser radiation direct from the source through interferometric spatial mode transformations.

Orbital angular momentum exchange in a picosecond optical parametric oscillator

We report on the orbital angular momentum (OAM) exchange among the interacting beams in an ultrafast optical parametric oscillator (OPO). The singly-resonant OPO is synchronously pumped by a picosecond vortex beam from a frequency-doubled Yb-fiber laser at 532 nm in the green. We demonstrate successful transfer of the pump OAM mode to the non-resonant idler beam tunable across 1109-1209 nm, with OAM as high as l_p=3. Controlling the cavity loss and spatial overlap between the resonant signal and the pump beam in the nonlinear crystal, we have generated signal and idler OAM mode combinations, (l_s,l_i) of (0,2) and (1,1), and (0,3) and (1,2) for pump OAM mode l_p=2 and 3, respectively. Using a pump power of 1 W, we have generated idler OAM mode of orders, l_i=1, 2, and 3, with maximum output powers of 202, 113, and 57 mW, respectively. To the best of our knowledge, this is the first report on controlled generation of OAM modes from an ultrafast OPO.

Generation of optical vortex array along arbitrary curvilinear arrangement

We propose an approach for creating optical vortex array (OVA) arranged along arbitrary curvilinear path, based on the coaxial interference of two width-controllable component curves calculated by modified holographic beam shaping technique. The two component curve beams have different radial dimensions as well as phase gradients along each beam such that the number of phase singularity in the curvilinear arranged optical vortex array (CA-OVA) is freely tunable on demand. Hybrid CA-OVA that comprises of multiple OVA structures along different respective curves is also discussed and demonstrated. Furthermore, we study the conversion of CA-OVA into vector mode that comprises of polarization vortex array with varied polarization state distribution. Both simulation and experimental results prove the performance of the proposed method of generating a complex structured vortex array, which is of significance for potential applications including multiple trapping of micro-sized particles.

Ultrashort vortex from a Gaussian pulse - An achromatic-interferometric approach

The more than a century old Sagnac interferometer is put to first of its kind use to generate an achromatic single-charge vortex equivalent to a Laguerre-Gaussian beam possessing orbital angular momentum (OAM). The interference of counter-propagating polychromatic Gaussian beams of beam waist ω_λ with correlated linear phase (ϕ₀ ≥ 0.025 λ) and lateral shear (y₀ ≥ 0.05 ω_λ) in orthogonal directions is shown to create a vortex phase distribution around the null interference. Using a wavelength-tunable continuous-wave laser the entire range of visible wavelengths is shown to satisfy the condition for vortex generation to achieve a highly stable white-light vortex with excellent propagation integrity. The application capablitiy of the proposed scheme is demonstrated by generating ultrashort optical vortex pulses, its nonlinear frequency conversion and transforming them to vector pulses. We believe that our scheme for generating robust achromatic vortex (implemented with only mirrors and a beam-splitter) pulses in the femtosecond regime, with no conceivable spectral-temporal range and peak-power limitations, can have significant advantages for a variety of applications.

Generation of optical vortex dipole from superposition of two transversely scaled Gaussian beams

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.

Non-coaxial superposition of vector vortex beams

Vector vortex beams are classified into four types depending upon spatial variation in their polarization vector. We have generated all four of these types of vector vortex beams by using a modified polarization Sagnac interferometer with a vortex lens. Further, we have studied the non-coaxial superposition of two vector vortex beams. It is observed that the superposition of two vector vortex beams with same polarization singularity leads to a beam with another kind of polarization singularity in their interaction region. The results may be of importance in ultrahigh security of the polarization-encrypted data that utilizes vector vortex beams and multiple optical trapping with non-coaxial superposition of vector vortex beams. We verified our experimental results with theory.

Strehl ratio: a tool for optimizing optical nulls and singularities

In this paper a set of radial and azimuthal phase functions are reviewed that have a null Strehl ratio, which is equivalent to generating a central extinction in the image plane of an optical system. The study is conducted in the framework of Fraunhofer scalar diffraction, and is oriented toward practical cases where optical nulls or singularities are produced by deformable mirrors or phase plates. The identified solutions reveal unexpected links with the zeros of type-J Bessel functions of integer order. They include linear azimuthal phase ramps giving birth to an optical vortex, azimuthally modulated phase functions, and circular phase gratings (CPGs). It is found in particular that the CPG radiometric efficiency could be significantly improved by the null Strehl ratio condition. Simple design rules for rescaling and combining the different phase functions are also defined. Finally, the described analytical solutions could also serve as starting points for an automated searching software tool.

Hermite-Gaussian modal laser beams with orbital angular momentum

A relationship for the complex amplitude of generalized paraxial Hermite-Gaussian (HG) beams is deduced. We show that under certain parameters, these beams transform into the familiar HG modes and elegant HG beams. The orbital angular momentum (OAM) of a linear combination of two generalized HG beams with a phase shift of π/2, with their double indices composed of adjacent integer numbers taken in direct and inverse order, is calculated. The modulus of the OAM is shown to be an integer number for the combination of two HG modes, always equal to unity for the superposition of two elegant HG beams, and a fractional number for two hybrid HG beams. Interestingly, a linear combination of two such HG modes also presents a mode that is characterized by a nonzero OAM and the lack of radial symmetry but does not rotate during propagation.