Astigmatic Beam Research Articles

Synthesis of astigmatic non-uniformly correlated beams.

We present a general strategy for synthesizing astigmatic random structured light beams by jointly manipulating the astigmatic phase and optical coherence. With it, we facilitate the creation of a distinct category of beams termed astigmatic non-uniformly correlated (ANUC) beams. Our study emphasizes the significant influence of the astigmatic phase on the optical spatial coherence distribution, resulting in novel propagation features. Furthermore, we elucidate their underlying physical nature. Experimentally, we successfully generate such beams, validating theoretical projections. Our findings hold promise for diverse applications requiring adaptable spectral density control.

Theoretical investigation on the effective coupling optical system between an astigmatic tapered diode laser beam and single-mode optical fibers

In this study, we theoretically investigate the coupling efficiency of tapered diode lasers to single-mode fibers in four different coupling systems using an astigmatic beam propagation algorithm. The fast-axis lens and slow-axis lens have been used to mitigate astigmatism, which is a characteristic of the tapered diode laser and then the beam coupling into different single-mode fibers. Designers should carefully balance the pursuit of high coupling efficiency with the need to minimize astigmatism sensitivity in the design of coupling systems.

Laser hazard classification of a line laser with an astigmatic extended source

Since lasers are used in a large variety of applications, new laser products have become more complex. To increase performance, like range or brightness, it is important to consider the maximum optical output that will not exceed laser safety limits. Exposure to an extended source laser results in a larger retinal image and a simplification of treating it as a point source unnecessarily restricts system performance. For laser beams where the location of the apparent source (beam waist) is different in each axis (astigmatic beams), the retinal image is asymmetric and is also a function of eye accommodation. Lasers with astigmatic beams are often evaluated as point sources because accommodation on the source in either beam axis can indicate that the source in that axis is a point source; however, the eye can only focus (accommodate) on one distance at a time. For a single accommodation of the eye, the source may be extended, and extended source lasers are considered less hazardous than point source lasers of the same output power because of the reduction of retinal irradiance (the power is distributed over a larger area). For a line laser with an astigmatic beam, a particular laser hazard class may allow for a higher laser output power than would be allowed if it were a point source laser.

Engineering Orbital Angular Momentum in Structured Beams in General Astigmatic Systems via Symplectic Matrix Approach

We studied theoretically and experimentally the propagation of structured Laguerre–Gaussian (sLG) beams through an optical system with general astigmatism based on symplectic ABCD transforms involving geometry of the second-order intensity moments symplectic matrices. The evolution of the coordinate submatrix ellipses accompanying the transformation of intensity patterns at different orientations of the cylindrical lens was studied. It was found that the coordinate submatrix W and the twistedness submatrix M of the symplectic matrix P degenerate in the astigmatic sLG beam with simple astigmatism, which sharply reduces the number of degrees of freedom, while general astigmatism removes the degeneracy. Nevertheless, degeneracy entails a simple relationship between the coordinate element Wxy and the twistedness elements Mxy and Myx of the submatrix M, which greatly simplifies the measurement of the total orbital angular momentum (OAM), reducing the full cycle of measurements of the Hermite–Gaussian (HG) mode spectrum (amplitudes and phases) of the structured beam to the only measurement of the intensity moment. Moreover, we have shown that Fourier transform by a spherical lens enables us to suppress the astigmatic OAM component and restore the original free-astigmatic sLG beam structure. However, with further propagation, the sLG beam restores its astigmatic structure while maintaining the maximum OAM.

Enhanced forward scattering of a cell in line optical tweezers with an astigmatic beam.

The line optical tweezers (LOT) has been proven to be an alternative technique to manipulating the biological cells because of the bigger potential compared with traditional optical tweezers with a highly focused spot. We deduce the 4 × 4 optical matrix of the astigmatic LOT to investigate the optical characteristics related to the systematic parameters. The comparison of the initial and scattered electric fields by the cell under the astigmatic and stigmatic LOT is implemented to illustrate that the forward scattered light from the astigmatic LOT is much stronger than that from the stigmatic LOT, so as to the cell deformations. It is demonstrated that the astigmatic LOT could provide a more efficient way to deform the cell not only in the focal plane, but also along the optical axis to screen large biomaterials in biomechanics.

Control of giant orbital angular momentum bursts of structured Laguerre-Gaussian beams in a medium with general astigmatism

We examined theoretically and experimentally the influence of astigmatic elements (for example, a cylindrical lens) on a structured Laguerre-Gaussian beam (sLG) when the lens axes are directed at an arbitrary angle to the laboratory coordinate axes (a general astigmatism). Although a structurally stable Laguerre-Gaussian (LG) beam contains a great number of axisymmetric modes (in the LG basis) with matching phases and amplitudes, their superposition already loses its original axial symmetry, but acquires new properties (for example, fast oscillations of the orbital angular momentum (OAM)), while the beam OAM cannot exceed the azimuthal number l of the original LG mode. The loss of axial symmetry occurs due to bringing phase and amplitude perturbations into each mode of the sLG beam, which destroy the ring dislocations. Since degenerate ring dislocations are formed by optical vortices with opposite topological charges, but with equal weights, their destruction is accompanied by appearing of vortex pairs in the form of topological dipoles (their number is equal to the radial number n). As a result, the mode spectrum of the sLG is extended to the value ±(2n + l). The astigmatic element (cylindrical lens) violates the equality of vortex weights in the dipoles, which leads to a sharp growing the OAM of the sLG beam. Moreover, the OAM can be controlled by changing the rotation of the cylindrical lens axes and the control parameters of the sLG beam. It is these processes that are discussed in detail in our article, both in theoretical and experimental aspects. We show that with a certain orientation of the cylindrical lens axes, the beam OAM can exceed the sum of the orbital and azimuthal numbers (OAM > n + l). Besides, we reveal that the intensity pattern of the astigmatic sLG beam can follow the rotation of the astigmatic element axes (the effect of the beam structure following the cylindrical lens axes) at certain relations between control parameters of the sLG beam and the astigmatic element.

Propagation characteristics of astigmatic elliptic vortex beams in nonlocal media with anisotropic nonlinearity

The propagation characteristics of the astigmatic elliptic vortex beam (AEVB) in nonlocal media with isotropic and anisotropic nonlinearities are analytically and numerically investigated. Three different kinds of dynamics are discussed: AEVB in nonlinear isotropic media, elliptic vortex beam in nonlinear anisotropic media, and astigmatic circular vortex beam (ACVB) in nonlinear anisotropic media. The isotropic nonlinearity cannot support the formation of elliptic vortex solitons for any input power, and the initial phase-front curvature (IPC) will induce the pulsating behavior of the AEVB. For anisotropic nonlinearity, when the nonlinear anisotropic parameter (NAP) of the medium and the initial ratio of the beam width satisfy γx/γy = (w0y/w0x)2, a quasi-stable elliptic vortex soliton can be obtained, in which the vortex angular velocity and vortex rotation angle evolve periodically. Circular vortex soliton cannot exist in nonlinear anisotropic media, and the rotation of the ACVB can be controlled by adjusting the NAP and the IPC. In both isotropic and anisotropic nonlinear media, the rotation direction of the vortex core is opposite to that of the beam envelope.

Quasi-optical design and analysis of a remote steering launcher for CFETR ECRH system

In order to optimize the operational safety and reliability of the upper launcher for the CFETR ECRH system, a design of the launcher for NTM control based on the remote steering concept is currently being carried out for comparison with the front steering equivalent. This paper presents the layout design and analysis of the quasi-optical system in the remote steering launcher. A 3D visual quasi-optical design tool has been developed for the quasi-optical system, which can parameterize modeling, perform general astigmatic beam calculation and show the accurate beam propagation path in the upper port. Three identical sets of quasi-optical modules are arranged in the launcher, and each one consists of two fixed double-curvature focusing mirrors, which focus and reflect the steering beams (−12°–12°) from two square corrugated waveguides. The beam characteristics at the resonance layer are described, and the average beam radius is < 100 mm. The peak head loads on the surfaces of the two fixed mirrors are 1.63 MW/m2 and 1.52 MW/m2. The position and size of the beam channel in the blanket are obtained, and the opening apertures on the launcher-facing and plasma-facing sides of the blanket module are 0.54 m2 and 0.4 m2, respectively.

Interaction of astigmatic hyperbolic sinusoidal Gaussian beams in strongly nonlocal nonlinear media

In this paper, we obtain analytical expressions for the co-propagation of two and four interacting astigmatic hyperbolic sinusoidal Gaussian beams in strongly nonlocal nonlinear media by using nonlocal nonlinear Schrödinger equation. Through numerical simulations, we characterize their interaction properties and differences between the interaction of two beams and four beams, primarily focusing on the transverse intensity distribution of beam clusters and the evolution of intensity along the axis. We find that in strongly nonlocal nonlinear media, the evolution of multiple interacting astigmatic hyperbolic sinusoidal Gaussian beams is periodic. Regardless of whether the beams are in-phase or out-of-phase, the interaction among multiple beams is always attractive. The difference lies in the fact that in the case of complete in-phase beams, there are two small intensity peaks at the center of the interaction region, whereas this is not the case for other scenarios. Furthermore, among the four beams, the evolution of the in-phase interaction between vertically adjacent beams is exactly opposite to the out-of-phase interaction between horizontally adjacent beams. This research provides valuable insights for interaction of multiple beams and optical wireless communication.

Method Comparison for Simulating Non-Gaussian Beams and Diffraction for Precision Interferometry.

In the context of simulating precision laser interferometers, we use several examples to compare two wavefront decomposition methods-the Mode Expansion Method (MEM) and the Gaussian Beam Decomposition (GBD) method-for their precision and applicability. To assess the performance of these methods, we define different types of errors and study their properties. We specify how the two methods can be fairly compared and based on that, compare the quality of the MEM and GBD through several examples. Here, we test cases for which analytic results are available, i.e., non-clipped circular and general astigmatic Gaussian beams, as well as clipped circular Gaussian beams, in the near, far, and extremely far fields of millions of kilometers occurring in space-gravitational wave detectors. Additionally, we compare the methods for aberrated wavefronts and their interaction with optical components by testing reflections from differently curved mirrors. We find that both methods can generally be used for decomposing non-Gaussian beams. However, which method is more accurate depends on the optical system and simulation settings. In the given examples, the MEM more accurately describes non-clipped Gaussian beams, whereas for clipped Gaussian beams and the interaction with surfaces, the GBD is more precise.

Reflective Spin–Orbit Geometric Phase from Planar Isotropic Interface

AbstractManipulating angular momentum of light relies on the change of geometric phase in anisotropic nanostructures or optical interface phenomena. Spin–orbit interactions demonstrated in normal incidence at a planar isotropic interface are conditioned by Brewster reflection, limited to the light beam with a single radial frequency in the k‐space. This study demonstrates a geometric (Pancharatnam–Berry) phase that overcomes Brewster angle limitations providing high variability in the modulation of light reflected from a planar isotropic interface. The examined geometric phase stems from the reflection anisotropy imitating the structural anisotropy of photoaligned liquid crystals and photonic metasurfaces. Using a geometric‐phase modulation of tightly focused light reflected from a glass slab, three modes of spin to orbital angular momentum conversion are demonstrated. The discovered reflective spin–orbit interaction allows for design of a double‐helix focusing sensor to be used in microscopy imaging for precise depth measurements (accuracy 109 nm and precision 7 nm in the range of 8 µm). Experiments with a focused astigmatic beam prove that a glass plate can perform very complex modulation of the geometric phase using illumination structuring. The results thus provide the foundation for the design of low‐cost geometric‐phase systems relying on the space‐variant reflection anisotropy.

Huge spikes and dips of the orbital angular momentum in structured Laguerre-Gaussian beams resistant to simple astigmatism

The article investigated conditions for shaping astigmatic-invariant structured Laguerre-Gaussian (LG) beams in the case of simple astigmatism. We have theoretically and experimentally confirmed that the conditions of astigmatic invariance are that the q-phase parameter of the structured LG (sLG) beam is equal to the arctangent of the ratio of the Rayleigh length z0 to the focal length fcyl of a cylindrical lens for a single amplitude parameter of epsilon;=1. For the rest amplitude parameter values, epsilon;NotEqual;1, the astigmatic invariance condition is set by the equality of the orbital angular momenta (OAM) of structured sLG and astigmatic-invariant sLG (asLG) beams. We have also found sharp spikes and dips of the OAM in astigmatic asLG beams in the region where OAM turns into zero. The height and depth of these spikes and dips significantly exceed the maximum and minimum OAM values in the conventional structured sLG beams. It has been shown that the occurrence of spikes and dips of the OAM is caused by a radical restructuring of the LG mode spectra in the form of their strong ordering. Theoretical calculations, accompanied by a computer simulation, and an experiment agree well with each other.

Astigmatic electron beam propagation

An astigmatic electron beam with an ellipticity ratio of approximately 2:1 was examined using the Enhanced Modified Faraday Cup (EMFC) diagnostic to measure its properties and show how the power density distribution varies near the beam waist. Results show that the beam has two power density peaks, one on either side of the beam crossover point, resulting from different focal distances of the major and minor axes of the elliptical beam shape. Quantification of the beam properties was used to establish a depth-of-field where the beam diameter and peak power densities are relatively constant. For the 1 kW beam studied here, the depth-of-field measured approximately ±5 mm from the beam crossover point, illustrating how electron beam diagnostics can be used to identify process control limits for repeatable and reliable welds under non-ideal electron beam power density distribution conditions.

Nonparaxial Tilted Waveobjects

Simple closed-form analytical expressions for tilted astigmatic wave beams and wavepackets that are exact solutions of the wave equation are constructed. They are obtained through two different but equivalent derivations, one is based on a complex shift in the Bateman-type solutions, the other employs their Lorentz transformation. Analytic expressions for the propagation invariants: energy, momentum and orbital angular momentum of tilted waveobjects with general astigmatism are presented.

Spot size estimation of flat-top beams in space-based gravitational wave detectors

Motivated by the necessity of a high-quality stray light control in the detection of the gravitational waves in space, the spot size of a flat top beam generated by the clipping of the Gaussian beam (GB) is studied. By adopting the mode expansion method (MEM) approach to simulating the beam, a slight variant of the definition of the mean square deviation (MSD) spot size for the MEM beam is proposed. This enables us to quickly estimate the spot size for arbitrary propagation distances. Given that the degree of clipping is dependent on the power ratio within the surface of an optical element, the power ratio within the MSD spot range is used as a measure of spot size. The definition is then validated in the cases of simple astigmatic Gaussian beam and nearly-Gaussian beam profiles. As a representative example, the MSD spot size for a top-hat beam in a science interferometer in the detection of gravitational waves in space is then simulated. As in traditional MSD spot size analysis, the spot size is divergent when diffraction is taken into account. A careful error analysis is carried out on the divergence and in the present context, it is argued that this error will have little effect on our estimation. Using the results of our study allows an optimal design of optical systems with top-hat or other types of non-Gaussian beams. Furthermore, it allows testing the interferometry of space-based gravitational wave detectors for beam clipping in optical simulations. This work will serve as a useful guide in the future system design of the optical bench and the sizes of the optical components.

Simplifying the Experimental Detection of the Vortex Topological Charge Based on the Simultaneous Astigmatic Transformation of Several Types and Levels in the Same Focal Plane.

It is known that the astigmatic transformation can be used to analyze the topological charge of a vortex beam, which can be implemented by using various optical methods. In this case, in order to form an astigmatic beam pattern suitable for the clear detection of a topological charge, an optical adjustment is often required (changing the lens tilt and/or the detection distance). In this article, we propose to use multi-channel diffractive optical elements (DOEs) for the simultaneous implementation of the astigmatic transformations of various types and levels. Such multi-channel DOEs make it possible to insert several types of astigmatic aberrations of different levels into the analyzed vortex beam simultaneously, and to form a set of aberration-transformed beam patterns in different diffraction orders in one detection plane. The proposed approach greatly simplifies the analysis of the characteristics of a vortex beam based on measurements in the single plane without additional adjustments. In this article, a detailed study of the effect of various types of astigmatic aberrations based on a numerical simulation and experiments was carried out, which confirmed the effectiveness of the proposed approach.

Investigation of Focusing Properties on Astigmatic Gaussian Beams in Nonlinear Medium.

Ultra-short laser filamentation has been intensively studied due to its unique optical properties for applications in the field of remote sensing and detection. Although significant progress has been made, the quality of the laser beam still suffers from various optical aberrations during long-range transmission. Astigmatism is a typical off-axis aberration that is often encountered in the off-axis optical systems. An effective method needs to be proposed to suppress the astigmatism of the beam during filamentation. Herein, we numerically investigated the impact of the nonlinear effects on the focusing properties of the astigmatic Gaussian beams in air and obtained similar results in the experiment. As the single pulse energy increases, the maximum on-axis intensity gradually shifted from the sagittal focus to the tangential focus and the foci moved forward simultaneously. Moreover, the astigmatism could be suppressed effectively with the enhancement of the nonlinear effects, that is, the astigmatic difference and the degree of beam distortion were both reduced. Through this approach, the acoustic intensity of the filament (located at the tangential focal point) increased by a factor of 22.8. Our work paves a solid step toward the practical applications of the astigmatism beam as the nonlinear lidar.

Twisted elliptical multi-Gaussian Schell-model beams and their propagation properties: comment.

The inadequacy of using beam propagation factors Mx2, My2 for general astigmatic beams as those analyzed in the paper J. Opt. Soc. Am. A37, 89 (2020)JOAOD60740-323210.1364/JOSAA.37.000089 is discussed, and the appropriate beam invariants to be considered are presented.

Modified astigmatic beam technique for laser writing.

The ultrafast laser writing of optical waveguides and devices is increasingly ubiquitous among the photonics community, mostly for its flexibility and three-dimensional fabrication capability. The well-known astigmatic beam technique is the simplest method to inscribe near-circular cross-section waveguides. In this paper, we report on a significant enhancement to the widely used astigmatic beam technique that makes it more flexible and yields a more circular waveguide cross section. By simply superposing a long-focus lens before the laser inscription objective lens, we demonstrate that the normalized squared radial deviation from a perfectly circular waveguide cross section can be reduced to <4×10-4, which is a significant improvement compared to >0.1 typically obtained using the standard astigmatic beam technique, or >0.7 with a Gaussian beam. The modified technique also makes it easy to use the full power delivered by the laser, which is not usually the case with the standard technique. A technique to optimize the waveguide shape prior to the inscription by in situ laser-induced plasma emission imaging is also discussed.

Average intensity and polarization evolution of aberrated partially coherent cosh-Airy beams propagating in ocean turbulence

In this paper, the cross-spectral density (CSD) of aberrated cosh-Airy beams in oceanic turbulence is first derived. And then, the corresponding CSD matrix elements can be obtained by the unified theory of coherence and polarization. Finally, the features of astigmatic cosh-Airy beams propagating in ocean turbulence, i.e. average intensity, spectral coherence and polarization properties, were investigated in detail using numerical simulation. It can be found that the astigmatism has different effects on the average intensity in x and y directions. And the distance of the polarization returning to its initial value is affected by the astigmatism coefficient, cosh modulation parameters and coherence length.