Astigmatic Beam Research Articles

Trapping and revolving micron particles by transformable line traps of optical tweezers

Optical line tweezers have been an efficient tool for the manipulation of large micron particles. In this paper, we propose to create line traps with transformable configurations by using the transverse electromagnetic mode-like laser source. We designed an optical path to simulate the generation of the astigmatic beams and line traps with a series of lenses to realize the rotational transformation with respect to the rotation angle of cylindrical lenses. It is shown that the spherical particles with diameters ranging from 5 μm to 20 μm could be trapped, aligned, and revolved in experiment. The periodical trapping forces generated by transformable line traps might open an alternative way to investigate the mechanical properties of soft particles and biological cells.

Investigation of multiple scattering in space and spatial-frequency domains: with application to the analysis of aberration-diverse optical coherence tomography.

Optical microscopy suffers from multiple scattering (MS), which limits the optical imaging depth into scattering media. We previously demonstrated aberration-diverse optical coherence tomography (AD-OCT) for MS suppression, based on the principle that for datasets acquired with different aberration states of the imaging beam, MS backgrounds become decorrelated while single scattering (SS) signals remain correlated, so that a simple coherent average can be used to enhance the SS signal over the MS background. Here, we propose a space/spatial-frequency domain analysis framework for the investigation of MS in OCT, and apply the framework to compare AD-OCT (using astigmatic beams) to standard Gaussian-beam OCT via experiments in scattering tissue phantoms. Utilizing this framework, we found that increasing the astigmatic magnitude produced a large drop in both MS background and SS signal, but the decay experienced by the MS background was larger than the SS signal. Accounting for the decay in both SS signal and MS background, the overall signal-to-background ratio (SBR) of AD-OCT was similar to the Gaussian control after about 10 coherent averages, when deeper line foci was positioned at the plane-of-interest and the line foci spacing was smaller than or equal to 80 µm. For an even larger line foci spacing of 160 µm, AD-OCT resulted in a lower SBR than the Gaussian-beam control. This work provides an analysis framework to gain deeper levels of understanding and insights for the future study of MS and MS suppression in both the space and spatial-frequency domains.

Propagation and transformation properties of rotating sinh-Gaussian beam in nonlinear media with spatial nonlocality

In this paper, by introducing a rotating coordinate system, the evolution and propagation of astigmatic sinh-Gaussian beam in nonlinear media with spatial nonlocality is investigated, and the transformation and propagation characteristics of astigmatic sinh-Gaussian beam in different transverse directions with different rotation angles are discussed. Some mathematical expressions of a rotating sinh-Gaussian beam are deduced, such as the propagation evolution, the beam width, the beam curvature, the critical power, etc. It is proved that the astigmatic sinh-Gaussian beam can keep the statistical width of the beam unchanged in any transverse direction during evolution, and the changes of beam width are diverse in two transverse directions. The influences of the rotation angle and the beam coefficients on the propagation characteristics are discussed and illustrated by numerical simulation.

Conservation of extremal ellipticity for coherent single mode Gaussian beams propagating in rotationally invariant media

We demonstrate that the conservation of extremal ellipticity for an astigmatic Gaussian beam propagating in a rotationally invariant medium, for example, an arbitrary sequence of free space propagation and stigmatic lenses, initially identified by Lo et al. (2017), is a direct consequence of the conservation of orbital angular momentum (OAM) of the beam. We derive explicit analytical expressions for the first few non-zero moments of the beam OAM and show that, apart from fundamental constants, they depend only on the beam’s extremal ellipticity. This unexpected connection uncovers the actual origin of a new propagation invariant, namely extremal ellipticity, for a broad class of coherent, single-mode Gaussian beams. We expect this principle to find use in various applications where spot circularity along an extended region of the beam is essential; such as laser micromachining, imaging, optical trapping, and inertial confinement fusion.

Cassegrain antenna for a laser diode source using an E-A system to improve the transmission efficiency.

To solve the serious loss problem for central energy of the Cassegrain antenna, this paper designs a beam-shaping system, named E-A system, to convert the elliptical divergent beam with astigmatism from a laser diode into an annular collimation beam. This E-A system, comprised only of lenses with quadratic surfaces, can simultaneously realize four functions, i.e., aberration correction, beam circularization, beam collimation, and dark hollow beam generation. By adjusting the parameters, the E-A system can be used to shape elliptical astigmatic beams with different parameters. Further, the E-A system can maintain good performance at wavelengths from 500 to 1647 nm. After considering various practical factors, the transmission efficiency of the entire transmitting system can be increased to 93.91% at a wavelength of 1550 nm.

Towards communication in a curved spacetime geometry

The current race in quantum communication – endeavouring to establish a global quantum network – must account for special and general relativistic effects. The well-studied general relativistic effects include Shapiro time-delay, gravitational lensing, and frame dragging which all are due to how a mass distribution alters geodesics. Here, we report how the curvature of spacetime geometry affects the propagation of information carriers along an arbitrary geodesic. An explicit expression for the distortion onto the carrier wavefunction in terms of the Riemann curvature is obtained. Furthermore, we investigate this distortion for anti de Sitter and Schwarzschild geometries. For instance, the spacetime curvature causes a 0.10 radian phase-shift for communication between Earth and the International Space Station on a monochromatic laser beam and quadrupole astigmatism; can cause a 12.2% cross-talk between structured modes traversing through the solar system. Our finding shows that this gravitational distortion is significant, and it needs to be either pre- or post-corrected at the sender or receiver to retrieve the information.

Structured laser beams: toward 2-μm femtosecond laser vortices

Structured ultrashort-pulse laser beams, and in particular eigenmodes of the paraxial Helmholtz equation, are currently extensively studied for novel potential applications in various fields, e.g., laser plasma acceleration, attosecond science, and fine micromachining. To extend these prospects further, in the present work we push forward the advancement of such femtosecond structured laser sources into the 2-μm spectral region. Ultrashort-pulse Hermite– and Laguerre–Gaussian laser modes both with a pulse duration around 100 fs are successfully produced from a compact solid-state laser in combination with a simple single-cylindrical-lens converter. The negligible beam astigmatism, the broad optical spectra, and the almost chirp-free pulses emphasize the high reliability of this laser source. This work, as a proof of principle study, paves the way toward few-cycle pulse generation of optical vortices at 2 μm. The presented light source can enable new research in the fields of interaction with organic materials, next generation optical detection, and optical vortex infrared supercontinuum.

Properties of hyperbolic sinusoidal Gaussian beam propagating through strong atmospheric turbulence

AbstractThis paper presents evolution of hyperbolic sinusoidal Gaussian (HSG) beam and its point‐like scintillation while propagating through turbulent atmosphere. We benefit from random phase screen approach to evaluate received field and scintillation. We see that astigmatic beams, which source parameters are not equal, are resistive against atmosphere considering intensity distribution. In case of scintillation, all selected HSG beams have less scintillation index than Gauss beam. In addition, astigmatism decreases scintillation at constant Gaussian source size. We anticipate that optical wireless communication devices can be designed using our outputs.

On the focusing of wide stripe laser diode astigmatic beams for highest power density

The focusing of wide stripe laser diode astigmatic beams to be as small as possible spots for highest power densities is analyzed. The “best” and “worst” alignment situations are identified for the first time. The significant differences among the focused spot sizes obtained in the best and worst alignments are shown by software raytracing examples. It is found that the conventional understanding that expanding the beam many times in the slow axis direction with the worst alignment can decrease the smallest focused spot is not correct. It is also found that by properly aligning the lenses, the astigmatism in the focused beam can be eliminated.

Propagation Properties of an Astigmatic Cos-Gaussian Beam through Turbulent Atmosphere

We use the extended Huygens-Fresnel integral to investigate the propagation properties of a cos-Gaussian beam (cosGB) with astigmatism in atmospheric turbulence. The intensity distribution behaviour along the propagation distance for an astigmatic cosGB in atmospheric turbulence are analytically and numerically demonstrated. Some novel phenomena are presented graphically, indicating that the intensity distribution and the on-axial intensity closely depend on the astigmatic parameter and the turbulent structure constant of the cosGBs in the atmospheric turbulence.

Propagation characteristics of focused astigmatic Gaussian beams in Kerr nonlinear media

When a powerful laser beam propagates in a Kerr nonlinear medium, the Kerr effect on the beam propagation characteristics is very significant. The astigmatic laser beams are often encountered in practice. Until now, much work has been carried out on the propagation characteristics of astigmatic laser beams in linear media, but a few researches have been reported about the propagation of astigmatic laser beams through nonlinear media. To the best of our knowledge, the propagation or the transformation of astigmatic laser beams through an optical system in a Kerr nonlinear medium has not been investigated. In this paper, the propagation characteristics of focused astigmatic Gaussian beams in a nonlinear Kerr medium are studied. The Kerr effect on the beam astigmatism and the focal shift of focused astigmatic Gaussian beams are investigated in detail, and the self-focusing focal length and focus control of focused astigmatic Gaussian beams in the Kerr nonlinear medium are also studied. For the beam spreading case, the analytical formula for each of the beam width, the beam waist position, and the focal shift of focused astigmatic Gaussian beams in the Kerr nonlinear medium is derived. It is shown that in the self-focusing medium, as the beam power increases (i.e. the self-focusing effect becomes stronger), the beam astigmatism becomes stronger, but the focal shift decreases. However, in a self-defocusing medium, as the beam power increases (i.e. the self-defocusing effect becomes stronger), the beam astigmatism becomes weaker, but the focal shift increases. On the other hand, for the beam self-focusing case, the analytical formula of the self-focusing focal length of focused astigmatic Gaussian beams in the Kerr nonlinear medium is derived. It is found that the number of foci can be controlled by applying beam astigmatism. The results obtained in this paper are of theoretical and practical significance.

Aberrations of plane-symmetrical mirror systems with freeform surfaces. Part II: closed-form aberration formulas.

The aberrations of reflective optical systems with planar symmetry are investigated in the most general case, with freeform surfaces and possibly different locations of the tangential and sagittal object and image. In this second and last paper, closed-form expressions are derived for the aberrations created by an individual mirror. We study two-mirror off-axis telescopes and establish a new family of designs that we show is simultaneously free of constant coma, linear astigmatism, and quadratic distortions (including smile and keystone). Analytical expressions for the intrinsic aberrations of an astigmatic beam are also derived.

Average intensity of astigmatic hyperbolic sinusoidal Gaussian beam propagating in oceanic turbulence

We derive the received intensity of astigmatic hyperbolic sinusoidal Gaussian(AHSG) beam propagating through oceanic turbulence. Huygens–Fresnel integral is evaluated to reach the expression at the receiver side. Effect of variations on turbulence parameters such as the rate of dissipation of the mean square temperature, the rate of dissipation of the turbulent kinetic energy per unit mass of fluid, and relative strength of the temperature and salinity fluctuations are examined. We observe that beam has a view having rings at close range but beam evolves into circular shape at a short/long distance depending on the parameters of oceanic turbulence. This evolution occurs faster when the rate of dissipation of the mean square temperature raises. We hope that our results will be used in underwater communication, imaging or range measurement applications.

Inclination shift signal: thickness or index measurement in transparent media by transmission of generally astigmatic Gaussian beams

The focus error signal is a widespread optical technique that harnesses the shape of a simply astigmatic Gaussian beam to produce an output signal with a well-defined linear range used for many different applications. However, general astigmatic Gaussian beams have not been extensively used for measuring purposes even though they have been known for decades. These beams have interesting properties which were used in this work as a mean to measure a change in the optical path and recover sample information. In this text, the formulae presented by E. Kochkina to represent generally astigmatic Gaussian beams are summarized, the principles of the proposed technique are set forth and two experimental results are presented as a validation of the proposal. A brief introduction to a different approach that enables the setup to perform simultaneous measurements of the thickness and refractive index is also given.

Propagation characteristics of astigmatic hyperbolic sinusoidal Gaussian beams in nonlocal nonlinear media

In this paper, the propagation characteristics of astigmatic hyperbolic sinusoidal Gaussian beams (AHSGB) in strongly nonlocal nonlinear media are discussed. The propagation expression of the AHSGB is theoretically derived and the evolution characteristics of the light intensity distribution, the beam width, and the phase curvature are analyzed by using mathematical and numerical methods. We find that the parameters of the hyperbolic sinusoidal function, the initial power and the initial position are important factors that influence the propagation behavior of the beam.

Quadratic Bessel-Gauss beams and the azimuthal angular spectra of Gaussian astigmatic beams

In this work, we establish the relationship existing between astigmatic Gaussian beams and Bessel-modulated Gaussian beams with quadratic radial dependence. We introduce an alternative representation of quadratic Bessel-Gaussian beams. This result permits us to expand the astigmatic Gaussian beams in a Fourier series with respect to the polar azimuthal angle with coefficients that are expressible in terms of Bessel-modulated Gaussian beams with quadratic radial dependence. The analysis presented also includes an analytic derivation of the power azimuthal spectral distribution associated with the decomposition in orbital angular momentum eigenmodes and a comprehensive characterization of the properties of this distribution as the beam parameters are varied.

Near field scattering for samples under forced flow

We describe a light scattering technique for characterizing colloidal samples under constant flow. It exploits the properties of speckles in the deep Fresnel region-the so-called near field speckles-providing absolute scattering measurements of the static form factor of the sample, as described extensively by Mazzoni et al. [Rev. Sci. Instrum. 84, 043704 (2013)] for static samples. We exploit a strongly astigmatic beam for illuminating the scattering volume with a light sheet a few microns thick. This largely improves the sensitivity of the method to small signals. Moreover, by flowing the sample in the direction perpendicular to the light sheet, the transit times are reduced to a minimum, allowing for fast measurements. We tested the instrument with suspensions of calibrated colloidal polystyrene spheres with a size comparable to the light wavelength. In particular, we recovered the static form factors of suspensions of spherical particles and the phase lag of the zero-angle scattering amplitude, which both compare well to Mie theory predictions. We then applied the method to colloidal fractal aggregates of sub-wavelength particles and measured their fractal dimension. The instrument is designed to be operational in continuous flow analysis systems.

Toroidally focused sensor array for real-time laser-ultrasonic imaging: The first experimental study

In this paper we report on the first toroidally focused 2D real-time laser-ultrasonic imaging system and a modified filtered back projection algorithm that can be used in the region near the waist of the astigmatic laser-ultrasonic probe beam. The system is capable of visualizing an acupuncture needle 0.2 mm in diameter located at ∼4 cm depth in water. The lateral spatial resolution is better than ∼0.32 mm and axial spatial resolution is ∼30 μm. The achieved frame rate is up to 30 Hz. The depth dependency of the sensitivity region width and lateral resolution are experimentally measured and discussed. The array is intended to be used as a part of combined real-time photoacoustic and laser-ultrasonic imaging system.

Effect of the astigmatic phase on the intensity of nonsingular beams during propagation

We investigated the effect of the astigmatic phase on the intensity distribution of coherent nonsingular beams during propagation. Compared with the conventional twisted beam, a beam carrying the astigmatic phase could be easily generated and operated by the phase hologram in experiment. It is found that rotating the hologram could change the rotation angle and direction of the intensity distribution. The speed of rotation is also affected by the twist strength coefficient. However, rotation does not occur in some special cases. By analyzing the simulation and experimental results, we proposed a symmetric transformation to explain the phenomenon we observed. The effect of the astigmatic phase is described as flipping the intensity distribution, where the direction of the symmetric axis is controlled by the rotation angle of the phase hologram. Whether rotation occurs depends on the symmetry of the intensity distribution along the symmetric axis in the initial in-plane. Meanwhile, the twist strength coefficient could control the rate of the symmetric transformation process and the divergence angle of the beam. The new interpretation might help to inspire the investigation of other types of astigmatic beams. Our research has some application prospects in the field of beam control and transmission, especially for scenes where a special intensity distribution of the beam is needed at a certain distance.

Multiple filamentation and control of properties of self-guided elliptical Gaussian laser beam

The spatial evolution of an elliptical Gaussian beam in fluoride glass (Kerr medium) is studied using nonlinear Schrodinger equation solved by split-step beam propagation method. Solutions obtained by numerical simulation are analysed to study the effect of variation of input beam ellipticity on the process of multiple filamentation in elliptical Gaussian beam, where emphasis is on the properties of the self-guided Gaussian laser beam by externally induced input beam astigmatism. Controlling the properties of self-guided laser beam is a necessity in generation of tailored filaments.