Propagation-invariant Beams Research Articles

Spin Hall Effect of Two-Index Paraxial Vector Propagation-Invariant Beams

We investigate a simple paraxial vector beam, which is a coaxial superposition of two single-ringed Laguerre–Gaussian (LG) beams, linearly polarized along the horizontal axis, with topological charges (TC) n and −n, and of two LG beams, linearly polarized along the vertical axis, with the TCs m and −m. In the initial plane, such a vector beam has zero spin angular momentum (SAM). Upon propagation in free space, such a propagation-invariant beam has still zero SAM at several distances from the waist plane (initial plane). However, we show that at all other distances, the SAM becomes nonzero. The intensity distribution in the cross-section of such a beam has 2m (if m > n) lobes, the maxima of which reside on a circle of a certain radius. The SAM distribution has also several lobes, from 2m till 2(m + n), the centers of which reside on a circle with a radius smaller than that of the maximal-intensity circle. The SAM sign alternates differently: one lobe has a positive SAM, while two neighbor lobes on the circle have a negative SAM, or two neighbor pairs of lobes can have a positive and negative SAM. When passing through a plane with zero SAM, positive and negative SAM lobes are swapped. The maximal SAM value is achieved at a distance smaller than or equal to the Rayleigh distance.

Acoustic diffraction–resistant adaptive profile technology (ADAPT) for elasticity imaging

Acoustic beam shaping with high degrees of freedom is critical for applications such as ultrasound imaging, acoustic manipulation, and stimulation. However, the ability to fully control the acoustic pressure profile over its propagation path has not yet been achieved. Here, we demonstrate an acoustic diffraction–resistant adaptive profile technology (ADAPT) that can generate a propagation-invariant beam with an arbitrarily desired profile. By leveraging wave number modulation and beam multiplexing, we develop a general framework for creating a highly flexible acoustic beam with a linear array ultrasonic transducer. The designed acoustic beam can also maintain the beam profile in lossy material by compensating for attenuation. We show that shear wave elasticity imaging is an important modality that can benefit from ADAPT for evaluating tissue mechanical properties. Together, ADAPT overcomes the existing limitation of acoustic beam shaping and can be applied to various fields, such as medicine, biology, and material science.

Topological Charge of Propagation-Invariant Laser Beams

If a vortex propagation-invariant beam is given by all its intensity nulls, then its topological charge (TC) can be defined easily: its TC is equal to the sum of topological charges of all optical vortices in these intensity nulls. If, however, a propagation-invariant beam is given as a superposition of several light fields, then determining its TC is a complicated task. Here, we derive the topological charges of four different types of propagation-invariant beams, represented as axial superpositions of Hermite–Gaussian beams with different amplitudes and different phase delays. In particular, topological charges are obtained for such beam families as the Hermite–Laguerre–Gaussian (HLG) beams and two-parametric vortex Hermite beams. We show that the TC is a quantity resistant to changing certain beam parameters. For instance, when the parameters θ and α of the HLG beams are altered, the beam intensity also changes significantly, but the TC remains unchanged.

Relativistic transformations of quasi-monochromatic paraxial optical beams

A monochromatic plane wave recorded by an observer moving with respect to the source undergoes a Doppler shift and spatial aberration. We investigate here the transformation undergone by a generic, paraxial, spectrally coherent quasimonochromatic optical beam (of finite transverse width) when recorded by a moving detector. Because of the space-time coupling intrinsic to the Lorentz transformation, the monochromatic beam is converted into a propagation-invariant pulsed beam traveling at a group velocity equal to that of the relative motion and which belongs to the recently studied class of ``space-time wave packets.'' We show that the predicted transformation from a quasimonochromatic beam to a pulsed wave packet can be observed even at terrestrial speeds.

Complex structured beam direct generation by coherent superposition of a complete set of degenerate eigenmodes.

Structured beams have played an important role in many fields due to their rich spatial characteristics. The microchip cavity with a large Fresnel number can directly generate structured beams with complex spatial intensity distribution, which provides convenience for further exploring the formation mechanism of structured beams and realizing low-cost applications. In this article, theoretical and experimental studies are carried out on complex structured beams directly generated by the microchip cavity. It is demonstrated that the complex beams generated by the microchip cavity can be expressed by the coherent superposition of whole transverse eigenmodes within the same order, thus forming the eigenmode spectrum. The mode component analysis of complex propagation-invariant structured beams can be realized by the degenerate eigenmode spectral analysis described in this article.

Experimentally unsupervised deconvolution for light-sheet microscopy with propagation-invariant beams

Deconvolution is a challenging inverse problem, particularly in techniques that employ complex engineered point-spread functions, such as microscopy with propagation-invariant beams. Here, we present a deep-learning method for deconvolution that, in lieu of end-to-end training with ground truths, is trained using known physics of the imaging system. Specifically, we train a generative adversarial network with images generated with the known point-spread function of the system, and combine this with unpaired experimental data that preserve perceptual content. Our method rapidly and robustly deconvolves and super-resolves microscopy images, demonstrating a two-fold improvement in image contrast to conventional deconvolution methods. In contrast to common end-to-end networks that often require 1000–10,000s paired images, our method is experimentally unsupervised and can be trained solely on a few hundred regions of interest. We demonstrate its performance on light-sheet microscopy with propagation-invariant Airy beams in oocytes, preimplantation embryos and excised brain tissue, as well as illustrate its utility for Bessel-beam LSM. This method aims to democratise learned methods for deconvolution, as it does not require data acquisition outwith the conventional imaging protocol.

Optical trapping and fluorescence control with vectorial structured light

Here we functionalized micro-scaled polymer beads with nano-scaled quantum dots and demonstrate optical trapping and tweezing, with in-situ fluorescence measurement, in an all-digital all-optical configuration. We outline the chemistry required to facilitate this, from deactivating the optical trapping environment to size, adhesion and agglomeration control. We introduce a novel holographic optical trapping set-up that leverages on vectorially structured light, allowing for the delivery of tuneable forms of light from purely scalar to purely vector, including propagation invariant flat-top beams for uniform illumination and tailored intensity gradient landscapes. Finally, we show how this has the potential to quench bleaching in a single wavelength trap by linear (spatial mode) rather than non-linear effects, advancing the nascent field of optics for chemistry.

Vector space-time wave packets

Space-time wave packets (STWPs) are propagation-invariant pulsed beams whose characteristics stem from the tight association between their spatial and temporal degrees of freedom. Until recently, only scalar STWPs have been synthesized in the form of light sheets. Here we synthesize vector STWPs that are localized in all dimensions by preparing polarization-structured spatiotemporal spectra and unveil the polarization distribution over the STWP volume via time-resolved complex field measurements. Such vector STWPs are endowed with cylindrically symmetric polarization vector structures, which require joint manipulation of the spatial, temporal, and polarization degrees of freedom of the optical field. These results may be useful in particle manipulation, and in nonlinear and quantum optics.

Orbital angular momentum of paraxial propagation-invariant laser beams.

For propagation-invariant laser beams represented as a finite superposition of the Hermite-Gaussian beams with the same Gouy phase and with arbitrary weight coefficients, we obtain an analytical expression for the normalized orbital angular momentum (OAM). This expression is represented also as a finite sum of weight coefficients. We show that a certain choice of the weight coefficients allows obtaining the maximal OAM, which is equal to the maximal power of the Hermite polynomial in the sum. In this case, the superposition describes a single-ringed Laguerre-Gaussian beam with a topological charge equal to the maximal OAM and to the maximal power of the Hermite polynomial.

Enhancement of image quality in planar Airy light-sheet microscopy via subtraction method

The use of propagation-invariant Airy beams enables a light-sheet microscopy with a large field-of-view. Without relying upon two-photon excitation or deconvolution-based processing to eliminate out-of focus blur caused by the side lobes, here, we present how the subtraction method is applied to enhance the image quality in digital scanned light-sheet microscopy with Airy beam. In the proposed method, planar Airy beam with the symmetric transversal structure is used to excite the sample. A hollow Airy beam with zero intensity at the focal plane is created, which is mainly used to excite the out-of-focus signal. By scanning the sample twice with the normal planar Airy beam and the hollow Airy beam, digital post-processing of the obtained images by subtraction allows for the rejection of out-of-focus blur and improves the optical sectioning, the axial resolution and the intensity distribution uniformity of the light-sheet microscopy.

An analytical approximation to measure the extinction cross-section using: Localized Waves

We present a general expression for the optical theorem in terms of Localized Waves. This representation is well-known and commonly used to generate Frozen waves, Xwaves, and other propagation invariant beams. We analyze several examples using different input beam sources on a circular detector to measure the extinction cross-section.

Spatiotemporal Helicon Wavepackets

Propagation-invariant or non-diffracting optical beams have received considerable attention during the last two decades. However, the pulsed nature of light waves and the structured property of optical media like waveguides are often overlooked. We here present a four-dimensional spatiotemporal approach that extends and unifies both concepts of conical waves and helicon beams, mainly studied in bulk media. By taking advantage of tight correlations between the spatial modes, the topological charges, and the frequencies embedded in an optical field, we reveal propagation-invariant (dispersion- and diffraction-free) space-time wavepackets carrying orbital angular momentum (OAM) that evolve on spiraling trajectories in both time and space in bulk media or multimode fibers. Besides their intrinsic linear nature, we show that such wave structures can spontaneously emerge when a rather intense ultrashort pulse propagates nonlinearly in OAM modes. With emerging technologies of pulse/beam shaping, multimode fibers and modal multiplexing, our proposed scheme to create OAM-carrying helicon wavepackets could find a plethora of applications.

Propagation-invariant laser beams with an array of phase singularities

In this work, we investigate multivortex beams with an infinite topological charge. Such optical vortices contain an array of an infinite, but countable, number of phase singularities (isolated intensity nulls), which typically have the unitary topological charge and are located either uniformly (or not uniformly) on a straight line (or on several crossing straight lines) in the beam transverse cross section. Such optical vortices are form invariant and their transverse intensity distribution is conserved on propagation, changing only in scale and rotation. The orbital angular momentum of such optical vortices is finite, since only a finite number of screw dislocations is located within the area of the notable intensity of the Gaussian beam, while the other phase singularities are in the periphery (and in the infinity), where the intensity is very small. Increasing the Gaussian beam waist radius leads to a parabolic growth of the orbital angular momentum of such beams.

Generalized optical theorem for Rayleigh scattering approximation

A general expression for the optical theorem for probe sources given in terms of propagation invariant beams is derived. This expression is obtained using the far field approximation for Rayleigh regime. In order to illustrate this results is revisited the classical and standard scattering elastic problem of a dielectric sphere for which the incident field can be any arbitrary invariant beam.

Optical Vortex Beam for Gentle and Ultraprecise Intrastromal Corneal Dissection in Refractive Surgery.

PurposeWe introduce a novel focus shaping concept for intrastromal corneal dissection that facilitates cleavage along corneal lamellae, and we analyze laser–tissue interactions governing cutting effectiveness and mechanical side effects.MethodsFocus shaping was achieved by a spiral phase plate that converts an incident Gaussian beam into a Laguerre–Gaussian beam with a helical phase. Such vortex beams have zero intensity at their center, are propagation invariant, and possess a ring focus equal in length to the Gaussian focus but with a larger diameter. Cutting precision and the required absorbed energy for flap dissection were compared for Gaussian and vortex beams on ex vivo porcine corneal specimens at pulse durations between 480 fs and 9 ps. Cutting quality and bubble formation were characterized by scanning electron microscopy and macro photography.ResultsWith the vortex beam, the cuts were much smoother. Bubble formation was markedly reduced because cutting can be performed close to the bubble threshold, whereas with the Gaussian beam energies well above threshold are needed. Although the incident energy at the flap dissection threshold was slightly larger for the vortex beam, the absorbed energy was much smaller and contributed more effectively to cutting. This reduced plasma-induced pressure more than sevenfold.ConclusionsThe vortex beam approach for corneal dissection is a simple, versatile, and cost-effective way of improving the precision of refractive surgery while reducing bubble formation and pressure-related mechanical side effects.Translational RelevancePhase plates for propagation invariant vortex beams are easily implemented in the beam path of next-generation clinical devices.

Shaping caustics into propagation-invariant light

Structured light has revolutionized optical particle manipulation, nano-scaled material processing, and high-resolution imaging. In particular, propagation-invariant light fields such as Bessel, Airy, or Mathieu beams show high robustness and have a self-healing nature. To generalize such beneficial features, these light fields can be understood in terms of caustics. However, only simple caustics have found applications in material processing, optical trapping, or cell microscopy. Thus, these technologies would greatly benefit from methods to engineer arbitrary intensity shapes well beyond the standard families of caustics. We introduce a general approach to arbitrarily shape propagation-invariant beams by smart beam design based on caustics. We develop two complementary methods, and demonstrate various propagation-invariant beams experimentally, ranging from simple geometric shapes to complex image configurations such as words. Our approach generalizes caustic light from the currently known small subset to a complete set of tailored propagation-invariant caustics with intensities concentrated around any desired curve.

Photopolymerization with high-order Bessel light beams.

We study photopolymerization with high-order Bessel light beams with phase singularities on-axis. Self-trapping and self-focusing of propagation-invariant light beams in a photopolymer allow the fabrication of extended helical microfibers with a length scale of a centimeter, which is more than an order of magnitude larger than the propagation distance of the Bessel light beams. We show the evolution of microfibers rotating at a rate proportional to the incident optical power, while the periodicity of the helical structures remains constant, irrespective of the laser power. This suggests that optical momentum transfer plays a predominant role in the growth and rotation of such fiber structures.

Planar Airy beam light-sheet for two-photon microscopy.

We demonstrate the first planar Airy light-sheet microscope. Fluorescence light-sheet microscopy has become the method of choice to study large biological samples with cellular or sub-cellular resolution. The propagation-invariant Airy beam enables a ten-fold increase in field-of-view with single-photon excitation; however, the characteristic asymmetry of the light-sheet limits its potential for multi-photon excitation. Here we show how a planar light-sheet can be formed from the curved propagation-invariant Airy beam. The resulting symmetric light sheet excites two-photon fluorescence uniformly across an extended field-of-view without the need for deconvolution. We demonstrate the method for rapid two-photon imaging of large volumes of neuronal tissue.

The existence and evolution of fast-decaying Bessel modes in cylindrical hollow waveguides and in free space

ABSTRACTThe fundamental problem of propagation invariant Bessel beams is that they are not square-integrable in the transverse direction, and are therefore associated with an infinite power flux. Hence, truncated Bessel beams are typically considered instead. These are generated by finite apertures or apodized by a Gaussian transmittance. We obtain a different square-integrable solution of the Bessel field distribution. We show that the cylindrical symmetric hollow waveguide as a resonator modulates its own field during its propagation. These fast-decaying modes satisfy Maxwell's equations and can be expressed in analytic form.

Generation of propagation-invariant vector beams with square array by use of 2D binary phase mask and pentagonal prism.

In this paper, we realize the generation of propagation-invariant vector beams with square array by use of a 2D binary phase mask and pentagonal prism in a typical Mach-Zehnder optical system. The binary phase mask set in the optical system is perpendicular to the optical axis, and its periodic orientation is 45° relative to the horizontal and vertical directions. One polarizer was used to produce the linearly polarized beam with the angle of 45° relative to the horizontal and vertical directions. One mirror in the Mach-Zehnder optical system was replaced by a pentagonal prism, as the light will be reflected twice inside the pentagonal prism. The intensity distribution of the two branches with the mirror and pentagonal prism have mirror symmetry, and the output optical field of the two branches has an orthogonal polarization state. By adjusting the position of the phase plate accordingly, the total optical field of the two branches can form a vector beam with a square array. The experimental results coincide with the simulation results very well and demonstrate the feasibility of this method.