Dynamic higher-order Bessel-Gauss beam interference generation of rotating beams

We report zero-th and high-order acoustic Bessel beams with broad depth-of-field generated using acoustic holograms. While the transverse field distribution of Bessel beams generated using traditional passive methods is correctly described by a Bessel function, these methods present a common drawback: the axial distribution of the field is not constant, as required for ideal Bessel beams. In this work, we experimentally, numerically and theoretically report acoustic truncated Bessel beams of flat-intensity along their axis in the ultrasound regime using phase-only holograms. In particular, the beams present a uniform field distribution showing an elongated focal length of about 40 wavelengths, while the transverse width of the beam remains smaller than 0.7 wavelengths. The proposed acoustic holograms were compared with 3D-printed fraxicons, a blazed version of axicons. The performance of both phase-only holograms and fraxicons is studied and we found that both lenses produce Bessel beams in a wide range of frequencies. In addition, high-order Bessel beam were generated. We report first order Bessel beams that show a clear phase dislocation along their axis and a vortex with single topological charge. The proposed method may have potential applications in ultrasonic imaging, biomedical ultrasound and particle manipulation applications using passive lenses.

Optical beam wander is one of the most important issues for free-space optical (FSO) communication. We theoretically derive a beam wander model for Bessel beams propagating in turbulent atmosphere. The calculated beam wander of high order Bessel beams with different turbulence strengths are consistent with experimental measurements. Both theoretical and experimental results reveal that high order Bessel beams are less influenced by the turbulent atmosphere. We also demonstrate the Bessel beams based orbital angular momentum (OAM) multiplexing/demultiplexing in FSO communication with atmospheric turbulence. Under the same atmospheric turbulence condition, the bit error rates of transmitted signals carried by high order Bessel beams show smaller values and fluctuations, which indicates that the high order Bessel beams have an advantage of mitigating the beam wander in OAM multiplexing FSO communication.

Higher-order Bessel-like optical beams can be created through off-axis coupling of light into a multimode fiber. Thanks to the aberration that is inherent in spherical surfaces, through directing the Bessel-like beam comprising multiple concentric rings onto a low-cost lens, we created multiple foci at different depths. Moreover, scanning of the optical fiber with a piezoelectric actuator in the lateral direction, we were able to acquire data from different targets located at different planes. After coupling back into the fiber, the reflected portions of light from different targets could be spatially differentiated and directed to different photo-detection units. The proposed architecture is particularly appealing for laser scanning endoscopy applications, as it does not require additional passive or active optical components for generating Bessel beams (axicons or spatial light modulators), therefore offering both miniaturized realization and high optical transmission. We've further demonstrated the tunability of foci separation via altering fiber-coupling conditions with tilt and translation stages. Overall, the proposed scanning method has paved the way for addressing multiple slices at single lateral scan, thus offering improved speed for imaging or ablation applications.

In this paper, a straightforward approach is presented to generate Bessel beam sources in three-dimensional finite-difference time-domain (FDTD) method. Based on the angular spectrum representation (ASR), the incident Bessel beam is described as a superposition of plane waves whose wavevectors covering a conical surface. This decomposition of Bessel beam is then approximated by a finite collection of plane waves, which are injected into FDTD simulation domain using the total-field/scattered-field (TF/ST) method. The present method's correctness and accuracy are verified by comparing the reconstructed field in FDTD with the original field. Far-field scattered diagrams of a dielectric sphere and a spheroid particle illuminated by a zero-order or a higher-order Bessel beam are calculated using FDTD. The results are compared with those calculated using the generalized Lorenz-Mie theory (GLMT) and surface integral equation method (SIEM). Very good agreements have been achieved, which partially indicate the correctness of our method. Internal and near-surface field distributions for a two-layer hemisphere particle, which are illuminated by Bessel beams, are also displayed to show the potentials of this approach in solving scattering problems of complex particles. This approach can also be applied to generate other structured beam sources in FDTD, which provides an access to solve structured beam scattering by complex particles using FDTD.

Optical dark traps such as Laguerre-Gaussian beams, modulated optical vortices, and high-order Bessel beams have been used in the micromanipulation of microparticles. Such optical traps are highly versatile, as they are able to trap both high- and low-index microparticles as well as to set them into rotation by use of the orbital angular momentum of light. Holography has been widely used to modulate the shape of an optical vortex for new optical traps. We show that, by designing the shape of a spiral phase plate and using electron-beam lithography for fabrication, one can modulate the amplitude and the phase of an optical vortex with respect to the specific shape of the spiral phase plate as required. Furthermore, to the best of our knowledge this is the first report of transferring orbital angular momentum from a spiral phase plate to an absorptive microparticle in an experiment. Hence, with this technique, optical dark traps can easily be designed and fabricated.

In this paper, we have performed experimental, analytical, and numerical studies of beams with topological charges of $\ifmmode\pm\else\textpm\fi{}1$ and $\ifmmode\pm\else\textpm\fi{}2$ formed by silicon binary phase axicons (BPAs) with spiral zone structures. The axicons were illuminated with the Novosibirsk free electron laser radiation (a continuous stream of 100-ps pulses at $f=5.6$ MHz). The cw power of the beams produced reached 30 W and can by doubled via antireflection coating of the axicons. The intensity distribution in the beam cross sections was in good agreement with the Bessel functions and was kept constant within a distance of about $L/r\ensuremath{\approx}190$ and 100, where the first ring radii of the beams r were 0.9 and 1.5 mm for the Bessel beams of the first and second orders, respectively. Although the characteristics of the beams (Bessel cross section, ``diffraction-free'' propagation, self-recovery after passing obstacles, and randomly inhomogeneous media) corresponded to the properties of ideal Bessel beams, their spatial Fourier spectrum (the image in the focal plane of the lens) was, instead of an ideal ring, intertwined segments of arcs with phases shifted by $\ensuremath{\pi}$, the number of which was equal to the double value of the topological charge. This feature can be used, for example, in a demultiplexing unit of a free vortex-wave communication system or for identification of beam topological charge. We also revisited Young's double-slit diffraction and rotation of beams obstructed by a half-plane, previously applied to Laguerre-Gaussian beam characterization, in the case of the Bessel beams. The Young diffraction pattern demonstrated in this case a complicated intensity-phase distribution. It was shown that the Bessel beams formed by BPAs have two important advantages, which can be used in applications, in comparison with other methods of generation, e.g., a combination of an axicon lens with a spiral phase plate. Although the phase jumps of the axicons are designed for a determined wavelength (141 $\ensuremath{\mu}\mathrm{m}$ in our case), the BPAs can form the beams at incident radiation with any wavelength, albeit with a reduced diffraction efficiency, and their cross section is the same for any wavelength.

We introduce a compact method for generating guide stars to enable direct wavefront sensing in Bessel two-photon microscopy. By sequentially modulating an axicon phase and a thin lens phase using a spatial light modulator (SLM), our approach achieves seamless switching between Bessel and Gaussian illumination beams without requiring mechanical movement or additional optical components. The Bessel beam provides an expanded field of view for imaging, while the Gaussian beam serves as a point-like guide star for wavefront sensing. Experimental validation in a Bessel two-photon light sheet microscope demonstrates that wavefront correction based on our method enhances the signal-to-noise ratio (SNR) by 7.3 times and improves axial resolution by 4.4 times.

The optical binding force (BF) of stratified chiral particles induced by Bessel beam is computed by using the Generalized Lorenz Mie theory. The axial intensity profile of such non-diffracting beams can suppress the influence of the axial intensity which then depended on the interactions between inter-particles. The arbitrarily polarized high order Bessel beam (HOBB) is described in terms of beam shape coefficients (BSCs) within the framework of generalized Lorenz-Mie theories (GLMT). We discuss the influence of the beam half-conical angles and chirality parameter in detail. Different illuminating Bessel beams with arbitrary polarizations are considered, and the corresponding BFs are analyzed. It is shown that the optical BF of stratified chiral spheres can be significantly depending on the incident beam polarizations and the interacting chiral particles handedness. In binding stratified chiral spheres, the out-layered chirality of the stratified chiral spheres should be chosen in accordance with the incident polarizations. This finding may give a recipe to understand the physical mechanism of interactions between multiple chiral stratified particles by using the analytical approach, which plays an important role in manipulating complex multi-layered chiral structures self-arrangement.

In this paper, the self-reconstruction property of astigmatic Bessel beam is studied experimentally and theoretically. Based on the Fresnel diffraction integral theory and Babinet principle, the general expression of the intensity distribution of astigmatic Bessel beams passing through a circular obstacle is derived. The cross-section light intensity at transmission distance of, 10, 30, and 80 mm after astigmatism of the astigmatic Bessel beam are occluded by circular obstacles. The self-reconstruction process of the light field is observed and verified by using an specially designed experimental setup. In the experiment, we choose He-Ne laser as a light source, collimate and expand the beam through a telescope system, and a zero-order astigmatic Bessel beam is generated by a beam vertically incident on the tilted axicon after the diaphragm. A circular obstacle with a radius of 0.2 mm is placed at a distance of 200 mm behind the axicon. Finally, the cross-section intensities at different distances are observed and recorded by a microscope. The experimental phenomena are in good agreement with the theoretical prediction. The results show that the reconstruction of the zero-order astigmatic Bessel beams will occur after passing through the on-axis and off-axis obstacles. And as the transmission distance increases, the outer contour size of the astigmatic Bessel beam becomes larger, and the number of central spot arrays increases, and the complete beam is gradually reconstructed. Particularly, this feature is different from the behavior of the non-diffracting Bessel beam, which maintains the light field unchanged during transmission and has a single central spot. It is expected to be applied to multi-layer multi-particle control. And a new optical property is discovered in the experiments: the reconstruction speed of the beam in the horizontal and vertical direction are not consistent in the reconstruction process, and there is a certain speed difference. Further, we add a spiral phase plate between the diaphragm and the axicon to produce a high-order astigmatic Bessel beam. And it is verified that the high-order astigmatism Bessel beam has the same self-reconstruction characteristics after being shielded by obstacles. Compared with the zero-order aperture system, the high-order beam can not only expand the operating range, but also use the orbital angular momentum carried by the beam to achieve light rotation, which makes the particle manipulation more flexible. The research proves the self-reconstruction characteristics of astigmatic Bessel beams theoretically and experimentally, and broadens the research range of astigmatic Bessel beams. The research results have practical significance and application value in the field of optical micro-manipulation.

The exact analytical solution for the acoustic scattering of a high-order (commonly known as generalized) Bessel beam (HOBB) by an elastic sphere immersed in an ideal fluid and centered along the beam axis is revisited. The far-field acoustic scattering field is expressed as a partial wave series involving the scattering angle relative to the beam axis, the order, and the half-conical angle of the wave number components of the generalized Bessel beam. Using an appropriate grouping of terms, the expressions for the incident and scattered pressures, as well as the scattering (complex) form function provided in a recent work are transformed into expressions involving the partial wave series starting from the order m of the generalized Bessel beam. In this new formulation, the scattering coefficients for a HOBB are found to equal those obtained from the study of sound scattering of plane progressive waves by an elastic sphere. This suggests that the (complex) form function presented here may be used to advantage toward studying the acoustic scattering of a HOBB by spherical shells, coated spheres, and coated spherical shells using their corresponding scattering partial wave coefficients available in standard and recent literature texts.

Bessel beams are nondiffracting light beams with large depth-of-focus and self-healing properties, making them suitable as a serial beam writing tool over surfaces with arbitrary topography. This property breaks the inherent resolution vs. depth-of-focus tradeoff of photolithography. One approach for their formation is to use circularly symmetric diffraction gratings. Such a ring grating was designed and fabricated for the extreme ultraviolet (EUV) wavelength of 13.5 nm, a candidate wavelength for future industrial lithography. Exposure of the aerial images showed that a Bessel beam with an approximately 1 mm long z-invariant central core of 223 nm diameter had been achieved, in good agreement with theory. Arbitrary patterns were written using the Bessel spot, demonstrating possible future application of Bessel beams for serial beam writing. Lithographic marks of ~30 nm size were also observed using a high resolution Bessel beam.

Bessel beams, characterized by their unique non-diffractive and self-healing properties, have been a focal point in optical research. They offer unique advantages in various applications, from high-resolution imaging to the enhancement of optical communication. However, traditional methods of Bessel beam generation face limitations in producing multiple beams simultaneously, which hinders the application of complex light manipulation and multiple beam pathways. In this work, by merging the wave steering function of zero-refractive index metamaterials and the phase tailoring functionality of dielectric metasurfaces, we have realized the generation of multi-directional Bessel beams with the hybrid metamaterials. The multidirectional Bessel beams are not only self-healing to the defects along the propagation paths but also robust to the defects in the Bessel beam generator. Notably, the intrinsic zero-index property facilitates the minimization of light crosstalk beyond the hybrid metamaterials, preventing interference and providing a disturbance-free environment for the generation of Bessel beams. Our results provide a new perspective on designing novel optical devices with multi-channel and open novel routes to steer the electromagnetic waves in nano-scale structures.

By mapping traditional amplitude modulation to spatial modulation and employing adaptive optics compensation technique, we propose and experimentally demonstrate a high-speed Bessel beam encoding/decoding free-space optical link through atmospheric turbulence. The Bessel beam encoding/decoding speed is not limited by the conventional slow switching response of a spatial light modulator (SLM) but is fully determined by the modulation rate of an intensity modulator, which easily supports tens of gigabits per second modulation and resultant encoding/decoding. We use an SLM loaded with a pseudorandom phase mask to emulate atmospheric turbulence in the laboratory environment. An adaptive optics closed loop is used to sense the phase distortion of an extra probe Gaussian beam and then compensate the distorted Bessel beams. A 20-Gbit/s Bessel beam encoding/decoding link with adaptive turbulence compensation is demonstrated in the experiment, showing favorable operation performance.

Spectral anomalies of focused high order Bessel beams in the neighborhood of focus

A perfect vortex beam (PVB) is a wavefront helically structured beam that has the capacity to transport Orbital Angular Momentum (OAM). PVB is typically generated by Bessel Gaussian beams, which can be modulated by phase modulation devices, such as spiral phase plates and SLMs. However, these methods are constrained by the redundancy of the operational devices and the singular order of the beams. This paper presents the design of a passive device that can generate PVB with a continuously variable order, utilizing the metasurface phase control technology and the Moiré lens principle. The device can only accomplish the continuous transformation of 0∼6 order PVB through simple mechanical rotation. Meanwhile, the structure maintains a rotation angle tolerance of -0.4° to +0.6°, the axial misalignment deviation between two metasurfaces can reach 1.5 λ, a beam inclination tolerance of ±3°, and a wavelength deviation tolerance of ±6 nm. This design offers a convenient solution for generating continuously variable-order PVBs and advances the integration of structured-beam optical platforms.