Near-Field Wireless Power Transfer, Sensing and Communication with Bessel Beams

The Bessel beam,characterized by its unique non-diffracting properties,holds promising applications.In this paper,we provide a detailed introduction and investigation into the theory and research of the Bessel beam,with a special focus on its generation and applications in the near-field region.We provide an introduction to the concepts,properties,and foundational theories of the Bessel beam.Additionally,the current study on generating Bessel beams and their applications is categorized and discussed,and potential research challenges are proposed in this paper.This review serves as a solid foundation for researchers to understand the concept of the Bessel beam and explore its potential applications.

Transverse manipulation of particles using Bessel beam of tunable size generated by cross-phase modulation

We report on a method to achieve multiple microscopic particles being trapped and manipulated transversely by using a size-tunable Bessel beam generated by cross-phase modulation(XPM)based on the thermal nonlinear optical effect.The results demonstrate that multiple polystyrene particles can be stably trapped simultaneously,and the number of the trapped particles can be controlled by varying the trapping beam power.In addition,the trapped particles can be manipulated laterally with micron-level precision by changing the size of J_(0)Bessel beam.This work provides a simple but efficient way to trap and manipulate multiple particles simultaneously,which would have potential applications in many fields such as cell sorting and transportation.

Generalization and propagation of spiraling Bessel beams with a helical axicon

A generalized type of spiral Bessel beam has been demonstrated by using a spatially displaced helical axicon （HA）. The topological charge of the spiraling Bessel beams is determined by the order of the input Laguerre Gaussian （LG） beam and the topological charge of the HA. The obtained spiraling Bessel beams have an LG type of modulation along their propagation direction and exhibit annihilation-reconstruction properties. Theoretical analysis is presented, including that of the stability, propagation distance, topological charge, and spiraling dynamic characteristics. The mathematical and numerical results show that the propagation distance and helical revolution of the spiraling Bessel beams can be controlled through choosing appropriate radius of the HA.

Propagation of Gauss-Bessel beams in turbulent atmosphere

This paper studies the propagation properties of Gauss-Bessel beams in a turbulent atmosphere. Based on the extended Huygens-Fresnel principle, it derives the intensity distribution expression for such beams propagating in a turbulent atmosphere. Then the influence of turbulence and source beam parameters on the beam propagation is studied in great detail. It finds that the intensity distribution of Gauss-Bessel beams will change into Gaussian profile in a turbulent atmosphere, and that stronger turbulence and smaller topological charges will lead to a faster changing.

Higher-order harmonics of general limited diffraction Bessel beams

In this paper, we extensively study the higher-order harmonic generation of the general limited diffraction m-th- order Bessel beam. The analysis is based on successive approximations of the Khokhlov-Zabolotskaya-Kuznetsov （KZK） equation. Asymptotic expansions are presented for higher-order harmonic Bessel beams in near and far fields. The validity of asymptotic approximation is also analyzed. The higher-order harmonic of the Bessel beam with the lowest zero-order is taken as a special example.

Local dynamical characteristics of Bessel beams upon reflection near the Brewster angle

We analytically and numerically study the local dynamical characteristics of the Bessel beams reflected from an airglass interface near the Brewster angle.A Taylor series expansion based on the angular spectrum component is applied to correct the reflection coefficients near the Brewster angle.Using a hybrid angular spectrum representation and vector potential method,the explicit expressions for the electric and magnetic field components of the reflected Bessel beams are derived analytically under paraxial approximation.The local energy,momentum,spin,and orbital angular momentum of the Bessel beams upon reflection near the Brewster angle are examined numerically by utilizing a canonical approach.Numerical simulation results show that the properties of these dynamical quantities for the Bessel beams near Brewster angle incidence change abruptly,and are significantly affected by their topological charge,half-cone angle,and polarization state.The present study has its importance in understanding the dynamical aspects of optical beams with vortex structure and diffraction-free nature during the reflection process.

Simulation of stimulated Raman scattering signal generation in scattering tissues excited by Bessel beams

Stimulated Raman scattering(SRS)microscopy has the ability of noninvasive imaging of specific chemical bonds and been increasingly used in biomedicine in recent years.Two pulsed Gaussian beams are used in traditional SRS microscopes,providing with high lateral and axial spatial resolution.Because of the tight focus of the Gaussian beam,such an SRS microscopy is difficult to be used for imaging deep targets in scattering tissues.The SRS microscopy based on Bessel beams can solve the imaging problem to a certain extent.Here,we establish a theoretical model to calculate the SRS signal excited by two Bessel beams by integrating the SRS signal generation theory with the fractal propagation method.The fractal model of refractive index turbulence is employed to generate the scattering tissues where the light transport is modeled by the beam propagation method.We model the scattering tissues containing chemicals,calculate the SRS signals stimulated by two Bessel beams,discuss the influence of the fractal model parameters on signal generation,and compare them with those generated by the Gaussian beams.The results show that,even though the modeling parameters have great influence on SRS signal generation,the Bessel beams-based SRS can generate signals in deeper scattering tissues.

Theory of Z-scan technique using Gaussian-Bessel beams with a phase object

This paper reports the theoretical study of combining Z-scan technique with Gauss-Bessel （GB） beams beside a phase object （PO） to measure the third-order nonlinear susceptibility components. By using this method, the sign of refractive index which depends on the shape of the close aperture Z-scan curve can be easily determined. Meanwhile, the magnitude of nonlinear coefficients can also be deduced by theoretical fit. The proposed method is advantageous for high sensitivity and imposes a lower stress in the cases of fragile materials, since small pulse energy is enough for the measurement of nonlinear coefficients. Predictions of the models are compared with Gaussian Z-scan measurement and GB Z-scan measurement. By using GB beams with a PO, the sensitivity of Z-scan measurements is found to be a factor of over 60 times greater than for Gaussian beams and 2 times greater than for Gaussian-Bessel beams.

Terahertz Bessel Beam Applied to Thickness Measurement of Ellipsometry Methods

This paper introduces a Terahertz (THz) ellipsometer thickness measurement method based on Bessel beams. The ellipsometry method is used to measure the thickness of film in the THz band. And the thickness of film could be measured in the range of hundreds of microns which the measurement of film thickness by ellipsometer is usually only a few hundred nm in visible light. In addition, the photon energy of the THz-wave is very low and has little damage to the film. The THz Bessel beam has the characteristics of self-healing and diffraction-free. It can make the film thickness measurement within the diffraction-free distance, which is conducive to the flexibility of the ellipsometer system. We use a multi-frequency method to measure film with two-dimensional finite different time domain (FDTD) to numerical simulation analysis of light intensity successfully.

Bessel–Gaussian beam-based orbital angular momentum holography

Orbital angular momentum(OAM), as a new degree of freedom, has recently been applied in holography technology.Due to the infinite helical mode index of OAM mode, a large number of holographic images can be reconstructed from an OAM-multiplexing hologram. However, the traditional design of an OAM hologram is constrained by the helical mode index of the selected OAM mode, for a larger helical mode index OAM mode has a bigger sampling distance, and the crosstalk is produced for different sampling distances for different OAM modes. In this paper, we present the design of the OAM hologram based on a Bessel–Gaussian beam, which is non-diffractive and has a self-healing property during its propagation. The Fourier transform of the Bessel–Gaussian beam is the perfect vortex mode that has the fixed ring radius for different OAM modes. The results of simulation and experiment have demonstrated the feasibility of the generation of the OAM hologram with the Bessel–Gaussian beam. The quality of the reconstructed holographic image is increased, and the security is enhanced. Additionally, the anti-interference property is improved owing to its self-healing property of the Bessel-OAM holography.

Two-photon polymerization of femtosecond high-order Bessel beams with aberration correction

In the femtosecond two-photon polymerization(2PP)experimental system,optical aberrations degrade the fabrication quality.To solve this issue,a multichannel interferometric wavefront sensing technique is adopted in the adaptive laser processing system with a single phase-only spatial light modulator.2PP fabrications using corrected high-order Bessel beams with the above solution have been conducted,and high-quality microstructure arrays of microtubes with 20μm diameter have been rapidly manufactured.The effectiveness of the proposed scheme is demonstrated by comparing the beam intensity distributions and 2PP results before and after aberration corrections.

Constructing ultra-long focal fields via tightly focused Bessel beams

We numerically demonstrate that the tight focusing of Bessel beams can generate focal fields with an ultra-long depth of focus(DOF).The ultra-long focal field can be controlled by appropriately regulating the order of the Bessel function and the polarization.An optical needle and an optical dark channel with nearly 100λDOF are generated.The optical needle has a DOF of~104.9λand a super-diffraction-limited focal spot with the size of 0.19λ^(2).The dark channel has a full-width at halfmaximum of~0.346λand a DOF of~103.8λ.Furthermore,the oscillating focal field with an ultra-long DOF can be also generated by merely changing the order of the input Bessel beam.Our results are expected to contribute to potential applications in optical tweezers,atom guidance and capture,and laser processing.

Generation of wavelength-independent subwavelength Bessel beams using metasurfaces

Bessel beams are of great interest due to their unique non-diffractive properties.Using a conical prism or an objective paired with an annular aperture are two typical approaches for generating zeroth-order Bessel beams.However,the former approach has a limited numerical aperture(NA),and the latter suffers from low efficiency,as most of the incident light is blocked by the aperture.Furthermore,an additional phase-modulating element is needed to generate higher-order Bessel beams,which in turn adds complexity and bulkiness to the system.We overcome these problems using dielectric metasurfaces to realize meta-axicons with additional functionalities not achievable with conventional means.We demonstrate meta-axicons with high NA up to 0.9 capable of generating Bessel beams with full width at half maximum about as small as~λ/3(λ=405 nm).Importantly,these Bessel beams have transverse intensity profiles independent of wavelength across the visible spectrum.These meta-axicons can enable advanced research and applications related to Bessel beams,such as laser fabrication,imaging and optical manipulation.

Sidelobe suppression in light-sheet fluorescence microscopy with Bessel beam plane illumination using subtractive imaging

The fluorescence from the out-of-focus region excited by the sidelobes of a Bessel beam is the major concern for light-sheet fluorescence microscopy （LSFM） with Bessel beam plane illumination. Here, we propose a method of applying the subtractive imaging to overcome the limitation of the conventional LSFM with Bessel beam plane illumination. In the proposed method, the sample is imaged twice by line scanning using the extended solid Bessel beam and the ring-like Bessel beam. By subtracting between the two images with similar out-of-focus blur, the improved image quality with the suppression of the Bessel beam sidelobes and enhanced sectioning ability with improved contrast are demonstrated.

Computation and analysis of the Bessel beam scattering by a submerged elastic sphere

Taking an elastic sphere for example, the acoustic scattering of a submerged object illuminated by a Bessel beam is studied. The partial wave series representation for an elastic sphere has been extended to the case of Bessel beam scattering. Referring to the scattering of a plane wave, the peak to peak intervals in backscattering form function caused by the interference of the specular wave and the Franz wave have been analyzed in geometry. The influence of the characteristic parameterβ of a Bessel beam on the peak to peak intervals has been indicated, and a predictive formula of the the first time. Meanwhile the elastic scattering peak to peak intervals has been established for of each partial wave has been separated based on the Resonance Scattering Theory. The influence of β on the pure elastic resonance has been studied further. The results show that selecting specific β can reduce the contribution of a certain partial wave. Therefore the resonance at the corresponding frequency and the nearby region in the backscattering is remarkably suppressed. The work of this paper could be helpful to the applications of Bessel beams on the acoustic detection of submerged objects.

Bessel-Beam Photoacoustic Microscopical Simulation Platform Based on k-Wave

We developed a Bessel-beam photoacoustic microscopical simulation platform by using the k-Wave: MATLAB toolbox. The simulation platform uses the ring slit method to generate Bessel beam. By controlling the inner and outer radius of the ring slit, the depth-of-field (DoF) of Bessel beam can be controlled. And the large volumetric image is obtained by point scanning. The simulation experiments on blood vessels were carried out to demonstrate the feasibility of the simulation platform. This simulation work can be used as an auxiliary tool for the research of Bessel-beam photoacoustic microscopy.

Micro-scale Additive Manufacturing Using the Optical Potential Generated by a Bessel Beam

In this study,we proposed a novel micro-scale additive manufacturing method based on the optical potential formed by a Bessel beam.The proposed technique is expected to show no deterioration in manufacturing resolution due to heat genera-tion,to be applicable to various materials,and to be able to be performed in an air environment.The basic principle of the proposed method involves accumulating and stacking particles dispersed in air by using optical radiation pressure.In this paper,the trajectory of the accumulated particles was numerically estimated and experimentally observed.The numerical and experimental results agreed well;specfially,the back ground flow carried the particles to the optical axis of the Bessel beam,and then the particles were localized at the bottom of the optical potential valley on the substrate.Finally,a pillar structure was fabricated with polystyrene particles having a diameter of 1 um,which indicated that the proposed technique was promising for practical applications.

Enhancement of phase conjugation degenerate four-wave mixing using a Bessel beam

We report on the enhancement of phase conjugation degenerate four-wave mixing(DFWM) in hot atomic Rb vapor by using a Bessel beam as the probe beam. The Bessel beam was generated using cross-phase modulation based on the thermal nonlinear optical effect. Our results demonstrated that the DFWM signal generated by the Bessel beam is about twice as large as that generated by the Gaussian beam, which can be attributed to the extended depth and tight focusing features of the Bessel beam. We also found that a DFWM signal with reasonable intensity can be detected even when the Bessel beam encounters an obstruction on its way, thanks to the selfhealing property of the Bessel beam. This work not only indicates that DFWM using a Bessel beam would be of great potential in the fields of high-fidelity communication, adaptive optics, and so on, but also suggests that a Bessel beam would be of significance to enhance the nonlinear process, especially in thick and scattering media.

A simple Bessel module with tunable focal depth and constant resolution for commercial two-photon microscope

The volumetric imaging of two-photon microscopy expands the focal depth and improves the throughput,which has unparalleled superiority for three-dimension samples,especially in neuroscience.However,emerging in volumetric imaging is still largely customized,which limits the integration with commercial two-photon systems.Here,we analyzed the key parameters that modulate the focal depth and lateral resolution of polarized annular imaging and proposed a volumetric imaging module that can be directly integrated into commercial two-photon systems using conventional optical elements.This design incorporates the beam diameter adjustment settings of commercial two-photon systems,allowing flexibility to adjust the depth of focus while maintaining the same lateral resolution.Further,the depth range and lateral resolution of the design were verified,and the imaging throughput was demonstrated by an increase in the number of imaging neurons in the awake mouse cerebral cortex.

基于格林函数法研究分数阶Bessel-Gaussian光束近场传输

为揭示FBG(fractional-order Bessel-Gaussian)光束在近场传输时的光强和相位演化情况,基于光传播的独立性和叠加性原理,通过引入虚光源点,并结合格林函数法,严格推导了FBG光束的非傍轴积分表达式,并进一步利用非傍轴下的各阶修正解,精确计算了FBG光束轴上的光强分布.计算结果表明:对于分数阶Bessel-Gaussian光束的远场传输,利用经典的傍轴近似理论可以得到准确的计算结果,但在近场传输时,傍轴近似理论的计算结果误差很大,只有利用非傍轴修正解才能精确研究FBG光束的近场光学传输.研究结果为将FBG光束更好地应用于近场光学奠定必要的理论基础.