Experimental investigation of Bessel beam characteristics

Scattered-light-sheet microscopy with sub-cellular resolving power

Since its first demonstration over 100 years ago, scattering-based light-sheet microscopy has recently re-emerged as a key modality in label-free tissue imaging and cellular morphometry; however, scattering-based light-sheet imaging with subcellular resolution remains an unmet target. This is because related approaches inevitably superimpose speckle or granular intensity modulation on to the native subcellular features. Here, we addressed this challenge by deploying a time-averaged pseudo-thermalized light-sheet illumination. While this approach increased the lateral dimensions of the illumination sheet, we achieved subcellular resolving power after image deconvolution. We validated this approach by imaging cytosolic carbon depots in yeast and bacteria with increased specificity, no staining, and ultralow irradiance levels. Overall, we expect this scattering-based light-sheet microscopy approach will advance single, live cell imaging by conferring low-irradiance and label-free operation towards eradicating phototoxicity.

Composite Diffraction-Free Beam Formation Based on Iteratively Calculated Primitives

To form a diffraction-free beam with a complex structure, we propose to use a set of primitives calculated iteratively for the ring spatial spectrum. We also optimized the complex transmission function of the diffractive optical elements (DOEs), which form some primitive diffraction-free distributions (for example, a square or/and a triangle). The superposition of such DOEs supplemented with deflecting phases (a multi-order optical element) provides to generate a diffraction-free beam with a more complex transverse intensity distribution corresponding to the composition of these primitives. The proposed approach has two advantages. The first is the rapid (for the first few iterations) achievements of an acceptable error in the calculation of an optical element that forms a primitive distribution compared to a complex one. The second advantage is the convenience of reconfiguration. Since a complex distribution is assembled from primitive parts, it can be reconfigured quickly or dynamically by using a spatial light modulator (SLM) by moving and rotating these components. Numerical results were confirmed experimentally.

Nonlinear Reconstruction of Images from Patterns Generated by Deterministic or Random Optical Masks-Concepts and Review of Research

Indirect-imaging methods involve at least two steps, namely optical recording and computational reconstruction. The optical-recording process uses an optical modulator that transforms the light from the object into a typical intensity distribution. This distribution is numerically processed to reconstruct the object's image corresponding to different spatial and spectral dimensions. There have been numerous optical-modulation functions and reconstruction methods developed in the past few years for different applications. In most cases, a compatible pair of the optical-modulation function and reconstruction method gives optimal performance. A new reconstruction method, termed nonlinear reconstruction (NLR), was developed in 2017 to reconstruct the object image in the case of optical-scattering modulators. Over the years, it has been revealed that the NLR can reconstruct an object's image modulated by an axicons, bifocal lenses and even exotic spiral diffractive elements, which generate deterministic optical fields. Apparently, NLR seems to be a universal reconstruction method for indirect imaging. In this review, the performance of NLR isinvestigated for many deterministic and stochastic optical fields. Simulation and experimental results for different cases are presented and discussed.

Transversal and axial modulation of axicon-generated Bessel beams using amplitude and phase masks for glass processing applications

The control of laser-induced microcracks in the volume of transparent materials is essential for scribing processes. In this paper, we investigate the effect of various amplitude and single-level phase masks on both transverse and axial intensity distribution of the conventional axicon-generated Bessel beams. Furthermore, we demonstrate the volumetric crack control induced by an asymmetrical central core with an appropriately selected intensity level to avoid the influence of peripheral intensity maxima. Proper alignment of cracks and intra-distance between the modifications results in the reduced separation stress of the scribed samples. Furthermore, the additional amplitude modulation of the incident Gaussian beam is introduced to flatten the axial intensity distribution of the axicon-generated Bessel beam.

Phase correlation arc and universal decay of entangled orbital angular momentum qubit states in atmospheric turbulence

In this study, we introduce the phase correlation arc of an orbital angular momentum (OAM) beam to investigate the evolution of OAM entanglement. We reveal that the entanglement decay of all OAM states of Laguerre-Gaussian modes in atmospheric turbulence is universal via both numerical predictions and experimental data. A similar evolution law is also theoretically confirmed to exist in Bessel-Gaussian modes. Finally, by using the phase correlation arc, the precise formula of the decay distance dependence on the OAM number is derived, and it exhibits excellent agreement with previous experimental conclusions.

Airy light-sheet Raman imaging

Light-sheet fluorescence microscopy has greatly improved the speed and overall photostability of optically sectioning cellular and multi-cellular specimens. Similar gains have also been conferred by light-sheet Raman imaging; these schemes, however, rely on diffraction limited Gaussian beams that hinder the uniformity and size of the imaging field-of-view, and, as such, the resulting throughput rates. Here, we demonstrate that a digitally scanned Airy beam increases the Raman imaging throughput rates by more than an order of magnitude than conventional diffraction-limited beams. Overall, this, spectrometer-less, approach enabled 3D imaging of microparticles with high contrast and 1 µm axial resolution at 300 msec integration times per plane and orders of magnitude lower irradiation density than coherent Raman imaging schemes. We detail the apparatus and its performance, as well as its compatibility with fluorescence light-sheet and quantitative-phase imaging towards rapid and low phototoxicity multimodal imaging.

Direct axial plane imaging of particle manipulation with nondiffracting Bessel beams

Optical manipulation with nondiffracting beams has been attracting great interest and finding widespread applications in many fields such as chemistry, physics, and biomedicine. Generally, optical manipulation is conducted in an optical microscopy system, which, in general, only allows for imaging motions of particles in the transverse plane, rendering the observation of dynamics processes occurring in the axial plane impractical. We propose and demonstrate an optical manipulation system that incorporates an axial plane imaging module. With this system, the trapping behavior in the transverse plane and the transportation process in the axial plane of a particle immersed in a Bessel beam were acquired simultaneously in real time.

Long-range quasi-non-diffracting Gauss-Bessel beams in a few-cycle laser field

Many applications ranging from nonlinear optics to material processing would benefit from pulsed ultrashort (quasi-)non-diffracting Gauss-Bessel beams (GBBs). Here we demonstrate a straightforward yet efficient method for generating such zeroth- and first-order GBBs using a single reflective spatial light modulator. Even in the sub-8-fs range there are no noticeable consequences for the measured pulse duration. The only effect is a weak "coloring" of the outer-lying satellite rings of the beams due to the spectrum spanning over more than 300 nm. The obtained beams have diffraction half-angles below 40 μrad and reach propagation distances in excess of 1.5 m.

Zeroth- and first-order long range non-diffracting Gauss-Bessel beams generated by annihilating multiple-charged optical vortices

We demonstrate an alternative approach for generating zeroth- and first-order long range non-diffracting Gauss–Bessel beams (GBBs). Starting from a Gaussian beam, the key point is the creation of a bright ring-shaped beam with a large radius-to-width ratio, which is subsequently Fourier-transformed by a thin lens. The phase profile required for creating zeroth-order GBBs is flat and helical for first-order GBBs with unit topological charge (TC). Both the ring-shaped beam and the required phase profile can be realized by creating highly charged optical vortices by a spatial light modulator and annihilating them by using a second modulator of the same type. The generated long-range GBBs are proven to have negligible transverse evolution up to 2 m and can be regarded as non-diffracting. The influences of the charge state of the TCs, the propagation distance behind the focusing lens, and the GBB profiles on the relative intensities of the peak/rings are discussed. The method is much more efficient as compared to this using annular slits in the back focal plane of lenses. Moreover, at large propagation distances the quality of the generated GBBs significantly surpasses this of GBBs created by low angle axicons. The developed analytical model reproduces the experimental data. The presented method is flexible, easily realizable by using a spatial light modulator, does not require any special optical elements and, thus, is accessible in many laboratories.

Tuning the resolution and depth of field of a lens using an adjustable ring beam illumination

A pair of axicons with an adjustable separation between them is used to generate a variable diameter ring beam with high efficiency. This beam illuminates a lens to produce quasi-diffraction-free beams with a tunable spot size and depth of field. We studied the generated beam characteristics while changing either the ring diameter or its thickness. Such a scheme has applications in adjustable imaging, including nondiffracting beam microscopy, material processing with an irradiance above a certain threshold value, and particle trapping/manipulation.

Improving axial resolution of Bessel beam light-sheet fluorescence microscopy by photobleaching imprinting

Light-sheet microscopy has been widely used in high-speed fluorescence imaging with low phototoxicity, while the trade-off between the field-of-view and optical sectioning capability limits its application in large-scale imaging. Although Bessel beam light-sheet microscopy greatly enhances the light-sheet length with the self-healing ability, it suffers from the strong side-lobe effect. To solve these problems, we introduce the photobleaching imprinting technique in Bessel beam light-sheet microscopy. By extracting the non-linear photobleaching-induced fluorescence decay, we get rid of the large concentric side lobe structures of the Bessel beam to achieve uniform isotropic resolution across a large field-of-view for large-scale fluorescence imaging. Both numerical simulations and experimental results on various samples are demonstrated to show our enhanced resolution and contrast over traditional Bessel-beam light-sheet microscopy.

Ultrasonic Bessel beam generation from radial modes of piezoelectric discs

We present comprehensive analytical and experimental investigations on ultrasonic Bessel beam generation from radial modes of piezoelectric disc transducers. The Bessel vibration pattern of the radial modes was experimentally measured using Laser Doppler Vibrometry and was found to be in very good agreement with those obtained from numerical simulations. Ultrasonic beam profiles from the first four radial modes of the piezoelectric disc were measured using a hydrophone in a water tank. The results obtained from the experimental scans were compared to the predictions from an analytical model and were found to be in very good agreement. Also, the Bessel beams generated from the radial modes (except the first) of the piezoelectric discs were found to have narrow beam width for the central lobe compared to those from an ideal piston source of same size. The proposed approach of using radial modes for Bessel beam generation finds applications in imaging, acoustic particle manipulation and trapping, and acousto-optics.

Generation of optical Bessel beams with arbitrarily curved trajectories using a magnetic-liquid deformable mirror

We propose a new strategy to curve the trajectory of the central lobe of a zero-order Bessel beam and a first-order Bessel beam along their propagation axis. Our method involves modifying the phase of a beam that is incident on an adaptive mirror. As examples, we show that the most intense lobe of the beam can follow a parabolic trajectory, a cubic trajectory, or a trajectory made by a combination of these orders. By using a phase correction emulating the effect of cylindrical mirrors, the central lobe always preserves its symmetry. Theoretical simulations were reproduced in the laboratory using a magnetic-liquid deformable mirror. The parabolic trajectory of the 60-μm central spot of a zero-order Bessel beam exhibits a 0.6-mm off-axis shift after 30-cm-length propagation.

Scattering of an arbitrary order acoustical Bessel beam by a rigid off-axis spheroid

In this study, the authors use the partial-wave series expansion method in the spherical coordinate system and provide a theoretical formula for the off-axis acoustical scattering by rigid prolate and oblate spheroids illuminated by an arbitrary-order Bessel beam to explore the physical characteristics of the off-axis far-field scattering (the axis of the Bessel beam is parallel to the axis of the spheroids). The proposed method is verified and several three-dimensional far-field directivity patterns of rigid spheroids illuminated by zeroth- and first-order Bessel beams are depicted to explore the off-axis scattering. A special emphasis is placed on the geometry size of the prolate and oblate spheroids, the half-cone angle of the Bessel beam, the order of the Bessel beam, and the offset position. Compared with the on-axis scattering, the derivation and calculation of the off-axis scattering takes into account the spherical harmonic function using a numerical integral procedure. In addition, no symmetry was observed in the patterns of the far-field acoustic scattering form function for the zeroth- and higher-order Bessel beams with the off-axis illumination. This investigation provides a tool for the exploration of the complex scattering problems of underwater non-spherical particles under the illumination of the Bessel beam.

Bessel-beam illumination in dual-axis confocal microscopy mitigates resolution degradation caused by refractive heterogeneities

One of the main challenges for laser-scanning microscopy of biological tissues with refractive heterogeneities is the degradation in spatial resolution that occurs as a result of beam steering and distortion. This challenge is particularly significant for dual-axis confocal (DAC) microscopy, which achieves improved spatial-filtering and optical-sectioning performance over traditional confocal microscopy through off-axis illumination and collection of light with low-numerical aperture (NA) beams that must intersect precisely at their foci within tissues. DAC microscope image quality is sensitive to positional changes and distortions of these illumination- and collection-beam foci. Previous studies have shown that Bessel beams display improved positional stability and beam quality than Gaussian beams when propagating through tissues with refractive heterogeneities, which suggests that Bessel-beam illumination may enhance DAC microscopy of such tissues. Here, we utilize both Gaussian and Bessel illumination in a point-scanned DAC microscope and quantify the resultant degradation in resolution when imaging within heterogeneous optical phantoms and fresh tissues. Results indicate that DAC microscopy with Bessel illumination exhibits reduced resolution degradation from microscopic tissue heterogeneities compared to DAC microscopy with conventional Gaussian illumination.

Fractional laser photothermolysis using Bessel beams

Fractional photothermolysis uses lasers to generate a pattern of microscopic columnar thermal lesions within the skin stimulating collagen remodeling. In this paper we investigate the use of Bessel beams as an alternative to conventional Gaussian beams in creating laser photothermal lesions of different aspect ratios in skin. We show for the first time the improved photothermal lesion depth-to-diameter aspect ratio using Bessel beams in ex vivo human skin as well as in numerical simulations using electric field Monte Carlo photon transport, finite difference methods and Arrhenius model. Bessel beams allow the creation of deep and narrow thermal lesions necessary for improved efficacy in fractional photothermolysis.

Enhancement of image quality and imaging depth with Airy light-sheet microscopy in cleared and non-cleared neural tissue

We have investigated the effect of Airy illumination on the image quality and depth penetration of digitally scanned light-sheet microscopy in turbid neural tissue. We used Fourier analysis of images acquired using Gaussian and Airy light-sheets to assess their respective image quality versus penetration into the tissue. We observed a three-fold average improvement in image quality at 50 μm depth with the Airy light-sheet. We also used optical clearing to tune the scattering properties of the tissue and found that the improvement when using an Airy light-sheet is greater in the presence of stronger sample-induced aberrations. Finally, we used homogeneous resolution probes in these tissues to quantify absolute depth penetration in cleared samples with each beam type. The Airy light-sheet method extended depth penetration by 30% compared to a Gaussian light-sheet.

Recent advances in imaging subcellular processes

Cell biology came about with the ability to first visualize cells. As microscopy techniques advanced, the early microscopists became the first cell biologists to observe the inner workings and subcellular structures that control life. This ability to see organelles within a cell provided scientists with the first understanding of how cells function. The visualization of the dynamic architecture of subcellular structures now often drives questions as researchers seek to understand the intricacies of the cell. With the advent of fluorescent labeling techniques, better and new optical techniques, and more sensitive and faster cameras, a whole array of questions can now be asked. There has been an explosion of new light microscopic techniques, and the race is on to build better and more powerful imaging systems so that we can further our understanding of the spatial and temporal mechanisms controlling molecular cell biology.

Mode-Division-Multiplexing of Multiple Bessel-Gaussian Beams Carrying Orbital-Angular-Momentum for Obstruction-Tolerant Free-Space Optical and Millimetre-Wave Communication Links

We experimentally investigate the potential of using 'self-healing' Bessel-Gaussian beams carrying orbital-angular-momentum to overcome limitations in obstructed free-space optical and 28-GHz millimetre-wave communication links. We multiplex and transmit two beams (l = +1 and +3) over 1.4 metres in both the optical and millimetre-wave domains. Each optical beam carried 50-Gbaud quadrature-phase-shift-keyed data, and each millimetre-wave beam carried 1-Gbaud 16-quadrature-amplitude-modulated data. In both types of links, opaque disks of different sizes are used to obstruct the beams at different transverse positions. We observe self-healing after the obstructions, and assess crosstalk and power penalty when data is transmitted. Moreover, we show that Bessel-Gaussian orbital-angular-momentum beams are more tolerant to obstructions than non-Bessel orbital-angular-momentum beams. For example, when obstructions that are 1 and 0.44 the size of the l = +1 beam, are placed at beam centre, optical and millimetre-wave Bessel-Gaussian beams show ~6 dB and ~8 dB reduction in crosstalk, respectively.

Characterizing the beam steering and distortion of Gaussian and Bessel beams focused in tissues with microscopic heterogeneities

Bessel beams have recently been investigated as a means of improving deep-tissue microscopy in highly scattering and heterogeneous media. It has been suggested that the long depth-of-field and self-reconstructing property of a Bessel beam enables an increased penetration depth of the focused beam in tissues compared to a conventional Gaussian beam. However, a study is needed to better quantify the magnitude of the beam steering as well as the distortion of focused Gaussian and Bessel beams in tissues with microscopic heterogeneities. Here, we have developed an imaging method and quantitative metrics to evaluate the motion and distortion of low-numerical-aperture (NA) Gaussian and Bessel beams focused in water, heterogeneous phantoms, and fresh mouse esophagus tissues. Our results indicate that low-NA Bessel beams exhibit reduced beam-steering artifacts and distortions compared to Gaussian beams, and are therefore potentially useful for microscopy applications in which pointing accuracy and beam quality are critical, such as dual-axis confocal (DAC) microscopy.

Gaussian beam in two-photon fluorescence imaging of rat brain microvessel

The critical optical properties of a Gaussian laser beam in two-photon or multiphoton fluorescence imaging, including the beam spot size, depth of focus, and intensity profile, are investigated for spatially locating nanoscale solutes in and surrounding the microvessels of rat brain.

Propagation of Bessel beams generated using finite-width Durnin ring

We have studied the increase of the power contained in Bessel beams generated using the Durnin ring technique, which is compatible with microelectromechanical systems technology. Increasing the ring width to increase the output power will lead to deviation from the Bessel beam profile and its diffraction properties. In this work, the effect of the ring width on the generated beam is investigated. An analytical expression for the generated beam depth of focus (DOF) is obtained. A Fourier optics model is also developed to estimate the transverse field profile. The theoretical predictions are assisted by numerical simulations and experimental measurements. The developed models allow engineering the beam diffraction properties to make the necessary compromise between the DOF and the amount of energy carried by the beam depending on the targeted application.

Controlling plasmonic hot spots by interfering Airy beams

We predict and demonstrate the generation of a plasmonic hot spot on the surface of a metal film by the interference of two Airy surface plasmons. We show that the position of the hot spot can be controlled by the distance between the excitation gratings as well as by the phase front of the initial excitation. The observed effect constitutes a planar analogy to Airy beam autofocusing and offers new opportunities for spatially resolved surface plasmon sensing and optical surface tweezers.

Generation of J0-Bessel-Gauss beam by a heterogeneous refractive index map

In this paper, we present the theoretical studies of a refractive index map to implement a Gauss to a J(0)-Bessel-Gauss convertor. We theoretically demonstrate the viability of a device that could be fabricated on a Si/Si(1-y)O(y)/Si(1-x-y)Ge(x)C(y) platform or by photo-refractive media. The proposed device is 200 μm in length and 25 μm in width, and its refractive index varies in controllable steps across the light propagation and transversal directions. The computed conversion efficiency and loss are 90%, and -0.457 dB, respectively. The theoretical results, obtained from the beam conversion efficiency, self-regeneration, and propagation through an opaque obstruction, demonstrate that a two-dimensional (2D) graded index map of the refractive index can be used to transform a Gauss beam into a J(0)-Bessel-Gauss beam. To the best of our knowledge, this is the first demonstration of such beam transformation by means of a 2D index-mapping that is fully integrable in silicon photonics based planar lightwave circuits (PLCs). The concept device is significant for the eventual development of a new array of technologies, such as micro optical tweezers, optical traps, beam reshaping and nonlinear beam diode lasers.

Bessel-like beam generation by superposing multiple Airy beams

We propose a way of generating Bessel-like non-diffracting beams based on the superposition of multiple Airy beams. We also demonstrate, through numerical simulations of the propagation dynamics of the Bessel-like beams, that these Bessel-like beams can be modified to show the feature of vortex power flow by controlling the initial positions of each single Airy beam.

Rapid three-dimensional isotropic imaging of living cells using Bessel beam plane illumination

A key challenge when imaging living cells is how to noninvasively extract the most spatiotemporal information possible. Unlike popular wide-field and confocal methods, plane-illumination microscopy limits excitation to the information-rich vicinity of the focal plane, providing effective optical sectioning and high speed while minimizing out-of-focus background and premature photobleaching. Here we used scanned Bessel beams in conjunction with structured illumination and/or two-photon excitation to create thinner light sheets (<0.5 μm) better suited to three-dimensional (3D) subcellular imaging. As demonstrated by imaging the dynamics of mitochondria, filopodia, membrane ruffles, intracellular vesicles and mitotic chromosomes in live cells, the microscope currently offers 3D isotropic resolution down to ∼0.3 μm, speeds up to nearly 200 image planes per second and the ability to noninvasively acquire hundreds of 3D data volumes from single living cells encompassing tens of thousands of image frames.

All-silica fiber Bessel-like beam generator and its applications in longitudinal optical trapping and transport of multiple dielectric particles

A Bessel-like beam was generated in a novel all-fiber integrated structure. A concentric ring intensity pattern was achieved by the multimode interference along the coreless silica fiber, which was then focused by the integrated micro-lens to result in a Bessel-like beam. The average beam diameter of 7.5 μm maintained over 500 μm axial length for a continuous wave Yb-doped fiber laser input oscillating at the wavelength of 1.08 μm. The generated beam was successfully applied to two-dimension optical trapping and longitudinal transport of multiple dielectric particles confirming its unique non-diffracting and self-reconstructing nature. Physical principle of operation, fabrication, and experimental results are discussed.

Apertured paraxial Bessel beams

The paraxial Bessel beam is obtained by applying an approximation in the wavenumbers. The scattering of the beams by a circular aperture in an absorbing screen is investigated. The scattered fields are expressed in terms of the Fresnel integrals by evaluating the Kirchhoff diffraction integral in the paraxial approximation. The results are examined numerically.

Compact all-fiber Bessel beam generator based on hollow optical fiber combined with a hybrid polymer fiber lens

We report a compact all-fiber Bessel beam generator using hollow optical fiber (HOF) and coreless silica fiber based on a self-assembled polymer lens. A nearly diffraction-free Bessel beam pattern was observed with its focused beam diameter of 20 microm maintained over a propagation distance of 550 microm. The generated Bessel beams were experimentally tested under various structural parameters such as the diameters of the HOF and operating wavelengths. A beam propagation method was applied to simulate the proposed device, which shows good agreement with the experimental observations.

Optical analysis of time-averaged multiscale Bessel beams generated by a tunable acoustic gradient index of refraction lens

Current methods for generating Bessel beams are limited to fixed beam sizes or, in the case of conventional adaptive optics, relatively long switching times between beam shapes. We analyze the multiscale Bessel beams created using an alternative rapidly switchable device: a tunable acoustic gradient index (TAG) lens. The shape of the beams and their nondiffracting, self-healing characteristics are studied experimentally and explained theoretically using both geometric and Fourier optics. By adjusting the electrical driving signal, we can tune the ring spacings, the size of the central spot, and the working distance of the lens. The results presented here will enable researchers to employ dynamic Bessel beams generated by TAG lenses.

Quasi-diffraction-free beams

A diffraction-free beam is obtained by the superposing of plane waves whose wave vectors make an angle with the propagation axis. These plane waves are realized with point sources that are distributed uniformly around a circle and an infinitely large aperture lens. After the field passes through the lens it has nondiffracting properties and is described by the zero-order Bessel function. Relaxing these conditions makes the beam diffraction free within only a limited region. The beam generated from such a geometry is referred to as a quasi-diffraction-free beam. The effects of the width of the annular source on the beam spread are discussed and compared with those for a Gaussian beam. Approximate expressions for quasi-diffraction-free beams are also obtained.

High-efficiency production of propagation-invariant spot arrays

Tailoring of the transverse intensity profiles of propagation-invariant optical fields is considered. The design of diffractive elements capable of realizing such fields by Fourier synthesis is discussed. High-efficiency realization of finite-aperture approximations of the constructed fields is demonstrated in a system consisting of two multilevel diffractive elements. The first element is a diffractive toroidal lens, which focuses the incident field into a ring pattern. The second diffractive element, located at the focal plane of the first element, introduces the phase modulation necessary to realize the desired transverse intensity profile behind a separate collimating lens. The influence of the fabrication errors of the diffractive elements on the fidelity of the propagation-invariant spot array is simulated, and system-integration aspects based on substrate-mode planar-integrated optics are considered.

Optical parametric oscillator pumped by a Bessel beam

We demonstrate operation of a KTP optical parametric oscillator (OPO) pumped by a Bessel beam for the first time to our knowledge. It is shown that the output of the OPO has a transverse profile, which is consistent with noncollinear phase-matching relations defined by a conical pump. The central spot and ring related to the pair of signal and idler beams were generated in the OPO. By adjusting the OPO cavity mirrors, we easily selected the lowest-order mode as well as the higher-order transverse modes in the central spot. Bessel beam pumping was shown to be useful, providing tubular beam coupling into OPO cavity modes. The OPO threshold pump energy was ~100 muJ in a 6-ns pulse.

Optical amplification of diffraction-free beams by photorefractive two-wave mixing and its application to laser Doppler velocimetry

The Fraunhofer diffraction pattern of a narrow annular slit is recorded holographically to generate a beam that approximates a diffraction-free Bessel beam. The experimental limitations resulting from the annular-slit parameters such as the opening width and the transmission coefficient are discussed. The reconstructed Bessel beam is amplified by two-wave mixing in a photorefractive crystal. Thus the efficient conversion of a relatively large beam with a constant (or Gaussian) intensity distribution into a nondiffracting beam is achieved entirely by direct physical interference. We show that diffraction-free beams reproduced and amplified in this way can be applied to the measurement of the velocity of small objects by the use of the laser Doppler technique. In addition, the advantages of Bessel beams, especially in measuring the velocity of solids, are discussed.

Holographic formation of a diode laser nondiffracting beam

We report for the first time, to our knowledge, the characteristics of a so-called nondiffracting beam produced by illumination of a binary-phase reflective holographic optical element with light from a diode laser. The Bessel beam has an intensity profile whose pattern changes little over distances of order 1 m and has a 1/e amplitude radius for the central lobe of ∼100 µm. This beam may have application for alignment of integrated optic elements in which unguided diffraction-free beams are used to align glass-slab elements containing interconnection holograms to a computer board. The aligning Bessel beam would be produced on reflection from a hologram on the glass-substrate interconnecting element. A single hologram may be used for different substrates having different lengths and functionality because of the large depth of field of the Bessel beam.