Axicon Research Articles

Finite Element Method Modelling for Extended Depth of Focus Acoustic Transducer

Abstract Extended depth of focus (DOF) with the high lateral resolution is the primary requirement of the transducer in scanning acoustic microscopy to generate high-resolution images of the 3-dimensional sample over a large depth. Traditionally, focused ultrasonic spherical transducers are used to tightly focus the acoustic waves generated from a piezoelectric material for a wide range of applications in industrial, medical, and other fields. Such transducers have a problem of narrow DOF which restricts the imaging range in depth. In the present work, we propose three different transducer designs such as single axicon, central flat axicon and double axicon, which enable the possibilities of high transverse resolution imaging over greater depths due to the significant increase in DOF. Finite element modeling (FEM) in COMSOL of a spherical, single axicon, central flat axicon, and double axicon transducer is systematically performed and compared in terms of transverse resolution, DOF, and acoustic pressure in the central lobe. In addition, the single axicon and double axicon transducer modeling are done for different apex angles. It is observed that the central flat axicon transducer allows customizable DOF and the double axicon transducer provides high lateral resolution and reduced pressure in the side lobes compared to a single axicon lens.

Spatiotemporal walk-off and improved focusing of plasma THz sources.

High-field THz sources with peak field strengths exceeding MV/cm are essential for nonlinear THz spectroscopy and coherent control of matter on ultrafast time scales. Two-color femtosecond laser plasma sources employing long filamentation have been reported as providing single-cycle, >MV/cm fields, with multi-decade spanning bandwidth and polarization control, making them promising sources for such experiments. In this work, we report the observation of spatiotemporal spreading of the THz pulse when standard off-axis parabolic mirrors are used for collection and focusing of long filament plasma-based THz pulses. This produces a flying focus for THz light, with the axial focal region propagating at a velocity of 1/3 the speed of light. The THz emission is then subsequently spread over a temporal width of ∼10 ps, approximately 100 times the THz pulse duration detected by electro-optic sampling at any single point along the focus. The consequences of this non-ideal focusing are a potential and drastic overestimation of the peak THz electric field based on energy measurements, as well as significant phase noise arising from beam pointing fluctuations. We show that this spatiotemporal spreading can be minimized using a simple axicon lens that perfectly collimates the extended filament source, resulting in improved spatial and temporal focusing of the THz pulse.

3D Printing of Optical Lenses Assisted by Precision Spin Coating

AbstractThough 3D printing shows potential in fabricating complex optical components rapidly, its poor surface quality and dimensional accuracy render it unqualified for industrial optics applications. The layer steps in the building direction and the pixelated steps on each layer's contour result in inevitable microscale defects on the 3D‐printed surface, far away from the nanoscale roughness required for optics. This paper reports a customized vat photopolymerization‐based lens printing process, integrating unfocused image projection and precision spin coating to solve lateral and vertical stair‐stepping defects. A precision aspherical lens with less than 1 nm surface roughness and 1 µm profile accuracy is demonstrated. The 3D‐printed convex lens achieves a maximum MTF resolution of 347.7 lp mm−1. A mathematical model is established to predict and control the spin coating process on 3D‐printed surfaces precisely. Leveraging this low‐cost yet highly robust and repeatable 3D printing process, the precision fabrication of multi‐scale spherical, aspherical, and axicon lenses are showcased with sizes ranging from 3 to 70 mm using high clear photocuring resins. Additionally, molds are also printed to form multi‐scale PDMS‐based lenses.

Nanosecond Laser Fabrication of Dammann Grating-like Structure on Glass for Bessel-Beam Array Generation

The generation of optical beam arrays with prospective uses within the realms of microscopy, photonics, non-linear optics, and material processing often requires Dammann gratings. Here, we report the direct fabrication of one- and two-dimensional Dammann grating-like structures on soda lime glass using a nanosecond pulsed laser beam with a 1064 nm wavelength. Using the fabricated grating, an axicon lens, and an optical magnification system, we propose a scheme of generation of a diverging array of zero-order Bessel beams with a sub-micron-size central core, extending longitudinally over several hundred microns. Two different grating fabrication strategies are also proposed to control the number of Bessel beams in an array. It was demonstrated that Bessel beams of 12 degrees conical half-angle in an array of up to [5 × 5] dimensions can be generated using a suitable combination of Dammann grating, axicon lens and focusing optics.

Rapid Fabrication of Yttrium Aluminum Garnet Microhole Array Based on Femtosecond Bessel Beam

High-aspect-ratio microholes, the fundamental building blocks for microfluidics, optical waveguides, and other devices, find wide applications in aerospace, biomedical, and photonics fields. Yttrium aluminum garnet (YAG) crystals are commonly used in optical devices due to their low stress, hardness, and excellent chemical stability. Therefore, finding efficient fabrication methods to produce high-quality microholes within YAG crystals is crucial. The Bessel beam, characterized by a uniform energy distribution along its axis and an ultra-long depth of focus, is highly suitable for creating high-aspect-ratio structures. In this study, an axicon lens was used to shape the spatial profile of a femtosecond laser into a Bessel beam. Experimental verification showed a significant improvement in the high aspect ratio of the microholes produced in YAG crystals using the femtosecond Bessel beam. This study investigated the effects of the power and defocus parameters of single-pulse Bessel beams on microhole morphology and size, and microhole units with a maximum aspect ratio of more than 384:1 were obtained. Based on these findings, single-pulse femtosecond Bessel processing parameters were optimized, and an array of 181 × 181 microholes in a 400 μm thick YAG crystal was created in approximately 13.5 min. The microhole array had a periodicity of 5 μm and a unit aspect ratio of 315:1, with near-circular top and subface apertures and high repeatability.

Acoustic Bessel-like beam generation using phononic crystals

Diffraction-free beams with large depth-of-field have a lot of potential in the field of acoustics, such as imaging, sensing, and particle manipulation. In this study, an acoustic Bessel-like beam is produced using an axicon-sonic crystal lens. The sonic crystal is created using cylindrical glass rods arranged in a triangular shape with a centered square lattice configuration. The numerical simulation between 4 and 8 kHz indicates that the axicon-sonic crystal converts the plane acoustic wave into a Bessel-like beam. The analysis of the beam indicates that the depth of field of this beam depends on the size and periodicity (lattice parameter) of the sonic crystal. The axicon lens also displays variable focal lengths at different frequencies. A graded index layer was implemented to mitigate the reflection caused by the significant impedance mismatch. Experimental validation of acoustic Bessel-like beam formation is also reported for the working frequencies. At 8 kHz, the measured range to the 50% on-axis intensity was 34λ, while the focus width at the same frequency was measured to be 2λ. The integration of three distinct design strategies—axicon shape, sonic crystal, and graded index—expands the possibilities for sound focusing applications.

Hollow Beam Shaper Based on Axicon Lens Group

Hollow Beam Shaper Based on Axicon Lens Group

Obstacle-tolerant terahertz wireless link using self-healing Bessel beams

Wireless communications using highly directive terahertz (THz) waves exhibit lower immunity to obstructions than microwaves, limiting their applications. This study demonstrates an obstacle-tolerant THz wireless link established by a self-healing Bessel beam at 300 GHz. The Bessel beam is generated by sending a Gaussian beam through a dielectric axicon lens. Furthermore, experiments were conducted to investigate the short-range transmission (98 mm) reception characteristics with and without the dielectric cubic obstacle (7.5 λ in size) and the metallic obstacle (22 λ in length and 8 λ in width) in the Gaussian beam and self-healing Bessel beam cross sections. The maximum attenuation of the received power due to obstruction was 8.8 and 2.2 dB for the Gaussian and Bessel beams, respectively, when the dielectric obstacle is placed in the middle of the transmission path (49 mm from a transmission lens). This study further investigated the bit error rate (BER) characteristics (1 Gbps, on–off keying) with the dielectric obstacle crossing the beam cross section. When the obstacle crosses the Gaussian beam, the BER degrades as the obstacle approaches the optical axis, breaking the wireless link. In contrast, when the obstacle crosses the Bessel beam cross section, the BER is maintained at <3.8 × 10−3 (the forward error correction limit), and the wireless link is maintained. A self-healing beam, such as the Bessel beam, makes the THz wireless link more tolerant than the Gaussian beam to obstacle and expand applications for THz wireless communications.

Real-Time Imaging of Plasmonic Concentric Circular Gratings Fabricated by Lens-Axicon Laser Interference Lithography.

Concentric circular gratings are diffractive optical elements useful for polarization-independent applications in photonics and plasmonics. They are usually fabricated using a low-throughput and expensive electron beam lithography technique. In this paper, concentric circular gratings with selectable pitch values were successfully manufactured on thin films of azobenzene molecular glass using a novel laser interference lithography technique utilizing Bessel beams generated by a combined lens-axicon configuration. This innovative approach offers enhanced scalability and a simplified manufacturing process on larger surface areas compared to the previously reported techniques. Furthermore, the plasmonic characteristics of these concentric circular gratings were investigated using conventional spectrometric techniques after transferring the nanostructured patterns from azobenzene to transparent gold/epoxy thin films. In addition, the real-time imaging of surface plasmon resonance colors transmitted from the concentric circular gratings was obtained using a 45-megapixel digital camera. The results demonstrated a strong correlation between the real-time photographic technique and the spectroscopy measurements, validating the efficacy and accuracy of this approach for the colorimetric studying of surface plasmon resonance responses in thin film photonics.

Fiber laser cutting of steel plate by twin spot beam setting in scanning direction

This study investigated the effects of laser beam intensity distribution on the reduction of dross height in fiber laser cutting of a steel plate with 3.2 mm thickness. A twin-spot beam was produced by splitting a single Gaussian beam into two beams using a special axicon lens, and these beams were set in the scanning direction for cutting experiments. The power ratio of two beams (R:F = Rear power:Front power) was varied to discuss the intensity balance for the effective reduction of dross. After cutting experiments, ray tracing analysis was conducted using an optical analysis to calculate the absorbed power density distributions in the kerf. A smaller dross height of 18 μm can be achieved at a power ratio of R:F = 8:2, and its value is lower than that by a single Gaussian beam. At a power ratio of R:F = 8:2, the front beam of lower power is irradiated at the upper part of the workpiece, and the rear beam of higher power is absorbed at the lower part of the workpiece. Thus, effective heat input to the lower part of the workpiece can contribute to a reduction of the dross height. Variation of power ratio in the rear and the front beams is effective in controlling the cutting front shape, and the uniformity of absorbed power in the thickness direction can be improved by setting the rear beam of about four times higher power to the front beam of lower power to obtain a smaller dross height in the case of a 3.2 mm steel plate.

Fabrication of a multilevel Fresnel axicon deep in fused silica by femtosecond laser machining.

This manuscript presents a simple approach to the manufacturing and optimization of a multilevel phase-only diffractive conical lens (Fresnel axicon or "fraxicon"). The method for recording deep type I modifications in fused silica was established and its ability proven. We showed the prospects and limitations of elements processed using this method. The fine and advanced parameters optimization allowed us to get a compensation mechanism for almost uniform refractive index change for each separate layer. The maximum diffraction efficiency of the fraxicon for a wavelength of 515 nm was ∼80%. The measured Bessel beam depth of field was compared with commercially available conical lens axicons and showed good agreement.

Non-Paraxial Effects in the Laser Beams Sharply Focused to Skin Revealed by Unidirectional Helmholtz Equation Approximation

Laser beams converging at significant focusing angles have diverse applications, including quartz-enhanced photoacoustic spectroscopy, high spatial resolution imaging, and profilometry. Due to the limited applicability of the paraxial approximation, which is valid solely for smooth focusing scenarios, numerical modeling becomes necessary to achieve optimal parameter optimization for imaging diagnostic systems that utilize converged laser beams. We introduce a novel methodology for the modeling of laser beams sharply focused on the turbid tissue-like scattering medium by employing the unidirectional Helmholtz equation approximation. The suggested modeling approach takes into account the intricate structure of biological tissues, showcasing its ability to effectively simulate a wide variety of random multi-layered media resembling tissue. By applying this methodology to the Gaussian-shaped laser beam with a parabolic wavefront, the prediction reveals the presence of two hotspots near the focus area. The close-to-maximal intensity hotspot area has a longitudinal size of about 3–5 μm and a transversal size of about 1–2 μm. These values are suitable for estimating spatial resolution in tissue imaging when employing sharply focused laser beams. The simulation also predicts a close-to-maximal intensity hotspot area with approximately 1 μm transversal and longitudinal sizes located just behind the focus distance for Bessel-shaped laser beams with a parabolic wavefront. The results of the simulation suggest that optical imaging methods utilizing laser beams with a wavefront produced by an axicon lens would exhibit a limited spatial resolution. The wavelength employed in the modeling studies to evaluate the sizes of the focus spot is selected within a range typical for optical coherence tomography, offering insights into the limitation of spatial resolution. The key advantage of the unidirectional Helmholtz equation approximation approach over the paraxial approximation lies in its capability to simulate the propagation of a laser beam with a non-parabolic wavefront.

Geometric-phase-based axicon lens for computational achromatic imaging.

Conventional optical imaging systems usually utilize several lenses within a precise assembly to eliminate chromatic aberration, which increases the difficulty of system integration. In recent years, with the rapid development of metasurfaces and liquid crystals (LCs), planar optical elements provide feasible solutions to realize flexible light manipulation and lightweight systems. However, there also exists chromatic aberration, which can be corrected but at the cost of a complex device design. Here, a geometric-phase-based axicon lens is utilized to correct chromatic aberration across a broadband wavelength with the assistance of a post-process algorithm. The axicon lens is fabricated through arranging orientations of liquid-crystal molecules with a standard photoalignment technique, and it produces an approximately invariant point spread function (PSF) at several discrete wavelengths, which is used as the prior information to extract the object in the blurred image. In the experiment, the reconstruction quality is significantly improved after the post-process algorithm. We expect our work to provide further development to reduce the dispersion with both the device design and the computational image technique.

Millimetric scale two-photon Bessel-Gauss beam light sheet microscopy with three-axis isotropic resolution using an axicon lens.

Typical light sheet microscopes suffer from artifacts related to the geometry of the light sheet. One main inconvenience is the non-uniform thickness of the light sheet obtained with a Gaussian laser beam. We developed a two-photon light sheet microscope that takes advantage of a thin and long Bessel-Gauss beam illumination to increase the sheet extent without compromising the resolution. We use an axicon lens placed directly at the output of an amplified femtosecond laser to produce a long Bessel-Gauss beam on the sample. We studied the dopaminergic system and its projections in a whole cleared mouse brain. Our light sheet microscope allows an isotropic resolution of in all three axes of the scanned volume while keeping a millimetric-sized field of view, and a fast acquisition rate of up to . With slight modifications to the optical setup, the sheet extent can be increased to 6mm. The proposed system's sheet extent and resolution surpass currently available systems, enabling the fast imaging of large specimens.

Printing Double-Network Tough Hydrogels Using Temperature-Controlled Projection Stereolithography (TOPS).

We report a new method to shape double-network (DN) hydrogels into customized 3D structures that exhibit superior mechanical properties in both tension and compression. A one-pot prepolymer formulation containing photo-cross-linkable acrylamide and thermoreversible sol-gel κ-carrageenan with a suitable cross-linker and photoinitiators/absorbers is optimized. A new TOPS system is utilized to photopolymerize the primary acrylamide network into a 3D structure above the sol-gel transition of κ-carrageenan (80 °C), while cooling down generates the secondary physical κ-carrageenan network to realize tough DN hydrogel structures. 3D structures, printed with high lateral (37 μm) and vertical (180 μm) resolutions and superior 3D design freedoms (internal voids), exhibit ultimate stress and strain of 200 kPa and 2400%, respectively, under tension and simultaneously exhibit a high compression stress of 15 MPa with a strain of 95%, both with high recovery rates. The roles of swelling, necking, self-healing, cyclic loading, dehydration, and rehydration on the mechanical properties of printed structures are also investigated. To demonstrate the potential of this technology to make mechanically reconfigurable flexible devices, we print an axicon lens and show that a Bessel beam can be dynamically tuned via user-defined tensile stretching of the device. This technique can be broadly applied to other hydrogels to make novel smart multifunctional devices for a range of applications.

Generation of a vortex point adjustable vortex array based on decentered annular beam pumping.

An adjustable optical vortex array (OVA) based on decentered annular beam pumping has been demonstrated in an end-pumped Nd:YVO4 laser. This method allows for not only the transverse mode locking of different modes, but also the ability to adjust the mode weight and phase by manipulating the position of the focusing lens and axicon lens. To explain this phenomenon, we propose a threshold model for each mode. Using this approach, we were able to generate optical vortex arrays with 2-7 phase singularities, achieving a maximum conversion efficiency of 25.8%. Our work represents an innovative advancement in the development of solid-state lasers capable of generating adjustable vortex points.

Extraction and manipulation of hydrocarbon droplets by ultrasound radiation

Acoustic tweezers are a method of using sound radiation forces to trap and manipulate objects. Previously, we demonstrated an acoustic tweezer capable of first creating the objects, droplets of CCl4 from a reservoir, before trapping and manipulating them. We achieved this using a single transducer whose field was modified by a low-profile fraxicon (Fresnel axicon) lens exhibiting specific near-field trapping zones and far-field Bessel beam behavior which enable the trapping process. Here, we extend the method to include another class of fluids, complex hydrocarbons, using conventional SAE30 motor oil in water. Furthermore, with the higher power levels used in this study we demonstrate the discovery of a second trapping region in the field generated by our transducer. The non-contact extraction and manipulation of organic and hydrocarbon fluid samples could have significant biological and environmental applications where a container would contaminate, destroy, or otherwise change the samples under investigation.

Axicon lenses with chiral-focusing properties modeling by means of analytical functions

Axicon lenses exhibit a large focal depth that generates an energy distribution, resulting in non-diffracting beams’ generation. These light structures are called Bessel beams and show numerous important applications in optical signal processing, imaging, transparent material processing, and even in metal drilling/cutting manufacturers. Asymmetrical and twisted axicon-lenses are boundary conditions on the Maxwell equation able to generate complex-structured light fields with specially designed intensity, phase, and polarization distributions. This paper presents a set of analytical functions that allows the definition of such surfaces with absolute freedom in relation to the lens profile. Obviously, before manufacturing any lens, it is necessary to compute its electromagnetic output in order to save resources. In this sense, we have studied some of these lenses by simulation using the well-known finite difference method in the time domain. Some necessary verification related to conservative magnitudes, such as the Poynting vector, have been done analytically and numerically. The numerical results show the distribution of iso-values corresponding to the electric field and 3D-vectorial representation of the chirality flux and the Poynting vector. Finally, by means of discrete fast Fourier transform, it is shown the field distributions as well as the power before and after the lens per frequency.

Hierarchical concentric surface patterns and metasurfaces on azobenzene molecular glass films using axicon interference lithography

Bessel laser beams generated by an axicon lens were used for the fabrication of hierarchical concentric surface patterns onto azobenzene molecular glass thin films. The resulting structures were characterized in details by atomic force and scanning electron microscopy, as well as surface profilometry, as the fabrication parameters were modified during the laser inscription process. It was found that the hierarchical concentric surface patterns on the azobenzene film reached overall heights that are surprisingly 5 times larger than the original film thickness. The presented axicon interference lithography technique was also used to fabricate novel metasurfaces on azobenzene thin films.

A Leaky-Wave Analysis of Resonant Bessel-Beam Launchers: Design Criteria, Practical Examples, and Potential Applicationsat Microwave and Millimeter-Wave Frequencies.

Resonant Bessel-beam launchers are low-cost, planar, miniaturized devices capable of focusing electromagnetic radiation in a very efficient way in various frequency ranges, with recent increasing interest for microwave and millimeter-wave applications (i.e., 3-300 GHz). In recent years, various kinds of launchers have appeared, with different feeding mechanisms (e.g., coaxial probes, resonant slots, or loop antennas), field polarization (radial, azimuthal, and longitudinal), and manufacturing technology (axicon lenses, radial waveguides, or diffraction gratings). In this paper, we review the various features of these launchers both from a general electromagnetic background and a more specific leaky-wave interpretation. The latter allows for deriving a useful set of design rules that we here show to be applicable to any type of launcher, regardless its specific realization. Practical examples are discussed, showing a typical application of the proposed design workflow, along with a possible use of the launchers in a modern context, such as that of wireless power transfer at 90 GHz.