Conical Lens Research Articles

Perfect vortex beams generation based on reflective geometric phase metasurfaces

Perfect vortex beam (PVB) is a propagating light field with radial intensity distribution independent of topological charge and carrying orbital angular momentum (OAM). PVBs can be generated through the Fourier transformation of a Bessel-Gaussian (BG) beam, which traditionally requires a precisely aligned optical setup consisting of a spiral phase plate, a conical lens, and a Fourier lens. However, such traditional schemes are usually bulky and unstable. Here, we have utilized a method that differs from conventional approaches, employing metasurfaces designed as planar Pancharatnam-Berry (PB) phase elements to substitute for all the required components. Unlike traditional methods based on reflective or refractive elements, metasurface elements can significantly reduce the system's footprint. Because the use of metallic metasurfaces allows for a more flattened design plane, in this paper, we have demonstrated the generation of PVB within the 8 GHz microwave frequency band based on a single-layer metallic metasurface. The metasurface is composed of a square ring metal structure, which can serve as a half wave plate to provide the required geometric phase distribution for incident circularly polarized light to generate PVB. By rigorously optimizing the parameters of the square-ring structures, we have generated vortex beams carrying OAM with different topological charges. These vortex beams exhibit a constant radial intensity distribution, which validates their "perfect" characteristics. In addition, we also extracted the mode purity of different vortex beams, so that the mode states of different vortex beams can be distinguished. These results provide broader value for the application of perfect vortex beams in communication.

Kinematic Features of Abrasive Processing of Lateral Surface of Flat-Convex Conical Lenses Using Free Rubbing Method

Kinematic Features of Abrasive Processing of Lateral Surface of Flat-Convex Conical Lenses Using Free Rubbing Method

Design of a dual hollow beam optical antenna based on a Fresnel lens-conical lens combination

To improve the transmission efficiency of Cassegrain antennas and enable the simultaneous transmission of signals with different wavelengths in the antenna system, this study introduces Fresnel lenses and conical lenses in front of the Cassegrain antenna at the transmitting end. Reflective mirrors and focusing lenses are introduced at the receiving end. A detailed description is provided of the design process for the Fresnel lens, as well as the impact of various parameters on the hollow radius when combined with the conical lens. Based on the laws of vector reflection and refraction, simulations are performed to track the propagation of light through the entire communication system and lens pairs, providing transmission efficiency plots of the antenna system under deflection and off-axis conditions. Taking into account practical factors such as lens chamfer, transmittance, Cassegrain antenna reflectance, and material dispersion, the transmission efficiency of the antenna system at 1550 nm wavelength can still reach 93.45%. The proposed method not only improves the transmission efficiency of Cassegrain antennas, but also enables the transmission of different information through the inner and outer layers of the antenna system.

Levitation of air-borne strong-absorbing nanoparticle clusters dominated by photophorestic force and migration behavior under thermophorestic force

In order to explore the levitation and migration behavior of strongly absorbing nanoparticle clusters in air by using laser technique, in this study trapping and levitating nanoparticle clusters is proposed based on the counter-propagated bi-Bessel beams, and then the clusters are released to observe and analyze their migration behaviors. Two Bessel beams are generated by a conical lens and polarizing beam splitter, arranged horizontally in reverse to form a three-dimensional optical trap. The stiffness of the optical trap can be controlled by adjusting the power ratio of the two Bessel beams. The particles in the levitation chamber are fluidized through weak airflow, and then captured and levitated by a light trap. A high-speed camera is used to record the levitation and migration process of clusters. The particle motion parameters can be obtained through image analysis. The strong-absorbing ultrafine coal particle clusters are first selected to conduct the experiments on their levitation and release migration. Then, the photophorestic force, gravity, buoyancy, drag force, and thermophorestic force acting on the clusters are calculated and analyzed. The experimental and computational results indicate that the photophorestic force of air-borne strong-absorbing nanoparticle clusters generated by laser illumination dominates the levitation; nanoparticle clusters can be stably levitated in a three-dimensional potential well formed by counter-propagated bi-Bessel beams, achieving dynamic equilibrium with gravity, buoyancy, drag, etc. by adjusting the levitation position. The relative instability parameter of levitation is used to evaluate the stability of air-borne strong-absorbing nanoparticle clusters, and the minimum relative instability of ultrafine coal particle clusters reaches 0.075. By analyzing the images of nanoparticle cluster recorded by high-speed camera after being released, the migration motion parameters of the cluster can be obtained, therefore the thermophorestic force acting on the cluster is accurately measured. For the ultrafine coal particle clusters with equivalent particle sizes in a range of approximately 13–21 μm, the magnitudes of their thermophorestic forces are in a range of 10<sup>–11</sup>–10<sup>–10</sup> N. As the cluster size increases, the thermophorestic force increases linearly, which is consistent with the theoretical calculation trend. The use of laser to levitate and release particles provides a novel approach for measuring and analyzing thermophorestic force, and also presents a novel manipulation tool for controlling and transporting particles in a gaseous medium.

Design and optimization of a conical electrostatic objective lens of a low-voltage scanning electron microscope for surface imaging and analysis in ultra-high-vacuum environment

Low-voltage scanning electron microscopy (LV-SEM) with landing energies below 5 keV has been widely used due to its advantages in mitigating the damage and charging effects to a specimen and enhancing surface information due to small interaction volume of electrons inside a specimen. Additionally, for elemental analysis of the surfaces of bulk specimens with Auger electron spectroscopy (AES) or electron energy loss spectroscopy (EELS), ultra-high-vacuum (UHV) environment is essential to maintain clean surfaces without the absorption of gas molecules during the electron beam irradiation for the acquisition of spectral data. In this study, we propose the optimal design and condition of a conical Electrostatic Objective Lens (EOL) for a UHV LV-SEM to achieve the high spatial resolution and secondary electron (SE) detection efficiency. The EOL is composed of only the three electrodes (retarding, focusing and booster electrodes) and the insulators, which is suitable for maintaining a UHV environment with less out-gassing. The cone angle of the EOL is determined as 60° to integrate a spectrometer in the UHV LV-SEM and in a large size and a higher tilt angle of the sample. Through the optimization with the simulations, the EOL achieves the minimized spherical and chromatic aberration coefficients of 0.05 and 0.03 mm at the sample side, respectively, at the landing energy of 50 eV and the shortest working distance (WD) of 1 mm for high-resolution imaging. In addition, the probe diameter of the optimized EOL is 2.3 nm at 1 keV and 5.7 nm at 50 eV with a WD of 1 mm and a probe current of 10 pA, which are comparable to previously studied compound objective lenses with magnetic and electrostatic lenses. Using a longer WD of 4 mm for analysis, the probe diameter was 5.4 nm at 1 keV and the SE detection efficiency was 83.3 % owing to the separated scintillator detector structure from the booster electrode.These results imply that the optimized EOL has the potential to be applied to a high-performance UHV LV-SEM for the surface imaging and analysis with a simple system configuration.

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.

Dielectrophoretic liquid lens driven by interdigitated sidewall electrodes.

This paper proposes a dielectrophoretic (DEP) liquid lens that is driven by interdigitated electrodes distributed on the sidewalls and has a structure similar to that of the electrowetting one produced by the company Corning. The interdigital electrodes are formed by winding double flexible wire electrodes wrapped in dielectric layers on the sidewall. Compared with the traditional planar electrode DEP lens, the proposed model ensures the stability of the optical axis of the liquid lens, simplifies the construction process of the interdigital electrode, realizes a continuous change in the focus from negative to positive, and reduces the response time. A truncated conical cavity dielectrophoretic liquid lens with an aperture of 5 mm is fabricated. When the voltage is 0-260 Vrms, it can reach shortest negative and positive focal lengths of -100 mm and 100 mm with a driving time of 190 ms and a relaxation time of 133 ms.

Tabletop 360-Degree Three-Dimensional Light-Field Display Based on Viewpoint-Fitting Encoding Algorithm for Reducing Facet Braiding.

Since the effect of the facet braiding phenomenon, the display quality of reconstructed image degrades with increasing depth of field in tabletop three-dimensional light-field display. Here, to analysis the facet braiding, the imaging process of the tabletop 360-degree three-dimensional light-field display based on conical lens array is mathematically modeled. A viewpoint-fitting encoding algorithm is proposed to reduce the effect of the facet-braiding phenomenon and improve the range of depth of field, which is optimized to form the best synthetic encoded image by fitting the reconstructed image seen by the simulated human eye to the parallax image captured at the corresponding location. The effectiveness of the proposed optimization algorithm is verified by simulation analysis and optical experiments, respectively. In the experiment, the clear depth of field range of the display system is increased from 13 cm to 15 cm, and the visualization effect of the reconstructed three-dimensional image is enhanced.

Highly Efficient Four-Rod Pumping Approach for the Most Stable Solar Laser Emission.

We report a significant numerical improvement in multi-rod laser efficiency, with an enhanced solar tracking error compensation capacity for a heliostat-parabolic system. The solar laser head was composed of a fused silica conical lens and a single conical pump cavity ensuring multiple passes through four 4.55 mm diameter, 15 mm length Nd:YAG rods. 0.76° tracking error width at 10% laser power loss, and total multimode laser power variation of 0.05% at ±0.1° solar tracking error and 0.30% at ±0.2° solar tracking error were numerically calculated, being 1.27, 74.80 and 21.63 times, respectively, more than the experimental record in solar tracking error compensation capacity attained with a dual-rod side-pumping horizontal prototype pumped by the same heliostat-parabolic system. Additionally, the end-side-pumping configuration of the four-rod solar laser-enabled 43.7 W total multimode solar laser power, leading to 24.7 W/m2 collection efficiency and 2.6% solar-to-laser power conversion efficiency, being 1.75 and 1.44 times, respectively, more than that experimentally obtained from the dual-rod side-pumping prototype. The significant improvement in solar tracking error compensation capacity with a highly efficient end-side-pumping configuration is meaningful because it reduces the cost of high-precision trackers for solar laser applications.

Design of ultra-compact augmented reality display based on grating waveguide with curved variable-period grating

Compact augmented reality (AR) display devices are necessary for the prevalence of AR technology. However, AR devices now usually have bulky size, which is not convenient for daily use. For waveguide AR system, the collimating optical system determines the thickness of the whole system. To address this challenge, we propose a grating waveguide system with curved grating. The function of both collimating lens and in-coupling grating is replaced by a variable-period curved grating, which can reduce the thickness of optical system significantly. We add a conical lens to correct the aberration without significant change of thickness. In our design, the thickness can be reduced by 39.3% compared with conventional grating waveguide system. The structure of grating is designed and optimized, and the average efficiency is over 70%. The stray light is analyzed and will not be seen by human eyes. The diagonal field of view (FOV) of the system reaches 36.6°.

The All-sky Spectrometer of Hot Cosmic Plasma

The main instruments for analyzing the processes occurring in cosmic plasma are energy and mass analyzers of charged particle beams. The analyzers’ operation is based on the separation of charged particles according to the energies of their motion or their masses in electric or magnetic fields. Currently, the top-hat analyzer is considered the main instrument for obtaining information about the state of cosmic plasma. However, it has a number of disadvantages: a significant time cycle for registering angular dependences in a total solid angle of 4π sr and low accuracy of determining the polar angles, which are associated with the need to rotate the analyzer during measurements. Over the past 20 years, plasma analyzers with a large viewing angle have been developed as an alternative to the top-hat analyzer. The design of the analyzer proposed in this work is capable of measuring plasma characteristics in a solid angle of 2π sr in one act of data registration. The all-sky spectrometer of hot cosmic plasma consists of two stages: the first stage is a conical lens of an original design, which serves to transform an extremely wide entrance flow of particles into a narrow cone-shaped beam; the second hexapole-cylindrical stage plays the role of an energy analyzer of a narrow cone-shaped flow. The paper describes the calculations and modeling of the proposed analyzer on the basis of original numerical and approximate analytical methods for designing systems of electron and ion optics. The main parameters of the device are calculated.

Achieving ultracold Bose–Fermi mixture of 87Rb and 40K with dual dark magnetic-optical-trap

We demonstrate that dual dark magnetic-optical-traps (MOTs) have great importance in the two-species 87Rb and 40K mixture compared with dual bright MOTs. The dark MOT has a little improvement in the trapping of single-species 87Rb or 40K gases compared with bright MOT. For the case of loading two-species 87Rb and 40K simultaneously, the improvement of 40K in the dual dark MOTs is mainly from the reduction of light-assisted collision losses. The dual dark MOTs employ a pair of conical lenses to produce the hollow beam for repump laser with high efficiency. The number and density of 87Rb and 40K atoms after evaporative cooling in the hybrid magnetic trap with dark MOT loading are compared with those in bright MOT. The atoms with large number and high density make it easier to realize the quantum degenerate of Bose–Fermi mixture.

3D Printed Linearly Polarized X-Band Conical Horn Antenna and Lens

A low-cost method to 3D print and metalize circular waveguide components is demonstrated using polylactic acid (PLA) and aluminum adhesive backed tape. A gradient index (GRIN) lens, an externally metalized thin-walled conical horn, and a WR90 rectangular to linearly polarized circular waveguide transition are simulated, fabricated, and measured. The horn and lens were both monolithic prints that were externally metallized to simplify the metallization process. Both the horn and lens have a measured operational bandwidth of 8.2 GHz to 12.4 GHz with an input reflection less than -15 dB and peak gain of 18.7 dBi at mid-band. The walls of the thin-wall horn are printed at a thickness such that the dielectric layer does not impact the performance of the horn while being robust enough to support external metallization. The lensed horn functioned as the support for the aluminum foil while also improving the radiation pattern by improving the E SLL by up to 15 dB compared to the thin-walled horn antenna.

Modeling of formation regularities of conical surfaces

The scheme of processing conical surfaces by grinding them to a flat tool is considered and a technical solution for the implementation of such processing is proposed. Using the created device allows implementing the group method of forming conical parts with a deviation of the generatrix of the cone from straightness of not more than ± 0.00012 mm. A mathematical model of the patterns of removal of stock from a conical part with a flat tool is developed. A formula is obtained for calculating the modulus of the sliding velocity at any point on the processed conical surface, which implements engineering methods for controlling the shaping of conical parts without conducting preliminary labor-intensive experimental studies. An optimization technique for the adjustment parameters of technological equipment was proposed. The most effective axicon processing modes were revealed at the stages of preliminary, medium and fine grinding, as well as at the polishing stage, depending on the technological heredity of the workpiece from the point of view of distribution of the stock to be removed over its surface. It has been established that changes in the eccentricity between the axes of rotation of the tool and the faceplate as well as the amplitudes of the reciprocating rotational movements of the latter practically do not affect both accuracy and processing productivity, therefore, in practice, these parameters can not be optimized, but their average values can be assigned. The operating modes of the basic lever grinding and polishing machine are established, at which the required accuracy of the working surface of the tool is provided, which directly affects the straightness of the generatrix of the cone. Studies of the regularities of the shaping of the side surface of a conical lens in the conditions of free grinding are carried out and the adjustment parameters of technological equipment that affect the quality and productivity of the processing process are determined.

3D Printed Sub-Terahertz All-Dielectric Lens for Arbitrary Manipulation of Quasi-Nondiffractive Orbital Angular Momentum Waves

Terahertz (THz) vortex waves carrying orbital angular momentum (OAM) hold great potential in dealing with the capacity crunch in wireless high-speed communication systems. Nevertheless, it is quite a challenge for the widespread applications of OAM in the THz regime due to the beam divergence and stringent alignment requirement. To address this issue, an all-dielectric lens (ADL) is proposed for the arbitrary manipulation of quasi-nondiffractive THz OAM waves (QTOWs). On the basis of the concept of the optical conical lens and the multivorticity metasurface, the beam number, the topological charge (TC), and the deflection angle as well as the nondiffractive depth of the generated THz OAM waves are controllable. For proof-of-concept, two ADLs are 3D printed to create single and dual deflected QTOWs, respectively. Remarkably, measured by a THz imaging camera, the desired QTOWs with high mode purity are observed in predesigned directions with a nondiffractive depth predefined theoretically. The proposed designs and experiments, for the first time, verified that the QTOWs could be achieved with a nondiffractive range of 55.58λg (λg = wavelength at 140 GHz) and large deflection angles of 30° and 45°.

Liquid crystal lens with tunable conical lens properties

A three-dimensional numerical calculation for analyzing reorientation in liquid crystal (LC) directors and optical phase retardation in an LC lens, which exhibits a tunable conical lens property, is developed. The proposed LC lens design employs a circular electrode, ring electrodes, and a circularly hole-patterned electrode employing a highly-resistive layer in a flat nematic cell. The three-dimensional tilt and azimuthal angle distributions are calculated. Subsequently, the conical phase retardation in the lens region can be estimated. The experimental results obtained for the optical phase profile agree well with the numerically calculated results.

Single-mode optical fibers coupling: Study of the field of view

Single mode Fiber (SMF) is commonly used in long distance applications as in optical communication. Coupling of the laser beam into SMF core to get high coupling efficiency is a challenging task in practice. The aim of our work is to study the impact of the field of view on the coupled light beam, taking into account well designed coupling lens to be sure that the focal spot has matched to the mode of propagation.Here in this article, a conical lens of 1.5 refractive index was used for light coupling process. The used criteria at HeNe laser of 0.5438 nm wavelength showed a degradation in the output signal due to generated distortion as the field of view increased from 0 to 6 degrees.

Wideband High-Gain Double-Sided Dielectric Lens Integrated With a Dual-Bowtie Antenna

A dual-bowtie antenna loaded with a double-sided dielectric lens is presented for wideband and high gain performance. The dielectric lens is a combination of the elliptical and conical frustum lenses formed on two sides (top and bottom) of a rectangular dielectric block, respectively. The conical frustum lens is mounted at the backside of the bowtie radiator to collect the radiated energy toward the elliptical lens. The bowtie antenna is fed by a coplanar strip (CPS) taper connected to a CPS-to-microstrip line (MSL) transition. The proposed lens-integrated antenna is fabricated and measured to have an operating bandwidth of 20.5–40.0 GHz. The antenna offers a peak gain of 15.1 dB. Also, the use of the double-sided dielectric lens helps to reduce the lens size of the equivalent gain by 31%. The overall size of the proposed lens antenna is 940 × 940 × 1008 mil.

Optoelectronic Device for Molecular Orientation of Functional Materials

A new approach to the development of an optoelectronic device for molecular orientation of functional materials is proposed. Results of the development of its main components are presented: a collimator for the light from an LED and a broad band polarizer with a large angular aperture. The problem of the collimation of a strongly diverging beam from an LED is examined. It is shown that the use of a modified conical lens offers promise for solving this problem. A broad-band polarizer with a large angular aperture, which is an important component of the optoelectronic device, is developed and fabricated on the basis of a multilayered structure.

Technological Features in Processing of Conical Lenses

The paper presents the technology of obtaining flat-conical lenses (axicons) by the method of free grinding a work-piece to a flat tool through a layer of abrasive suspension. For this, theoretical and experimental studies of the regularities of stock removal from the base of the cone and its lateral surface have been carried out. The processing modes have been identified that ensure both uniform operation of the flat surface of the part and enhanced removal of the allowance in the edge or central zone of this surface. During the study of the processing of the conical surface, the set-up parameters of the technological equipment have been established, at which there is a minimum deviation of the generatrix of the cone from straightness and maximum productivity of the process. The stages of processing conical lenses are proposed, which allow to assign the optimal sequence of operations in the manufacture of this type of parts from blanks of a cylindrical shape in cases where the ratio of the height of the cone to the diameter of its base H/d £ 0.5. The main stages of processing include: grinding of the bases of cylindrical blanks with maintaining their mutual parallelism with a given accuracy; polishing one of the cylinder bases to achieve the required roughness and deviation from non-flatness; fastening a cylindrical blank to an auxiliary plane-parallel glass plate using molecular cohesion forces; mechanical fastening of a cylindrical work-piece with a collet adapter mandrel for a plane-parallel glass plate; applying the nearest sphere to the second base of the cylindrical blank; drawing a conical surface on the spherical part of a plano-convex lens; grinding and polishing the conical surface to achieve the required roughness and straightness of the cone generatrix. The degree of efficiency of the setup parameters of the machine has been revealed depending on the technological heredity of the work-piece from the point of view of the distribution of the allowance to be removed over the machined surface.