Conical Lens Research Articles

Conical Double-Dielectric Fresnel Zone Lens and Antenna

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A conical double-dielectric phase-reversal Fresnel-zone plate (FZP) lens is introduced. We present the lens design equations as functions of cone opening angle. As an example, the phase-reversal lens has been applied to four millimeter-wave antennas with different lens opening semi-angles: 45<formula formulatype="inline"><tex>$^{\circ}$</tex></formula>, 60<formula formulatype="inline"> <tex>$^{\circ}$</tex></formula>, and 75<formula formulatype="inline"><tex>$^{\circ}$</tex> </formula> (conical lenses) and 90<formula formulatype="inline"><tex>$^{\circ}$</tex> </formula> (plane lens). The radiation characteristics of these antennas have been calculated and contrasted one-to-another, and to those with the same semi-angles and linear dimensions binary (half-open) FZP lens antennas. The double-dielectric FZP conical arrangement can serve as a conical antenna lens and a radome simultaneously. </para>

High-resolution energy analyzer for photoelectron diffraction studies

This paper presents a design of a novel instrument for X-ray photoelectron diffraction and X-ray photoelectron holography measurements—compact electron spectrometer characterized by a high sensitivity as well as a high energy and spatial resolution. The design is based on a combination of axially symmetric 90° sector spherical deflector with second-order spatial focusing preceded by hollow conical deceleration immersion lens. The range of photoelectron energies, accepted by the spectrometer, varies from 0 up to several thousand electron volts, so that the analyzer can be used for studies of both valence and core electron levels. The analyzer can provide (with the radius of the beam path inside the spherical deflector of 50 mm) for the energy resolution of Δ E/ E=10 −4. This resolution can be achieved in angle-resolved experiments with the angular resolution of 0.25° for electrons collected from the extended area on the sample plane up to 4 mm 2 or more and the range of initial polar or azimuthal angles up to 60°. Alternatively, the same resolution can be achieved in the spectromicroscopy mode, with the accepted solid angle of 0.5 sr. In both cases, the acceptance of the analyzer is about an order of magnitude larger than the acceptance of high-resolution energy analyzers conventionally used in such studies.

Axicon lens for coherent matter waves

We have realized a conical matter wave lens. The repulsive potential of a focused laser beam was used to launch a Bose-Einstein condensate into a radially expanding wavepacket whose perfect ring shape was ensured by energy conservation. In spite of significant interactions between atoms, the spatial and velocity widths of the ring along its radial dimension remained extremely narrow, as also confirmed by numerical simulations. Our results open the possibility for cylindrical atom optics without the perturbing effect of mean-field interactions.

Dark optical lattice of ring traps for cold atoms

We propose a new geometry of optical lattice for cold atoms, namely a lattice made of a 1D stack of dark ring traps. It is obtained through the interference pattern of a standard Gaussian beam with a counter-propagating hollow beam obtained using a setup with two conical lenses. The traps of the resulting lattice are characterized by a high confinement and a filling rate much larger than unity, even if loaded with cold atoms from a MOT. We have implemented this system experimentally, and obtained a lattice of ring traps populated with typically 40 atoms per site with a life time of 30 ms. Applications in statistical physics, quantum computing and Bose-Einstein condensate dynamics are conceivable.

Fractal conical lenses

A conical lens is an optical element that produces a continuous focal segment along the optical axis. In this paper we introduce a more general optical device: the fractal conical lens (FCL). As the profile of a FCL is generated using the Cantor function, we show that a classical conical lens is a particular case of these fractal lenses. FCLs are distinguished by the fractal focal segments they produce along the optical axis. The influence of the Fresnel number on the axial irradiance generated by these lenses is investigated.

Conical octopole ion guide: Design, focusing, and its application to the deposition of low energetic clusters

A design of a radio-frequency (rf) octopole ion guide with truncated conical rods arranged in a conical geometry is presented. The performance is tested in a cluster deposition apparatus used for the soft-landing of size-selected clusters on well-characterized substrates used as a model system in heterogeneous catalysis in ultrahigh vacuum. This device allows us to focus 500pA of a mass-selected Ni20+ cluster ion beam from 9mm down to a spot size of 2mm in diameter. The transmittance is 70%±5% at a rf voltage of 420Vpp applied over an amateur radio transceiver with an interposed homemade amplifier-transformer circuit. An increase of the cluster density by a factor of 15 has been achieved. Three ion trajectories are simulated by using SIMION6, which are relevant for this focusing device: transmitted, reflected, and absorbed. The observed effects in the simulations can be successfully explained by the adiabatic approximation. The focusing behavior of the conical octopole lens is demonstrated by experiment and simulations to be a very useful technique for increasing molecule or cluster densities on a substrate and thus reducing deposition time.

Mechanical fabrication of precision microlenses on optical fiber endfaces

We present a purely mechanical means of producing highly concentric spherical lenses at the endfaces of optical fibers. The production process has two stages. First, conical lenses are produced in a grinding process that ensures excellent concentricity. Then, the conical lenses are transformed to spherical lenses using a novel process called loose abrasive blasting. The cone grinding is carried out on a microgrinding machine, which has a sophisticated control system that enables the production of precision conical lenses. The blasting is carried out on a diamond blasting machine. Plots showing automatic centering performance of the microgrinding machine and scanning electron microscopy images of the conical and spherical lenses are presented.

Formation of extended plasma channels in a condensed medium upon axicon focusing of a femtosecond laser pulse

The formation of plasma channels of a femtosecond laser pulse in the bulk of fused silica is studied by numerical simulation, and the advantages of using a conical lens (axicon) over conventional parabolic lenses are shown. It is found that the length of the plasma channel formed with the help of an axicon exceeds the length of the channel formed upon lens focusing.

A New, Highly Sensitive Time-of-Flight Mass Spectrometer Consisting of a Flangeon-type Conical Ion Lens System and a Proto-type Daly Detector for Exhaust Gas Analysis Based on the Jet-REMPI Technique

For the analysis of trace amounts of hazardous organic compounds, we developed a new ion detection system for supersonic jet resonance-enhanced multiphoton laser ionization mass spectrometry. High sensitivity and selectivity have been achieved by combining a proto-type Daly detector, a newly designed conical ion lens, and a potential switch that can perform the function of a mass selector. This ion detection system enables us to bring the jet nozzle closer to the ionization point. The detection sensitivity has thus been improved totally by more than 100 times compared with that obtained by the parallel-plate electrodes and micro-channel plate. We succeeded in assembling a flangeon-type ion extraction electrode consisting of a conical ion lens and a potential switch.

Micro gradient-index conical lenses: simulation and fabrication methods

In this paper, a micro gradient-index conical lens, which has a larger acceptance angle than a conventional microlens, is presented. Methods on how to simulate these lenses in commercial optical design software CodeV are introduced, and the effects of several index profiles and cone shapes are compared in simulation. Results show that a micro gradient-index conical lens has a four times larger acceptance angle compared with a microlens. Additionally, conical lenses with a Gaussian-index profile show a larger acceptance angle than those with a solid refractive index. Fabricated conical lenses show an acceptance angle of more than 27 degrees for a detection threshold of 50%, which agrees with the simulation result.

Focusing characteristics of curvilinear half-open Fresnel zone plate lenses: plane wave illumination

A diffraction field-focusing equation based on a specific conical-segment linearization procedure is derived for the Fresnel zone plate (FZP) lens of arbitrary curved profile and is applied for contrasting plane, spherical, parabolic and conical zone plate lenses, convex-side illuminated by a paraxial plane wave front. Two sets of 100-GHz curvilinear and plane FZP lenses are studied numerically with regards to their dimensions, axial focusing intensity and footprint, and frequency bandwidth. For the first set , where the curvilinear and plane lenses share a common lens base aperture and have equal focal lengths, the following new finding has resulted: regardless of their different in shape profiles the FZP lenses have equal zone numbers and produce similar axial focusing. The second set also consists of plane, spherical, parabolic and conical lenses. They share a common apex, and have equal in diameter base apertures and focal lengths but different thicknesses. For such disposition and proportions, the FZP lenses possess different zone numbers and focusing parameters (gain, efficiency, footprint and bandwidth). The belief that the curvilinear FZP have superior (or inferior) electromagnetic characteristics, compared to those of the plane FZP lens with equal number of zones is not in general true. Their relative focusing qualities can vary significantly depending on the lens positioning and dimensions.

The quasi-optical analysis of Bessel beams in the far infrared

We discuss the Gaussian beam mode analysis of Bessel beams, eigen-solutions of the wave-equation in cylindrical polar coordinates which neither change form nor spread out as they propagate. Approximate, limited diffraction finite aperture, pseudo-Bessel beams having intense on-axis spots with large depths of field can be produced experimentally in the far infrared by using plastic conical lenses, known as axicons. We illustrate the physical insight provided by Gaussian beam mode analysis of such systems. Such pseudo-Bessel beams can be usefully approximated by high-order Gaussian–Laguerre modes, which have similar propagation characteristics. The size of the on-axis spot produced by an axicon, and its depth of focus, can be estimated from a single best-fit high-order Gaussian–Laguerre mode, and a more detailed description of behaviour can be achieved by adding a few additional modes of neighbouring orders. The strength of Gaussian beam mode analysis is that it is straightforward to model the propagation of Bessel beams through complex systems of long wavelength optical components, such as apertures, mirrors, and lenses. We report the experimental generation and measurement of a 0.1 THz Bessel beam, and show that useful performance is possible for an axicon having a scale size just one order of magnitude greater than the wavelength. This work confirms the technical feasibility of designing and building long-wavelength optical systems based on Bessel beams.

TEARES: a toroidal energy- and angle-resolved electron spectrometer

The toroidal energy- and angle-resolved electron spectrometer (TEARES) is a state-of-the-art high-resolution electron detector, which measures both the energy and ejection angle of electrons simultaneously over a range of angles. A double-focussing cylindrical slit entrance lens transports and focusses electrons that are ejected near the plane perpendicular to the main axis of the spectrometer and which originate from an interaction volume of approximately 1 mm 3 to the entrance of the toroidal analyser. In addition, the lens adjusts the kinetic energy of the electrons to be analysed to match the pass energy of the analyser with a relatively constant unit magnification. The toroidal deflector analyser is comprised of an inner and an outer toroidal sector, which disperses and focuses the electrons according to their energy in the radial dimension, it is defined by a spherical radius of 125 mm, a cylindrical radius of 120 mm and a sector angle of 142°. These dimensions have been chosen to ensure optimum focussing properties. A 1 mm high entrance slit provides an analyser resolution (ΔE/PE) of 0.0081 (=1/125). A single-focussing conical slit exit lens transports, demagnifies, focuses and accelerates the electrons from the exit of the analyser onto an imaging detector. Electrons travel through the spectrometer with their initial angular direction preserved. The whole of the spectrometer has no blind spots and incorporates a working distance defined by a 38–40 mm radius. The TEARES system is designed to operate over a kinetic energy range of <0.5≤KE≤1000 eV and a pass energy range of ∼0.5≤PE≤25 eV with a useful angular range of ∼230°.

Ultrasonic Characterization of Degradation of Aging Epoxy Coating

Acoustic impedance of aging epoxy coating in nuclear plant is measured for evaluation of the degradation of the epoxy coating using a new ultrasonic measurement technique that uses a specially designed conical acoustic lens to determine the reflection coefficient (reflectance) of the epoxy coating. Reflection waves measured at two different vertical positions slightly apart from each other are subtracted and used to calculate the acoustic impedance of the epoxy coating. Epoxy coated concrete specimens are fabricated and degraded artificially under accelerated aging conditions to determine the acoustic impedance of the films. Experimental results show that the acoustic impedance is very sensitive to the degradation of coating and can be applied to evaluate the quality of the epoxy coating quantitatively.

Study on conical columns with different conical angles for semi-preparative liquid chromatography

The dynamic flow profiles and separation performances in conically shaped preparative liquid chromatographic columns (inlet i.d. larger than outlet i.d.) with three different angles (7, 10 and 15°) were studied and compared with cylindrical column of the same length and internal volume. The shapes of dynamic flow profiles were studied by on-column visualization method. The transparent chromatographic columns made of polymethyl methacrylate (PMMA), packed with C 18 bonded silica, were immerged into a cubic pool filled with glycerol to eliminate the cylindrical and conical lens effect. The flow profiles of colored iodine solution in the columns were observed clearly using cyclohexane as mobile phase since the refractive indices of C 18, column wall and the mobile phase are very close. In the conical column of 15° (20–7 mm i.d.) the mobile phase in the central region migrated slower than in wall region as it moved toward the column outlet, while in the conical column of 7° (17–11 mm i.d.) the mobile phase in the central region migrated faster than in wall region just like in cylindrical column. We found that a plug-like flow profile was generated in the conical column of 10° (18–9 mm i.d.) during the whole migration process. A carmine and brilliant blue mixture was used as a probe to test the separation ability of the columns. The resolutions of the two compounds on the conical column of 7, 10, 15° and on the cylindrical column were 0.6, 1.57, 1.29 and 0.8, respectively.

Quasi-stationary stage of a nonequilibrium optical discharge in the field of a Bessel wave beam

The self-consistent stationary distributions of the field and plasma produced by Bessel wave beams in a gas with the ionization and Kerr nonlinearities are studied analytically. Using a stationary model based on the condition of a constant field amplitude in the ionized region, the structures are considered to be formed by Bessel beams of two types: with an azimuthal electric field equal to zero at the symmetry axis and a quasitrans-verse field having a maximum at the axis. A specific feature of the plasma channel formed in the first case is the presence of a nonionized region in its central part (tubular discharge), whose radius is independent of the incident power. In the second case, the channel is continuous. The relation is found between the incident radiation power and the external radius of the discharge. It is shown that the Kerr nonlinearity, which is especially important at small divergence angles of the beam, enhances the maximum plasma density and reduces the discharge radius. The parameters of plasma structures produced upon focusing a Gaussian beam by a conical lens are estimated using the model proposed.

Development of a four-element conical electron lens dedicated to high resolution Auger electron–ion(s) coincidence experiments

A four-element conical electron lens has been developed in view of its integration to a double toroidal electron energy analyzer (DTA) dedicated to Auger electron–ion coincidence measurements. The lens design, using electron trajectory numerical simulations, was entirely guided by the perspective of analyzing energetic electrons with high resolution in the multicoincidence regime. The design, construction, and experimental characterization stages of this electron optics system are described in this article. Emphasis is put on the importance of third generation synchrotron radiation sources when performing such multicoincidence experiments.

Characterization and modelling of the hollow beam produced by a real conical lens

The properties of the hollow beam produced by a conical lens are studied in detail. In particular, the impact of a rounded vertex is examined. It is shown that it could lead to drastic changes in the transverse distribution of the hollow beam, determined by the ratio between the transverse size of the incident beam and the size of the blunt area. An adequate choice for this ratio allows us to either minimize the losses or optimize the distribution symmetry.

Test of a conical lens using a two-beam shearing interferometer

We describe a two-beam shearing interferometric technique for testing refractive conical lenses. The optical configuration requires two mutually coherent plane wave fronts transmitted through the conical lens under test. The method can also be considered as an interferometric fringe projection technique in which a fringe pattern produced by the two interfering wave fronts is projected through the optical elements. We describe the principle of the method and present application of the technique for determining the angle formed by the flat surface and the conical surface of a refractive conical lens.

Axially symmetric hollow beams using refractive conical lenses

We explore the possibility of producing several beam shapes with conical or cylindrical geometry using conical lenses. We discuss optical schemes for generation of hollow laser beams; with 3D intensity distribution surrounding all directions, a dark core region can be obtained. These optical fields are important for the confinement of cold atoms in 2D or 3D blue dipole potentials.