Symmetric Lens Research Articles

Semiconductor laser collimation and shaping design based on the combination of a rotationally symmetrical lens and a cylindrical lens

A dual-lens collimation and shaping system which is composed of a rotationally symmetric lens and an aspherical cylindrical lens is proposed in this paper. The system design method is discussed in detail, and the divergent elliptical laser beams are finally converted into collimated circular beams. The simulation results show that the maximum divergence angle of the beams can be collimated to 2.58 µrad, the standard deviation of the edge beam radius samples (SDRS) can be decreased from the original 4.227 to 0.135 mm, and the ratio of beam waist (RBW) drops from 1.554 to 1.0093 in the case of the output beam radius of 40 mm. The effects of transmission distance, astigmatism, wavelength deviation, light source offset, and lens offset on the collimation shaping effect are discussed. The collimation system can be widely used in long-distance optical communication systems and the design method in this paper can provide some new ideas for optical design researchers.

Harnessing surface plasmon polaritons from nanogroove plasmonic lenses to enhance the EM fields around plasmonic nanoantennas

In this paper, we present a device—consisting of a bowtie nanoantenna surrounded by either an asymmetric plasmonic nanogroove or a symmetric plasmonic nanogroove—that allows improved excitation of the bowtie nanoantenna via interaction between the bowtie nanoantenna and the surface plasmon polaritons (SPPs) generated from the nanogrooves. We study the effect of both a linear plasmonic nanogroove as well as a circular plasmonic nanogroove (i.e., a circular nanogroove plasmonic lens) on the EM fields around a bowtie nanoantenna placed at a certain distance from the nanogroove. We show that the electric field enhancement of a bowtie nanoantenna can be significantly improved by the interaction between the bowtie nanoantenna and the SPPs generated from the nanogrooves. We employed FDTD simulations to calculate quantities such as the electric field enhancements and power coupling into SPPs as well as a finite difference eigenmode solution to obtain dispersion relation of the nanogrooves. The geometrical parameters of the symmetric nanogroove and asymmetric nanogroove were optimized to couple maximum light into SPPs. We show that the bowtie nanoantenna surrounded by a single asymmetric nanogroove plasmonic lens produces a SERS electromagnetic enhancement factor (EMEF) of 1010—even when the gap between the arms of the bowtie nanoantenna is as large as 10 nm—which is three orders of magnitude higher than SERS EMEF of a stand-alone bowtie nanoantenna and one order of magnitude higher than the SERS EMEF of a bowtie nanoantenna surrounded by a single symmetric nanogroove plasmonic lens. In addition, the effect of the radius of nanogroove plasmonic lenses is studied. The calculation of collection efficiencies of Raman signal from the proposed nanostructures shows that ∼62% Raman signal can be collected from the bowtie nanoantenna surrounded by a symmetric nanogroove plasmonic lens or an asymmetric nanogroove plasmonic lens (PL) compared to 10% Raman signal collected from only a bowtie nanoantenna on a silica substrate.

Design and characterization of a compact Einzel lens for portable quadrupole mass spectrometry (QMS)

Quadrupole mass spectrometry (QMS) offers better resolution, selectivity and sensitivity than the metal-oxide, field effect transistors and thermal-based gas sensors. However, existing QMS systems are unsuitable for field applications. The miniaturized QMS requires dimensionally scaled components with comparable performance to the conventional bulky systems. For a portable quadrupole mass spectrometry, a compact focusing ion system is required to transfer the maximum number of ions from the ion source to the filter. The present paper discusses the design of a miniature focusing Einzel lens and the effect of design parameters on its performance. The three-cylindrical axially symmetric compact Einzel lens assembly was designed using commercially available software. The relationship between the design parameters is explored for compact and low-powered ion optics. The beam focal length was tuned by varying the bias voltage. The dimensions, as well as voltages across the Einzel lens, were reduced significantly to open a new way for portable point-of-care applications. At an applied voltage of 70 V, the focal length of the ions is 11 mm without being scattered, which is favorable for a portable quadrupole mass filter. The designed Einzel lens was fabricated using micromachining techniques and characterized at a vacuum of 3.05 × 10−4 mbar. The developed lens system shows a current output of 0.114 µA at 72 V lens voltage. A current of 94.8 µA is observed with a background noise of 0.01 µA for the system with nitrogen (28 amu) as the sample.

Inferring Properties of Dark Galactic Halos Using Strongly Lensed Gravitational Waves

Abstract Gravitational waves (GWs) can be deflected, similarly to electromagnetic (EM) waves, by massive objects through the phenomenon of gravitational lensing. The importance of GW lensing for GW astronomy is becoming increasingly apparent in the GW detection era, in which nearly 100 events have already been detected. As current ground-based interferometers reach their design sensitivities, it is anticipated that these detectors may observe a few GW signals that are strongly lensed by the dark halos of intervening galaxies or galaxy clusters. Analyzing the strong lensing effects on GW signals is, thus, becoming important to understand the lens’ properties and correctly infer the intrinsic GW source parameters. However, one cannot accurately infer lens parameters for complex lens models with only GW observations because there are strong degeneracies between the parameters of lensed waveforms. In this paper, we discuss how to conduct parameter estimation of strongly lensed GW signals and infer the lens parameters using additional EM information, including the lens galaxy’s axis ratio and the GW source-hosting galaxy’s lensed images. We find that for simple spherically symmetric lens models, the lens parameters can be well recovered using only GW information. On the other hand, recovering the lens parameters requires systems in which four or more GW images are detected with additional EM observations for nonaxially symmetric lens models. Combinations of GW and EM observations can further improve the inference of the lens parameters.

A new approach for fast field calculation in electrostatic electron lens design and optimization

In electron optics, calculation of the electric field plays a major role in all computations and simulations. Accurate field calculation methods such as the finite element method (FEM), boundary element method and finite difference method, have been used for years. However, such methods are computationally very expensive and make the computer simulation challenging or even infeasible when trying to apply automated design of electrostatic lens systems with many free parameters. Hence, for years, electron optics scientists have been searching for a fast and accurate method of field calculation to tackle the aforementioned problem in the design and optimization of electrostatic electron lens systems. This paper presents a novel method for fast electric field calculation in electrostatic electron lens systems with reasonably high accuracy to enable the electron-optical designers to design and optimize an electrostatic lens system with many free parameters in a reasonably short time. The essence of the method is to express the off-axis potential in an axially symmetrical coordinate system in terms of derivatives of the axial potential up to the fourth order, and equate this to the potential of the electrode at that axial position. Doing this for a limited number of axial positions, we get a set of equations that can be solved to obtain the axial potential, necessary for calculating the lens properties. We name this method the fourth-order electrode method because we take the axial derivatives up to the fourth order. To solve the equations, a quintic spline approximation of the axial potential is calculated by solving three sets of linear equations simultaneously. The sets of equations are extracted from the Laplace equation and the fundamental equations that describe a quintic spline. The accuracy and speed of this method is compared with other field calculation methods, such as the FEM and second order electrode method (SOEM). The new field calculation method is implemented in design/optimization of electrostatic lens systems by using a genetic algorithm based optimization program for electrostatic lens systems developed by the authors. The effectiveness of this new field calculation method in optimizing optical parameters of electrostatic lens systems is compared with FEM and SOEM and the results are presented. It should be noted that the formulation is derived for general axis symmetrical electrostatic electron lens systems, however the examples shown in this paper are with cylindrical electrodes due to the simplicity of the implementation in the software.

Large viewing angle integral imaging 3D display system based on a symmetrical compound lens array.

We propose a large viewing angle integral imaging 3D display system based on a symmetrical compound lens array (SCLA). The display system comprises a high-resolution 2D display panel, an SCLA, and a light shaping diffuser. The high-resolution 2D display panel presents an elemental image array, the SCLA modulates the light rays emitted from the 2D display panel to form 3D images in space, and the light shaping diffuser eliminates the gaps between 3D pixels of the 3D images. We find that the lateral aberration is a crucial factor that affects the resolution of the reconstructed 3D image. The symmetrical structure of the SCLA enables a reduced focal length and the elimination of lateral aberration, improving the viewing angle and the 3D image resolution simultaneously. The experimental results confirm that the proposed display system increases the viewing angle to 68.6°, achieving a comparable resolution of the full field of view while maintaining a simple structure.

Semi-analytical finite ray-tracing through the quadratic symmetric GRIN lens.

The propagation of light within a gradient index (GRIN) media can be analyzed with the use of differential equations for a given non-homogenous refractive index profile. Numerical methods are often necessary to perform ray-tracing in GRIN media; however, analytical solutions exist for several types of GRIN lenses. In this paper, paraxial and non-paraxial differential equations are derived to calculate the ray path in a GRIN lens. It is shown that the paraxial equation has an analytical solution for a GRIN media with a quadratic profile within the paraxial region. The analytical solution can be obtained by using Legendre polynomials or by the Frobenius method involving a power series. Using the Legendre or Frobenius solution, one can calculate the refractive indices along the ray path. A new recursive relationship is proposed to map the trajectory of light at finite heights. To illustrate the finite ray-tracing method utilizing a non-paraxial differential equation, two lenses (with spherical and elliptical iso-indicial contours) are considered. The lenses' back focal distances, for rays entering the lenses at varying finite heights, are calculated. For each lens, its spherical aberration is estimated. The effective focal length and the shape of the principal surface are also obtained. The accuracy of the results is then compared to the numerical ray-tracing using an optical design software, Zemax OpticStudio. The predicted spherical aberration for the spherical lens differs from numerical ray-tracing by less than λ14 at the marginal zone, while the error for the effective focal length is less than λ100.

Symplectic numerical methods in optics and imaging: ray tracing in spherical gradient-index lenses and computer-generated image rendering.

This paper provides an introduction to symplectic numerical integration techniques and examines various optical applications. We first outline the fundamentals of Hamiltonian optics and detail the construction of a symplectic method via the splitting technique. Numerical experiments involving a selection of spherically symmetric gradient-index lenses compare the accuracy of various first-, second-, and fourth-order symplectic methods with equivalent nonsymplectic methods. The best-performing methods are then further tested as part of an image rendering task involving nonlinear ray tracing, comparing the trace time required by each method. Future improvements, recommendations, and uses for symplectic ray tracing are also considered.

Lensing of gravitational waves: Efficient wave-optics methods and validation with symmetric lenses

Lensing of gravitational waves: Efficient wave-optics methods and validation with symmetric lenses

The contribution of image minification to discomfort experienced in wearable optics.

Wearable optics have a broad range of uses, for example, in refractive spectacles and augmented/virtual reality devices. Despite the long-standing and widespread use of wearable optics in vision care and technology, user discomfort remains an enduring mystery. Some of this discomfort is thought to derive from optical image minification and magnification. However, there is limited scientific data characterizing the full range of physical and perceptual symptoms caused by minification or magnification during daily life. In this study, we aimed to evaluate sensitivity to changes in retinal image size introduced by wearable optics. Forty participants wore 0%, 2%, and 4% radially symmetric optical minifying lenses binocularly (over both eyes) and monocularly (over just one eye). Physical and perceptual symptoms were measured during tasks that required head movement, visual search, and judgment of world motion. All lens pairs except the controls (0% binocular) were consistently associated with increased discomfort along some dimension. Greater minification tended to be associated with greater discomfort, and monocular minification was often-but not always-associated with greater symptoms than binocular minification. Furthermore, our results suggest that dizziness and visual motion were the most reported physical and perceptual symptoms during naturalistic tasks. This work establishes preliminary guidelines for tolerances to binocular and monocular image size distortion in wearable optics.

Top-shaped asteroids as Lens-shaped bodies

Several asteroids are known to be shaped like toy tops. This paper models Top-Shaped Asteroids (TSAs) as Homogeneous Symmetric Lenses (HSLs), and derives their rotational, self-gravitational, and total energies as functions of their mass, density, and angular momentum. Then we raise, test, and ultimately reject the hypothesis that TSAs take the shape of lowest total energy, subject to the constraint that they keep the same mass, density, and angular momentum, while remaining HSLs. Other processes must control the shapes of TSAs. For completeness, we also describe a Core-Mantle Model for TSAs, as well as an Inverted Core-Mantle Model, and derive their self-gravitational energies, along with their rotational energies. The gravitational potential at the center of an HSL then is derived.

Average paraxial power of a lens and visual acuity

To provide a solution for average paraxial lens power (ApP) of a lens. Orthogonal and oblique sections through a lens of power F were reduced to a paraxial representation of lens power followed by integration. Visual acuity was measured using lenses of different powers (cylinders of − 1.0 and − 2.0D) and axes, mean spherical equivalent (MSE) of S + C/2, ApP and a toric correction, with the order of correction randomised. A digital screen at 6 m was used on which a Landolt C with crowding bars was displayed for 0.3 s before vanishing. The general equation for a symmetrical lens of refractive index (n), radius of curvature R, in medium of refractive index n1, through orthogonal (theta) and oblique meridians (gamma) as a function of the angle of incidence (alpha) reduces for paraxial rays (alpha sim 0) to F_{n,R} left( {alpha ,theta ,gamma } right)left. right|_{alpha sim 0} = frac{{n - n_{1} }}{R}cos^{2} theta cos^{2} gamma. The average of this function is F_{n,R} left( {alpha ,theta ,gamma } right)left. right|_{alpha sim 0} = frac{{n - n_{1} }}{4R} providing a solution of frac{F}{4} for ApP.For central (p = 0.04), but not peripheral (p = 0.17) viewing, correction with ApP was associated with better visual acuity than a MSE across all tested refractive errors (p = 0.04). These findings suggest that frac{F}{4} may be a more inclusive representation of the average paraxial power of a cylindrical lens than the MSE.

Graded index all-dielectric lens antenna designed by phase manipulation and optical path rescaling

A rotationally symmetric all-dielectric lens antenna is designed by defining the phase function inside the dielectric directly via a closed-form series formula. The refractive index of the lens is modified using state-of-the-art optical path rescaling to keep the refractive index within practical values. The lens optimization is done using the genetic algorithm in MATLAB, where each case is evaluated by conducting linked ray tracing and full-wave electromagnetic simulation in COMSOL. A lens prototype is shown to provide a directivity enhancement of 5.1 dB compared to the optimal conical horn antenna, an improvement of 2 dB compared to the Luneburg lens, and an improvement of 3.8 dB compared to a reference graded index lens. All the examined cases shared a similar length of 5λ for the center frequency of 10 GHz. The prototype lens antenna has a maximum refractive index of 2.1, a reflection coefficient of −22 dB, and a side-lobe level of −25 dB at the center frequency of 10 GHz. The lens’ performance is consistent in the 9–11 GHz band supported by the standard circular waveguide. The results from a prototype with a discretized refractive index simulated in CST Studio Suite are in excellent agreement with the ones with a continuous refractive index profile simulated in COMSOL.

Characterization of rotational symmetry and noise in multifocal contact lens power maps

AbstractPurpose: Spherical multifocal contact lenses are typically designed with a rotationally symmetrical power profile. Imperfections in the raw material, manufacturing and measurement process can break this symmetry, altering the intended lens design. The purpose of this work is to develop a method to separate the intended symmetric design profile from the asymmetries and to give the spatial distribution of the measurement noise uncertainty in diopters.Methods: NIMO TR1504 (Lambda‐X) version V.2.13.2 has been used to measure the local power map of various multifocal contact lenses. From the map, a set of radial power profiles is obtained for different angles (0°, 180°), (0°, 360°). A symmetrical lens should show a constant radial profile for different angles, while asymmetries manifest as differences in the set of radial power profiles. They are analysed using a Principal Components Method (PCA) implemented in MATLAB.Results: The method displays a map of the symmetric radial profile of the lens, another map of the deviations with spatial structure indicating the angles where the deviations are stronger (rotational asymmetries), and noise with three separated components (spatially random variations). Asymmetries of the order of 0.17D (with maximums of 0.4D), and random noise values of 0.12D were found in some lenses.Conclusions: The characterization of multifocal contact lens prescription is important in visual optics. The prescription perceived by the patient depends on the distribution of the radial power profile on the pupil. That is the reason why asymmetries and imperfections estimation is important. The method developed in this work allows to calculate a diopter equivalent number for them.

Effect of Outer Polepiece Shroud Geometry on Bipolar Lens and Studying its Properties

In this paper, several innovative designs of axially symmetrical magnetic dipole lenses, which are bipolar lenses with different geometries, were designed, where the outer pole arm indicated by the symbol was changed (hp) with current density (σ = 6 A/mm2) and after designing them, the engineering variables were studied in terms of magnetic properties, then the optical properties were studied in terms of aberrations, i.e. the coefficient of spherical aberration and the coefficient of chromatic aberration, where it was found that there were slight changes in the corresponding spherical aberration As for chromatic aberration and focal length, no noticeable changes occurred.

Broadband flattened underwater acoustic Luneburg lens

Conventional Luneburg lenses are symmetric circular gradient-index lens with no aberration, but they are restricted by their circular focal surface. Here, we show the design, realization and measurement of an underwater acoustic Luneburg lens with flattened focal surface. The flattened lens is designed by using the quasi-conformal transformation technique and constructed by metamaterials based on air-filled photosensitive resin. Through numerical simulations and experimental studies, the flattened lens is demonstrated to have excellent focusing performance for the incident plane waves propagating at desired angles over a broad frequency band from 20 kHz to 35 kHz. The proposed flattened Luneburg lens can be potentially applied in the applications such as biomedical imaging, underwater acoustic sensing and communication.

Modeling the external flow of a novel HorseShoe receiver and the evaluation of thermal performance

The linear receiver of a Parabolic Trough Collector is the most critical element in the entire system. The Universal Vacuum Air Collector concept is the most extended type of receiver in both experimental and industrial facilities. Besides their considerable cost, their efficiency usually drops as operation time passes. This is mainly due to a partial loss of vacuum in the evacuated annulus between the absorber and the glass cover. An alternative design called HorseShoe receiver is proposed in this work, whose main goal is to maintain the thermal performance throughout its entire lifespan. This innovative receiver is indicated for low-to-medium temperature ranges, which is particularly suitable for solar heat for industrial processes. It consists of a horseshoe-like cavity absorber having its upper border insulated. In addition, two main advantages can be taken by using two symmetric lenses as glass cover: reconcentrate solar radiation into the cavity (improvement of the intercept factor) and protect stratification conditions (reduction of thermal losses). A transient numerical model with customized boundary conditions has been implemented to evaluate both thermal performance and temperature difference in the absorber domain, which is critical for the thermal stress conditions. For that purpose and as a key contribution, not only the Heat Transfer Fluid (HTF) temperature but also the heat transfer coefficient in the duct are set. In particular, HTF temperature ranges from 80 °C to 220 °C and the inner heat transfer coefficient from 600 W/(m 2 ⋅ K) to 1800 W/(m 2 ⋅ K). Results show that numerical thermal performance is above 96%, which is mainly due to the reduction of thermal radiation losses, where the absorber active surface emittance is ϵ a b s = 0 . 3 . Since no inclination of the receiver has been considered in this initial study, it is shown that the air inside the cavity is stratified, which reduces convective losses. Moreover, temperature difference between the coldest and the hottest spot of the absorber is no higher than 30 K, which is affordable from a technical point of view. A polynomial heat losses correlation is also provided, whose parameters are on the same order of those by conventional receiver correlations available in the literature. • A new concept of solar linear cavity receiver (HorseShoe receiver) is proposed. • Thermal losses have been evaluated numerically. • Thermal performance is above 96% under the selected operation conditions. • The symmetric lenses enhance air stratification. • Most of the thermal losses are due to thermal radiation.

Spherical lens aberration minimization method for short-range free-space light transmission

Spherical aberrations of lenses lead to increased spot radii on the focal plane. Several methods, such as optimizing thickness and radii or building lens groups, are known to minimize these spherical aberrations. Here, an innovative method for spherical aberration minimization is introduced; it can be used for short-range free-space optical communication systems, such as unit power afocal relay trains, lens waveguides, and periodic lens systems. This spherical aberration compensation principle is based on the combination of two identical spherical convex lenses at an optimal distance. Due to the higher refractive power for rays with an larger axis distance, rays from the outer area of the first lens intersect the inner area of the second lens, and vice versa. With this setup, the radial refractive power deviation of the two lenses compensate each other. Analytic calculations and numerical simulations are done to confirm this behavior, and measurements using two symmetric spherical lenses with polymer optical fibers as light feed confirm the calculations. Simulations and measurements show a very good matching behavior except for an unknown systematic error. At a lens distance of 300 mm, the optical attenuation decreased by ∼2 dB compared with a very small lens distance. This leads to the conclusion that this proposed spherical aberration minimization method works as theoretically predicted.

Gravitational lensing in Kerr–Newman anti de Sitter spacetime

The method of Rindler and Ishak enables one to study how light is bent in the vicinity of a non-rotating and spherically symmetric gravitational lens. This method mainly aims to investigate the role of cosmological constant in the consequent path. In this paper, we use the extension of Rindler–Ishak method (RIM) in order to evaluate the deflection angle of null geodesics in the equatorial plane of Kerr–Newman anti de Sitter (KNAdS) spacetime. We then use astrophysical data to see the effect of rotation and charge on the bending angle of light for seven distinct stars and two black holes under the assumption of having a KNAdS background with a negative cosmological constant Λ.

Green and wide acceptance angle solar concentrators.

A low-toxicity photopolymer was employed to prepare holographic solar concentrators (HSCs). The main aim of this study is to obtain a versatile holographic element to concentrate the sunlight from different relative positions of the Sun during the day, avoiding the need of expensive tracking systems. Multiplexed holographic elements that combine symmetric and asymmetric holographic lenses of low frequency (545 l/mm) have been recorded in the same plate to concentrate the sunlight from sunrise to sunset. The holographic behavior of HSCs has been studied by measuring the angular diffraction efficiency at 633 nm (close to the maximum response of silicon cells). The efficiency of the complete system "HSC-solar cell" has been evaluated by measuring the short-circuit current (Isc) under solar illumination at different incident angles. This study overcomes the trade-off between good efficiency and high incident acceptance angle, showing an important breakthrough to obtain wide acceptance angle systems.