Gradient Index Materials Research Articles

Ultra-high-aperture infrared triplet with a GRIN lens: modeling stages of composite gradient-index material and potential possibilities of the optical system

Ultra-high-aperture infrared triplet with a GRIN lens: modeling stages of composite gradient-index material and potential possibilities of the optical system

REFORMULATED STRAIN GRADIENT (RSG) ELASTICITY THEORY FOR FREE VIBRATION OF THERMAL BI-DIRECTIONAL FG MICROBEAM

This research examines the vibrational response of a micro-scale Euler beam made from two-directional functionally graded (2D-FG) materials and subjected to thermal effects. By employing a reformulated strain gradient elasticity (RSGE) approach, the equations of motion using Hamilton’s principle for clamped -clamped and clamped-simply boundary conditions are derived and solved them using Galerkin's approach. The investigation explores the impact of temperature, gradient index, and parameters length scale materials on the bidirectional graded microbeam's dynamic characteristics. Furthermore, the normalized frequency, as based on the current reformulated strain gradient elasticity microbeam model, consistently emerges as higher than that derived from the classical model.

Imaging stretching and displacement using gradient-index elements during the lens design process.

In this study, we propose an approach to stretch or translate images using gradient-index (GRIN) elements with a rotationally symmetric shape in lens systems. In this method, the GRIN material, instead of optical surfaces, are utilized to enable a breaking of rotational symmetry for the two image translations. GRIN expression with anamorphic and tilting terms is introduced. A pair of GRIN elements in front of the given system alters the magnification in two orthogonal directions using the anamorphic terms in the expression, which realizes image stretching. A pair of GRIN elements with tilting terms is used after the given system tilts the optical path to achieve a transverse displacement of the image. The structure of the given system remains unchanged when these translations are performed. A design method for the GRIN elements is presented. Additionally, a design example is presented whose image is stretched by 1.33 times in one direction and displaced to one side of its axis to demonstrate the feasibility of the proposed approach. The approach in this study may enable novel imaging GRIN lens system designs with flexible image positions or special optical functions.

A 3D Printed Nearly Isotropic Luneburg Lens Antenna for Millimeter-Wave Vehicular Networks

A three-dimensional (3D) printed Luneburg lens with nearly isotropic properties is presented. The cubical-lattice-type and the rod-type gradient-index materials are employed together to construct the novel printable spherical lens geometry, whose nearly isotropic properties improve the antenna radiation characteristics significantly. The dual-polarized radiation beam generated by the lens antenna can steer in a wide angular range with stable performance throughout a wide operating band. A prototype with an equivalent radius of 16.8 mm is printed and measured in the Ka-band. An impedance bandwidth of more than 40% for |S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sub> | of less than −17.5 dB, a gain of up to 21.3 dBi, and promising radiation patterns with the dual polarization scanning in an angular range of ±60° are obtained experimentally. With the advantages of satisfying operating performance and ease of realization, the lens investigated in this paper would be an attractive candidate for the wireless applications in millimeter-wave vehicular networks.

Unveiling True 3D Nanoscale Microstructural Evolution in Chalcogenide Nanocomposites: A Roadmap for Advanced Infrared Functionality

AbstractThe design of multiphase optical nanocomposites necessitates the understanding of coexisting phases’ morphology and chemistry which have deterministic impacts on light–matter interaction. A prominent example is gradient refractive index (GRIN) materials proposed to realize an arbitrarily shaped, single optical component with minimal chromatic aberration. Ge‐As‐Pb‐Se materials are promising for GRIN due to their ability to exhibit spatially varying volume fraction of high‐index Pb‐rich phases in low index matrices. These materials are characterized to date, exclusively using transmission electron microscopy to reveal their phase separation and induced crystalline phase(s). It is found in the study that the intrinsic 2D perspective of the technique has hindered the identification of true morphology. To clarify this ambiguity, atom probe tomography (APT) is utilized to gain the first‐ever observation of the nanocomposites’ microstructure and its evolution upon heat treatment in a 3D space. The APT‐quantified geometry and chemistry of coexisting phases are considered to predict the effective media's optical behaviors which closely match experimental data, enabling the establishment of the material's predictive and accurate process–structure–property relationship. Findings in the study demonstrate the robustness and advantage of the APT‐assisted characterization in the design and realization of GRIN materials.

Analytical and Numerical Investigation of Buckling Behavior of Functionally Graded Sandwich Plate with Porous Core

ABSTRACT This research presents a new analytical model for the buckling analysis of a functionally graded rectangular sandwich plate with all edges simply supported and subjected to in-plane loading conditions. The sandwich plate comprises a porous metal core with an isotropic metal that serves as a skin. The functionally graded core metal has a varied distribution of porosities in accordance with the plate thickness, which may lead to variation in material properties. By considering classical plate theory principles, the kinematic relations are used to obtain the analytical solution. The effects of changing gradient index, elastic parameters, porosity distribution, slenderness ratio, boundary conditions, and core materials on buckling stresses and dynamic response of functionally graded sandwich plates are presented. A numerical study on elastic buckling using finite element analysis (FEA) was employed to examine the accuracy of the proposed analytical solution. From the obtained results, it is found that the porosity coefficients play significant influences on the buckling behavior and reliability of the FG sandwich structures.

Inkjet-/3D-/4D-Printed Perpetual Electronics and Modules: RF and mm-Wave Devices for 5G+, IoT, Smart Agriculture, and Smart Cities Applications

With the revolutionary developments in the fields of millimeter-wave (mm-wave) and Internet of Things (IoT) technologies and the billion devices promised to be implemented by the end of the decade, the realization of inexpensive, low-power, and intelligent systems is highly desirable. Additive manufacturing (AM) is a technology seeing widespread adoption due to its ability to enable rapid prototyping for iterative design; its reduced setup costs, facilitating economic small-batch production; and its ability to significantly reduce waste by-products, resulting in both environmental benefits as well as lower manufacturing costs. On the other hand, current lithography-based manufacturing technologies-a huge contributor to the growing RF and 5G wireless electronics industry-require extensive design verification, have longer turnaround times, and produce harmful byproducts. Although AM can offer time and cost benefits under the correct conditions, among the more impactful demonstrations of the manufacturing technology are the novel topologies enabled by design rules that allow feature sets, including nonorthogonal planes, conformal surfaces, multimaterial deposition, simultaneous thick- and thin-film deposition [1], complex 3D structures, integrated voids, and gradient index materials.

Temperature-tuned and excellent omnidirectional bending of light to the normal for energy concentration in an index-continuous structure

We present an alternative concept for omnidirectional bending of light and concentration of energy in an index-continuous structure, comprising two gradient-index SiOx (0≤x≤2) layers and a thermochromic VO2 layer. The concept helps to overcome the constraints of conventional optics that are nonadjustable and only functional at designed wavelengths. The advantages of both gradient-index and thermochromic materials are combined in this work to realize temperature-tuned omnidirectional concentration of energy. Using a double-coated ICS component of AIR/SiOx/SUB/SiOx/VO2 for light manipulation and application near the visible spectrum range, this concept was numerically and experimentally demonstrated. The incoming light under oblique incident angles (0°–80°) was bent effectively and concentrated regardless of polarization. Favorable results demonstrated that a notably high energy concentration efficiency Pe (1.93–2.52) was achieved by varying the ambient temperatures (25–75 °C). This concept is general and can be applied in a variety of elements in light energy-efficient devices.

Optical analogues to the equatorial Kerr\u2013Newman black hole

Optical analogues to black holes allow the investigation of general relativity in a laboratory setting. Previous works have considered analogues to Schwarzschild black holes in an isotropic coordinate system; the major drawback is that required material properties diverge at the horizon. We present the dielectric permittivity and permeability tensors that exactly reproduce the equatorial Kerr–Newman metric, as well as the gradient-index material that reproduces equatorial Kerr–Newman null geodesics. Importantly, the radial profile of the scalar refractive index is finite along all trajectories except at the point of rotation reversal for counter-rotating geodesics. Construction of these analogues is feasible with available ordinary materials. A finite-difference frequency-domain solver of Maxwell’s equations is used to simulate light trajectories around a variety of Kerr–Newman black holes. For reasonably sized experimental systems, ray tracing confirms that null geodesics can be well-approximated in the lab, even when allowing for imperfect construction and experimental error.

Mapping of index of refraction profile for polymer gradient index optics using confocal Raman spectroscopy

Scanning confocal Raman microscopy is proposed to measure a gradient index (GRIN) profile at an optical surface. The Raman microscope is calibrated to index of refraction for a binary copolymer GRIN material, and then the index of refraction is mapped on the plano surface of a GRIN polymer lens. The measurement deduces axial shift of 680 μm and identifies lateral tilt or decenter with respect to the nominal position of the GRIN profile. Results suggest that the mapping method is a nondestructive way to measure the GRIN profile of a GRIN lens and its positioning within the lens geometry, to within the sampling precision of the Raman microscope.

Predictive model for indentation of elasto-plastic functionally graded composites

In this paper, the complex phenomena of the elastic and elastoplastic indentation responses of functionally graded materials (FGMs) are studied in the framework of frictional contact mechanics using finite element method. The proposed model accounts for the continuous gradation of all the elastic and plastic properties of the indented material along its thickness using power law function and Tamura, Tomota and Ozawa (TTO) model. Classical Coulomb's friction law is utilized to model the friction effect throughout the contact interface. The model is implemented in ANSYS FE software and utilized to simulate the axisymmetric frictional contact of an FGM substrate and a rigid spherical indenter. Parametric studies are performed to investigate the effects of friction coefficient, gradient index, and FGM-constituent materials on the frictional indentation behaviors of elastic and elastoplastic FGMs under loading/unloading pattern. Results show that the frictional contact response of elastoplastic FGMs can be controlled by appropriate choice of the gradient index. Using obtained numerical results, an empirical equation is derived to predict the normalized residual indentation depth for elastoplastic FGMs by knowing the gradient index and a single material parameter under frictional spherical indentation.

Fabrication of cylindrical active GRIN media by laser-assisted radial dopant diffusion: A proof of concept

This work introduces a new approach to prepare active GRadient-INdex (GRIN) materials by gradually doping commercial silica cylindrical substrates with different optically active ions or materials by the Laser Zone Melting (LZM) process. Scanning Electron Microscopy (SEM) combined with energy dispersive X-ray (EDX) analysis demonstrate that the dopants are gradually incorporated into the cylindrical substrate under controlled penetration depths. This simple, environmentally respectful fabrication method opens the possibility to manufacture versatile GRIN optical elements on a large scale and reduced cost.

Material selection for GRIN-based achromatic doublets.

We use first-order optical principles to examine the ability of gradient index (GRIN) lenses to correct chromatic aberrations. We consider radial GRIN lenses with flat surfaces, with a flat diffractive surface, and with curved surfaces. We model the GRIN material system as a locally varying, subwavelength blend of three materials. In this model, we demonstrate that the color-correcting properties of each lens type can be expressed solely in terms of the dispersion properties of the base materials. We find, at this level of approximation, that the material condition for a two-material GRIN achromat with curved surfaces is identical to that for a homogeneous doublet achromat comprised of the same two materials. For the more general case of three-material, ternary GRIN elements, we use the theory to develop a figure-of-merit-based optimization approach. This allows us to identify promising material combinations without first fabricating a GRIN element. The optimization approach can be applied to alternate GRIN geometries and arbitrary glass catalogs. We use our model to search a large, commercial glass catalog to identify the best achromatic glass combinations for the three different GRIN lenses described above. Significant numerical effort was required to identify which glass combinations performed best. Ternary glass combinations are necessary to achieve good achromatic performance for flat geometries. Diffraction combined with a graded-index enables improved color correction for the same optical power or nearly a factor of two increase in power for the same level of color correction. Glass pairs that perform well as an achromatic doublet also perform well chromatically when blended in a GRIN singlet.

Multibeam 3-D-Printed Luneburg Lens Fed by Magnetoelectric Dipole Antennas for Millimeter-Wave MIMO Applications

A 3-D-printed Luneburg lens with a novel simplified geometry is presented. The rod-type structures are employed as the unit cell of the gradient-index material to realize the required permittivity distribution in the lens. A prototype designed in the Ka-band is manufactured successfully by using a commercial 3-D printing facility. The substrate-integrated waveguide fed magnetoelectric (ME)-dipole antenna with endfire radiation is introduced as the feed for the Luneburg lens due to its wideband performance and compact configuration. By combining the lens with a set of the ME-dipoles, a millimeter-wave (mm-wave) multibeam Luneburg lens antenna is designed, fabricated, and measured. An overlapped impedance bandwidth of wider than 40% that can cover the entire Ka-band and mutual coupling below -17 dB are verified by the fabricated prototype. Nine stable radiation beams with a scanning range between ±61°, gain up to 21.2 dBi with a variation of 2.6 dB, and radiation efficiency of around 75% are achieved as well. With the advantages of good operating features, low fabrication costs, and ease of integration, the proposed multibeam Luneburg lens antenna would be a promising candidate for the fifth-generation (5G) mm-wave multiple-input multiple-output (MIMO) applications in 28 and 38 GHz bands.

Superfocusing plate of terahertz waves based on a gradient refractive index metasurface

A new scenario to realize superfocusing of terahertz waves based on a gradient index (GRIN) metasurface is proposed. To design the GRIN material, a robust algorithm is presented and numerically demonstrated to retrieve the constitutive effective parameters (permittivity and permeability) of the metasurface from the measurement of S parameters. In addition, a new kind of unit cell with a simple structure is designed to verify the theory of effective parameters. By computing the effective refractive index of the unit cell using the algorithm, we design a plate with a thickness of approximately 0.11λ0 (free-space wavelength) at 0.967 THz to superfocus terahertz waves in one dimension. We also revise the theory of superfocusing to make full use of the coupling effect among the cells in the plate and are able to demonstrate it. Comprehensive simulations of focusing are provided, and the full width at half-maximum beam width reaches up to 0.167λ0 at a distance of 0.2λ0. The focusing depth can be further enhanced by decreasing the cell size of the metasurface. This work is beneficial for metasurface design, super-resolution imaging, and other applications in the near field.

Hybrid micro-optical elements by laser-based fabrication of Fresnel lenses on the end face of gradient index lenses.

Fresnel lenses are fabricated directly upon the end face of gradient index (GRIN) lenses by F2-laser machining at 157 nm wavelength. The employed laser processing technique combines a mask projection configuration at 25-x demagnification with a rotation of the structured lens. The ablation characteristics of the GRIN materials require very high pulse fluences with typical values above 7 J/cm2. Topography measurements on the Fresnel lenses reveal a good contour accuracy with residual deviations from the design profile well below 100 nm. Such hybrid optical elements, combining GRIN lenses with diffractive lenses in one element, can serve as the basis for high-performance micro-optical imaging systems with diameters up to 2 mm. Examples of possible applications include imaging sensors like proximity sensors or color-corrected microscope objectives with high numerical aperture for endoscopy applications.

An analytical study of sound transmission through corrugated core FGM sandwich plates filled with porous material

Abstract The main objective of this research work is focused on sound transmission loss analysis of corrugated core functionally graded material (FGM) sandwich plates filled with porous material, wherein two types of FGM sandwich structures are considered, which include one with FGM face sheets and homogeneous ceramic or metal core, and the other with FGM core and homogeneous face sheets. To model the process of sound propagation between fluid and solid, the equivalent fluid model with effective density and bulk modulus is used to describe the sound wave propagation through porous sound absorptive material. The corrugated cores are approximated as a series of uniformly distributed translational and rotational springs to link the sandwich structure. Fluid-structure coupling is considered by imposing velocity continuity condition at fluid-structure interfaces. By using the space harmonic approach and virtual work principle, the sound transmission loss is described analytically. The validity of the proposed theoretical model is verified by comparisons with previously published numerical results. Based on the developed theoretical mode, the influences of the FGM properties, gradient index, sandwich type, skin-core-skin ratios and porous material type on sound transmission loss are subsequently presented.

Directional Acoustic Wave Manipulation by a Porpoise via Multiphase Forehead Structure

For acoustic waves, in general the source must be much larger than the wavelength to produce directional waves, yet porpoises have efficient biosonar systems that break this size rule. How? This study reveals that the porpoise's forehead is a natural gradient-index material, and key to production and control of directional beams. The whale's compression of the multiphase structure of its forehead effectively manipulates the view angle of the beam. Aside from advancing our knowledge of cetaceans, these results could inspire the development of human-made metamaterials for our own subwavelength applications.

Propagation of a Vector Cosine-Gaussian Correlated Beam Through an Active GRIN Medium

This paper presents a convenient approach that uses the tensor method to study the propagation of a nonuniformly correlated electromagnetic Cosine-Gaussian Schell-model (ECGSM) beam through an active gradient-index (GRIN) medium. It is shown that the initial correlation structure has a significant influence on the intensity gain; an ECGSM beam ( n = 1) experiences more gain than a conventional electromagnetic Gaussian Schell-model (EGSM) beam ( n = 0). The inhomogeneous gain induced by the medium leads to a nonlinear modulation of beam parameters such as the spectral intensity, coherence, and polarization. Although the gain leads to a broadening of the beam width, the coherence gradually decreases, which yields a useful guideline for manipulating active GRIN materials to generate numerous partially coherent beams. It is found that the polarization ellipse in the center of a conventional EGSM beam gradually evolves into circular polarization. However, the state of polarization of a nonuniformly correlated ECGSM beam gradually changes into linear polarization. The ability to manipulate light beams using active GRIN materials opens an alternative avenue for the generation of complex vector beams, which promises important supports in the fields of waveguide amplifiers, beam shaping, optical sensors, and beam transformer devices.

Effect of thermal environment on free vibration and buckling of partially cracked isotropic and FGM micro plates based on a non classical Kirchhoff's plate theory: An analytical approach

A non classical analytical model is presented for free vibration of the cracked rectangular isotropic and functionally graded micro plates in the presence of thermal environment. The new approach is based on the combination of classical plate theory and the modified couple stress theory. The crack terms are based on the Line Spring Model whereas the thermal environment is accommodated in the form of thermal moment and in-plane forces. The solution for fundamental frequencies of the cracked plate is obtained by discounting geometric nonlinearity. A non classical relation for geometrically linear thermal buckling phenomenon of a cracked micro-plate is also proposed. The variation of critical buckling temperature and fundamental frequency with uniform rise in temperature of the cracked plate is studied for various crack length ratios, gradient index and internal material length scale parameter. Furthermore the variation of the buckling coefficient with plate aspect ratio and thickness of the cracked micro-plate is established. A comparison is presented between the classical results and present results as affected by thermal environment and microstructure of the plate. It is concluded that the presence of cracks affects the critical buckling temperature and fundamental frequencies of micro plates. The consideration of size effect increases the buckling temperature which shows the significance of the internal material length scale parameter in the presence of thermal environment.