Gradient Refractive Index Structure Research Articles

Gradient refractive index tellurite glass-ceramics for miniaturized and lightweight MWIR imaging

Tellurite glasses are highly anticipated for creating gradient refractive index (GRIN) lenses, which have the potential to be applied in the lightweight and miniaturization of optical imaging systems to improve their performance. However, it is still challenging to precipitate pure crystalline phases in tellurite glasses after heat treatment to control the refractive index via spatial variation of nanocrystal distribution. Here, we present a novel method for fabricating axial telluride GRIN glass via a gradient heat-treatment technique. Through the selection of glass composition and control of the heat treatment process, pure phase Bi4TeO8 nanocrystals with a high refractive index (n) can be precipitated in telluride glass with a lower refractive index. This allows the axial telluride GRIN structure of maximum refractive index difference Δn ∼ 0.1 to be obtained by modulating the spatial distribution and concentration of Bi4TeO8 nanocrystals. This work not only demonstrates the feasibility of producing GRIN lenses from tellurite glass but also lays the foundation for the future development of medium wave infrared (MWIR) imaging.

Equalization system of low differential mode delay few-mode fibers based on the neural network MIMO algorithm.

In recent years, with the development of information networks, higher requirements for transmission capacity have been recommended. Yet, at the same time, the capacity of single-mode fiber is rapidly approaching the theoretical limit. The multidimensional multiplexing technique is an effective way to solve this problem. Since the high differential mode delay (DMD) of transmission fiber increases the complexity of demultiplexing in equalization algorithms, we use an intelligent design method to optimize the trench-assisted gradient refractive index structure in this paper. The maximum DMD of the optimized optical fiber structure is 19.6 ps/km. A least mean squares-feedforward neural network constant modulus algorithm (LMS-FNNCMA) is also designed by using the theory of the least mean squares (LMS), constant modulus algorithm (CMA), and the multiple input multiple output (MIMO) neural networks. In order to verify the accuracy of the algorithm, a polarization division multiplexing-wavelength division multiplexing-mode division multiplexing (PDM-WDM-MDM) optical transmission system is constructed through simulation. The algorithm successfully realizes the de-crosstalk over a transmission distance of 1200 km at a rate of 1.2 Tbps under simulation conditions.

Elastic P-wave manipulation utilizing functionally graded parallel plate gradient refractive index structures

This paper presents a new Gradient Refractive Index (GRIN) structure, which utilizes a series of thin plates made of functionally graded material separated by narrow gaps, to control elastic P-wave fields. The proposed technique is demonstrated through two basic examples of wave manipulation: focusing and deflecting, but has the potential for a wide range of applications. To verify the theoretical calculations, COMSOL Multiphysics simulation software was utilized to solve the full Navier–Lamé equations. Overall, the results of this study demonstrate the effectiveness of the proposed GRIN structure in manipulating elastic P-wave fields.

Hollow core-shell nanocoatings with gradient refractive index structure for enhanced photovoltaic performance

Hollow structure-based multifunctional coatings with broadband antireflectivity, self-cleaning performance, stability, and durability can be applied to photovoltaic (PV) modules to maintain high transmittance and increase solar cell power generation. This research prepared bilayer hollow composite nanoparticles by improving and optimizing the nanoparticle synthesis and volume ratios. The optimal volume ratio of hollow SiO2 to TiO2 was determined using refractive index, transmittance, surface area, photocatalysis, and thermogravimetry. With the modification effect of methyltriethoxysilane, the refractive index interval of the composite coating was obtained, while giving the coating better hydrophobicity. A three-layer broadband antireflective coating (HT-TGBA) with a gradient refractive index structure was prepared using pre-designed simulation software. Various morphological and structural characterizations of HT-TGBA nanoparticles were performed. The transmittance of HT-TGBA-coated glass was significantly improved compared with that of uncoated glass. Its self-cleaning properties were confirmed by photocatalysis and surface hydrophobicity. Damp heat, abrasion tests, and pencil hardness tests proved the excellent durability of HT-TGBA, and measurements of sustained water contact angles demonstrated its stability. The short-circuit current density and photoelectric conversion efficiency were significantly improved by dip-coating HT-TGBA onto mini-modules. These results demonstrate that HT-TGBA has broad application prospects, supporting future large-scale applications of composite coatings in PV modules.

Infrared GRIN GeS2–Sb2S3–CsCl chalcogenide glass–ceramics

AbstractChalcogenide glasses show a unique potential for creating gradient refractive index (GRIN) lenses, which would reduce the size and weight of infrared thermal imaging system and remain/improve its performance. Here, we propose a new method that forms a GRIN chalcogenide glass–ceramics (GCs) by creating low refractive index (n) CsCl nanocrystals within a high n GeS2–Sb2S3 glass matrix. After specific gradient thermal treatment, the GRIN structure of Δn ∼ 0.04 was formed through the gradient precipitation of CsCl. This work would pave a new path to design the GRIN chalcogenide GCs through a selective crystallization of halide crystals with low n.

Enhanced photonic spin Hall effect of reflected light from a doubly linear gradient-refractive-index material.

The photonic spin Hall effect (SHE), manifesting itself as spin-dependent splitting of light, holds potential applications in nano-photonic devices and precision metrology. However, the photonic SHE is generally weak, and therefore its enhancement is of great significance. In this paper, we propose a simple method for enhancing the photonic SHE of reflected light by taking advantage of the gradient-refractive-index (GRIN) material. The transverse shifts for a normal (homogeneous) layer and linear GRIN structure with three different types (singly increasing, singly decreasing, and doubly linear ones) are theoretically investigated. We found that the doubly linear GRIN materials exhibit the prominent photonic SHE of reflected light, which is mainly due to the Fabry-Perot resonance. By optimizing the thickness and the lower (higher) refractive index of the doubly linear GRIN layer, the transverse shift for a horizontally polarized incident beam can nearly reach its upper limitation (i.e., half of the beam waist). These findings provide us a potential method to enhance the photonic SHE, and therefore establish a strong foundation for developing spin-based photonic devices in the future.

Highly Transparent and Wide Viewing Optical Films Using Embedded Hierarchical Double-Shell Layered Nanoparticles with Gradient Refractive Index Surface.

The essential improvements in the performance of light-diffusing materials for wide viewing angles in potential optoelectronic applications have attracted considerable attention. In this study, a simple and unprecedented strategy is proposed to simultaneously provide exceptional light scattering performance and high optical transparency for transparent optical thin films using hierarchical double-shell nanoparticles possessing a refractive index gradient on the nanoparticle surface. The hierarchical SiO2/TiO2/poly(methyl methacrylate) (PMMA) double-shell layered nanoparticles induce enhanced light scattering properties by their nanolayered gradient refractive index structure. Fourier transform infrared spectroscopy and scanning electron microscopy-energy-dispersive X-ray spectroscopy analyses show the successful formation of the multiple nanolayered structure of the double-shell nanoparticles. The synthesized SiO2/TiO2/PMMA nanoparticles with a diameter of 40 nm and a TiO2 layer thickness of 4.5 nm exhibit the highest diffuse reflectance of 87% in the visible region. An ultraviolet-light-cured optical film with an extremely low content of double-shell nanoparticles exhibits efficient light scattering characteristics while maintaining high optical transparency. This study provides a facile yet effective, scalable approach to improve the viewing angle performances of optoelectronic devices and paves the new way for further studies on the wide applications of light scattering phenomenon using optically active hierarchical nanoparticles with multiple refractive indices.

Monolithic Chalcogenide Optical Nanocomposites Enable Infrared System Innovation: Gradient Refractive Index Optics

AbstractThe size and weight of conventional imaging systems is defined by costly non‐planar lenses and the complex lens assemblies required to minimize optical aberrations. The ability to engineer gradient refractive index (GRIN) optics has the potential to overcome constraints of traditional homogeneous lenses by reducing the number of components in optical systems. Here, an innovative strategy to realize this goal based on monolithic GRIN media created in Ge‐As‐Se‐Pb chalcogenide infrared nanocomposites is presented. A gradient heat treatment to spatially modulate the volume fraction of high refractive index Pb‐rich nanocrystals within a glass matrix is utilized, providing a GRIN profile while maintaining an optical transparency. A first‐ever correlation of material chemistry and microstructure, processing protocol, and optical property modification resulting in a prototype GRIN structure is presented. The integrated approach and mechanistic understanding illustrated by this versatile modification paradigm provides a platform for new optical functionalities in next‐generation imaging applications.

Hybrid Nanostructured Antireflection Coating by Self-Assembled Nanosphere Lithography

Broadband antireflection (AR) coatings are essential elements for improving the photocurrent generation of photovoltaic modules or the enhancement of visibility in optical devices. In this paper, we report a hybrid nanostructured antireflection coating combination that is a clean and efficient method for fabricating a nanostructured antireflection coating (ARC). A multilayer thin-film was introduced between the ARC and substrate to solve the significant problem of preparing nanostructured ARCs on different substrates. In this way, we rebuilt a gradient refractive index structure and optimize the antireflective property by simply adjusting the moth-eye structure and multilayers. Subwavelength-structured cone arrays were directly patterned using a self-assembled single-layer polystyrene (PS) nanosphere array as an etching mask. Nanostructure coatings exhibited excellent broadband and wide-angle antireflective properties. The bottom-up preparation process and hybrid structural combination have the potential to significantly enhance the broadband and wide-angle antireflective properties for a number of optical systems that require high transparency, which is promising for reducing the manufacturing cost of nanostructured AR coatings.

Acoustic Absorption Characteristics of New Underwater Omnidirectional Absorber**Supported by the National Natural Science Foundation of China under Grant Nos 51575201 and 11204098.

We investigate a new underwater omnidirectional absorber with acoustic black hole effect to realize a broadband omnidirectional acoustic wave absorption. Based on multiple scattering theory, a two-dimensional axisymmetric model of underwater omnidirectional absorber comprised of an acoustic gradient refractive index structure and a hollow core is developed, and the mechanisms of omnidirectional absorption and dissipation of acoustic waves are studied. The numerical results indicate that the omnidirectional absorber developed here can achieve the omnidirectional absorption of incident acoustic waves in a broadband frequency and can effectively reduce the backscattering of acoustic waves. It potentially provides a new notion for underwater acoustic coating design.

Gradient refractive index structure of phosphor‐in‐glass coating for packaging of white LEDs

AbstractA gradient refractive index (GRIN) structure, with a gradual increase in the refractive index from the glass substrate, was successfully obtained by multilayer screen printing for white light‐emitting diodes (w‐LEDs) packaging. Each phosphor‐in‐glass (PiG) coating consisted of B2O3–SiO2–ZnO glass matrix and yellow phosphor. The gradually increased refractive index (1.62, 1.72, and 1.82) of glass matrices were obtained from higher molecular weight of La2O3 and WO3. After sintering at 600°C, no obvious interface was observed and the phosphor particles were mixed thoroughly in the glass matrix. When the phosphor content was 50 wt%, the white‐light emission was obtained. Compared with those based on the nongradient and low‐refractive PiG coating, the luminous efficacy of w‐LEDs constructed by the PiG coating with GRIN was enhanced. It shows that the GRIN structure is beneficial to improve the luminous efficacy of w‐LEDs.

Atmospheric-Window-Matching Hierarchical Broadband Infrared Absorber Realized by Lithography-Free Fabrication

An ultra-broadband selective absorber has been realized with a hierarchical structure through integrating vacuum impedance matched structure, quarter wavelength structure and gradient refractive index structure. Through optimizing the design parameters of the proposed hierarchical structure, an ultra-broadband infrared absorber covering three major atmospheric windows (0.7~2.5 μm, 3~5 μm and 8~14 μm) has been numerically and experimentally demonstrated. An overall absorption up to 80% covering all the three major atmospheric infrared windows and a ratio of the total absorptions within and beyond the windows as high as 5.88, has been achieved with the developed absorber. The high absorption and spectral selectivity of the absorber make it promising for sensitive broadband infrared spectroscopy detection. The proposed hierarchical structure also provides great design freedom with many tunable factors, making it convenient to extend the design for other applications. In addition, we developed a cost-effective lithography-free method for the fabrication of this structure. The design flexibility and fabrication convenience of this hierarchical structure render it suitable for the development of tailored selective broadband absorbers for targeted applications.

Energy Transfer Using Gradient Index Metamaterial

The gradient refractive index structure in this paper is used to increase the quantum of energy transfer. This is done by improving the directive gain of the pyramidal horn antenna at a frequency of 10 GHz. A three-dimensional array of closed square rings is placed in front of the horn antenna aperture to form a gradient refractive index structure. This structure increases the directive gain by 1.6 dB as compared to that of the conventional horn antenna. The structure nearly doubles the wireless power transfer quantum between the transmitter and the receiver when placed at both ends. The increase in the directivity is achieved by converting the spherical wave emanating from the horn to a plane wave once it passes through the structure. This transformation is realized by the gradient refractive index structure being placed perpendicular to the direction of propagation. The gradient refractive index is constructed by changing the dimensions of a closed square ring placed in the unit cell of the array. The change in the refractive index gives rise to an improvement of the half power beam width and side lobe level compared to that of the normal horn. The design and simulation were done using CST Studio software.

Sharp bend in two-dimensional optical waveguide based on gradient refractive index structure.

In this work, we propose the design of a sharp bend in a two-dimensional optical waveguide which has super-ellipse curve boundaries and a gradient refractive index structure in its core. Numerical simulations are presented to show the efficient light propagation in the waveguide bend, as well as the efficient light coupling between the proposed waveguide bend and a straight waveguide, for TE0 and TM0 modes. The proposed design strategy is also useful for designing other compact optical and photonic components.

Transmission properties of defect modes in one-dimensional photonic crystals containing gradient refractive index defects

The gradient refractive index (GRIN) defect layer is introduced into one-dimensional photonic crystal (1D PC) to develop the optical filters needed. The transmission properties of 1D PC with GRIN defect layer were investigated based on the finite difference time domain (FDTD) method. Defect mode was obtained according to the GRIN distribution functions. With a GRIN structure in the defect layer, simulation results show that the position and width of the photonic band gap can be effectively modulated by varying the thickness and GRIN distribution functions of defect layer and the parameters of symmetrical layers. The new study provides a certain reference for photonic band gap engineering and designing the photonic-based devices.

Geometry-invariant GRIN lens: iso-dispersive contours

A dispersive model of a gradient refractive index (GRIN) lens is introduced based on the idea of iso-dispersive contours. These contours have constant Abbe number and their shape is related to iso-indicial contours of the monochromatic geometry-invariant GRIN lens (GIGL) model. The chromatic GIGL model predicts the dispersion throughout the GRIN structure by using the dispersion curves of the surface and the center of the lens. The analytical approach for paraxial ray tracing and the monochromatic aberration calculations used in the GIGL model is employed here to derive closed-form expressions for the axial and lateral color coefficients of the lens. Expressions for equivalent refractive index and the equivalent Abbe number of the homogeneous equivalent lens are also presented and new aspects of the chromatic aberration change due to aging are discussed. The key derivations and explanations of the GRIN lens optical properties are accompanied with numerical examples for the human and animal eye GRIN lenses.

Geometry-invariant gradient refractive index lens: analytical ray tracing

A new class of gradient refractive index (GRIN) lens is introduced and analyzed. The interior iso-indicial contours mimic the external shape of the lens, which leads to an invariant geometry of the GRIN structure. The lens model employs a conventional surface representation using a coincoid of revolution with a higher-order aspheric term. This model has a unique feature, namely, it allows analytical paraxial ray tracing. The height and the angle of an arbitrary incident ray can be found inside the lens in a closed-form expression, which is used to calculate the main optical characteristics of the lens, including the optical power and third-order monochromatic aberration coefficients. Moreover, due to strong coupling of the external surface shape to the GRIN structure, the proposed GRIN lens is well suited for studying accommodation mechanism in the eye. To show the power of the model, several examples are given emphasizing the usefulness of the analytical solution. The presented geometry-invariant GRIN lens can be used for modeling and reconstructing the crystalline lens of the human eye and other types of eyes featuring a GRIN lens.

Efficient optical absorption in thin-film solar cells

In order to improve the optical absorption of hydrogenated amorphous silicon (a-Si:H) thin film solar cells, a new structure consisted of ITO layer with the nonresonant nanoparticles embedded in it and a-Si:H layer, is proposed. By optimizing both the thickness of a-Si:H layer and nanoparticles size, the effects of Fabry-Perot resonance and the scattering of incident light are discussed and analyzed. It is demonstrated that the enhanced optical absorption can be achieved due to the coupling of incident light and nanostructure, simultaneously the proposed structure can be considered as gradient refractive index structure to restrain the reflection at the interface of ITO and a-Si:H thin film.

Broadband antireflection of block copolymer/homopolymer blend films with gradient refractive index structures

The factors that influence the broadband antireflection of block copolymer/homopolymer blend films were systematically investigated. The gradient refractive index structure, which was generated by removing the PMMA content from a film of PS-b-PMMA/PMMA blends, contributed to the broadband antireflection. The volume fraction of the PMMA block (fPMMA), the total degree of polymerization (N) and the weight percent of the homopolymer played a key role in the formation of the gradient porosity index inner structure. By increasing χN, the PS porous structure was kept from collapsing after removal of the PMMA domain, which led to a stable gradient porosity ratio structure and higher transmittance. While increasing fPMMA, the PMMA domains changed from a dispersed phase to a continuous phase, which caused the residual PS structure to collapse more easily and the transmittance decreased. The best broadband antireflective properties were achieved from the 45 mg mL−1 solution of PS-b-PMMA (Mn = 68 000–33 500, fPMMA = ∼25%) blended with 30 wt% PMMA: a mean transmittance of 98.4% at full spectrum, and >98.0% in the visible–NIR range between 600 nm and 2000 nm.

Refractive index of the crystalline lens in young and aged eyes

Background: When the ageing crystalline lens is modelled on the basis of a constant equivalent lens, the changes in ocular dimensions would lead to an increase in power of the order of two dioptres. A comparable increase in myopia is usually not evident with increasing age and this inconsistency has been referred to as the lens paradox. It has been proposed that this paradox can be resolved if the refractive index is modelled as a gradient refractive index. The purpose of this paper was to study differences in the equivalent, gradient and surface refractive index of the crystalline lens between a young and old age group.Methods: Biometric data was collected for 96 subjects: 48 young adults with an age range 19 to 31 years (mean 22.10 ± 2.93 years) and 48 old adults with an age range 49 to 61 years (mean 53.88 ± 3.88 years). The equivalent refractive index was determined for each subject by paraxial ray tracing and a merit function based on refractive error and Purkinje image height. The refractive index gradient was determined by modelling the crystalline lens as a bi‐elliptical iso‐indicial structure in a three‐surface Gullstrand‐Emsley schematic eye and a merit function based on the surface power, the gradient refractive index power and the equivalent power of the lens. The central refractive index of the lens was assumed to be 1.406.Results: The differences between the groups included a decrease in the mean equivalent refractive index from 1.427 ± 0.007 to 1.418 ± 0.006, an increase in surface refractive index from 1.386 ± 0.007 to 1.394 ± 0.006 with a concurrent change in the gradient refractive index profile. The refractive index changes maintained a constant mean lens power in each group.Conclusions: The so‐called ‘lens paradox’ whereby an increase in the power of the crystalline lens does not lead to an increase in myopia is resolved by a decrease in the equivalent refractive index of the lens or when modelled as a gradient refractive index structure, by an increase in the surface refractive index and an associated change in gradient for an assumed central refractive index of 1.406.