Gradient Refractive Index Lens Research Articles

Optically anisotropic porous silicon microlenses with tunable refractive indexes and birefringence profiles

The effect of spatially varying birefringence on the focusing behavior of porous silicon (PSi) and porous silicon dioxide (PSiO2) gradient refractive index (GRIN) lenses is investigated. Both materials attain broad, tunable refractive indexes and birefringence profiles, with PSi having a maximum birefringence of ∼0.26 and PSiO2 a reduced maximum birefringence of ∼0.03 at 633 nm. These GRIN lenses exhibit polarization-dependent split focusing behavior, wherein the divergence angle between the twin foci increases with the birefringence gradient. PSi’s large birefringence allows the divergence angle to be tuned such that light focuses away from the center of the lens. These GRIN elements demonstrate how tunable birefringent materials can be used to engineer polarization-selective optical responses.

Radial gradient refractive index (GRIN) infrared lens based on spatially resolved crystallization of chalcogenide glass

While widely used in the visible, radial gradient refractive index (GRIN) lenses are still elusive in the IR waveband. In this paper we introduce a new method based on spatially resolved crystallization of chalcogenide glass to produce such lenses. Optical and structural properties of 80 GeSe2–20 Ga2Se3 glass ceramic samples are measured. A shift of refractive index is induced by increasing the density of nanocrystals. By placing the sample into a tailored thermal profile, spatially controlled crystallization is achieved. To our knowledge this constitutes the first fabrication of an optically functional radial GRIN in the IR. We also introduce a method to characterize the index profile non-destructively, which is a necessary step for embedding GRIN into commercial systems.

Optical development in the zebrafish eye lens.

The optics of the eye is the key to a functioning visual system. The exact nature of the correlation between ocular optics and eye development is not known because of the paucity of knowledge about the growth of a key optical element, the eye lens. The sophisticated optics of the lens and its gradient of refractive index provide the superior optical quality that the eye needs and which, it is thought, has a major influence on the development of proper visual function. The nature of a gradient refractive index lens, however, renders accurate measurements of its development difficult to make and has been the reason why the influence of lens growth on visual function remains largely unknown. Novel imaging techniques have made it possible to investigate growth of the eye lens in the zebrafish. This study shows measurements using X-ray Talbot interferometry of three-dimensional gradient index profiles in eye lenses of zebrafish from late larval to adult stages. The zebrafish lens shows evidence of a gradient of refractive index from the earliest stages measured and its growth suggests an apparent coincidence between periods of rapid increase in refractive index in the lens nucleus and increased expression of a particular crystallin protein group.

Ultrawideband Antipodal Tapered Slot Antenna With Gradient Refractive Index Metamaterial Lens

This letter proposes an ultrawideband and high-gain antipodal tapered slot antenna (ATSA) with a gradient refractive index (GRIN) lens. The GRIN lens consisting six metamaterial lenses is placed in the maximum radiation direction of the ATSA to greatly enhance its radiation capability. We found that the proposed GRIN lens antenna has a wide impedance bandwidth of 175.7% (0.84–13 GHz) and −3 dB gain bandwidth of 65.8% (5.86–11.6 GHz). Its gain is averagely increased by 4.81 dB in the whole operating band, and the maximum gain reaches 20.55 dBi at 9.5 GHz. The simulation and measured results demonstrate that the designed GRIN lens antenna has an excellent performance and is suitable for short-pulse ground penetrating radar systems.

Interview

Oskar Björkqvist Oskar Björkqvist, from the KTH Royal Institute of Technology in Sweden, talks to us about his submission “Additive manufactured dielectric Gutman lens”, and the potential ubiquity of 3D-printed antennae, page 1318. I am a recently graduated electrical engineer with a specialisation in electromagnetics. At the time we authored this paper I was affiliated with the Division for Electromagnetic Engineering at KTH Royal Institute of Technology in Stockholm, Sweden, which specialises in wave propagation and antennas. They have worked in close collaboration with industry recently to prepare for the launch of 5G, amongst other projects. Some of the topics we focus our research on are transformation optics, metasurfaces and lens antennas, such as the one in this publication. Some people in my research group had started using these new RF-compatible 3D printing filaments to make customised layers and bodies of dielectric. I came across a few papers where people had been looking at 3D printing dielectric lenses, but none of them seemed to have turned to the cheapest and most commercially available form of 3D printing, known as ‘fused filament fabrication’. This led us to the idea that we could probably make similar lenses with a normal desktop 3D printer. Some initial simulations showed promising results, and we were able to print and measure a first working prototype soon after. Since then we have developed a few different versions of these lenses, one of which we decided to publish here in Electronics Letters. We have in this work shown that it is fully feasible to make a gradient refractive index lens, which historically have been relatively complex to manufacture, by very simple means. The fact that the entire antenna can be made in a single piece, by a single machine, suggests that pretty much anyone with access to a 3D printer could make their own low cost, high gain antennas using this method – not to mention the fact that the source 3D models can very easily be redistributed. I'd like to imagine that the method could be well suited for applications where weight and form factor of an antenna plays a role, as this plastic lens is in general relatively light weight and could assume many different shapes with the use of transformation optics. We are further confident that the method also is applicable to even higher frequency bands than the one we have considered here, possibly stretching into the mm-wave regime. Not being an expert in 3D printing technology, it was at times not easy to know how well a 3D model might translate into a printed object. The small details in the models and the limited spatial resolution of a desktop 3D printer necessitated us iterating a few different methods for generating the models and different geometries of our unit cells, which are the ‘building blocks’ we use to create the lens. Still being relatively new to this field, I have not yet experienced any significant changes first-hand. It is however evident to me that working with antennas and electromagnetics in general clearly has changed the last couple of decades as an effect of the IT revolution – the simulation tools we have now are extremely powerful and the process of designing, manufacturing and evaluating a design is probably easier than ever. Our publication in this edition of Electronics Letters is perhaps a good example – the time from conceiving the idea to measuring the first prototype spanned over only a few weeks and could be done pretty much single-handedly, only with the help of a computer and a relatively simple 3D printer. I suspect that we will see more of this way of working in the future and that research groups will to a greater extent be able to manufacture their designs by themselves, which is likely to speed up the process of conducting research significantly.

Microtopography‐Guided Radial Gradient Circle Array Film with Nanoscale Resolution

Distribution of multimaterials at arbitrary positions with nanoscale resolution and over a large area substrate is essential to future advances in functional graded materials. Such stringent requirements are highly beyond the reach of current techniques, although newly developed 3D printing technologies are addressed. Here, a radial gradient circle array film with the distribution accuracy up to ≈18 nm is fabricated by using microtopographic substrate. A mathematical model is developed to guide the distribution of position, size, shape, and type of materials on an arbitrary section for the given morphology of substrate. The periodic electrical and mechanical properties of the radial gradient circle film are identified, which can be beneficial for further functionalization and applications, such as gradient refractive index lenses, microcoils, and microantennas.

Far-Field Wireless Power Transfer Using GRIN Lens Metamaterial at GHz Frequency

In this letter, the far-field wireless power transfer up to 6-m distance from the transmitting horn antenna (Tx) aperture using a new design gradient refractive index lens metamaterial (GRIN MM) is proposed for the first time, which increases the efficiency of power transfer. Double-sided-S-shaped GRIN MM unit cell dimensions are optimized for the operating frequency of 2.45 GHz. The D-dot sensor is placed at 6-m distance from the Tx aperture to measure the electric field without and with the proposed GRIN MM and hence the power density. The same amount of power is received experimentally without GRIN MM as obtained by the Friis transmission equation, thus validating the theoretical and experimental analysis. Experimentally, it is observed that due to the point directive beam obtained after passing through the GRIN MM array, 86% more power is received with it compared to without it, thus increasing the maximum theoretical power received.

An Analytical Inverse Approach to Design GRIN Lenses

An analytical inverse method to design lenses of isotropic inhomogeneous refractive index (RI) distribution is presented, where the wave ray propagation is described by the eikonal equation. We show that some particular RI distributions can be obtained by the angles of incidence and emergence when the rays pass through the surfaces of the lenses. This method is applied to design lenses that perfectly focus rays or bend them to arbitrary angles. In addition, gradient refractive index (GRIN) devices are proposed, able to generate self-bending acoustic beams and obtain illusion shadows of arbitrary objects. The ray tracing and finite elements method simulation results indicate the validity of the method. The method may have potential applications in designing acoustic and optic GRIN devices for controlling energy flux, such as medical imaging, therapeutic ultrasound, acoustic levitation, energy isolation, acoustic and optic camouflaging, etc.

Analysis and Experimental Validation of an Optimized Gradient-Index Phononic-Crystal Lens

Harvesting flexural energy has emerged as a viable means for driving low-power electronic devices. This study presents an optimized phononic gradient refractive index (GRIN) lens, which has important applications in focusing and harvesting elastic waves in fields such as structural health monitoring and wearable electronics. Also presented is a general framework for optimizing GRIN lenses, using multiple-scattering computations and ray-tracing analysis. Experimental results for an actual, optimized lens exhibit significant increase in focused power, with significant shortening of focal distance.

High-performance lens antenna using high refractive index metamaterials**Project supported by the National Natural Science Foundation of China (Grant Nos. 61761010 and 61461016), in part by the Natural Science Foundation of Guangxi Zhuang Autonomous Region, China (Grant No. 2015jjBB7002), in part by the Guangxi Key Laboratory of Wireless Wideband Communication and Signal Processing, and in part by the Innovation Project of

In this paper, a high refractive index metamaterial (HRM), whose element is composed of bilayer square patch (BSP) spaced by a dielectric plate, is proposed. By reducing the thickness of the dielectric plate and the gap between adjacent patches, the BSP can effectively enhance capacitive coupling and simultaneously suppress diamagnetic response, which significantly increases the refractive index of the proposed metamaterial. Furthermore, the high refractive index region is far away from the resonant region of the metamaterial, resulting in broadband. Based on these characteristics of BSP, a gradient refractive index (GRIN) lens with thin thickness (0.34λ0, where λ0 is the wavelength at 5.75 GHz) is designed. By using this lens, we then design a circularly polarized horn antenna with high performance. The measurement results show that the 3-dB axial ratio bandwidth is 34.8% (4.75 GHz∼ 6.75 GHz) and the antenna gain in this frequency range is increased by an average value of 3.4 dB. The proposed method opens up a new avenue to design high-performance antenna.

Polarization Tomography of Residual Stresses in Cylindrical Gradient-Index Lenses

In most cases, cylindrical structures with a gradient refractive index (GRIN) are formed on the basis of diffusion technology. The refractive index and the residual stresses in them are axially symmetrical. The distortion determined by diffusion and the thermal internal stresses in them are simulated by the fictive temperature of residual stresses. The use of the integral photoelasticity for the reconstruction of residual stresses in GRIN lenses is usually limited to the case of a planar deformed state. In this study, this algorithm is extended to the case of the axial change of residual stresses. It is assumed that the illumination procedure is carried out in the sample cross section. The optical problem is solved within the quasi-isotropic approximation. The reconstruction is based on measuring the characteristic parameters of polarized light passed through the sample and on the combined solution of the thermoelasticity problem.

Longitudinal intravital imaging of the femoral bone marrow reveals plasticity within marrow vasculature

The bone marrow is a central organ of the immune system, which hosts complex interactions of bone and immune compartments critical for hematopoiesis, immunological memory, and bone regeneration. Although these processes take place over months, most existing imaging techniques allow us to follow snapshots of only a few hours, at subcellular resolution. Here, we develop a microendoscopic multi-photon imaging approach called LIMB (longitudinal intravital imaging of the bone marrow) to analyze cellular dynamics within the deep marrow. The approach consists of a biocompatible plate surgically fixated to the mouse femur containing a gradient refractive index lens. This microendoscope allows highly resolved imaging, repeatedly at the same regions within marrow tissue, over months. LIMB reveals extensive vascular plasticity during bone healing and steady-state homeostasis. To our knowledge, this vascular plasticity is unique among mammalian tissues, and we expect this insight will decisively change our understanding of essential phenomena occurring within the bone marrow.

Gain enhancement of the ultra-wideband tapered slot antenna using broadband gradient refractive index metamaterial

In this article, a broadband gradient refractive index (GRIN) metamaterial is designed and used to enhance the gain of the tapered slot antenna (TSA). The proposed GRIN is implemented using nonresonant parallel-line unit cell with different refractive index values. GRIN lens are placed in front of the tapered slot direction in the direction of x-axis. The designed GRIN metamaterials have broad bandwidth (2-12 GHz) characteristics due to the nonresonant parallel-line elements which is suitable for the ultra-wideband frequency band. The measurement results indicates that the radiated beam becomes more directive with narrow beam width. The measured reflection coefficient is below −10 dB over the frequency bandwidth of 3-11 GHz. The peak gain of TSA is obtained up to 14 dB at 10 GHz using GRIN lens.

Fast varifocal two-photon microendoscope for imaging neuronal activity in the deep brain.

Fluorescence microendoscopy is becoming a promising approach for deep brain imaging, but the current technology for visualizing neurons on a single focal plane limits the experimental efficiency and the pursuit of three-dimensional functional neural circuit architectures. Here we present a novel fast varifocal two-photon microendoscope system equipped with a gradient refractive index (GRIN) lens and an electrically tunable lens (ETL). This microendoscope enables quasi-simultaneous imaging of the neuronal network activity of deep brain areas at multiple focal planes separated by 85-120 µm at a fast scan rate of 7.5-15 frames per second per plane, as demonstrated in calcium imaging of the mouse dorsal CA1 hippocampus and amygdala in vivo.

A Defective 1-D Photonic Crystal-Based Chemical Sensor in Total Internal Reflection Geometry

In this paper, we introduce and analytically demonstrate a novel chemical sensor based on defective 1-D photonic crystals in total internal reflection geometry, where a gradient refractive index (GRIN) defect layer is located at the end of the structure. This configuration creates an open sensing interface for real-time detection with ultrahigh sensitivity. Using the GRIN lens in the structure not only helps to tune the resonance wavelength to a desired value but also as a consequence of its special refractive index distribution function, a ring-shaped reflectance distribution appears on the output plane of the structure that plays a key role in finding the optimized refractive index of the defect layer and achieving the best resonance of the cavity modes. The resonance angle of the cavity modes is highly sensitive to the effective refractive index of the fluid flowing above the sensor. The refractive index variation of $\Delta n_{F}=10^{-8}RIU$ that causes $\Delta \theta =3.2\times 10^{-6}$ degrees shift at the resonance angle can be detected by this sensor.

Theoretical and Experimental Study of the Diffraction Intensity of Gradient Refractive-Index Lenses

We develop the wave-optics approach for calculating the diffraction distribution of gradient refractiveindex lenses and observing the diffraction pattern of gradient refractive-index lenses in the experiments. The results of our calculation are in good agreement with the experimental results obtained. We show that the diffraction can be regarded as a method to check the quality of the refractive-index distributions of gradient refractive-index lenses.

Directive Beam of the Monopole Antenna Using Broadband Gradient Refractive Index Metamaterial for Ultra-Wideband Application

This paper introduces a novel technique to enhance the gain of the basic monopole antenna by using broadband gradient refractive index (GRIN) metamaterial. The proposed GRIN is designed by using a parallel-line unit cell metamaterial with different refractive index. A seven GRIN lens is placed on the omnidirectional printed basic monopole antenna, perpendicularly. Due to the non-resonant and subwavelength properties of the parallel-line elements, the proposed GRIN metamaterial lens has a broad bandwidth property with low loss. The simulation and measurement results confirmed that the beam is more directive with narrow beam width. The measured reflection coefficient of the GRIN antenna is below -10 dB over the frequency bandwidth of 3.4-11 GHz. Due to GRIN lens, the peak gain of the basic monopole antenna is increased by 5.3 dB at 8.8 GHz.

A liquid thermal gradient refractive index lens and using it to trap single living cell in flowing environments.

A gradient refractive index (GRIN) lens has a great potential for on-chip imaging and detection systems because of its flat surface with reduced defects. This paper reports a liquid thermal GRIN lens prepared using heat conduction between only one liquid, and uses it as a tunable optical tweezer for single living cell trapping in a flowing environment. This liquid GRIN lens consists of a trapezoidal region in the upper layer which is used to establish a GRIN profile by the heat conduction between three streams of benzyl alcohol with different temperatures, and subsequently a rhombus region in the lower layer with compensation liquids to form a steady square-law parabolic refractive index profile only in transverse direction. Simulations and experiments successfully show the real-time tunability of the focusing properties. The focal length can be modulated in the range of 500 μm with the minimum focal length of 430 μm. A considerable high enhancement factor achieves 5.4 whereas the full width at half maximum is 4 μm. The response time of the GRIN lens is about 20 ms. Based on this enhancement, tunable optical trapping for single human embryonic kidney 293 cell in the range of 280 μm is demonstrated by varying the focal length and working distance which is difficult for solid optical tweezers. The considerable quality of this liquid GRIN lens indicates on-chip applications especially in high quality optical imaging, detection and cells' handling.

High-magnification super-resolution FINCH microscopy using birefringent crystal lens interferometers.

Fresnel incoherent correlation holography (FINCH) microscopy is a promising approach for high-resolution biological imaging but has so far been limited to use with low-magnification, low-numerical-aperture configurations. We report the use of in-line incoherent interferometers made from uniaxial birefringent α-barium borate (α-BBO) or calcite crystals that overcome the aberrations and distortions present with previous implementations that employed spatial light modulators or gradient refractive index lenses. FINCH microscopy incorporating these birefringent elements and high-numerical-aperture oil immersion objectives could outperform standard wide-field fluorescence microscopy, with, for example, a 149 nm lateral point spread function at a wavelength of 590 nm. Enhanced resolution was confirmed with sub-resolution fluorescent beads. Taking the Golgi apparatus as a biological example, three different proteins labelled with GFP and two other fluorescent dyes in HeLa cells were resolved with an image quality that is comparable to similar samples captured by structured illumination microscopy.

Compact fiber optic dual-detection confocal displacement sensor.

We propose a dual-detection confocal displacement sensor (DDCDS) with a compact fiber-based optical probe. This all-fiber-optic sensor probe is simple and robust, since it only requires simple alignment of a gradient refractive index lens and a double-clad fiber (DCF). The DDCDS is composed of two point detectors, one coupled to a single mode fiber and the other coupled to a multimode fiber, which are used to measure the light intensity from a core and an inner clad of a DCF, respectively. The ratio of the axial response curves, measured by the two detectors, can be used to obtain a linear relationship between the axial position of the object plane and the ratio of the intensity signals. We demonstrate the performance of the proposed method by measuring micromovement and fast vibration.