Plasmonic Antennas Research Articles

An exploratory simulation study and prediction model on human brain behavior and activity using an integration of deep neural network and biosensor Rabi antenna

The plasmonic antenna probe is constructed using a silver rod embedded in a modified Mach-Zehnder interferometer (MZI) ad-drop filter. Rabi antennas are formed when space-time control reaches two levels of system oscillation and can be used as human brain sensor probes. Photonic neural networks are designed using brain-Rabi antenna communication, and transmissions are connected via neurons. Communication signals are carried by electron spin (up and down) and adjustable Rabi frequency. Hidden variables and deep brain signals can be obtained by external detection. A Rabi antenna has been developed by simulation using computer simulation technology (CST) software. Additionally, a communication device has been developed that uses the Optiwave program with Finite-Difference Time-Domain (OptiFDTD). The output signal is plotted using the MATLAB program with the parameters of the OptiFDTD simulation results. The proposed antenna oscillates in the frequency range of 192 THz to 202 THz with a maximum gain of 22.4 dBi. The sensitivity of the sensor is calculated along with the result of electron spin and applied to form a human brain connection. Moreover, intelligent machine learning algorithms are proposed to identify high-quality transmissions and predict the behavior of transmissions in the near future. During the process, a root mean square error (RMSE) of 2.3332(±0.2338) was obtained. Finally, it can be said that our proposed model can efficiently predict human mind, thoughts, behavior as well as action/reaction, which can be greatly helpful in the diagnosis of various neuro-degenerative/psychological diseases (such as Alzheimer's, dementia, etc.) and for security purposes.

Achieving High Temporal Resolution in Single‐Molecule Fluorescence Techniques Using Plasmonic Nanoantennas

AbstractSingle‐molecule fluorescence techniques are essential for investigating the molecular mechanisms in biological processes. However, achieving sub‐millisecond temporal resolution to monitor fast molecular dynamics remains a significant challenge. The fluorescence brightness is the key parameter that generally defines the temporal resolution for these techniques. Conventional microscopes and standard fluorescent emitters fall short in achieving the high brightness required for sub‐millisecond monitoring. Plasmonic nanoantennas are proposed as a solution, but despite huge fluorescence enhancement having been obtained with these structures, the brightness generally remains below 1 million photons/s/molecule. Therefore, the improvement of temporal resolution is overlooked. This article presents a method for achieving high temporal resolution in single‐molecule fluorescence techniques using plasmonic nanoantennas, specifically optical horn antennas. This work demonstrates about 90% collection efficiency of the total emitted light, reaching a high fluorescence brightness of 2 million photons/s/molecule in the saturation regime. This enables observations of single molecules with microsecond binning time and fast fluorescence correlation spectroscopy measurements. This work expands the applications of plasmonic antennas and zero‐mode waveguides in the fluorescence saturation regime toward brighter single‐molecule signal, faster temporal resolutions, and improved detection rates to advance fluorescence sensing, DNA sequencing, and dynamic studies of molecular interactions.

A Body-Wide RF Energy Harvester Based on Textile Surface Plasmonic Antenna Array for Wearable Wireless Power Transmission

This brief demonstrated a body-wide RF energy harvester based on textile spoof surface plasmon (SSP) antenna array for wearable wireless power transmission. This harvester includes four patch antennas and SSP waveguides to form an SSP antenna array integrated with clothing to harvest the incident RF energy. Then, a loop and rectifier are integrated and fabricated in the same plane to extract, combine, rectify and output DC power from the multi-path harvested energy in a contactless way and without a complex matching network. They are fabricated with a simple structure, entirely off-the-shelf flexible and textile materials, and a proven fabrication technique. Finally, it is worn on the body to output DC power of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$108.89~\mu \text{W}$ </tex-math></inline-formula> when illuminated with a power density of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$7.96~\mu \text{W}$ </tex-math></inline-formula> /cm2 at 2.4-2.45 GHz Industrial Scientific Medical (ISM) band. This design could be applied to power the potential wearable sensors wirelessly.

THz antennas design, developments, challenges, and applications: A review

SummaryTerahertz (0.1–10 THz) wireless communication will be the future technology to reach a top‐notch data rate. THz is one of the most promising candidates for 6G systems because it provides enormous bandwidth, up to 100 GHz, and a massive data rate of up to 1 Tbps. THz antennas, antenna arrays, and MIMO antenna arrays in 6G are hot research topics for implementing 6G wireless communication systems. The 6G aims to continue to enhance the features of the 5G as it is capable of achieving the maximum high‐speed data rate, excellent reliable communication, massive connectivity, and very low latency connectivity. The 6G requirements need high‐gain antenna arrays and MIMO antenna arrays to combat the effect of atmospheric losses in high frequencies. An in‐depth discussion of the planar THz antennas that have been extensively used in THz applications like imaging, sensing, and Internet‐of‐Things (IoT) has been conducted. The study of the THz antennas, antenna arrays, and MIMO antennas on different conducting materials such as copper and graphene, which are designed on different dielectric substrates such as polyimide, quartz, liquid crystalline polymer, and polytetrafluoroethylene, has been carried out in detail. Metamaterial, photoconductive, plasmonic antennas, and THz beamforming are significant parts of THz communications. This paper also provides antennas and antenna arrays based on them.

Purcell Factor for Plasmon-Enhanced Metal Photoluminescence

We present an analytical model for the plasmonic enhancement of metal photoluminescence (MPL) in metal nanostructures with a characteristic size below the diffraction limit. In such systems, the primary mechanism of MPL enhancement is the excitation of localized surface plasmons (LSP) by recombining carriers, followed by photon emission due to LSP radiative decay. For plasmonic nanostructures of arbitrary shape, we obtain a universal expression for the MPL Purcell factor that describes the plasmonic enhancement of MPL in terms of the metal dielectric function, LSP frequency, and system volume. We find that the lineshape of the MPL spectrum is affected by the interference between direct carrier recombination processes and those mediated by plasmonic antenna, which leads to a blueshift of the MPL spectral band relative to LSP resonance in scattering spectra observed in numerous experiments.

An ultra-thin high-efficiency plasmonic metalens with symmetric split ring transmitarray metasurfaces

Metasurface lenses (or metalenses) have aroused great attentions and efforts in the community of metamaterials or metasurfaces due to its ultrathin device dimension and superior focusing performances. High-efficiency transmissive metalenses with an ultra-thin device thickness are an important aspect especially in the low frequency by using plasmonic transmitarray antennas. In this paper, an ultra-thin plasmonic metalens with only 0.1λ (λ is working wavelength, the aperture size is 7λ) device thickness is designed by changing the radius of the proposed symmetric complementary split ring resonator antenna metasurfaces. Thanks to its high transmittance and large phase shift of the plasmonic meta-atoms, the designed metalens achieves both high transmissive efficiency of 80% and high focusing efficiency of 50% on the focal plane of F = 4.6λ in the simulations. The designed ultra-thin plasmonic metalens has a moderate large numerical aperture of 0.67 (NA = 0.67). In order to verify its high working efficiency of the proposed plasmonic metalens, a sample is also fabricated and a much higher focusing efficiency of 65% is realized in the measurements. The influence of the open angles of the symmetric split ring transmitarray metasurface on the focusing performances such as working efficiency and NA of the designed metalens is also studied and analyzed finally, which can add new degree of freedoms to optimize its focusing performance. The presented studies can facilitate the development of high-efficiency metalenses in the low frequency and have significant potential applications in high-resolution microwave imaging, high-gain metalens antennas and others.

Frequency-domain terahertz spectroscopy using long-carrier-lifetime photoconductive antennas.

We present a telecommunication-compatible frequency-domain terahertz spectroscopy system realized by novel photoconductive antennas without using short-carrier-lifetime photoconductors. Built on a high-mobility InGaAs photoactive layer, these photoconductive antennas are designed with plasmonics-enhanced contact electrodes to achieve highly confined optical generation near the metal/semiconductor surface, which offers ultrafast photocarrier transport and, hence, efficient continuous-wave terahertz operation including both generation and detection. Consequently, using two plasmonic photoconductive antennas as a terahertz source and a terahertz detector, we successfully demonstrate frequency-domain spectroscopy with a dynamic range more than 95 dB and an operation bandwidth of 2.5 THz. Moreover, this novel approach to terahertz antenna design opens up a wide range of new possibilities for many different semiconductors and optical excitation wavelengths to be utilized, therefore bypassing short-carrier-lifetime photoconductors with limited availability.

Photothermal Conversion of Solar Infrared Radiation by Plasmonic Nanoantennas for Photovoltaic-Thermoelectric Hybrid Devices

Photovoltaics have become one of the low-cost options for electricity generation. However, the lack of absorption of the near-infrared and infrared solar spectrum intrinsically limits its efficiency. Here, we present an approach for photothermal conversion of solar infrared radiation in photovoltaic-thermoelectric systems using plasmonic nanoantennas. Through numerical calculations-driven shape engineering, we identified Ni diabolo nanoantennas as efficient solar infrared spectrum harvesters. Nanofabrication with electron-beam lithography further revealed its impact on nanoantenna optical properties at the single-nanoantenna level. In the large-scale low-cost approach, however, photothermal surfaces of nanocone plasmonic antennas, made with a simple and robust fabrication process, still deliver a significant 6.1 °C temperature increase under solar infrared illumination. The reported results pave the way toward the development of hybrid photovoltaic-thermoelectric systems with an optimal utilization of the solar spectrum.

Tailoring the directional dependent emitter interaction based plasmonic antenna character of Ag–Au heterodimer

Based on the concept of optical nanoantennas, light-matter interaction between metal heterodimer (Ag and Au spherical nanoparticles) and single dipole emitter system are numerically simulated utilizing a MATLAB toolbox MNPBEM17 based on boundary element method (BEM). The precise position and orientation of the dipole emitter systematically controls not only the (non)radiative losses, but also the efficiency of excitation (absorption) and respective emission processes in the vicinity of the plasmonic optical antenna system. The overall (non)radiative decay rates and associated surface charge distributions help estimate the spatio-directional dependency of dipole emitter emission, analogous to that of the SERS enhancement. Furthermore, the Poynting vector analysis of our present hybrid plasmonic antenna system effectively assesses the flow of electromagnetic energy, thus accounting for improvement in both near- and far-field propagation modes. The calculation of Purcell factor and coupling strength along with quantum yield evaluate the detailed optical response of a nanoantenna characteristics simultaneously based on the dipole emitter position and orientation, offering better scope for understanding the underlying mechanisms governing such intriguing interactions in complex geometries as well.

Promoting 2D Material Photodetectors by Optical Antennas beyond Noble Metals

AbstractThe distinctive layered crystal structures and diverse properties of 2D layered materials (2DLMs) have established them as prospective building blocks for implementing next‐generation optoelectronics. One critical predicament in terms of light sensing is the weak absorption caused by the atomic‐scale thickness, as well as the limited effective wavelength range/low spectral selectivity constrained by the intrinsic band structures. Despite the fact that numerous noble metal antennas are harnessed for enhancing the light–matter coupling, they suffer from exorbitant cost and narrow resonant optical windows. To this end, a number of non‐noble plasmonic optical antennas have been developed to improve the light‐sensing properties of 2DLM photodetectors, and tremendous advances have been accomplished. Herein, a comprehensive overview of this subject is provided based on four aspects; namely, non‐noble metal antenna promoted 2DLM photodetectors, heteroatom doped semiconductor antenna promoted 2DLM photodetectors, non‐stoichiometric semiconductor antenna promoted 2DLM photodetectors, and MXene antenna promoted 2DLM photodetectors. The focus is on the device structures, preparation, and underlying mechanisms. In the end, the challenges are highlighted, and potential strategies addressing them are proposed, which aim to navigate the upcoming exploration in the related domains and fully exert the pivotal role of non‐noble plasmonic optical antennas toward advancing 2DLM photodetectors.

Amine Functionalization Within Hierarchically‐Porous Zeotype Framework for Plasmonic Catalysis over PdAu Nanoparticles

AbstractPlasmonic catalysis has revealed improved product yield and selectivity in various chemical transformation reactions over the past decade. In this report, the effect of tertiary amine (‐NR3) functionalization on the surface of hierarchically‐porous zeotype (HP‐AlPO‐5) materials to enhance the plasmon‐mediated catalysis, utilizing a combination of the plasmonic antenna (Au) and catalytic reactor (Pd) nanoparticles (NPs) was investigated. The catalysts have been characterized using enhanced techniques such as HAADF‐STEM, FT‐EXAFS, and probe‐based FT‐IR to reveal the proximity and interaction between bimetallic NPs, and thermal stability of amines in the presence of Au or PdAu NPs. Interestingly, a four‐fold enhancement in the Suzuki‐Miyaura coupling reaction product yield was obtained over PdAu/HP‐AlPO‐5‐NR3 when compared with the analogous plasmonic catalyst with no amine functionalization under visible light irradiation. A range of amines were functionalized and their influence in the nucleation, uniform growth and stabilization of catalytic active site (Pd) and formation of electron‐rich species under visible light irradiation has also been investigated. The presence of tertiary amine in the nanostructured catalyst enhanced the turnover number (TON) significantly under light irradiation conditions in comparison to dark conditions. This study provides an enriched understanding of plasmon‐driven chemistry, where the maximized reaction rate enhancement requires the existence of active metal species and the formation of electron‐enriched species under light irradiation conditions.

Substrate engineering of plasmonic nanocavity antenna modes.

Plasmonic nanocavities have emerged as a promising platform for next-generation spectroscopy, sensing and photonic quantum information processing technologies, benefiting from a unique confluence of nanoscale compactness and integrability, ultrafast functionality and room-temperature viability. Harnessing their unprecedented optical field confinement and enhancement properties for such diverse application domains, however, demands continued innovation in cavity design and robust strategies for engineering their plasmonic mode characteristics, with the aim of optimizing spatial and spectral matching conditions for strong light-matter interaction involving embedded quantum emitters. Adopting the canonical gold bowtie nanoantenna, we show that the complex refractive index, n + ik, of the substrate material provides additional design flexibility in tailoring the properties of plasmonic nanocavity modes, including their resonance wavelengths, hotspot locations, intracavity field polarization and radiative decay rates. In particular, we predict that highly refractive (n ≥ 4) or highly absorptive (k ≥ 4) substrates provide two complementary approaches to engineering nanocavity modes that are especially desirable for coupling two-dimensional quantum materials, featuring namely an elevated hotspot with a dominantly in-plane polarized near-field, as well as a strongly radiative character. Our study elucidates the benefits and intricacies of a largely unexplored facet of nanocavity mode manipulation, beyond the widely practiced synthetic control over the cavity topology or physical dimensions, and paves the way for plasmonic cavity quantum electrodynamics with two-dimensional excitonic matter.

Ultraviolet Nanophotonics Enables Autofluorescence Correlation Spectroscopy on Label-Free Proteins with a Single Tryptophan.

Using the ultraviolet autofluorescence of tryptophan amino acids offers fascinating perspectives to study single proteins without the drawbacks of fluorescence labeling. However, the low autofluorescence signals have so far limited the UV detection to large proteins containing several tens of tryptophan residues. This limit is not compatible with the vast majority of proteins which contain only a few tryptophans. Here we push the sensitivity of label-free ultraviolet fluorescence correlation spectroscopy (UV-FCS) down to the single tryptophan level. Our results show how the combination of nanophotonic plasmonic antennas, antioxidants, and background reduction techniques can improve the signal-to-background ratio by over an order of magnitude and enable UV-FCS on thermonuclease proteins with a single tryptophan residue. This sensitivity breakthrough unlocks the applicability of UV-FCS technique to a broad library of label-free proteins.

Refractive Index Measurement Using SOI Photodiode with SP Antenna toward SOI CMOS-Compatible Integrated Optical Biosensor.

This paper proposes a new optical biosensor composed of a silicon-on-insulator (SOI) p-n junction photodiode (PD) with a surface plasmon (SP) antenna. When the phase-matching condition between two lateral wavelengths of the diffracted light from the SP antenna and the waveguiding mode in the SOI PD is satisfied, we observe sharp peaks in the spectroscopic light sensitivity. Since the peak wavelength depends on the RI change around the SP antenna corresponding to the phase-matching condition, the SOI PDs with an SP antenna can be applied to the optical biosensor. The RI detection limit is evaluated in the measurements with bulk solutions, and 1.11 × 10-5 RIU (refractive index unit) can be obtained, which is comparable to that of a surface plasmon resonance (SPR) sensor, which is well known as a representative optical biosensor. In addition, the response for intermolecular bonds is estimated by the electromagnetic simulations using the finite-difference time-domain (FDTD) method to clarify its ability to detect biomolecular interactions. The results of this paper will provide new ground for high-throughput label-free biosensing, since a large number of SOI PDs with an SP antenna can be easily integrated on a single chip via an SOI complementary metal-oxide-semiconductor (CMOS) fabrication process.

A super asymmetric cross antenna structure with tunable dual-frequency resonances.

The detection performance of traditional infrared spectroscopy can be very limited in the case of molecular vibrational modes with low absorption cross-sections. On account of its electric field enhancement, plasmonic antenna can be combined with infrared spectroscopy to realize surface enhanced infrared detection and characterization of molecules. In this work, a super asymmetric cross antenna structure with tunable dual-frequency resonance and a high enhancement factor is designed. By systematically studying the transmission spectrum and charge distribution of this super asymmetric cross antenna structure, the physical origin of the dual-frequency resonance and its tunability are characterized in detail. In addition, in order to target desired molecular ensembles, the relationship between the resonance frequency and electric-field intensity of the two resonance modes and the parameters of structure and incident light are examined, yielding an enhancement factor close to 100 in the desired frequency region. Finally, the experimental results show that the proposed super asymmetric cross antenna structure can indeed generate dual-frequency resonances, agreeing reasonably with the theoretical results. It is believed that the super asymmetric cross antenna structure can be widely used to sensitively detect trace molecules, and in monolayered chemistry and bio-molecules, allowing their structures and dynamics to be studied using nonlinear infrared spectroscopy.

Au@C/Pt core@shell/satellite supra-nanostructures: plasmonic antenna-reactor hybrid nanocatalysts.

Integration of plasmonic nanoantennas with catalytically active reactors in deliberately designed hybrid supra-nanostructures creates a dual-functional materials platform, based upon which precise modulation of catalytic reaction kinetics becomes accomplishable through optical excitations of plasmon resonances. Here, we have developed a multistep synthetic approach that enables us to assemble colloidal Au@C/Pt core@shell/satellite supra-nanostructures, in which the Au core functions as a light-harvesting plasmonic nanoantenna, the Pt satellites act as catalytically active reactors, and the C shell serves as a nanoscale dielectric spacer separating the reactors from the antenna, respectively. By adjusting several synthetic parameters, the size of the Au core, the thickness of the C shell, and the surface coverage of Pt satellites can all be tuned independently. Choosing Pt-catalyzed cascade oxidation of 3,3',5,5'-tetramethylbenzidine in an aerobic aqueous environment as a model reaction, we have systematically studied the detailed kinetic features of the catalytic reactions both in the dark and under visible light illumination over a broad range of reaction conditions, which sheds light on the interplay between plasmonic and catalytic effects in these antenna-reactor nanohybrids. The plasmonic antenna effect can be effectively harnessed to kinetically modulate multiple crucial steps during the cascade reactions, benefiting from plasmon-enhanced interband electronic transitions in the Pt satellites and plasmon-enhanced intramolecular electronic excitations in chromogenic intermediate species. In addition to the plasmonic antenna effect, photothermal transduction derived from plasmonic excitations can also provide significant contributions to the kinetic enhancements under visible light illumination. The knowledge gained from this work serves as important guiding principles for rational design and structural optimization of plasmonic antenna-reactor hybrid nanomaterials, endowing us with enhanced capabilities to kinetically modulate targeted catalytic/photocatalytic molecule-transforming processes through light illumination.

Programmable Beam-Steering Capabilities Based on Graphene Plasmonic THz MIMO Antenna via Reconfigurable Intelligent Surfaces (RIS) for IoT Applications

The approaching sixth-generation (6G) communication network will modernize applications and satisfy user demands through implementing a smart and reconfigurable system with a higher data rate and wider bandwidth. The controllable THz waves are highly recommended for the instantaneous development the new technology in wireless communication systems. Recently, reconfigurable intelligent surfaces (RIS), also called codded/tunable programmable metasurfaces, have enabled a conspicuous functionality for THz devices and components for influencing electromagnetic waves (EM) such as beam steering, multi-beam-scanning applications, polarization variation, and beam focusing applications. In this article, we proposed a graphene plasmonic two-port MIMO microstrip patch antenna structure that operates at a 1.9 THz resonance frequency. An E-shape MTM unit cell is introduced to enhance the isolation of the antenna from −35 dB to −54 dB. An implementation of controllable and reconfigurable surfaces based on graphene meta-atoms (G-RIS) placed above the radiating patches with a suitable separated distance to control the radiated beam to steer in different directions (±60°). The reconfigurable process is carried out via changing the (ON/OFF) meta-atoms states to get a specific code with a certain beam direction. The gain enhancement of the antenna can be implemented through an artificial magnetic conductor (AMC) based on graphene material. The G-AMC layer is located underneath the (MIMO antenna, G-RIS layer) to improve the gain from 4.5 dBi to 10 dBi. The suggested antenna structure results are validated with different techniques CST microwave studio and ADS equivalent circuit model. The results have asymptotic values. So, the proposed design of the MIMO antenna that is sandwiched between G-RIS and G-AMC is suitable for IoT applications.

Miniaturized Spoof Plasmonic Antennas with Good Impedance Matching.

The ability of spoof surface plasmon polaritons (SSPPs) to confine electromagnetic fields in a subwavelength regime enables the design of miniaturized antennas. However, the impedance matching scheme for miniaturized spoof plasmonic antennas has not been studied systematically. In this paper, we propose a general method in the antenna design based on SSPPs, providing a feasible solution to impedance matching at the feeding point of miniaturized spoof plasmonic antennas. To verify the method, a prototype of a planar spoof plasmonic dipole antenna is simulated, fabricated and measured, of which the dipole arm length is reduced by 35.2% as compared with the traditional dipole antenna. A peak gain level of 4.29 dBi and the radiation efficiency of about 94.5% were measured at 6 GHz. This general method can be extended to solve the impedance matching problem in the design of other spoof plasmonic devices.

Ultralong Lifetime of Plasmon-Excited Electrons Realized in Nonepitaxial/Epitaxial Au@CdS/CsPbBr3 Triple-Heteronanocrystals.

Combination of the strong light-absorbing power of plasmonic metals with the superior charge carrier dynamics of halide perovskites is appealing for bio-inspired solar-energy conversion due to the potential to acquire long-lived plasmon-induced hot electrons. However, the direct coupling of these two materials, with Au/CsPbBr3 heteronanocrystals (HNCs) as a prototype, results in severe suppression of plasmon resonances. The present work shows that interfacial engineering is a key knob for overcoming this impediment, based on the creation of a CdS mediate layer between Au and CsPbBr3 forming atomically organized Au-CdS and CdS-CsPbBr3 interfaces by nonepitaxial/epitaxial combined strategy. Transient spectroscopy studies demonstrate that the resulting Au@CdS/CsPbBr3 HNCs generate remarkably long-lived plasmon-induced charge carriers with lifetime up to nanosecond timescale, which is several orders of magnitude longer than those reported for colloidal plasmonic metal-semiconductor systems. Such long-lived carriers extracted from plasmonic antennas enable to drive CO2 photoreduction with efficiency outperforming previously reported CsPbBr3 -based photocatalysts. The findings disclose a new paradigm for achieving much elongated time windows to harness the substantial energy of transient plasmons through realization of synergistic coupling of plasmonic metals and halide perovskites.

Plasmonic high gain graphene-based antenna array design for ultra wide band terahertz applications

Graphene, which consists of one atomic slide made from the Carbon, and it utilized in various of the implementations like the chemical, the thermal, the mechanical, and the electrical. In this research article, a high gain plasmonic antenna array is proposed for the utilizations of the terahertz (THz) regime on the basis of the graphene material. Also, the surface plasmon polariton (SPP) waves phenomena which emerged at THz in graphene are demonstrated the suggested antenna is composed of (4*6) graphene patches and a graphene Nano ribbon feeder to excite the patches deposed on the lumina layer. The simulated antenna was designed and investigated via the utilizing of the CST software. The obtained outcomes show that the antenna operation frequency bands covered a large band at the 2.6-10, 2.28-2.5, 1.87-2.14, and 1.4-1.6 THz with an S11 ≤ -10 dB and an expedient antenna gain in the operating frequency ranges.