Spherical Wavefront Research Articles

Ultra‐wide Band Antipodal Vivaldi Antenna Using Metasurface Lens for Gain and Front‐To‐Back Ratio (FBR) Improvement

AbstractThis paper addresses the limited gain of conventional Antipodal Vivaldi Antenna (AVA) at higher frequencies. We propose a novel Metamaterial Lens Vivaldi Antenna (MLVA) design that overcomes this limitation by integrating an exponentially tapered antenna lens and a strategically placed Near Zero Refractive Index (NRZI) metamaterial lattice. The MLVA achieves exceptional wideband performance with a −3 dB gain bandwidth exceeding 148.6% from 3.7 to 25 GHz. The result demonstrates a peak realized gain of 11.8 dBi at 11.2 GHz, compared to 9.1 dBi conventional AVA, especially beyond 5 GHz. The compact MLVA design measures only 120 × 78 × 1.524 mm3 (1.48 × 0.96 × 0.0188λ03) λ0 where free‐space wavelength is the lowest frequency and is fabricated on RO4350 B substrate with a 50‐Ω SMA connector. Key features of the design include exponential flaring, and trapezoidal lens geometries chosen for their inherent ability to effectively collimate and direct the spherical wavefront. The incorporation of a dielectric lens and metasurface further enhances gain and Front‐to‐Back Ratio (FBR) by directing the majority of energy in the end‐fire direction. Experimental results validate the effectiveness of the proposed design, confirming simulation predictions. These outstanding characteristics make the MLVA a promising candidate for diverse wireless communication and radar applications demanding high data rates across a broad frequency range.

Investigative photometry experiments on planar extended-light sources

The inverse-square decay law of the illuminance of a point light source with distance is a common notion of basic optics theory, which is readily demonstrated to be a direct consequence of the propagation of spherical wave fronts with the centre at the light source. It is far less common to address the experimental verification of this law and, even less, to study the illuminance decay with the distance of extended light sources, which somehow represent an unknown topic. We propose a scientific experiment where the light sensor of a smartphone is used to collect illuminance data as a function of the source-to-sensor distance and orientation. Through this procedure, students can realize the limit of validity of the inverse-square law and determine the luminance flux of the chosen point-like light source (e.g. the white LED flashlight of a smartphone). More interestingly, when dealing with extended sources (e.g. the LCD of a laptop displaying a white image) subtle characteristics of the decay trend emerge, particularly for distances lower that the source size. A detailed analysis of these characteristics is presented though a process allowing student engagement in a real scientific investigation, envisaging steps of data acquisition through experimental measurements, model construction on the basis of the observed patterns, and finally model testing. We provide a guided formulation for the general modelling of planar emitters, starting from the theoretical treatment of Lambertian sources. In this way, students are able to quantify the luminous emission also for extended sources and their deviation from a Lambertian behaviour.

Gain enhancement of mm-wave antenna using graded index lens integrated frequency selective surface for 5G NR FR2 applications

In this study, the gain of a printed antenna is boosted for utilization in 5G systems by employing a phase-oriented graded index-type lens system. In the prescribed design, various metamaterial unit cells are arranged as arrays with radial phases for the graded meta lens to optimize transmission characteristics. The suggested arrangement creates a meta lens with spatially varying surface impedance and locally varying refractive index, allowing the conversion of spherical wavefronts into planar wavefronts for beam collimation in the 5G band. The focal length-to-diameter ratio (f/d) is fixed at 0.38 in this prescribed design. The integration of the FSS structure with the patch antenna enhances the efficiency above 98% and increases gain by 2.635dBi owing to the focusing effect of the properly placed lens. The prescribed planar lens is easy to realize during manufacturing compared to 3D lenses. The meta lens integrated patch yields a gain of around 8.936dBi at 29 GHz. The performance of the lens antenna is evaluated through simulation studies and then validation of results is performed with experimental arrangement to ensure accuracy and reliability of the suggested methodology for gain enhancement of the functioning antenna at FR2 5G spectrum.

Spin-orbital conversion of the light field immediately behind an ideal spherical lens

The Richards-Wolf equations not only adequately describe a light field distribution at the sharp focus, but are also able to describe a light field distribution just behind an ideal spherical lens, i.e. on a converging spherical wavefront. Knowing all projections of light field strength vectors behind the lens, longitudinal components of the spin angular momentum and orbital angular momentum (SAM and OAM) can be derived. In this case, the longitudinal projection of the SAM just behind the lens either remains zero or decreases. This means that the spin-orbital conversion (SOC), where part of the “spin transfers orbit”, occurs just behind the ideal spherical lens. Notably, the sum of the longitudinal projections of SAM and OAM is conserved. Regarding the spin Hall effect, it is revealed that rather than forming just behind the lens, it appears as focusing occurs. Thus, we find that while just behind the lens there is no Hall effect, it becomes maximally pronounced in the focal plane. It is because just behind the ideal spherical lens, two optical vortices with topological charges (TCs) –2 and 2 and opposite-sign spins (with right and left circular polarization) are generated. However, the total spin is equal to zero because the two vortices have the same amplitudes. The amplitudes of the optical vortices become different in the course of focusing and in the focal plane and, therefore, areas with opposite-sign spins (Hall effect) are formed. We also present a general form of the incident light fields whose longitudinal component is zero in the focal plane. In this case, the SAM vector can only have the longitudinal non-zero component. The notion of the SAM vector elongated only along the optical axis in the focal plane is applied for solving magnetization problems.

Retinal image quality for multifocal lenses with on- and off-axis annular zones.

Multi-focal intra-ocular or contact lenses, intended to increase depth of focus, conventionally have annular zones of additional refractive power, generating wavefront rings of coaxial spherical surfaces. It is, however, possible to influence depth of focus by changing not only the curvature of the wavefront, i.e., refractive power, in the annulus, but also the tilt, i.e., circularly symmetrical linear radial deviation imposed on the spherical wavefront. Employing the example of a single annulus bifocal, retinal image light distributions in the two regimes are calculated, using standard diffraction theory. Four measures of retinal image quality in through-focus scans show that plus power additions and wavefront tilts operate almost interchangeably. In testing these lenses, attention needs to be paid to the detailed operating characteristics of measuring devices of the Shack-Hartmann type to ensure that their grain and precision is compatible with the framework of the analysis.

Design Formulas for Flat Gradient Index Lenses With Planar or Spherical Output Wavefront

Design Formulas for Flat Gradient Index Lenses With Planar or Spherical Output Wavefront

High-precision spherical wavefront calibration method for shack-hartmann wavefront sensor

High-precision spherical wavefront calibration method for shack-hartmann wavefront sensor

Принцип преобразования сигналов в фотонных телекоммуникационных устройствах с использованием объёмных Фурье-голограмм

The relevance of the transition to a new element base for the construction of tele-communication systems and devices with improved technical characteristics based on photonics technologies, including holographic photonics, is shown. To improve the technical characteristics and expand the functionality of the equipment of telecommunication systems in the construction of their structures, it is proposed to use volumetric Fourier holograms. The principle of converting the information parameters of electrical signals in a photonic telecommunication de-vice with a volumetric Fourier hologram into the corresponding parameters of a holographic interferogram is formulated and a block diagram of this principle is developed. It is indicated that for the practical use of the principle of electro-optical signal conversion in photonic telecommunication devices with optical modulators and volumetric Fourier holograms in their design, each stage of the implementation of this principle must be considered as a separate task. The functional purpose of individual elements of the structural scheme of the transformation principle is described. Possible methods of modulation of the parameters of the luminous flux in a photonic telecommunication device with a volumetric Fourier hologram are shown. Variants of structural schemes of holographic pho-tonic devices with reflective and reflective-transmitting Fourier holograms, re-spectively, are presented. Mathematical relations are given that determine the nature of the distribution of the intensity of the light flux on the interferogram formed in the plane of the volumetric Fourier hologram. The influence of a volumetric Fourier hologram on the parameters of a coherent light flux is considered. It is noted that a holographic interferogram formed in the plane of a volumetric Fourier hologram is projected into the searchlight zone while maintaining the amplitude-phase relations between interfering light streams, but with a change in the scale of the projected interferogram. Recommendations on the use of the principle of signal conversion in photonic telecommunication devices using volumetric Fourier holograms have been developed. The influence of electro-optical and acousto-optical modulators of a coherent light flux with a spherical wavefront on the position of its phase center is explained. It is indicated that the sensitivity of the parameters of the holographic interferogram to changes in the voltage of the modulating electrical signal can be adjusted by changing the parameters of the elements of the optical circuit of the holographic photonic telecommunication de-vice and the recording conditions of the volumetric Fourier hologram. A reasonable conclusion is made about the feasibility of constructing photonic telecommunication devices using optical light flux modulators in combination with volumetric Fourier holograms.

Stochastic dynamic analysis of floating bridges exposed to inhomogeneous and irregular waves

As future floating bridges gets longer, the likelihood of significant inhomogeneous wave conditions across them increase. Consequently, a proper assessment of the effects of inhomogeneous wave conditions is needed. In this paper, we present an approach to model inhomogeneous sea states by representing the stochastic process using generalized harmonic decomposition, retaining the coherency inherent in Airy wave theory. The methodology is applied to a concept model of a floating bridge to cross the Bjørnafjord in Norway, which is more than five kilometres wide. The paper emphasizes on frequency-domain simulation, but the required steps to generate time-domain representations are given. To suggest what might be critical considerations in design, the response effects due to some selected conceptual inhomogeneities are highlighted. For varying wave heights alone, it is found that it is likely conservative to approximate the inhomogeneous sea state as homogeneous by assuming the harshest conditions across the full width of the strait. By modulating the mean wave angle of a 100-year swell sea state, a spherical wave front matching the curvature of the bridge girder is found to produce significantly more severe response than the homogeneous reference swell; an increase of 14% of the maximum axial force response is found. Furthermore, a proper treatment of the coherency for swell sea states is found to be crucial, in contrast to typical wind sea conditions.

Acoustic impedance measurement method using spherical waves

The mechanical properties and composition of materials can be better understood through ultrasonic non-destructive testing. Ultrasound is a valuable tool for characterizing elastic moduli, material microstructure, morphological conditions, and correlated acoustical/mechanical properties. Although ultrasound measurement techniques like transmission and pulse-echo are well-established, there is a growing demand for new technologies to facilitate automated inspection and enhance the widespread application of this method. This paper presents a novel approach to evaluate the characteristic acoustic impedance of a sample using measurements of reflected spherical waves. Employing a spherical sound source makes the energy distribution more uniform in all directions, minimizing measurement errors caused by system alignment. Additionally, that configuration aids in determining the experiment's geometry. The impedance was evaluated by analysis of the spherically reflected Gaussian-modulated sinusoidal pulses, which are less susceptible to noise interference. The acquired signal is fitted into a mathematical model to calculate the acoustic impedance, considering the decrease in sound pressure amplitude at the spherical wavefront according to the inverse distance law. Materials with a wide range of impedances (2 MRayl < Z < 46 MRayl) were measured to validate the method. The experimental impedances exhibited statistically significant agreement with values obtained via through-transmission impedance evaluation. The linear regression indicates a bias of 0.02 MRayls and an overall relative error of 1.7 % between the methods. This experimental setup holds promise for accurately assessing submerged structures, offering potential advantages for quantitative inspection.

Estimation of the sensitivity of optical measurements using a holographic interferometer

Various interferometers used for high-precision spectroscopic measurements are considered, and the choice of a holographic interferometer based on the spatial-spectral method of holographic interferometry is justified, with the help of which the movements of the phase center of a coherent light flux in a wide dynamic range are measured in real time and measurement information is recorded digitally. On the basis of mathematical relations proposed by the authors in previous publications and based on the results of experimental studies, the sensitivity of a holographic interferometer to spatial displacements of phase centers (focus points) of light streams – point light sources forming a holographic interferogram is numerically estimated. The dependence of the level of the normalized intensity of the luminous flux in the central region of the holographic interferogram on the movement of the actual point light source along the normal to the plane of the Fourier hologram is established. Based on the results of mathematical modeling, it is shown that the sensitivity of the holographic interferometer to the movements of a real point light source along the normal to the plane of the Fourier hologram depends on the parameters of the optical scheme of the holographic interferometer when exposing the hologram and during measurements. At the same time, the sensitivity of the holographic interferometer to the indicated displacements of a real point light source can only be evaluated experimentally. It is proposed to increase the sensitivity of the holographic interferometer by using a thin collecting lens in its optical scheme. For the first time, a mathematical relation was obtained and investigated for the gain coefficient of the light flux phase with a spherical wavefront, which makes it possible to numerically estimate the increase in sensitivity of a holographic interferometer implementing the spatial-spectral method of holographic interferometry with known parameters of a thin collecting lens in an optical scheme. It is shown that the sensitivity of a holographic interferometer to the movements of an imaginary point light source along the normal to the plane of the Fourier hologram is 2.86 times greater than its sensitivity to the same movements of a real point light source. It is established that the sensitivity of a holographic interferometer with a volumetric Fourier hologram and a thin collecting lens in its design can be increased by at least an order of magnitude compared to the sensitivity of known optical interferometers. The results of assessing the sensitivity of a holographic interferometer implementing the spatial-spectral method of holographic interferometry to the movements of point sources of real and imaginary light fluxes, as well as the obtained ratio for the gain of the light flux phase gain by a thin collecting lens will be useful for high-precision measurements of linear and angular displacements of objects, as well as for the construction of photonic device designs. Based on the results of the study, an experimental sample of an acousto-electric converter was developed and manufactured on the basis of a holographic interferometer, which has high sensitivity in wide dynamic and frequency ranges and is intended for use in acoustic location of unmanned aerial vehicles.

Vector Light Field Immediately behind an Ideal Spherical Lens: Spin–Orbital Conversion, Additional Optical Vortices, Spin Hall Effect, Magnetization

The Richards–Wolf formulas not only adequately describe a light field at a tight focus, but also make it possible to describe a light field immediately behind an ideal spherical lens, that is, on a converging spherical wave front. Knowing all projections of light field strength vectors behind the lens, the longitudinal components of spin and orbital angular momenta (SAM and OAM) can be found. In this case, the longitudinal projection of the SAM immediately behind the lens either remains zero or decreases. This means that the Spin–Orbital Conversion (SOC) effect where part of the “spin goes into orbit” takes place immediately behind the lens. And the sum of longitudinal projections of SAM and OAM is preserved. As for the spin Hall effect, it does not form right behind the lens, but appears as focusing occurs. That is, there is no Hall effect immediately behind the lens, but it is maximum at the focus. This happens because two optical vortices with topological charges (TCs) 2 and −2 and with spins of different signs (with left and right circular polarization) are formed right behind the lens. However, the total spin is zero since amplitudes of these vortices are the same. The amplitude of optical vortices becomes different while focusing and at the focus itself, and therefore regions with spins of different signs (Hall effect) appear. A general form of initial light fields which longitudinal field component is zero at the focus was found. In this case, the SAM vector can only have a longitudinal component that is nonzero. The SAM vector elongated only along the optical axis at the focus is used in magnetization task.

Digital holographic interferometry method for tracking detector modules displacement

In high energy particle physics scattering experiments, the precision of the reconstructed particle tracks can be fundamental. For this reason, a method for detecting the displacement of tracking detector modules is developed. The modules are silicon planes mounted on a frame and used in the MUonE project, which aims at a precision measurement of the scattering angle of elastic muon-electron scattering. From the scattering angle, the hadronic contribution to the anomalous magnetic moment of the muon is extracted. To achieve the desired accuracy, the position of the tracking detector planes must be monitored. The allowable relative displacements must be less than 10 μ m. To meet the specifications and to monitor as large an area of the detector as possible, a digital holographic interferometer was developed. It is based on a novel lens-less design in off-axis holographic geometry. Light from a fiber-coupled laser source is split by a fiber beam splitter, with one output used to illuminate the detector plane and the other for the reference beam. The two beams produce an interference pattern on a CMOS image sensor. To obtain relative displacement information, successive images are superimposed on an initial reference image and reconstructed by solving the Rayleigh-Sommerfeld diffraction integral taking into account the spherical wavefronts of the beams. The interference fringes that appear in the reconstructed holographic image provide a measure of the relative displacement of the detector plane compared to the initial position. The performance of the reconstruction method used was verified with the proposed setup at a real tracking station.

Dual-Functional Tunable Metasurface for Meta-Axicon with a Variable Depth of Focus and Continuous-Zoom Metalens.

Optical metasurfaces have been widely investigated for their versatile ability to manipulate wavefront and miniaturize traditional optical components into ultrathin planar devices. The integration of metasurfaces with multifunctionality and tunability has fundamentally transformed optics with unprecedented control over light propagation and manipulation. This study introduces a pioneering framework for the development of tunable metasurfaces with multifunctionality, and an example of a tunable metasurface of dual functionalities is proposed and numerically verified as one of the tunable meta-axicon for generating Bessel beams with a variable depth of focus (DOF) and a continuous-zoom metalens. Specifically, this design achieves dual-functional phase modulation by helicity-multiplexing from the combination of the geometric phase as well as the propagation phase and realizes tunability for both functionalities through rotational actuation between double metasurface layers. As a result, dual functionalities with continuous tunability of the proposed TiO2 metasurface are enabled independently for the left and right circularly polarized (LCP and RCP) incidences at 532 nm. Specifically, LCP light triggers the metasurface to function as a tunable axicon, generating non-diffracting Bessel beams with variable numerical apertures (NA) and DOFs. Conversely, the RCP incidence induces it to operate as a continuous-zoom metalens and generates variable spherical wavefront focusing on diverse focal lengths. This study not only initially implements the design of tunable meta-axicon, but also achieves the integration of such a tunable meta-axicon and continuous-zoom metalens within a single metasurface configuration. The proposed device could find potential applications in biological imaging, microscopic measurement, laser fabrication, optical manipulation, multi-plane imaging, depth estimation, optical data storage, etc.

Comprehensive tool for a phase compensation reconstruction method in digital holographic microscopy operating in non-telecentric regime.

Quantitative phase imaging (QPI) via Digital Holographic microscopy (DHM) has been widely applied in material and biological applications. The performance of DHM technologies relies heavily on computational reconstruction methods to provide accurate phase measurements. Among the optical configuration of the imaging system in DHM, imaging systems operating in a non-telecentric regime are the most common ones. Nonetheless, the spherical wavefront introduced by the non-telecentric DHM system must be compensated to provide undistorted phase measurements. The proposed reconstruction approach is based on previous work from Kemper's group. Here, we have reformulated the problem, reducing the number of required parameters needed for reconstructing phase images to the sensor pixel size and source wavelength. The developed computational algorithm can be divided into six main steps. In the first step, the selection of the +1-diffraction order in the hologram spectrum. The interference angle is obtained from the selected +1 order. Secondly, the curvature of the spherical wavefront distorting the sample's phase map is estimated by analyzing the size of the selected +1 order in the hologram's spectrum. The third and fourth steps are the spatial filtering of the +1 order and the compensation of the interference angle. The next step involves the estimation of the center of the spherical wavefront. An optional final optimization step has been included to fine-tune the estimated parameters and provide fully compensated phase images. Because the proper implementation of a framework is critical to achieve successful results, we have explicitly described the steps, including functions and toolboxes, required for reconstructing phase images without distortions. As a result, we have provided open-access codes and a user interface tool with minimum user input to reconstruct holograms recorded in a non-telecentric DHM system.

Sub-Array-Based Millimeter Wave Massive MIMO Channel Estimation

Combination of millimeter wave (mmWave) and massive multiple input multiple output (MIMO) forms a promising technology for future sixth generation networks. As the number of antennas increases, propagation channel starts yielding spherical wavefronts, for which the traditional channel estimation algorithms are no longer applicable. To overcome this technical gap, a novel MIMO channel estimation scheme based on the assumption of spherical wavefront is proposed in this work. The large antenna array is first divided into several sub-arrays, and then the channel estimation is performed for each sub-array based on the orthogonal matching pursuit algorithm. In addition, the joint estimation of angle of arrivals and departures (AoAs and AoDs) of each uniform planar sub-array is transformed into separate estimation by dimensionality reduction. Next, an iterative estimation is performed using Taylor expansion to continuously approximate the real grid points to recover the AoAs/AoDs. Lastly, the superiority of the proposed algorithm is verified by numerical simulations, where the proposed algorithm exhibits the best NMSE performance, compared with the existing MIMO channel estimation methods.

Toward 6G Holographic Localization: Enabling Technologies and Perspectives

In the last years, we have experienced the evolution of wireless localization from being a simple add-on feature for enabling specific applications to becoming an essential characteristic of wireless cellular networks, as for sixth generation (6G) cellular networks. This paper illustrates the importance of radio localization and its role in almost all cellular generations. Also, it speculates on the idea of holographic localization where the characteristics of electromagnetic (EM) waves, including the spherical wavefront in the near-field, are fully controlled and exploited to achieve better wireless localization. Along this line, we briefly overview possible technologies, such as large intelligent surfaces, and challenges to realize holographic localization. To corroborate our vision, we also include a numerical example that confirms the potentialities of holographic localization.

Visibility region and correlation in ELAA-MIMO LoS scenarios under planar and spherical wavefront propagation

Channel is one of the critical aspects of designing reliable wireless communication systems by accurately modeling the signal propagation along different physical scenarios where the wireless data transmission occurs. Although several channel models have already been developed for Massive MIMO (M-MIMO) systems, the novel extra-large array aperture multiple-input-multiple-output (ELAA-MIMO) systems impose a new challenge in the development of wireless channel models due to the proximity between users, scatterers, and the base station (BS) array, by establishing the spherical wavefront hypothesis. Spherical wavefront propagation and visibility regions (VR) are known as phenomenons that physically affects the ELAA-MIMO system performance and channel modeling, being essential for practical deployments of the next-generation wireless communications (B5G). In this work, we model and discuss the critical parameters of Line-of-Sight (LoS) M-MIMO and recent ELAA-MIMO channel models, such as physical aspects and generation of these wireless channels. We aim to provide insights on the parameters setting and VR determination based on a power threshold criterion to be considered in specific LoS ELAA-MIMO channel modeling.

A Novel THz Massive MIMO Beam Domain Channel Model for 6G Wireless Communication Systems

In this paper, a three dimensional (3D) geometry based stochastic model (GBSM) considering planar antenna array is firstly proposed for the sixth generation (6 G) terahertz (THz) massive multiple-input multiple-output (MIMO) wireless communication systems. Then, a novel beam domain channel model (BDCM) is derived from the proposed GBSM based on the Fourier transform matrix from the spatial domain to the angle domain in horizontal and vertical directions simultaneously. The THz propagation characteristics, including non-negligible diffuse scattering and limited order of reflection, are considered in these two channel models. In addition, the proposed GBSM and BDCM can capture the spherical wavefront and spatial non-stationarity characteristics in massive MIMO channels by deriving steering vectors of near-field clusters and partly visible clusters, respectively. The angle-domain sparsity property of the BDCM can be observed, which helps reduce the complexity of the GBSM and improve the mathematical tractability. Typical statistical properties of the proposed GBSM and BDCM are derived and compared. The effects of the spherical wavefront on space-time-frequency correlation functions (STF-CFs) and channel capacity are also studied for the proposed GBSM and BDCM. The power leakage of the BDCM caused by the spherical wavefront and visible region (VR) is thoroughly analyzed. It is found that the statistical properties of the GBSM and BDCM fit well and are considerably influenced by the spherical wavefront and VRs.

A Novel 3D Beam Domain Channel Model for UAV Massive MIMO Communications

Due to the agile maneuverability, unmanned aerial vehicles (UAVs) have shown great promise for on-demand communications in the next-generation wireless networks. Considering the massive multiple-input multiple-output (MIMO) configuration, this paper proposes a novel three-dimensional (3D) beam domain channel model (BDCM) for UAV communications. Through dividing the large antenna array into several sub-arrays and classifying multipath components as near-field and far-field components, the proposed BDCM takes the spherical wave front (SWF) and array non-stationarity into account. Channel statistical properties including spatial-temporal-frequency correlation function (STF-CF), root-mean-squared (RMS) Doppler spread, beam spread, channel matrix collinearity (CMC), and stationary time interval are derived and simulated for the proposed BDCM. Influences of SFW and non-stationary properties on the statistical properties and system performance are analyzed. Simulation results show that, compared with the equivalent geometry-based stochastic model (GBSM), the proposed BDCM has better temporal correlation, while BDCM and GBSM are equivalent in the system performance evaluation. Furthermore, the performance of the proposed BDCM is evaluated in terms of accuracy, complexity, and pervasiveness. The results show that the proposed BDCM can represent massive MIMO channel properties accurately with low complexity and good compatibility.