... The diffraction barrier is a fundamental characteristic of light-matter interaction, which refers to the minimum size at which electromagnetic waves can be confined. This limit prevents the localization of light in nanoscale regions smaller than the wavelength, as exemplified by the limited resolution in conventional optical microscopes (Abby's criterion) [14]. In regards to the miniaturization of integrated photonics for data transmission, such as waveguides that steer light within a circuit chip component, diffraction becomes a significant challenge. ...
... This configuration will serve as a reference for the subsequent comparison to highlight how the Bragg diffraction is a constraint that affects the performance of periodic structures, and thwarts their operation in high-frequencies. The dispersion and transmission analysis of the suggested structures are constructed using the eigenvalue and harmonic computations predicated on solving the Helmholtz equation [14], using the Finite Element Method (FEA). ...
... Extending their operation range to much higher frequencies remains a priority, and this aspect is accomplished only through the development of advanced fabrication techniques to synthesize subwavelength structures, which is a result of technological miniaturization progress [26]. The Bragg limit in the cermet changes from 1.1 × 10 14 Hz for the standard isotropic structure, to 4.01 × 10 14 Hz the for the anisotropic case, a fourfold alleviation of the diffraction problem. Modal analysis also revealed large photonic band gaps, a feature with many implications in energy harvesting and electromagnetic wave guiding. ...
Rationally constructed materials have enabled access to optical capabilities beyond nature’s limitations, thanks to advances made in both theory and experiment. These synthetic composites allow subwavelength confinement of electromagnetic energy and facilitate unparalleled control over different aspects of electromagnetic waves (polarization, amplitude, frequency, etc.). However, the diffraction phenomenon is severely hindering the efficacy and performance of dielectric photonic components. Diffraction causes the electromagnetic wave to spread and deviate from its intended path, thereby, making the collimated light beam scatter, leading to lower power density and inaccurate targeting. This is particularly detrimental for applications requiring precise control of high-frequency with shorter wavelengths. Herein, we report on the effect of anisotropic geometrical scaling of dielectric photonic crystals to alleviate the diffraction barrier along the Γ → X path of the irreducible Brillouin region. Thus, achieving the long-sought goal of high-frequency electromagnetic wave steering. We harness the full weight of modal and harmonic analysis based on the Finite Element Method to demonstrate that scaling the direction perpendicular to the wave’s propagation reduced by fourfold the diffraction limit from 100 THz to 400 THz.
... Based on the first-order Born approximation [2], ultrasonic tomography is one of these strategies [3], which is known to be a potentially valuable method of imaging objects with a similar acoustical impedance to that of the surrounding homogeneous medium such as in soft tissue characterization [4] and underwater acoustics [5]. But difficulties arise when it is proposed to obtain quantitative tomograms using acoustical parameters such as the velocity or the attenuation of the wave or tomograms of more highly contrasted media such as in the case of hard tissues [6], industrial process tomography [7], [8], etc. Finding solutions here involves either using iterative schemes [9] and/or performing extensive studies on the limitation of the first-order Born approximation [10]. ...
Ultrasound tomography is crucial due to its capability to deliver detailed, real-time, and non-invasive imaging. This is essential for early diagnosis, treatment planning, and guiding medical procedures. Its affordability, portability, and safety make it a versatile tool in medical and non-medical fields alike, driving ongoing advancements in technology and applications. The Distorted Born Iterative Method (DBIM) is an advanced technique used in ultrasound tomography to iteratively restore images, improving upon the standard Born approximation by addressing some of its limitations. However, the DBIM also has its own set of disadvantages when used for iterative image restoration, resulting in computational complexity, noise sensitivity, convergence issues, etc. In this paper, we introduce a new method for image reconstruction in ultrasound tomography by using the algebraic method. The numerical results indicate that this method has a shorter computational time and achieves high-resolution reconstructions and accurate solutions.
... Although the perovskite-nanocrystals-based method is capable of sensing three-dimensional (3D) light-direction, its large-scale application is relatively costly and complex. While, with the design goals of ultra-small, high-precision, and wide-sensing-range, angle-sensors relying on lenses or gratings suffer a sharp decrease in accuracy when their scales approach or are smaller than the wavelength due to the diffraction limitation [15]. ...
High-precision, ultra-thin angular detectable imaging upon a single pixel holds significant promise for light field detection and reconstruction, thereby catalyzing advancements in machine vision and interaction technology. Traditional light-direction angle sensors relying on optical components like gratings and lenses face inherent constraints from diffraction limits in achieving device miniaturization. Recently, angle sensors via coupled double nanowires have demonstrated prowess in attaining high-precision angle perception of incident light at sub-wavelength device scales, which may herald a novel design paradigm for ultra-compact angle sensors. However, the current approach to measure the three-dimensional (3D) incident light direction is unstable. In this paper, we propose a flexible segmented concentric nanorings structure capable of discerning the 3D light-direction based on its sensitivity character to both elevation (θ) and azimuth (ϕ) angles at a micrometer device scale. Through deep learning (DL) analysis and prediction, our simulations reveal that for angle scanning with a step size of 1o, the device can still achieve a detection range of 0∼360o for azimuth and 45o∼90o for elevation, with an average accuracy of 0.19o, and DL can further solve some data aliasing problems to expand the sensing range. Our design broadens the angle sensing dimension based on mutual resonance coupling among nanorings segments, and through waveguide implementation or sensor array arrangements, the detection range can be flexibly adjusted to accommodate diverse application scenarios.
... Through this effect, incident angles can be obtained according to the changing rules of the self-images [10]. However, angle sensors that rely on lenses or gratings are limited by diffraction theory [11]. When a sensor's scale is close to or smaller than the wavelength of the detection light, its accuracy will sharply decrease due to the minimal recognizable half wavelength limits between two adjacent imaged spots, and this makes it difficult to achieve the design goal of ultra-thin sensors with deep miniaturization. ...
High-precision, ultra-thin angular detectable imaging upon a single pixel holds significant promise for light-field detection and reconstruction, thereby catalyzing advancements in machine vision and interaction technology. Traditional light-direction angle sensors relying on optical components like gratings and lenses face inherent constraints from diffraction limits in achieving device miniaturization. Recently, angle sensors via coupled double nanowires have demonstrated prowess in attaining high-precision angle perception of incident light at sub-wavelength device scales, which may herald a novel design paradigm for ultra-compact angle sensors. However, the current approach to measuring the three-dimensional (3D) incident light direction is unstable. In this paper, we propose a sensor concept capable of discerning the 3D light-direction based on a segmented concentric nanoring structure that is sensitive to both elevation angle (θ) and azimuth angle (ϕ) at a micrometer device scale and is validated through simulations. Through deep learning (DL) analysis and prediction, our simulations reveal that for angle scanning with a step size of 1°, the device can still achieve a detection range of 0∼360° for ϕ and 45°∼90° for θ, with an average accuracy of 0.19°, and DL can further solve some data aliasing problems to expand the sensing range. Our design broadens the angle sensing dimension based on mutual resonance coupling among nanoring segments, and through waveguide implementation or sensor array arrangements, the detection range can be flexibly adjusted to accommodate diverse application scenarios.
... In polystyrene suspensions containing 0.2μm and 0.5μm particles, these particle sizes are smaller than or comparable to a portion of the light's wavelength. Consequently, longer wavelengths more readily bypass the particles, whereas shorter wavelengths are more likely to interact with them [37]. For polystyrene suspensions with 1μm particles, the particle size exceeds the wavelength, facilitating interactions between the light waves and the particles. ...
Polystyrene microplastics are now widely distributed in aquatic environments, encompassing natural waters, bottled water, and even biological fluids such as blood and urine. These microplastics negatively affect such processes as underwater communication, underwater detection, and blood flow imaging. In this work, a suspension of polystyrene microspheres was chosen as the subject of investigation. Monodisperse polystyrene microspheres with diameters of 0.2μm, 0.5μm, and 1μm were used to create uniform scattering environments in water. Incident wavelengths of 470nm, 532nm, and 670nm were selected, respectively. The study examines which type of polarized light maintains its polarization most effectively. For polystyrene suspensions containing 0.2μm particles, parallel polarized light demonstrated superior polarization retention at the 532nm and 670nm wavelengths. In all other instances, right-handed circular polarized light exhibited better polarization retention. This phenomenon can be tentatively explained by the vector Fokker-Planck approximation. According to the vector Fokker-Planck approximation, the retention of circular polarization is correlated with the asymmetry parameter g. Circular polarization preserves its helicity and handedness during propagation through anisotropic random media. By contrast, linear polarization states become randomized more rapidly. This reversal occurs as the anisotropy of the environment decreases. The investigation also addresses which wavelength demonstrates enhanced polarization retention. Longer wavelengths exhibit improved polarization retention. Both parallel and right-handed circular polarized light achieve optimal polarization retention at the 670 nm wavelength. The outcomes of this research are anticipated to aid in endeavors such as underwater communication, underwater detection, and blood flow imaging techniques.
... In polystyrene suspensions containing 0.2μm and 0.5μm particles, these particle sizes are smaller than or comparable to a portion of the light's wavelength. Consequently, longer wavelengths more readily bypass the particles, whereas shorter wavelengths are more likely to interact with them [37]. For polystyrene suspensions with 1μm particles, the particle size exceeds the wavelength, facilitating interactions between the light waves and the particles. ...
Polystyrene microplastics are now widely distributed in aquatic environments, encompassing natural waters, bottled water, and even biological fluids such as blood and urine. These microplastics negatively affect such processes as underwater communication, underwater detection, and blood flow imaging. In this work, a suspension of polystyrene microspheres was chosen as the subject of investigation. Monodisperse polystyrene microspheres with diameters of 0.2μm, 0.5μm, and 1μm were used to create uniform scattering environments in water. Incident wavelengths of 470nm, 532nm, and 670nm were selected, respectively. The study examines which type of polarized light maintains its polarization most effectively. For polystyrene suspensions containing 0.2μm particles, parallel polarized light demonstrated superior polarization retention at the 532nm and 670nm wavelengths. In all other instances, right-handed circular polarized light exhibited better polarization retention. This phenomenon can be tentatively explained by the vector Fokker-Planck approximation. According to the vector Fokker-Planck approximation, the retention of circular polarization is correlated with the asymmetry parameter g. Circular polarization preserves its helicity and handedness during propagation through anisotropic random media. By contrast, linear polarization states become randomized more rapidly. This reversal occurs as the anisotropy of the environment decreases. The investigation also addresses which wavelength demonstrates enhanced polarization retention. Longer wavelengths exhibit improved polarization retention. Both parallel and right-handed circular polarized light achieve optimal polarization retention at the 670 nm wavelength. The outcomes of this research are anticipated to aid in endeavors such as underwater communication, underwater detection, and blood flow imaging techniques.
... where (q y , q z ) is the in-plane wavevector, κ o and κ e are decrements of field decay from the boundary, and k 0 = ω/c is the wavevector in vacuum. The expressions are obtained from solving the Fresnel equation system [108]. The form of eigenvectors (A1) and (A2) is especially useful. ...
Surface polaritons in an anisotropic media possess a strong dependence of the wave vector on the propagation direction, which is called the isofrequency contour. This can lead to the fact that polariton propagation is possible only in a limited range of angles in the boundary plane. Notable examples are Dyakonov surface waves at the boundary of two dielectrics and hyperbolic plasmons in a hyperbolic metamaterial. Exact closed-form solutions of the polariton dispersion equation are known only in special cases: in a weakly anisotropic medium and in an arbitrary medium for highly symmetric directions of polariton propagation. This work provides an universal exact solution in algebraic form for a surface polariton at the interface of arbitrary isotropic and uniaxial media for the case of the optic axis parallel to the boundary. As an example, it is used to analyze the shapes of isofrequency contours of surface polaritons. The work brings together previously scattered results of studies on surface polaritons of various types in uniaxial media. In addition, two cases not previously considered in the literature are analyzed in detail here. The first corresponds to the boundary of an isotropic metal and a Type I hyperbolic medium, for which the existence of a surface polariton is predicted. In the second case, “elliptic” surface polaritons at the boundary of an isotropic dielectric and an anisotropic metal-like medium are analyzed.
... Further, in Figure 4a,b, we evaluate the laser absorption percentage in the spintronic heterostructures. Poynting's theorem is used to estimate the absorption allocation of the excitation laser in the individual layer based on the experimentally observed reflectance and transmittance from the samples (Section S6, Supporting Information regarding absorption calculation, including the application of Poynting's theorem [60] ). From Figure 4b, we find that the SAF heterostructure exhibits the same fluence absorption, 19.1%, in both the NiFe layers, suggesting the formation of equal spin current density. ...
The broken inversion symmetry at the ferromagnet (FM)/heavy‐metal (HM) interface leads to spin‐dependent degeneracy of the energy band, forming spin‐polarized surface states. As a result, the interface serves as an effective medium for converting spin accumulation into 2D charge current through the inverse Rashba–Edelstein effect. Exploring and assessing this spin‐to‐charge conversion (SCC) phenomenon at the FM/HM interface can offer a promising avenue to surpass the presumed limits of SCC in bulk HM layers. Spintronic heterostructures are utilized as a platform to measure the SCC experienced by photoexcited spin currents. Therefore, FM/HM heterostructures emitting terahertz electric field upon illumination by femtosecond laser pulses enable quantitative measure of the ultrafast SCC process. This results demonstrate a robust interfacial spin‐to‐charge conversion (iSCC) within a synthetic antiferromagnetic heterostructure, specifically for the NiFe/Ru/NiFe configuration, by isolating the SCC contribution originating from the interface and the bulk heavy‐metal (HM). Through the measurements of the emitted terahertz pulse, the iSCC at the NiFe/Ru interface is identified to be ≈27% of the strength as compared to SCC from the highest spin‐Hall conducting heavy‐metal, Pt. The results thus highlight the significance of interfacial engineering as a promising pathway for achieving efficient ultrafast spintronic devices.
... The angular resolution of an imaging system depends on the sharpness of its impulse function [15]. For a diffraction limited telescope, this response depends on 1) the wavelength of the observed light, λ; 2) the telescope's diameter, D. For an ideal scenario with a circular aperture, the full width at half maximum (FWHM) of the impulse function is λ/D [16]. ...
Point source detection algorithms play a pivotal role across diverse applications, influencing fields such as astronomy, biomedical imaging, environmental monitoring, and beyond. This article reviews the algorithms used for space imaging applications from ground and space telescopes. The main difficulties in detection arise from the incomplete knowledge of the impulse function of the imaging system, which depends on the aperture, atmospheric turbulence (for ground-based telescopes), and other factors, some of which are time-dependent. Incomplete knowledge of the impulse function decreases the effectiveness of the algorithms. In recent years, deep learning techniques have been employed to mitigate this problem and have the potential to outperform more traditional approaches. The success of deep learning techniques in object detection has been observed in many fields, and recent developments can further improve the accuracy. However, deep learning methods are still in the early stages of adoption and are used less frequently than traditional approaches. In this review, we discuss the main challenges of point source detection, as well as the latest developments, covering both traditional and current deep learning methods. In addition, we present a comparison between the two approaches to better demonstrate the advantages of each methodology.
The planar laser-induced fluorescence (PLIF) method has been widely applied for measuring the thickness of liquid films. To identify the liquid–gas interface, however, PLIF-based methods require an artificial threshold value of brightness or a calibration curve between the thickness and the brightness, limiting its application in measuring unknown film thickness. To overcome the drawbacks, we propose a new method, time-variant PLIF (T-PLIF), which employs an index of time variance of brightness to detect the interface. We first establish the mathematical principle of T-PLIF, wherein the time variance of a phase-dependent variable becomes the maximum exactly at the time-averaged position of the wavy interface. We then perform experiments for a well-controlled downward annular liquid film flow to test the reliability of T-PLIF. We demonstrate that T-PLIF measures liquid film thickness of with the accuracy of to the theoretical reference and with . T-PLIF is able to quantify the film thickness with no need for any pre-/post-calibration or artificial threshold values. We further confirm the applicability of T-PLIF to the wavy film flow sheared by an airflow up to by measuring the phase velocity and wavelength, which well matches the theoretical results.
Surface plasmon polaritons (SPPs) describe the excitation of photons coupled with free charge carriers at the interface of metals (visible) or doped semiconductors (infrared). While SPPs in the mid-infrared spectral range have been demonstrated in 2D materials such as graphene, their short propagation length combined with weak confinement in bulk materials has prevented real-space imaging of those SPPs. Here, we demonstrate real-space imaging of propagating SPPs on the doped semiconductors CdO and InAs with tunable plasma frequencies in the infrared via scattering-type scanning near-field optical microscopy. Adding a thin film of phase-change materials (PCMs) to these doped semiconductors increases the polariton confinement, leading to simplified SPP imaging and SPP resonator fabrication. We investigate optically written circular resonators of the plasmonic PCM In 3 SbTe 2 on CdO with near-field spectroscopy and Fabry-Perot resonators of the dielectric PCM Ge 3 Sb 2 Te 6 on InAs with far-field spectroscopy. Our work enables rapid prototyping of reconfigurable SPP resonators in mid-infrared.
The thermoelectric, magneto-optic, and electronic characteristics of the materials Ba2GdXO6 (X = Nb, & U) have been computed, using first principles investigations. The GGA + U potential approximation is used to predict the ground state characteristics of the materials. The materials are found to have a stable crystallographic structure by obtaining the tolerance factor in the cubic (Fm-3 m) symmetries. They are also found to be thermodynamically and dynamically stable. The electronic band structures suggest that the Ba2GdNbO6 is direct band gap semiconducting with band gaps of 2.3 eV (spin up) and 2.5 eV (spin down) and the half-metallic nature of Ba2GdUO6. The DOS predicts the magnetic nature of the materials. The integral values 7 (µB) and 8 (µB) of total magnetic moments of Ba2GdNbO6 and Ba2GdUO6, respectively, support the ferromagnetic nature of the materials. The ferromagnetic nature of the material was determined by analyzing the energy–volume optimization curve at the most stable configuration, in comparison with the antiferromagnetic (AFM) and non-magnetic (NM) phases. The optical characteristics, including the real and imaginary parts of the dielectric functions, along with other optical parameters, have been computed and discussed to understand the optical behavior of the materials. The overall ZT and PF analysis of the materials suggests that the Ba2GdUO6 shows excellent thermoelectric performance as compared to the Ba2GdNbO6 material. The thermoelectric, magneto-optic, and electronic characteristics of the materials Ba2GdXO6 (X = Nb, U) have been computed using first principles investigations. The GGA + U potential approximation is employed to predict the ground state characteristics, while the main focus remains on GGA + U. However, band gap values were also calculated using the HSE06 functional, yielding 5.358 eV for Ba2GdNbO6 (spin up), 5.384 eV for Ba₂GdNbO₆ (spin down), 4.420 eV for Ba₂GdUO₆ (spin up), and 3.891 eV for Ba₂GdUO₆ (spin down), confirming that these materials are direct band gap semiconductors. The materials demonstrate a stable crystallographic structure within cubic (Fm-3 m) symmetries, verified by tolerance factor calculations, indicating thermodynamic and dynamic stability. The electronic band structures classify Ba2GdNbO6 as a direct band gap semiconductor, while Ba₂GdUO₆ exhibits half-metallic behavior. The DOS analysis further suggests the magnetic nature of the materials, with total magnetic moments of 7 µB and 8 µB for Ba2GdNbO6 and Ba2GdUO6, respectively, supporting their ferromagnetic character. This ferromagnetic nature is confirmed by energy–volume optimization, where ferromagnetic configurations show greater stability compared to antiferromagnetic (AFM) and non-magnetic (NM) phases. Optical properties, including the real and imaginary parts of the dielectric functions, along with other optical parameters, have been calculated to elucidate the materials’ optical behavior. The ZT and power factor (PF) analyses indicate that Ba2GdUO6 exhibits superior thermoelectric performance compared to Ba2GdNbO6.
The control of polarization, an essential property of light, is of wide scientific and technological interest. The general problem of generating arbitrary time-varying states of polarization (SOP) has always been mathematically formulated by a series of linear transformations, i.e. a product of matrices, imposing a serial architecture. Here we show a parallel architecture described by a sum of matrices. The theory is experimentally demonstrated by modulating spatially-separated polarization components of a laser using a digital micromirror device that are subsequently beam combined. This method greatly expands the parameter space for engineering devices that control polarization. Consequently, performance characteristics, such as speed, stability, and spectral range, are entirely dictated by the technologies of optical intensity modulation, including absorption, reflection, emission, and scattering. This opens up important prospects for polarization state generation (PSG) with unique performance characteristics and applications in spectroscopic ellipsometry, spectropolarimetry, communications, imaging, and security.
When performing ultrasonic testing of pipes of various diameters using antenna arrays and matrices, two technologies for imaging reflectors-the total focusing method (TFM) and the digital aperture focusing (DAF)-are widely used. If the pipe diameter is greater than a hundred wavelengths, the DAF can be utilized for reflector imaging, considering multiple reflections from boundaries while assuming that the test object is flat. The errors in forming the DAF image of reflectors will be minimal in this case. However, if the pipe diameter is several tens of wavelengths and the wall thickness is approximately half the pipe diameter, then to obtain a quality DAF image of the reflectors, the geometry of the test object must be taken into account. This paper examines the features of image formation when recording echo signals with an antenna array or matrix while scanning both the outer and inner surfaces of the test object. Numerical and model experiments demonstrate that to achieve high-quality DAF images of reflectors when scanning the outer surface of a thick-walled pipe with a small diameter, both an antenna array and an antenna matrix can be used. This is due to the presence of the physical focusing effect of the ultrasonic field. However, when scanning the inner surface of a thick-walled pipe with a small diameter, echo signals must be recorded using an antenna matrix to reconstruct the image of the reflectors due to the defocusing effect.
Many animals exhibit structural colors, which are often iridescent, meaning that the perceived colors change with illumination conditions and viewing perspectives. Biological iridescence is usually caused by multilayers or other periodic structures in animal tissues, which selectively reflect light of certain wavelengths and often result in a shiny appearance---which almost always comes with spatially varying highlights, thanks to randomness and irregularities in the structures. Previous models for biological iridescence tend to each target one specific structure, and most models only compute large-area averages, overlooking spatial variation in iridescent appearance.
In this work, we build appearance models for biological iridescence using bird feathers as our case study, investigating different types of feathers with a variety of structural coloration mechanisms. We propose an approximate wave simulation method that takes advantage of quasi-regular structures while efficiently modeling the effects of natural structural irregularities. We further propose a method to distill our simulation results into distributions of BRDFs, generated using noise functions, that preserve relevant statistical properties of the simulated BRDFs. This allows us to model the spatially varying, glittery appearance commonly seen on feathers. Our BRDFs are practical and efficient, and we present renderings of multiple types of iridescent feathers with comparisons to photographic images.
In recent decades, there has been an increasing interest in the search for structures that enable confining and manipulating light at the nanometer scale. However, the diffraction limit of light poses a fundamental challenge in achieving resolution beyond the wavelength of the illuminating light, restricting the fabrication and imaging of sub-wavelength structures and thus impeding progress in the field of nano-optics. The initial section of this chapter illustrates this limitation by demonstrating that waveguides—structures designed to direct light along specific directions—made of traditional dielectric materials are not suitable for confining light in nanometric volumes at visible or longer wavelengths.
In the subsequent sections, we discuss considerable advances that have been made to overcome this limitation. All are based on leveraging polaritons—hybrid light matter excitations—to achieve nanoscale confinement and control of light. We will show that polaritons can propagate along interfaces between materials with permittivities of different signs as a result of the strong interaction between light and collective dipolar matter oscillations. Then, we offer a comprehensive overview of propagating polaritons. Initially, these were explored in bulk metals and polar crystals, and subsequently in graphene and hexagonal boron nitride with the advent of van der Waals (vdW) and two-dimensional (2D) materials. We also put a special focus on the mid-infrared (mid-IR) frequency range, a technologically important spectral region, and we highlight the role that anisotropy plays in the properties of propagating polaritons. Finally, we introduce alpha-phase molybdenum trioxide, the main material studied in this thesis. This vdW semiconductor supports the propagation of strongly anisotropic polaritons along its surface, promising unprecedented control of light and the flow of energy at the nanoscale.
In this chapter, organized in a tutorial style, we present a detailed derivation of the dispersion relation of electromagnetic modes in a biaxial slab. We show that our general dispersion relation successfully reduces to several known limiting cases of interest, such as uniaxial and isotropic slabs or semi-infinite crystals, among others. We manage to reduce the general dispersion relation to simple analytical expressions for short wavelength of the modes and small slab thicknesses, which are of great interest for the study of anisotropic polaritons in van der Waals (vdW) slabs. To demonstrate the validity of our analytical approximations, we compare them to full-wave simulations, finding an excellent agreement.
Most of the results reported in this chapter were developed in collaboration with Kirill Voronin (Moscow Institute of Physics and Technology, Russia), and published in “Analytical approximations for the dispersion of electromagnetic modes in slabs of biaxial crystals”, by Gonzalo Álvarez-Pérez, Kirill V. Voronin et al., in Physical Review B 100, 235408 (2019).
Hybrid integration of solid-state quantum emitters (QEs) into nanophotonic structures opens enticing perspectives for exploiting multiple degrees of freedom of single-photon sources for on-chip quantum photonic applications. However, the state-of-the-art single-photon sources are mostly limited to two-level states or scalar vortex beams. Direct generation of high-dimensional structured single photons remains challenging, being still in its infancy. Here, we propose a general strategy to design highly entangled high-dimensional spin-orbital single-photon sources by taking full advantage of the spatial freedom to design QE-coupled composite (i.e., Moiré/multipart) metasurfaces. We demonstrate the generation of arbitrary vectorial spin-orbital photon emission in high-dimensional Hilbert spaces, mapping the generated states on hybrid-order Bloch spheres. We further realize single-photon sources of high-dimensional spin-orbital quantum emission and experimentally verify the entanglement of high-dimensional superposition states with high fidelity. We believe that the results obtained facilitate further progress in integrated solutions for the deployment of next-generation high-capacity quantum information technologies.
We propose a novel hybrid classical-quantum approach for image processing based on polar Walsh basis functions. Using this approach, we present an algorithm for the removal of the circular banding noise (including Airy pattern noise) and the azimuthal banding noise. This approach is based on a formulation of Walsh basis functions in polar coordinates for image representations. This approach also builds upon an earlier work on a hybrid classical-quantum algorithm for Walsh-Hadamard transforms. We provide two kinds of polar representations using uniform area measure and uniform radial measure. Effective smoothening and interpolating techniques are devised relevant to the transformations between Cartesian and polar coordinates, mitigating the challenges posed by the non-injectivity of the transformation in the context of digital images. The hybrid classical-quantum approach presented here involves an algorithm for Walsh-Hadamard transforms, which has a lower computational complexity of compared to the well-known classical fast Walsh-Hadamard transform, which has a computational complexity of . We demonstrated the applicability of our approach through computational examples involving the removal of the circular banding noise (including Airy pattern noise) and the azimuthal banding noise.
A disposable miniature radiometer has been developed using optical filters for spectral separation. Limitations in accurately retrieving irradiance from the broad-band measurement results can be attributed to the broad-band filters. This paper proposes an algorithm for spectral irradiance using broad-band optical filter data (SIBOF algorithm) to achieve precise retrieved irradiance through four correction steps. First, the algorithm uses an energy ratio method to adjust the broad-band data to narrow-band data. The energy ratio is derived from the reference lamp spectrum and measured optical filter transmissivities. Second, the algorithm corrects for filter transmissivity differences by multiplying the normalized spectral transmissivities by calibration coefficients. The third step involves polarization correction, compensating for additional transmissivity caused by polarization effects from the film overlying on the cosine collector, thus eliminating errors due to film polarization. The fourth step involves radiative heating correction, where fitting curves and coefficients are used to analyze the relationship between irradiance deviation and actual irradiance to correct the data. Standardized tests indicate that, after applying the four corrections, the results are highly consistent with the irradiance from the reference radiometer, demonstrating that these correction steps constitute a reliable algorithm for spectral irradiance using broad-band optical filter data. In April 2024, a 20-day sea fog sounding observation was conducted at the Qianliyan Ocean Station. The irradiance data from the miniature radiometers before launch were corrected and compared with those measured by the reference radiometer on the ground. Results indicate that the irradiance retrieved through the algorithm was in good agreement with the measurements from the reference radiometer, validating its performance across various weather conditions.
PixPol is an in-water multi-spectral polarized upwelling radiance distribution fisheye camera system. Its imaging sensors utilize a pixel-level polarizer structure allowing for polarimetric retrieval from one image capture, offering an advantage compared to other in-water polarimetric fisheye camera systems that require information from multiple images. When submerged, PixPol images a scene from which the first three Stokes parameters are derived at an angular resolution of 1° within a field of view that encompasses all azimuthal angles up to an elevation of 43° from nadir. For all viewing angles, Stokes parameter I and the linear polarization parameters, Q / I and U / I , are retrieved with an inter-pixel uncertainty of ±5%, ±0.02, and ±0.02, respectively. From these parameters, an uncertainty of ±0.01 is attained for the degree of linear polarization and ±0.9° for the angle of linear polarization. A description of the camera system, its radiometric and polarization calibration, and the associated uncertainties are described. Example images of the distribution of downwelling polarized light in the sky just above the ocean’s surface and upwelling polarized light just below the surface are provided.
We give different integral representations of the Lommel function s μ , ν ( z ) involving trigonometric and hypergeometric 2 F 1 functions. By using classical results of Pólya, we give the distribution of the zeros of s μ , ν ( z ) for certain regions in the plane ( μ , ν ) . Further, thanks to a well known relation between the functions s μ , ν ( z ) and the hypergeometric 1 F 2 function, we describe the distribution of the zeros of 1 F 2 for specific values of its parameters.
We review the classical Fermat principle, a fundamental result in the calculus of variations. By determining the Euler–Lagrange equations for the optical path length functional in homogeneous, isotropic media, we review how to obtain the classical ray equations in terms of the refractive index of a material. Staying in the variational framework, we discuss how the Weierstrass–Erdmann corner condition for parametric variational integrals leads to the classical Snell’s Law of refraction. We then discuss many variants of Snell’s Law, looking at both refraction and reflection. Finally, we focus on liquid crystal optics by taking the optical path length functional to be the one with integrand being the effective refractive index obtained in the previous chapter. Connections to recent results in the literature are provided along the way, and we end with a discussion about Snell’s Law with absorption.
In this chapter we review optical aberrations in third order geometric optics and focus on wave aberration functions. After a systematic review of aberrations, we consider a two dimensional lens design problem. The problem is the following: Given the first surface of an optical lens in two dimensions, what is the second surface such that the lens containing a liquid crystal layer between the surfaces refracts the extraordinary ray into a given fixed point? We then consider an inverse optical problem; namely, given a desired light ray trajectory, what nematic director can be imposed in order to obtain such trajectory?
This chapter is devoted to a brief review of liquid crystals, providing both a physical background and a mathematical background. Namely, we discuss the various competing theories for nematic liquid crystals: the Oseen–Frank model, Eriksen model, and Landau–de Gennes theory. We describe some of the mathematics used to understand defects and classical director deformations (bend, splay, and twist). We also derive formulas for the effective refractive indices for a nematic liquid crystal, based on both definitions of light ray discussed in the previous chapter. We also derive a formula for the effective refractive index for a biaxial nematic liquid crystal. This chapter is meant to serve as a brief introduction to liquid crystals to those more familiar with the mathematical optics aspects. In particular, we also provide a short review of some recent mathematical results.
Starting from the equations of macroscopic electromagnetism, we derive the geometric optics regime as a limiting case. We discuss the different types of anisotropy possible and then focus on the optical indicatrix in uniaxial and biaxial media. From the optical indicatrices, we show how to obtain the Fresnel surfaces for the ordinary and extraordinary waves and how this relates to the classical Eikonal equation. The permittivity can be written in terms of appropriate refractive indices and director fields by using the constitutive relation , where is the electric flux density and is the electric field. Finally, the definition of light ray is explored; in the case of anisotropic media, it is necessary to distinguish between the direction of propagation of light rays and the direction of propagation of energy flux.
In this last chapter, we provide a brief summary of the previous chapters. We then enumerate a number of open directions where this research could lead to, starting from determining a more general Snell’s Law and then revisiting the challenges of absolute instruments. Moreover, we suggest a way to ease the restrictions of an absolute instrument by considering what we call nearly absolute instruments, where instead of no aberrations being present, one allows for a small amount of wave aberrations. Related to this and the associated wave aberration function, we consider the optical transfer function as a measure of the image quality of an optical system. Here we make interesting connections between the very concrete optical transfer function and harmonic analysis techniques related to oscillatory integrals. We also say a few words about incorporating topological objects into this geometric optics analysis, such as skyrmions, hopfions, and heliknotons. Finally, we provide some directions related to helical media (especially, cholesteric liquid crystals) and detail a short conclusion.
This chapter illustrates the challenges associated with obtaining absolute instruments, i.e., devices that stigmatically image a region of 3D. The starting point is an analogy between mechanics and optics which relates the refractive index for an “optical” problem to a potential in a “mechanics” problem. There are deep mathematical connections between absolute instruments and superintegrable systems. We review some essentials of separable Hamiltonians and superintegrable systems, starting from Hamilton equations of motion. The main issue we encounter is that the relevant mechanical potential depends on velocity, so separation of variables (in order to obtain a separable Hamiltonian) is not straightforward. Moreover, if we wish to use liquid crystals to construct absolute instruments, the relevant Hamiltonian is actually quadratic in the momentum variables. Finally, we make an interesting connection between absolute instruments to Riemannian geometry (more precisely, Wiedersehen manifolds) through the so-called Wiedersehenmannigfaltigkeit.
This chapter continues the variational focus by first deriving the Euler–Lagrange equation for the optical path length functional with effective refractive index from previous chapters. Next, we show under what conditions one can find a minimizer of this functional in a particular class of allowable trajectories. This is then extended to the case of rectifiable curves when the director is at least smooth. This uses a lower semicontinuity argument and the Dunford–Pettis Theorem. We then consider the Hamiltonian formulation (rather than the usual Lagrangian formulation) and provide a brief review of Riemannian geometry concepts necessary to understand light rays as geodesics under a certain geometry, i.e., with a certain metric. We obtain the geodesic equations for the optical path length functional and provide a number of examples. Finally, we discuss broken extremals, which are typical in optics problems when an abrupt change of materials occurs. We discuss the possibility of obtaining discontinuous extremals, with explicit calculations done in two dimensions.
This study focuses on the influence of low-concentration additions of NiCl2 on the overall properties of lead arseborate oxide glasses. In this regard, small amounts, in grams, of NiCl2 were added, separately, to the main constituents of the lead-arseboarte glass, according to the chemical formula [23 wt% B2O3–11 wt.% Na2O–20 wt. CaO–23 wt.% PbO–23 wt.% As2O3] % + x NiCl2, where x = 0.25, 0.5, 0.75, and 1 g, to prepare a glass series of four samples using the fast quenching technique. The structural and optical characterizations of the prepared samples have been described based on X-ray diffraction (XRD) measurements, Fourier transform infrared charts (FTIR), and UV–Vis spectra. The X-ray diffraction (XRD) patterns did not contain any crystalline peaks but only two broad humps which revealed that all samples possess short-range order structures. At the same time, the FTIR charts showed different structural units. The UV–Vis spectra demonstrated that the absorption edge spectra changed to a higher wavelength with an increase in NiCl2 dopants, accompanied by a drop in optical transmittance, particularly in the visible range. As the NiCl2 dopants increased, the values of the optical energy gaps reduced while the mass attenuation remained constant, and the effective atomic number, bulk density, microhardness, absorption index, and characteristic relaxation time increased. Regardless of sample thickness, a novel methodology has been proposed to determine both the optical band gaps and the optical loss. The novel method and the widely used one (Tauc relation) demonstrated excellent agreement. The results suggest the NiCl2-rich sample is a primary material for radiation shielding applications as a carrier for radioactive sources and preserving them, or for preserving radioactive waste and high-reflection and UV-blocking glass coating.
The widespread introduction of antenna arrays into the practice of ultrasonic testing has made it possible to obtain images of reflectors using either phased array technology or digital focusing of aperture (DFA) technology. However, many current regulatory documents governing the rules for conducting ultrasonic nondestructive testing in nuclear power engineering, petrochemistry, gas production industry, etc. require determining the equivalent dimensions of reflectors. The present article proposes a method for calculating the DAF-DGS array to determine the diameter of an equivalent flat-bottomed hole (FBH) when analyzing an image. It is shown that it is more efficient to work not with the amplitude of the image, but with the integral amplitude. Numerical experiments have shown the accuracy of the order of mm in determining the FBH diameter. In model experiments, the accuracy of determining the FBH diameter was better than 0.2 mm in absolute value. Keywords: antenna array, DGS curve, full matrix capture (FMC), total focusing method (TFM), digital focusing of aperture (DFA)
The spacer layer imaging method (SLIM) is widely used to measure the thickness of additive and lubricant films, in lubricant development and evaluation, and for fundamental research into elastohydrodynamic lubrication and tribofilm formation mechanisms. The film thickness measurement, as implemented on several popular tribometers, provides powerful, non-destructive in-situ mapping of film topography with nanometre-scale height sensitivity. However, the results can be highly sensitive to experimental procedure, machine condition, and image analysis, in some cases reporting unphysical film thickness trends. The prevailing image analysis techniques make it challenging to interrogate these errors, often hiding their multivariate nonlinear behaviour from the user by spatial averaging. Herein, several common ‘silent errors’ in the SLIM measurement, including colour matching to incorrect fringe orders, and colour drift due to the optical properties of the system or film itself, are discussed, with examples. A robust suite of novel a priori and a posteriori methods to address these issues, and to improve the accuracy and reliability of the measurement, are also presented, including a novel, computationally inexpensive circle-finding algorithm for automated image processing. In combination, these methods allow reliable mapping of films up to at least 800 nm in thickness, representing a significant milestone for the utility of SLIM applied to elastohydrodynamic contact.
Graphical abstract
Free-space diffractions are an optical phenomenon where light appears to "bend" around the geometric edges and corners of scene objects. In this paper we present an efficient method to simulate such effects. We derive an edge-based formulation of Fraunhofer diffraction, which is well suited to the common (triangular) geometric meshes used in computer graphics. Our method dynamically constructs a free-space diffraction BSDF by considering the geometry around the intersection point of a ray of light with an object, and we present an importance sampling strategy for these BSDFs. Our method is unique in requiring only ray tracing to produce free-space diffractions, works with general meshes, requires no geometry preprocessing, and is designed to work with path tracers with a linear rendering equation. We show that we are able to reproduce accurate diffraction lobes, and, in contrast to any existing method, are able to handle complex, real-world geometry. This work serves to connect free-space diffractions to the efficient path tracing tools from computer graphics.
The problem of detecting weak signals in the presence of a bright and contrasting background in scanning optical technical visual systems is discussed. Creating appropriate digital signal processing algorithms to solve it is important for automatic remote sensing systems working in a hard and aggressive environment. For such a problem, the major task is obtaining an acceptably low false alarm rate while at the same time maintaining a high probability detection of useful signal. The main focus of the proposed chapter is concentrated on the method based on sequential viewing of all elements of the area of responsibility of the visual system and fixing those elements where the detector detected the signal source. Mathematics aspects of one-step cyclic searching and post-detector signal processing are discussed. The search procedure is presented as a branched transition graph, where the nodes of the graph represent possible states, and the edges of the graph represent possible transitions of the search system from one state to another. Analytical expressions are obtained that determine the mathematical expectation and dispersion of the signal detection and identification time, provided that a single-cycle search has been carried out.
Material relevant from a physicist’s point of view is addressed in this chapter. The emphasis is on understanding Cauchy’s theorem, the residue theorem, etc. by following a numerical approach—performing hands-on computations. I have found that students appreciate this and understand analytic functions, and singularities better if a concrete numerical approach is adopted in addition to the standard methods. Python programmes and figures elucidate the content. Figures show the properties of poles and essential singularities; why is it called essential? Its nasty behaviour is made explicit. Topics such as analytic continuation and the stationary phase approximation are also discussed.
This study examines the physical characteristics of Co2Te3O8 in the spiroffite structure using an ab initio approach. The optimization of the Co2Te3O8 structure, in both nonmagnetic and magnetic states, indicates that the magnetic state is more stable than the non-magnetic one. Thermodynamic properties under various temperatures and pressures, calculated via the quasi-harmonic approximation, reveal that the specific heat capacity of spiroffite Co2Te3O8 conforms to the Debye model and satisfies the Dulong and Petit limits. The electrical, magnetic, and optical properties of Co2Te3O8 are investigated using the GGA and TB-mBJ approximations. Analysis of the density of states and the band structure indicates that spiroffite Co2Te3O8 exhibits semiconductor characteristics in both the spin up and spin down channels. The study is extended to apply hydrostatic pressure to assess the electronic and magnetic properties of both unstrained and strained structures of Co2Te3O8. It is found that within the investigated pressure range (0–15 GPa), no structural changes are observed. Furthermore, a slight decrease in the spin up gap is noted, while no appreciable changes are observed in the spin down gap. Moreover, the investigation into the spin-polarized thermoelectric properties of the material reveals that it achieves a high figure of merit, approximately 0.99, across broad temperature spectra. This performance highlights its suitability as a candidate for thermoelectric power generation. Finally, optical properties calculations on spiroffite Co2Te3O8 reveal efficient absorption in the ultraviolet region.
In 1948, Dennis Gabor proposed the concept of holography, providing a pioneering solution to a quantitative description of the optical wavefront. After 75 years of development, holographic imaging has become a powerful tool for optical wavefront measurement and quantitative phase imaging. The emergence of this technology has given fresh energy to physics, biology, and materials science. Digital holography (DH) possesses the quantitative advantages of wide-field, non-contact, precise, and dynamic measurement capability for complex-waves. DH has unique capabilities for the propagation of optical fields by measuring light scattering with phase information. It offers quantitative visualization of the refractive index and thickness distribution of weak absorption samples, which plays a vital role in the pathophysiology of various diseases and the characterization of various materials. It provides a possibility to bridge the gap between the imaging and scattering disciplines. The propagation of wavefront is described by the complex amplitude. The complex-value in the complex-domain is reconstructed from the intensity-value measurement by camera in the real-domain. Here, we regard the process of holographic recording and reconstruction as a transformation between complex-domain and real-domain, and discuss the mathematics and physical principles of reconstruction. We review the DH in underlying principles, technical approaches, and the breadth of applications. We conclude with emerging challenges and opportunities based on combining holographic imaging with other methodologies that expand the scope and utility of holographic imaging even further. The multidisciplinary nature brings technology and application experts together in label-free cell biology, analytical chemistry, clinical sciences, wavefront sensing, and semiconductor production.
Digital in-line holographic microscopy (DIHM) is a non-invasive, real-time, label-free technique that captures three-dimensional (3D) positional, orientational, and morphological information from digital holographic images of living biological cells. Unlike conventional microscopies, the DIHM technique enables precise measurements of dynamic behaviors exhibited by living cells within a 3D volume. This review outlines the fundamental principles and comprehensive digital image processing procedures employed in DIHM-based cell tracking methods. In addition, recent applications of DIHM technique for label-free identification and digital tracking of various motile biological cells, including human blood cells, spermatozoa, diseased cells, and unicellular microorganisms, are thoroughly examined. Leveraging artificial intelligence has significantly enhanced both the speed and accuracy of digital image processing for cell tracking and identification. The quantitative data on cell morphology and dynamics captured by DIHM can effectively elucidate the underlying mechanisms governing various microbial behaviors and contribute to the accumulation of diagnostic databases and the development of clinical treatments.
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