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Based on the Collins formula and the moment's method, the analytical expressions for the beam field propagation through an ABCD system, the beam propagation factor (M2-factor) and the kurtosis factor of a vortex higher-order cosine-hyperbolic-Gaussian beam (vHOChGB) are derived. It is shown that the propagation characteristics are determined by the beam structure parameters, such as the decentered parameter b, the cosh order N and the topological charge m. The kurtosis parameter is dependent, besides the structure beam parameters, on the propagation distance. Numerical examples are presented to discuss the influence of the parameters b, N and m on the propagation characteristics of vHOChGB in free space. This research may be beneficial to the applications involving vortex beams in optical communications, beam splitting, and micromanipulation of particles. [ABSTRACT FROM AUTHOR]

Quantum key distribution (QKD) is a swiftly advancing field with the great potential to be ubiquitously adopted in quantum communication applications, attributed to its unique capability to offer ultimate end-to-end theoretical security. However, when transitioning QKD from theory to practice, environmental noise presents a significant impediment, often undermining the real-time efficacy of secure key rates. To uphold the operation of QKD systems, a myriad of protocols and experimental designs have been proposed to counteract the effects of noises. Even with real-time variations, the primary component of environmental noise can be modeled as a unitary evolution or background noise, which can be compensated or reduced with various noise-reducing schemes. This review provides an overview of design strategies for reducing noises in practical QKD systems under various circumstances. These strategies are evaluated based on their principles and suitability in real-world applications. Through this review, we aim to provide readers with a clear understanding of the logic behind these noise-reducing QKD designs, facilitating a smoother start of research and engineering in this field. [ABSTRACT FROM AUTHOR]

In the framework of the generalized Huygens–Fresnel diffraction integral and paraxial approximation theory, the propagation features of the general model vortex higher-order cosh-Gaussian beam (GMvHchGB) in a free space (FS) and a gradient-index medium (GIM) are studied. The analytical formulas of the GMvHchGB propagating through the considered media are derived. According to the derived formulas, some numerical examples of the normalized intensity distributions and corresponding phase structure of the GMvHchGB in both FS and GIM are performed under different parameter conditions during propagation setups. The obtained results show that the beam with higher decentered parameters, the GMvHchGB propagating in FS case cannot maintain its initial shape during the propagation process, whereas the beam propagation in the GIM case will keep the original shape unchanged with a repeated self-focusing along propagation distances. Finally, the numerical results of both intensity and phase distributions demonstrated that the beam order N significantly influences the vortex property of the beam, which enhances the clear importance of the current work. [ABSTRACT FROM AUTHOR]

A new investigation of controllable vortex anomalous hollow Hermite beam (CVAHHB) as a general form of anomalous hollow beam is introduced. Based on the integral of Huygens-Fresnel, analytical propagation formulas of a CVAHHB in a paraxial ABCD optical system are derived. Our numerical results show that the evolution features of the received intensity pattern upon propagation in free space are affected by controllable beam parameters, Hermite orders and topological charge. Additionally, the intensity and phase distributions of the beam propagating in Fractional Fourier Transform (FRFT) gradually and periodically evolve with respect to the order of the FRFT. The shape of the considered beam depends strongly on the FRFT order and the incident beam parameters. Our results could potentially support the applications of the CVAHHB in optical trapping and laser optics. [ABSTRACT FROM AUTHOR]

This work introduces a new kind of laser beam called Laguerre-Whittaker-Gaussian beams (LWGBs) in terms of Laguerre and Whittaker functions in the source plane. Applying the integral of Huygens-Fresnel, a propagation formula of LWGBs traversing a paraxial ABCD optical system is derived. The variation of the intensity distribution of the propagated LWGBs with the beam structure parameters, such as the beam orders (m, n) and the topological charge l, is discussed with some graphical representations. The results reveal that m, n and l have a considerable impact on the beam's properties as it propagates in free space. Also, in a thin lens in a free space, it is found that the focal length affects the beam shape. In the case of the Fourier transform system, it is observed that the intensity pattern of the LWGBs is more focused with the decrease of the focal length. This research is helpful for optical communication and optical trapping because the beam studied has a zero intensity in the center. [ABSTRACT FROM AUTHOR]

This paper investigates the propagation characteristics of chirped Pierce-Gaussian beams in both free space and PT-symmetric media using the stepwise Fourier method. An in-depth analysis is conducted on the effects of the truncation factor, chirp factor, modulation depth, and gain/loss coefficient of the medium. When the wave propagates in free space, the truncation factor modulates its focusing intensity, and the initial chirp controls the direction of beam deflection. Conversely, when propagated via a PT-symmetric medium, the Pierce-Gaussian beam emits a soliton at the focal point and attains reliable propagation. The modulation strength P and gain/loss coefficient W0 of the PT-symmetric medium impact the shedding soliton's peak intensity and oscillation period. Meanwhile, the beam's initial chirp parameter c can regulate the peak intensity of the shedding soliton. The results of this study offer a significant theoretical foundation for understanding the dynamics of the propagation of specialized beams. [ABSTRACT FROM AUTHOR]

Let C be a set of n axis-aligned cubes of arbitrary sizes in R 3 in general position. Let U : = U (C) be their union, and let κ be the number of vertices on ∂ U ; κ can vary between O(1) and Θ (n 2) . We present a partition of cl (R 3 \ U) into O (κ log 4 n) axis-aligned boxes with pairwise-disjoint interiors that can be computed in O (n log 2 n + κ log 6 n) time if the faces of ∂ U are pre-computed. We also show that a partition of size O (σ log 4 n + κ log 2 n) , where σ is the number of input cubes that appear on ∂ U , can be computed in O (n log 2 n + σ log 8 n + κ log 6 n) time if the faces of ∂ U are pre-computed. The complexity and runtime bounds improve to O (n log n) if all cubes in C are congruent and the faces of ∂ U are pre-computed. Finally, we show that if C is a set of arbitrary axis-aligned boxes in R 3 , then a partition of cl (R 3 \ U) into O (n 3 / 2 + κ) boxes can be computed in time O ((n 3 / 2 + κ) log n) , where κ is, as above, the number of vertices in U (C) , which now can vary between O(1) and Θ (n 3) . [ABSTRACT FROM AUTHOR]

High-precision time–frequency is widely used in time measurement, satellite navigation, scientific research, and other fields. With the rapid development of optical clock technology, the fractional frequency instability and uncertainty of optical clock have reached 10−18 orders of magnitude, which is expected to contribute to generating the International Atomic Time and may even be used to redefine the "second" in the future. Therefore, the long-distance transfer of time–frequency signals between optical atomic clocks is of great significance. Free-space optical frequency transfer technology is one of the important technologies for solving the space-based optical clock comparison because of its high transfer precision and easy networking characteristics. In order to solve the long-distance space-based optical clock comparison, this paper investigates a free-space active phase noise compensation method using an Acousto-Optic Modulator (AOM), based on the traditional optical fiber phase noise compensation scheme. This new method is more flexible and scalable than the optical fiber time–frequency transfer technology. The optical frequency transfer over a 64 m free-space link is demonstrated. The fractional frequency transfer instability during free running is 9.50 × 10−16 at 1 s, and 4.44 × 10−16 at 2000 s, and the fractional frequency instability after compensation is 7.10 × 10−17 at 1 s, 3.07 × 10−19 at 2000 s, which is about 1–3 orders of magnitude better than that in free running, and provides a feasible scheme for space-based optical clock comparison. [ABSTRACT FROM AUTHOR]

White-collar workers around the world are reconfiguring their ways of working. Some have found their way out, performing office work outdoors, through walk-and-talks, outdoor meetings, or reading sessions. Working outdoors has proved both invigorating and challenging. This qualitative interview study aims to develop a conceptual framework concerning the implications of white-collar workers incorporating the outdoors into their everyday work life. Applying a constructivist grounded theory approach, 27 interviews with a total of 15 participants were systematically analyzed. Findings evolved around the following categories: practicing outdoor office work, challenging the taken-for-granted, enjoying freedom and disconnection, feeling connected and interdependent, promoting health and well-being, enhancing performance, and finally adding a dimension to work. These categories were worked into a conceptual model, building on the dynamic relationship between the practice of working outdoors on one hand, and how this challenges the system in which office work traditionally takes place on the other. Interviews reflected the profound learning process of the employees. Drawing on the concepts of free space and resonance, we demonstrate how performing office work outdoors may unlock a transformative potential by opening up connectedness and interdependence and contribute to a sustainable work life as well as overall sustainable development. [ABSTRACT FROM AUTHOR]

Operating in urban waters with an autonomous vessel can be challenging. The autonomous vessel must be able to react quickly and detect obstacles to avoid collisions and risky maneuvers. Exteroceptive sensors such as LiDAR and RADAR have typically been used with great success in the maritime domain, but the measurements are often too sparse to represent smaller obstacles during docking and other maritime operations. However, other sensor modalities, such as stereo cameras, can provide both appearance and dense depth information. In this paper, we present a stereo camera-based free space estimation method for the maritime domain. The mapping of navigable areas is crucial for path planning and collision avoidance systems. To robustly estimate the free space, we use vertically oriented rectangular segments known as stixels. We utilized both stereo correspondences and a recent image segmentation network trained on a large, generalized dataset to create the stixels. To validate our approach, we analyzed the estimated free space, evaluating both the accuracy and consistency in the estimated depth over time. We demonstrate the approach using a real dataset recorded with a stereo camera mounted on an autonomous ferry and compare its accuracy against measurements from a LiDAR.

This article explores how collaborative self-study, initiated by experienced challenges and insecurity in new roles, contributes to the professional development of teacher educators. We document how four vocational teacher educators created a free space for self-development in a self-study process of dialogue and collective reflective inquiry. This study was initiated during the 2019/2020 academic year as we facilitated a school-based mentor course for vocational high school teachers. We analyze personal reflective journals written during and after mentoring sessions, group meetings, and throughout the process. Drawing on the self-study tradition within educational research, we examine the dilemmas, challenges, and opportunities this experience presented for our roles as teacher educators. The results indicate that investing time in group meetings established an atmosphere of mutual trust and developed the self-study group as a free space. Furthermore, we show the value of collaborative self-study as a tool for individual and collective self-understanding and professional development for teacher educators. Our experiences indicate that a self-study group must be self-selected to achieve an open and trusting process. Furthermore, the study shows that creating free space in academia is possible but highlights a need for academia to recognize free space and self-study as integral parts of the work culture. [ABSTRACT FROM AUTHOR]

Measurement-device-independent quantum key distribution (MDI-QKD) has demonstrated significant security in countering detection-side attacks, expanding the practical applications of quantum communication over fiber-based links. Nevertheless, implementing MDI-QKD over free-space links presents challenges, including fluctuations in transmittance induced by atmospheric turbulence. Adaptive optics (AO) provides an effective means to mitigate the impact of atmospheric turbulence. Here we investigate the feasibility of extending AO to free-space MDI-QKD, using a satellite-based MDI-QKD model and an elliptic-beam model to describe the probability distribution of transmittance (PDT). Through comprehensive numerical simulations, we assess the impact of communication distance and turbulence intensity on PDT, highlighting the effectiveness of AO optimization in enhancing the practicality of the protocol over free-space links. The results provide valuable insights for future research in the field of free-space quantum communication. [ABSTRACT FROM AUTHOR]

In this work, we propose to give a new mathematical formulation of the Ince–Gaussian beams (IGBs) in terms of generalized Laguerre–Gaussian beams. This new expression reproduces the well-known Ince–Gaussian modes. Based on this expansion and the Huygens–Fresnel diffraction integral, the analytical expression describing the electric field amplitude and the intensity distribution of the IGBs propagating through paraxial ABCD optical system are derived. Numerical simulation and analysis of the propagation of IGBs in free space, thin lens and Fractional Fourier transform system are computed and discussed in details. The results of this work can be regarded as complementary investigation on elliptical beams such as IGBs. [ABSTRACT FROM AUTHOR]

This paper attempts to reinterpret asylum theory (1954) propounded by Ortwin Henssler (1923–2017) as a free-space theory of education, as a way of grasping the problematic nature of 'pedagogical protection.' The theoretical potential of Henssler's thought has been more appreciated, accepted, and developed in Japan than in his native Germany. First, I outline Henssler's theory of asylum and show how his theory has been received and developed in Japan, especially in the fields of historical researches. Secondly, I discuss the possibility of reading Henssler's thought of asylum as a theory of 'pedagogical protection.' Thirdly, I consider whether it is possible to interpret 'free space' in education based on the model of asylum. Finally, I delineate some prospects for and challenges involved in connecting the theory of asylum to the theory of education. [ABSTRACT FROM AUTHOR]

The primary goal of this study is to design a simple antenna that has a wide bandwidth and low return loss for biomedical applications. The paper shows the recommended antenna's three-stage modeling, with the goal of assessing every important parameter while a Teflon or polytetrafluoroethylene (PTFE) polymer substrate is used. In order to better comprehend, a comparison with prior studies employing teflon and similar substrate materials is conducted for the proposed patch antenna. The analysis includes the phantom model, evaluating performance criteria such as specific absorption rate (SAR), return loss, bandwidth, and gain values relevant to biomedical applications. The antenna works at two different frequencies: 9.73 and 9.39 GHz, one in free space and another in a skin-cotton layer. The bandwidth of the antenna is 4.067 GHz in free space at the resonance frequency of 9.73 GHz, where the return loss is -62.18 dB. The performance of the proposed antenna in the field of biomedical applications, its underlying reasons, and its impacts are discussed in detail in this study. [ABSTRACT FROM AUTHOR]

High-precision time–frequency is widely used in time measurement, satellite navigation, scientific research, and other fields. With the rapid development of optical clock technology, the fractional frequency instability and uncertainty of optical clock have reached 10−18 orders of magnitude, which is expected to contribute to generating the International Atomic Time and may even be used to redefine the “second” in the future. Therefore, the long-distance transfer of time–frequency signals between optical atomic clocks is of great significance. Free-space optical frequency transfer technology is one of the important technologies for solving the space-based optical clock comparison because of its high transfer precision and easy networking characteristics. In order to solve the long-distance space-based optical clock comparison, this paper investigates a free-space active phase noise compensation method using an Acousto-Optic Modulator (AOM), based on the traditional optical fiber phase noise compensation scheme. This new method is more flexible and scalable than the optical fiber time–frequency transfer technology. The optical frequency transfer over a 64 m free-space link is demonstrated. The fractional frequency transfer instability during free running is 9.50 × 10−16 at 1 s, and 4.44 × 10−16 at 2000 s, and the fractional frequency instability after compensation is 7.10 × 10−17 at 1 s, 3.07 × 10−19 at 2000 s, which is about 1–3 orders of magnitude better than that in free running, and provides a feasible scheme for space-based optical clock comparison.

In this paper, we introduce a new laser beam called Bessel higher-order cosh-Gaussian (BHChG) beam and analyzed its propagation properties through a paraxial ABCD optical system. The analytical expression of the diffracted beam is derived based on the extended Huygens–Fresnel integral and some numerical examples of BHChG beam propagating in a free space, through a thin lens and a Fractional Fourier transform system are exposed. The results reveal that the behavior of the output BHChG beam is affected by the optical system and the source beam parameters. The propagation of some laser beams through a paraxial ABCD optical system is deduced as particular case from the present study such as the fundamental Gaussian beam, the Bessel-Gaussian beam, the cosh-Gaussian beam, the Bessel-cosh-Gaussian beam and the Higher-order-cosh-Gaussian beam. The outcomes can be helpful for free-space optical communication, remote sensing and optical micromanipulation. [ABSTRACT FROM AUTHOR]

A new level of freedom is made possible by orbital angular momentum (OAM), which can be used to create twisted ultrasonic motors for particle manipulation and control. For steady and free‐flowing particle management, it is essential to produce acoustic OAM beams of high order and high quality. However, this task is difficult due to the phased array's fundamental restriction of insufficient resolution or aperture. Herein, a generic approach is presented to inverse design that may be used to improve the OAM beam quality and produce twisted ultrasonic motors in free space. In comparison to the previous direct‐design method, up to a 14% improvement in amplitude uniformity and a 12 dB improvement in signal‐to‐noise ratio (SNR) of OAM modes are achieved. These notable benefits enable the ultrasonic motor to operate with a straightforward and compact system while enabling steady particle rotation in free space with an undersampled phased array, which is not possible with the conventional technique. This study paves the way for effective particle control, high‐fidelity communication, and other OAM‐based technologies by providing an inverse‐design framework for optimizing OAM. [ABSTRACT FROM AUTHOR]

A new level of freedom is made possible by orbital angular momentum (OAM), which can be used to create twisted ultrasonic motors for particle manipulation and control. For steady and free‐flowing particle management, it is essential to produce acoustic OAM beams of high order and high quality. However, this task is difficult due to the phased array's fundamental restriction of insufficient resolution or aperture. Herein, a generic approach is presented to inverse design that may be used to improve the OAM beam quality and produce twisted ultrasonic motors in free space. In comparison to the previous direct‐design method, up to a 14% improvement in amplitude uniformity and a 12 dB improvement in signal‐to‐noise ratio (SNR) of OAM modes are achieved. These notable benefits enable the ultrasonic motor to operate with a straightforward and compact system while enabling steady particle rotation in free space with an undersampled phased array, which is not possible with the conventional technique. This study paves the way for effective particle control, high‐fidelity communication, and other OAM‐based technologies by providing an inverse‐design framework for optimizing OAM.

The study focuses on the behavior of pulsed Laguerre higher-order cosh-Gaussian (LHChG) beam propagating through a paraxial ABCD optical system. The formula for propagation is derived using the extended Huygens-Fresnel principle and Fourier Transform method. The investigation analyzes how transverse positions and initial beam parameters affect the spectral intensity of the beam. It also examines the relative spectral shift of the beam at different radial coordinates through numerical calculations. The findings show that the spectral intensity is influenced by beam order and pulse duration. From our main results, one derives some particular cases of the considered beam such as the Laguerre cosh-Gaussian (LChG), Laguerre-Gaussian (LG), and Gaussian beams. Physical explanation for the spectral transition of the analyzed beam in a paraxial ABCD optical system is provided. The research has practical applications in information coding and transmission. [ABSTRACT FROM AUTHOR]

This study investigates the impact of the surrounding free space on the topology optimization (TO) of electro-active polymers (EAPs). It is well understood that, under the application of an electric field, the deformation of an EAP is not solely determined by the field distribution within the body, but also by the distribution in the free space surrounding it. This is particularly true for electronic EAP, which are emerging as leading candidates for developing artificial muscles. Our study specifically focuses on understanding the influence of the free space in the context of density-based TO. We model the free space as an extended void region around the design domain. Our numerical experiments focus on EAP actuators and take into account their geometrical nonlinear behavior. The results show that incorporating the surrounding free space has a significant impact on the performance of the optimized EAPs with low electric permittivity. This makes it essential to consider in real-world applications. [ABSTRACT FROM AUTHOR]

Quantum teleportation is one of the fundamental primitives of quantum cryptography. In order to achieve a wider range of high-capacity information transfer, we propose a free-space quantum teleportation (QT) protocol with orbital angular momentum (OAM) multiplexed continuous variable (CV) entangled states. The preparation of the entangled states is accomplished by the spontaneous four-wave mixing (SFWM) process occurring in a hot 85 Rb vapor cell, and the mode selection for the Bell-state measurement is achieved by employing the balanced homodyne detection technique. The fidelity of teleporting EPR entangled states carrying different topological charges via a Kolmogorov-type atmospheric turbulence channel is derived, and the superiority of enhancing the system channel capacity via OAM multiplexing is demonstrated. Our work provides a feasible scheme to implement high-capacity quantum communication in atmospheric environments. [ABSTRACT FROM AUTHOR]

The results of analysis of the effect of Raschig ring wall thickness in dumped packings on energy consumptions during column equipment operation with reference to drying tower of sulfuric acid production plant are presented. Regression equations and graphical relationships of specific surface and free volume of dumped Raschig ring packing as well as of hydraulic resistance and energy consumptions during operation of the column equipment with Raschig ring wall thickness are presented. [ABSTRACT FROM AUTHOR]

This work presents a generalized angle-dependent ray transfer function that can accurately map the angular and spatial distribution of light intensities on the tissue surface onto a camera image plane in a non-contact camera-based imaging system. The method developed here goes beyond existing ray transfer models that apply to angle-averaged tomographic data alone. The angle-dependent ray transfer operator was constructed using backward ray tracing based on radiation surface theory. The proposed method was validated using numerical phantoms and experimental data from an actual non-contact imaging system. [ABSTRACT FROM AUTHOR]

Image analysis techniques are expanding in agriculture and, for being fast, simple, and not destroying samples, they are interesting alternatives in the detection of immature rice seeds. Therefore, the aim of this study was to evaluate the quality of rice seeds using X-ray, multispectral and chlorophyll fluorescence image analysis techniques. Initially, with the seeds identified and numbered, radiographic images were obtained to determine the free space (area between the endosperm + embryo and the glumes). Subsequently, with the same seeds used in the X-ray, multispectral and chlorophyll fluorescence images were acquired, and then the computerized seedling analysis was performed with the SVIS® software. It was concluded that rice seeds that do not germinate or originate abnormal seedlings have free space equal to or greater than 18.68%, higher reflectance in the spectral bands with wavelength from 590 nm to 780 nm (41.46% to 64.21%, respectively) and in the band of 970 nm (75.65%), in addition to having chlorophyll fluorescence values equal to or greater than 40.58 and 112.92 at excitation/emission energies of 630/700 nm and 645/700 nm, respectively. [ABSTRACT FROM AUTHOR]

The finite sampling bandwidth of an analog-to-digital converter has a negative effect on the continuous-variable quantum key distribution (CVQKD), which leaves a potential loophole for an eavesdropper and weakens the practical security of the system. To compensate for the loss in free space, we deploy an adaptive optics (AO) unit in the detector of the CVQKD system with discrete modulations. Since the closed-loop control bandwidth of the embedded AO unit can be optimized with the sampling frequency, the practical security of the system can be enhanced in terms of the secret key rate. The security analysis is demonstrated on the basis of the derived secret key rate with numerical simulations, providing a feasible implementation of CVQKD in realistic free-space environments. [ABSTRACT FROM AUTHOR]

This work presents a generalized angle-dependent ray transfer function that can accurately map the angular and spatial distribution of light intensities on the tissue surface onto a camera image plane in a non-contact camera-based imaging system. The method developed here goes beyond existing ray transfer models that apply to angle-averaged tomographic data alone. The angle-dependent ray transfer operator was constructed using backward ray tracing based on radiation surface theory. The proposed method was validated using numerical phantoms and experimental data from an actual non-contact imaging system.

This article presents a summary of the work done on the development of a new algorithm for mobile robot navigation in unknown dynamic environment. The developed humanlike algorithm uses a free-space attraction (Agoraphilic) concept for robot navigation. The algorithm presented in this article is an advanced development of the Agoraphilic navigation algorithm. The Agoraphilic algorithm does not look for obstacles (problems) to avoid but rather for free spaces toward the goal (solutions) to follow. The original Agoraphilic while it was able to overcome the limitations of the traditional algorithms had its own limitations in navigating robots in environments cluttered with moving obstacles. The new Agoraphilic Navigation Algorithm under Dynamic Environment (ANADE) was developed to overcome those limitations. ANADE consists of seven main modules reported in this article. The objects tracking and objects prediction methodologies developed for the algorithm estimate future growing free-space passages toward the goal. The algorithm generates a time-varying single attractive force to pull the robot through the free space toward the predicted (future) growing free-space passages leading to the goal. The new algorithm was tested, not only through simulation, but also through experimental work. Summary of the experimental results is presented and discussed in this article. [ABSTRACT FROM AUTHOR]

The electrical properties of materials and their dependence on frequency and temperature are indispensable in designing electromagnetic devices and systems in various areas of engineering and science for both basic and applied researches. A free-space transmission/reflection method measuring the free-space scattering parameters of a material under test (MUT) located at the middle of transmit/receive antennas in a free space is suitable for non-destructively testing the MUT without prior machining or physical contact in high-frequency range. This paper describes a planar offset short applicable to the calibration of a quasi-optic based free-space material measurement system in the millimeter-wave frequency range. The measurement results of the dimensional and electrical properties for the three fabricated planar offset shorts with the phase difference of 120° between the reflection coefficients of the planar shorts in the W-band (75–110 GHz) are presented.

A locally convex space (lcs) E is said to have an ω ω -base if E has a neighborhood base { U α : α ∈ ω ω } at zero such that U β ⊆ U α for all α ≤ β . The class of lcs with an ω ω -base is large, among others contains all (LM)-spaces (hence (LF)-spaces), strong duals of distinguished Fréchet lcs (hence spaces of distributions D ′ (Ω) ). A remarkable result of Cascales-Orihuela states that every compact set in an lcs with an ω ω -base is metrizable. Our main result shows that every uncountable-dimensional lcs with an ω ω -base contains an infinite-dimensional metrizable compact subset. On the other hand, the countable-dimensional vector space φ endowed with the finest locally convex topology has an ω ω -base but contains no infinite-dimensional compact subsets. It turns out that φ is a unique infinite-dimensional locally convex space which is a k R -space containing no infinite-dimensional compact subsets. Applications to spaces C p (X) are provided. [ABSTRACT FROM AUTHOR]

An apparatus for measuring the W-band (75â€"110 GHz) complex permittivity of dielectrics at 1000 °C was developed. This apparatus allows for measurements at approximately twice the temperature of previously published high temperature free-space measurement systems while maintaining similar precision. Challenges were addressed related to high temperature measurements, including temperature uniformity, the accuracy of temperature measurements, and preventing temperature related changes to mm-wave measurement systems. The details of complex permittivity extraction from the measured S-parameters are discussed. Sources of error related to permittivity measurement and mathematical models were identified and are discussed in detail herein. Thermally-cycled, mm-wave absorbing, aluminum nitride ceramic composites containing varying levels of molybdenum additives were measured over the range of 25 °Câ€"1000 °C. These measurements were compared to the same composites before thermal cycling. It was found that ceramic composites are largely stable after thermal cycling in terms of dielectric properties despite the presence of visible surface modifications. [ABSTRACT FROM AUTHOR]

This instrumental case study illustrates the necessity of free spaces within antiracist teacher education. The author uses antiracism and free spaces as a theoretical lens to examine the experiences of 11 social studies teacher educators (SSTEs) who teach and research antiracist social studies. The findings portray the SSTEs' need for free space to persevere in antiracist teacher education as well as to improve their scholarship in antiracist social studies education, yet the SSTEs do not explicitly include the need for a free space within their course syllabi and readings for pre-service teachers. Based on these findings, the author argues the need to consider how free spaces can be extended to teacher education instruction and to alumni who desire to be K-12 antiracist educators. [ABSTRACT FROM AUTHOR]

A terahertz (THz) attenuation calibration system is developed using a photoacoustic (PA) detector for free-space beams. Based on the principle of the PA detector, the system measures the THz attenuation by substituting radio frequency (RF) attenuation with audio frequency (AF) attenuation. The AF attenuation at 1 kHz is directly calibrated using an inductive voltage divider (IVD) as the reference standard. The calibration is demonstrated for metalized film attenuators up to 20 dB at 0.11 THz. A Gunn oscillator with a corrugated horn antenna is used as the source, and its radiated beam is collimated using an off-axis parabolic mirror. Sources of uncertainties are also discussed in detail, and the expanded uncertainty is found to be 0.40–0.46 dB ($k = 2$). [ABSTRACT FROM AUTHOR]

We present in this work the propagation properties of Generalized Humbert-Gaussian beams (GHGBs) passing through a paraxial ABCD optical system. Based on the extended Huygens-Fresnel integral, the analytical expression of the intensity distribution for GHGBs is derived and some numerical simulations are performed for particular cases in free space, thin lens in a free space and graded refractive index system. Our results show that the comportment of several particular cases of these beams during the propagation is influenced by the beam orders and the characteristic parameters of the system. [ABSTRACT FROM AUTHOR]

Electrically parallel and optically uncoupled triple and septuple oxide confined vertical-cavity surface-emitting laser (VCSEL) arrays emitting at about 980 nm where each VCSEL has an oxide aperture diameter (φ) of ∼7.5 μm transmit data at 40 Gbps at room temperature (RT) in a back-to-back test configuration using standard two-level non-return-to-zero pulse amplitude modulation at bias current densities (J) of 17.4 and 10.3 kA/cm2, respectively. Reference single VCSELs processed with the VCSEL arrays on the same wafer pieces with φ ∼7.5, 13.5, and 19.5 μm transmit data at up to 45, 40, and 35 Gbps at RT at J of 20.4, 13.3, and 10.7 kA/cm2, respectively, where the latter two single VCSELs have total emitting areas nearly equal to the total additive emitting areas of the triple and septuple VCSEL arrays, respectively. The RT optical output power at J ∼10 and 15 kA/cm2 is 11.4 and 17.2 mW for the triple arrays and 31.1 and 45.9 mW for the septuple arrays, respectively. By increasing the number of emitters in an array for a fixed φ per VCSEL from 3 to 7 we increase the total optical output power and simultaneously we decrease the J required for error free digital data transmission at 40 Gbps. [ABSTRACT FROM AUTHOR]

In this paper, we have introduced a general formula of a new laser beam with a nearly Flattened-top profile. The propagation properties of this beam, called Generalized Flattened Hermite-cosh-Gaussian (GFHChG) beam are studied in detail. Based on the Huygens–Fresnel integral, an analytical expression of the intensity distribution for GFHChG passing through a paraxial ABCD optical system is developed. Several particular cases such as the propagation of the flattened Gaussian beam, the cosh-Gaussian beam, the higher and squared cosh-Gaussian beam and the Hermite-cosh-Gaussian beam are deduced from our result. Numerical simulations are also given in free space and through a circular thin lens in a free space to study the comportment of this beam during propagation. [ABSTRACT FROM AUTHOR]

Optical wireless communication has attracted significant interest recently in industry and academia. This special issue features a collection of inter-related papers with the intention to cover all necessary multidisciplinary challenges to realize optical wireless networks. We hope that this special issue will serve as a comprehensive reference and that it will be a resource which fosters many more new ideas for this rapidly emerging field. This article is part of the theme issue 'Optical wireless communication'. [ABSTRACT FROM AUTHOR]

Polarization encoding has been extensively used in quantum key distribution (QKD) implementations along free-space links. However, the calculation model to characterize channel transmittance and quantum bit error rate (QBER) for free-space QKD has not been systematically studied. As a result, it is often assumed that misalignment error is equal to a fixed value, which is not theoretically rigorous. In this paper, we investigate the depolarization and rotation of the signal beams resulting from spatially-dependent polarization effects of the use of curved optics in an off-axis configuration, where decoherence can be characterized by the Huygens–Fresnel principle and the cross-spectral density matrix (CSDM). The transmittance and misalignment error in a practical free-space QKD can thus be estimated using the method. Furthermore, the numerical simulations clearly show that the polarization effect caused by turbulence can be effectively mitigated when maintaining good beam coherence properties.

Abstract Background Focusing with a 4 π parabolic mirror allows for concentrating light from nearly the complete solid angle, whereas focusing with a single microscope objective limits the angle cone used for focusing to half solid angle at maximum. Increasing the solid angle by using deep parabolic mirrors comes at the cost of adding more complexity to the mirror’s fabrication process and might introduce errors that reduce the focusing quality. Methods To determine these errors, we experimentally examine the focusing properties of a 4 π parabolic mirror that was produced by single-point diamond turning. The properties are characterized with a single 174Yb + ion as a mobile point scatterer. The ion is trapped in a vacuum environment with a movable high optical access Paul trap. Results We demonstrate an effective focal spot size of 209 nm in lateral and 551 nm in axial direction. Such tight focusing allows us to build an efficient light-matter interface. Conclusion Our findings agree with numerical simulations incorporating a finite ion temperature and interferometrically measured wavefront aberrations induced by the parabolic mirror. We point at further technological improvements and discuss the general scope of applications of a 4 π parabolic mirror.

A miniaturized tag antenna is presented in this paper, for operating in the RFID UHF American band, in free space or in a metallic environment. The proposed antenna is printed on a single layer FR4 substrate, and designed first to work in a free space. The shape of the π-match allowed us to achieve a good matching between the antenna impedance and that of the chip. The correspondence between simulation results in CST and HFSS pushed us to manufacture a prototype of our tag. After that, we simulated the proposed antenna in a metallic area, by adding a square metal plate separated with the antenna by a foam-layer, in order to test the performance of the tag in this environment. An optimization procedure enabled us to achieve a good performance when operating in metallic surroundings. Finally, we tested the reading range of the manufactured tag. We obtained a good range of about 6.5m. The final design of our proposed tag has a simple structure, a dimension of 51×26,63×0.8 mm3 and which is reduced by 88,64% compared to the calculated theoretical dimensions of a patch antenna operating at the resonant frequency of 915 MH. [ABSTRACT FROM AUTHOR]

Free space algorithms are kind of graphics-based methods for path planning. With previously known map information, graphics-based methods have high computational efficiency in providing a feasible path. However, the existing free space algorithms do not guarantee the global optimality because they always search in one connected domain but not all the possible connected domains. To overcome this drawback, this article presents an improved free space algorithm based on map decomposition with multiple connected domains and artificial bee colony algorithm. First, a decomposition algorithm of single-connected concave polygon is introduced based on the principle of concave polygon convex decomposition. Any map without obstacle is taken as single-connected concave polygon (the convex polygon map can be seen as already decomposed and will not be discussed here). Single concave polygon can be decomposed into convex polygons by connecting concave points with their visible vertex. Second, decomposition algorithm for multi-connected concave polygon (any map with obstacles) is designed. It can be converted into single-connected concave polygon by excluding obstacles using virtual links. The map can be decomposed into several convex polygons which form multiple connected domains. Third, artificial bee colony algorithm is used to search the optimal path in all the connected domains so as to avoid falling into the local minimum. Numerical simulations and comparisons with existing free space algorithm and rapidly exploring random tree star algorithm are carried out to evaluate the performance of the proposed method. The results show that this method is able to find the optimal path with high computational efficiency and accuracy. It has advantages especially for complex maps. Furthermore, parameter sensitivity analysis is provided and the suggested values for parameters are given. [ABSTRACT FROM AUTHOR]

Free space algorithms are kind of graphics-based methods for path planning. With previously known map information, graphics-based methods have high computational efficiency in providing a feasible path. However, the existing free space algorithms do not guarantee the global optimality because they always search in one connected domain but not all the possible connected domains. To overcome this drawback, this article presents an improved free space algorithm based on map decomposition with multiple connected domains and artificial bee colony algorithm. First, a decomposition algorithm of single-connected concave polygon is introduced based on the principle of concave polygon convex decomposition. Any map without obstacle is taken as single-connected concave polygon (the convex polygon map can be seen as already decomposed and will not be discussed here). Single concave polygon can be decomposed into convex polygons by connecting concave points with their visible vertex. Second, decomposition algorithm for multi-connected concave polygon (any map with obstacles) is designed. It can be converted into single-connected concave polygon by excluding obstacles using virtual links. The map can be decomposed into several convex polygons which form multiple connected domains. Third, artificial bee colony algorithm is used to search the optimal path in all the connected domains so as to avoid falling into the local minimum. Numerical simulations and comparisons with existing free space algorithm and rapidly exploring random tree star algorithm are carried out to evaluate the performance of the proposed method. The results show that this method is able to find the optimal path with high computational efficiency and accuracy. It has advantages especially for complex maps. Furthermore, parameter sensitivity analysis is provided and the suggested values for parameters are given. [ABSTRACT FROM AUTHOR]

We review two concepts in description of free space in the zeolite-like frameworks: topological (natural tiling) and geometrical-topological (Voronoi net). Advantages and disadvantages as well as similarities and differences of both concepts are discussed. We also consider the packing model of zeolite framework assemblage, which is derived from the natural tiling approach. New statistical data are given for natural tilings and Voronoi models of all known 239 zeolite frameworks. A route to modeling and prediction of new zeolite frameworks is outlined. [ABSTRACT FROM AUTHOR]

Highlights • An accuracy of 0.2% can be realized with waveguide method in low UC content (0–2%) detection. • The waveguide method is superior to the free space method in terms of measurement accuracy. • The accuracy of using the magnitude as the measurement parameter is lower than that of using the phase. Abstract To compare the performances of different microwave measure methods in UC content determination, we have developed two measurement systems that can be operated in 12–15 GHz band, including one based on free space method, and the other based on waveguide method. The fly ash samples with UC content in 0–20% are measured. In addition, this paper specifically studies the test results in the 0–2% low UC content range using the waveguide method. The measurement range and measure accuracy are analyzed to evaluate these methods. For measurement range, free space method can realize wider measurement range of UC content compared with waveguide method. For accuracy, the error of UC content is used as an accuracy indicator to evaluate accuracies under different test modes. The calculated accuracy indicators can verify the following conclusions. The waveguide method is superior to the free space method and the accuracy of using the magnitude as the measurement parameter is lower than that of using the phase in both measurement systems. [ABSTRACT FROM AUTHOR]

The information and communication technology (ICT) is increasingly involved in the measurement, operation, control and protection of the cyber-physical power system (CPPS). As one of the most promising communication infrastructure projects, Starlink is a satellite Internet constellation being constructed by SpaceX for providing global Internet access, which can benefit the network service supply for the communication-enabled power system equipment in locations where the network access is unreliable, expensive, or completely unavailable. In this letter, the future applications of the Starlink space network in CPPSs are explored: the communication infrastructure and transmission parameters are discussed, and the corresponding test case was emulated in real-time on the heterogeneous co-emulation platform to validate the proposed concept of space network enhanced cyber-physical power system. [ABSTRACT FROM AUTHOR]

Commercial light‐emitting diodes are a low‐cost and energy‐efficient solution for the implementation of optical wireless communication, known as visible light communication (VLC). This technology has a huge growing interest, being recently a research spotlight in the scientific community, especially due to the increasing popularity and rapid development of self‐sustainable smart houses and the Internet of Things. As the VLC link is free space, big challenges arise in its implementation. To improve the VLC performance, this work proposes an enhanced system solution integrating an optical amplifier. In this context, organic–inorganic hybrids incorporating a blue‐emitting conjugated polymer with high quantum yield (>50%) were synthesised and processed as planar waveguides. The waveguides were tested in a testbed scenario, showing a signal amplitude improvement of 2.5 dB, establishing the proposed approach as a promising cost‐effective solution for optical amplification in VLCs. [ABSTRACT FROM AUTHOR]

Orbital angular momentum (OAM) multiplexing has caused a lot of concerns and researches in recent years because of its great spectral efficiency and many OAM systems in free space channel have been demonstrated. However, due to the existence of atmospheric turbulence, the power of OAM beams will diffuse to beams with neighboring topological charges and inter-mode crosstalk will emerge in these systems, resulting in the system nonavailability in severe cases. In this paper, we introduced independent component analysis (ICA), which is known as a popular method of signal separation, to mitigate inter-mode crosstalk effects; furthermore, aiming at the shortcomings of traditional ICA algorithm’s fixed iteration speed, we proposed a joint algorithm, CSO-ICA, to improve the process of solving the separation matrix by taking advantage of fast convergence rate and high convergence precision of chicken swarm algorithm (CSO). We can get the optimal separation matrix by adjusting the step size according to the last iteration in CSO-ICA. Simulation results indicate that the proposed algorithm has a good performance in inter-mode crosstalk mitigation and the optical signal-to-noise ratio (OSNR) requirement of received signals (OAM+2, OAM+4, OAM+6, OAM+8) is reduced about 3.2 dB at bit error ratio (BER) of 3.8 × 10 −3 . Meanwhile, the convergence speed is much faster than the traditional ICA algorithm by improving about an order of iteration times. [ABSTRACT FROM AUTHOR]