Cosine Beam Research Articles

Customized quasi-zero-stiffness metamaterials for ultra-low frequency broadband vibration isolation

Quasi-zero-stiffness (QZS) metamaterials play an important role in ultra-low frequency vibration mitigation. In this study, a customized QZS metamaterial is proposed to isolate ultra-low frequency broadband vibration and its isolation performance is verified. A representative unit cell (RUC) that satisfies both optimal QZS performance and minimum size is designed for the metamaterial and optimized by matching the parameters of positive stiffness heart-shaped beam with the properties of negative stiffness cosine beam. Then, a new composite structure with multiple RUCs is designed by matching the optimal mass block for each RUC to meet the vibration isolation requirements of ultra-low frequency and broadband. The transmissibility test is performed, and the isolator made of the metamaterial is then integrated into an underwater glider to test the vibration isolation performance. The results show that the proposed QZS metamaterial can isolate broadband vibrations of 3.2 to 60 Hz and the isolator can attenuate the vibration signals of gliders to the background noise in air and water. Therefore, the customized metamaterial can be used in the engineering case of ultra-low frequency broadband vibration isolation and the design method of the metamaterial can be used for reference by other equipment.

An Intriguing Interpretation of 1D and 2D Non-Diffracting Modes in Cosine Profile

We provide a simple analysis based on ray optics and Dirac notation for 1D (one-dimensional) and 2D (two-dimensional) non-diffracting modes in the cosine profile, which are often called Cosine beams. We explore various kinds of structured modes formed by the superposition of two 1D Cosine beams. We then went on to understand the properties of the Bessel beams in terms of Cosine beams. For the first time, we report on the generation of three-dimensional tunable needle structures based on the interference of 1D Cosine beams. These size-tunable optical needles can have multiple advantages in material processing. Also, we report, for the first time, on the Talbot effect in Cosine beams. Straightforward mathematical calculations are used to derive analytical expressions for Cosine beams. The present method of demonstrating Cosine beams may be utilized to understand other structured modes. The Dirac notation-based interference explanation used here can provide new researchers with an easy way to understand the wave nature of light in a fundamental aspect of interferometric experiments as well as in advanced-level experiments such as beam engineering technology, imaging, particle manipulation, light sheet microscopy, and light–matter interaction. We also provide an in-depth analysis of similarities among Cosine, Bessel, and Hermite–Gaussian beams.

Programmable Multi-stable Structure Based on Cosine Beam

Mechanical metamaterials with multi-stable properties are an emerging field of interest. In this paper, we present a novel 3D bi-stable cell element with negative stiffness characteristics designed based on a cosine-curved beam. Static compression simulations were performed for the single-cell model and the series model. Using “E” and “F” states as programming units, five array models were designed to analyze the stiffness variation rules. Dynamic simulations were conducted to compare the energy absorption rate and collision force of the model with variable stiffness. The conclusion shows that the structure has multi-stable and negative stiffness characteristics, and its stiffness can be adjusted in the range of 113.0 to 197.6 N/mm. Additionally, the energy absorption rate can be adjusted in the range of 8% to 65%. This study has made the structure configurable after manufacturing, breaking through the application limitations of predefined objects, and broadening its application prospects.

Highly sensitive SPR curvature sensor based on graded-index fiber.

At present, fiber curvature sensors based on surface plasmon resonance (SPR) are mostly of the multimode fiber core type or cladding type. These types have many SPR modes, resulting that the sensitivity cannot be adjusted and is difficult to improve. In this Letter, a highly sensitive SPR curvature sensor based on graded-index fiber is proposed. The light-injecting fiber is eccentrically connected with the graded-index fiber to inject single-mode light. Due to the self-focusing effect, the light beam propagates in the graded-index multimode fiber with a cosine trajectory, and the cosine beam contacts the flat grooved sensing region fabricated on the graded-index fiber to generate SPR. Due to the single transmission mode of the proposed fiber SPR sensor, the curvature sensing sensitivity is greatly improved. By changing the light injection position of the graded-index multimode fiber, the sensitivity can be adjusted. The proposed curvature sensing probe has a high sensitivity and can identify the bending direction. When bending in the X direction, the sensitivity reaches 5.62 nm/m-1, and when bending in the - X direction, the sensitivity reaches 4.75 nm/m-1, which provides a new scheme for highly sensitive and directionally identifiable curvature measurement.

Eliminating Primary Beam Effect in Foreground Subtraction of Neutral Hydrogen Intensity Mapping Survey with Deep Learning

In neutral hydrogen (H i) intensity mapping (IM) survey, foreground contamination on cosmological signal is extremely severe, and systematic effects caused by radio telescopes further aggravate the difficulties in subtracting foreground. We investigate whether the deep-learning method, the 3D U-Net algorithm, can play a crucial role in foreground subtraction when considering the systematic effect caused by the telescope’s primary beam. We consider two beam models, i.e., the Gaussian beam and Cosine beam models. The traditional principal component analysis (PCA) method is employed as a preprocessing step for the U-Net method to reduce the map dynamic range. We find that in the case of the Gaussian beam, the PCA method can effectively clean the foreground. However, the PCA method cannot handle the systematic effect induced by the Cosine beam, and the additional U-Net method can improve the result significantly. To show how well the PCA and U-Net methods can recover the H i signal, we also derive the H i angular power spectrum and H i 2D power spectrum after performing foreground subtraction. It is found that in the case of Gaussian beam, the concordance with the original H i map using U-Net is better than that using PCA by 27.4%, and in the case of Cosine beam, the concordance using U-Net is better than that using PCA by 144.8%. Therefore, the U-Net–based foreground subtraction can efficiently eliminate the telescope primary beam effect and shed new light on recovering H i power spectrum for future H i IM experiments.

Propagation of cosine beam in uniaxial crystal orthogonal to optical axis

ABSTRACTIn this paper, we analyze the intensity and phase changes of cosine beam(CB) propagating uniaxial crystal orthogonal to optical axis. Received field is derived based upon Huygens–Fresnel integration. Main objective of this paper is to present intensity and phase evolution of cosine beam in uniaxial crystals first time in the literature. However, behavior of other untraditional beams is studied, reaction of cosine beam against uniaxial crystal is not studied previously. We analyze the results considering source beam settings, crystal structure, and propagation distance. Our results indicate that matrix view in intensity profile evolves into straight lines along propagation axis. In other point of view, symmetric cosine beam has constant phase at close distance and periodic oscillation is observed at middle at far distance. We believe that results of this study will be beneficial for optical tracking and other optical applications.

Generation of diffraction-free beams using resonant metasurfaces

Several metasurface diffraction-free beam generators are designed by using a set of resonant V-shaped nanoholes. Cosine beams, Bessel beams and cosine Bessel beams are generated through the corresponding metasurface structures with V-shaped nanoholes arranged in different ways. Theoretical analysis provides the design mechanism for these diffraction-free beam generators, numerical simulations and experiment measurement give the powerful verification for the generation of diffraction-free beams. The proposed diffraction-free beam generators have advantages of ultra-thin thickness, compact structure, ease to manufacture and flexibility to operate. The generated diffraction-free beams show high efficiency, polarization independence and validity for any visible wavelength. The compact design is benefit to the applications of diffraction-free beams in nanometer fabrication, optical integrated imaging and optical micromanipulation.

Cosine beam: diffraction-free propagation and self-healing.

In this paper we revisit the nondiffracting properties of the cosine beam (CB). Since the CB is of infinite extension and not physically realizable, we use two apodization pupils to manage its transverse extent: the first one is a Gaussian apodized pupil, giving rise to the cosine-Gauss (CG) beam, and the second one is a window (aperture) apodized pupil, giving rise to the cosine-windowed beam. Based on the second-order intensity moments, we demonstrate analytical expressions for the CG beam width and its nondiffracting range as a function of some key parameters. By considering the CG beam a standing wave resulting from the superposition of two oppositely oblique traveling Gaussian beams, we extend the study to higher-order CG beams. The latter is generated by the superposition of two oppositely oblique Hermite-Gauss (HGn) beams of order n, giving birth to a standing nondiffracting Hermite-cosine-Gauss (HCGn) beam of order n. We also demonstrate the expressions of the higher-order CG beam width and its nondiffracting range zmax. After demonstrating the nondiffracting nature of the HCG beam family, we test their ability to self-heal and recover against obstacles, and we show the limit distance from which HCGn beams self-heal as a function of obstruction size and CG parameter. The results of this paper are of big interest in fields involving structured light such as particle manipulation, imaging, and light sheet microscopy.

The non-diffracting nature of truncated Hermite-Gaussian beams.

Using the asymptotic formula of the Hermite polynomials for higher-orders n≫1, an elegant mathematical expression that makes Hermite-Gaussian beams and cosine beams equivalent is obtained. Two factors of merit, the similarity and the power content ratio, are used to quantify the degree of equivalence between the two beams. These results yield a new nondiffracting Hermite-Gaussian beam in one dimension (1D) and that is easily extended to 2D.

On the beam shape coefficients of fundamental nondiffracting beams

In generalized Lorenz–Mie theory (GLMT) applied to structured beams the evaluation of beam shape coefficients (BSCs) constitutes a challenge. In this paper, we propose to calculate BSCs of fundamental nondiffracting beams, cosine beams, Bessel beams, Mathieu beams and parabolic beams. The aim of our method is the use of the Whittaker integral related to a scalar nondiffracting beam, and well known angular spectrum decomposition. Also, we exploit the relationship between solutions of scalar Helmholtz equation to expand the BSCs of nondiffracting beams in terms of higher order Bessel Beams (HOBB) BSCs. Some numerical simulations and discussions are given to validate our results.

Shaping self-accelerating Bessel-like optical beams along arbitrary trajectories by magnetic fluid deformable mirror

<sec> With the development of laser technology, the application scope of nondiffracting beams, such as Bessel beams, Mathieu beams, cosine beams, and parabolic beams, which remain invariant along their propagation, continues to expand. During its propagation, the main lobes of these beams tend to bend towards off-axis position, which is called self-accelerating (or self-bending) property. A Bessel-like beam with self-acceleration can realize the propagation of the main lobe along a curved trajectory while maintaining the non-diffraction. Because of the above property, Bessel-like beams have been utilized in various areas such as guiding particles along arbitrarily curved trajectories, self-accelerating beams in nonlinear medium, plasma guidance, and laser-assisted guiding of electric discharges around objects. </sec><sec> In this paper, we propose a method of bending the trajectory of Bessel-like beams by using a magnetic fluid deformable mirror (MFDM) instead of traditional spatial light modulator (SLM) and Pancharatnam-Berry (PB) phase manipulation. The MFDM provides a method without pixelation, where all parameters can be rapidly modified for fine-tuning. Furthermore, compared with the conventional deformable mirror, the MFDM has the advantages of a continuous and smooth mirror surface, large shape deformation, low manufacture cost, easy extension, and large inter-actuator stroke. Therefore, it is easy for the MFDM to generate the ideal shape of an axicon. Firstly, according to geometric analysis, the asymmetrical mirror profile to produce a self-accelerating Bessel-like optical beam is proposed. The proposed mirror profile can be used to compensate for the difference in optical path length for each annular slice of the axicon. If a collimated Gaussian beam is incident on the mirror combining the axicon and the asymmetrical mirror profiles, which can obtain Bessel-like beams with arbitrarily curved trajectories. Secondly, the resultant of the self-accelerating Bessel-like beams along parabolic trajectories is validated by the simulation in MATLAB. Finally, a prototype of MFDM consisting of the dual-layer arrays of miniature electromagnetic coils, a Maxwell coil and the magnetic fluid filled in a circular container is fabricated for the experiment. The experimental results show that the Bessel-like beams propagate along the parabolic trajectories, with the MFDM used, and the accuracy of the curved trajectories is verified. The proposed method in this paper opens a new experimental way to the study of Bessel-like beam; the theoretical approach can also be generalized mathematically for other non-paraxial beam propagation. </sec>

Theoretical analysis on the elasticity of a novel accordion cellular honeycomb core with in-plane curved beams

Flexible skin is an essential component for morphing wind turbine blade to maintain a smooth profile and bear aerodynamic loads during morphing. Cellular honeycomb cores with low in-plane and high out-of-plane stiffness are potential candidates for support structures of flexible skin. Honeycomb structure also requires zero Poisson’s ratio to avoid unnecessary stress and strain during one-dimensional morphing. A novel accordion cellular honeycomb core of close-to-zero Poisson’s ratio with in-plane corrugated U-type beams was proposed as a solution for these problems. The elastic properties of the structure are illustrated through a combination of theoretical analysis and finite element analysis. Results show that better in-plane morphing and out-of-plane load-bearing capabilities can be obtained with parameters of larger height-to-length ratio, spacing-to-length ratio and vertical beam to U-type beam thickness ratio as well as smaller thickness-to-length ratio. Results of comparisons on properties of the proposed honeycomb with two existing accordion honeycombs reveal that the in-plane elastic modulus of the proposed structure is as low as about 56% of that of the accordion honeycomb with V-type beams and 79% of that of the accordion honeycomb with cosine beams, showing better in-plane property but weaker out-of-plane load-bearing capability. Nevertheless, the out-of-plane load-bearing capability can be reinforced by increasing the vertical beam to U-type beam thickness ratio. Smaller driving force and less energy consumption are required by the proposed honeycomb core than conventional structures during morphing. The methods and results could be used for predictions of elasticity in design of sandwich morphing skin with similar cellular honeycomb cores.

Generation and applications of non-diffraction beam

In recent years, with the development of laser technology, various non-diffraction beams each with a central spot unchanged after a long distance propagation, have been generated, they being the Bessel beam, higher Bessel beam, Mathieu beam, higher Mathieu beam, cosine beam, parabolic beam, and Airy beam. Diffraction-free beams are widely used in laser drilling, laser precision alignment, optical precision control, optical micromanipulation, optical communication, plasma guidance, light bullet, synthesis of autofocusing beam, nonlinear optics, etc. In this paper, the expressions, generation methods and corresponding experimental results of the various non-diffraction beams are presented. There are many ways to generate the Bessel beam, they being circular slit, computed hologram, spherical aberration lens, resonant cavity, axicon, and metasurface. The main methods of generating the non-diffraction beams are summarized, and each method is analyzed in depth from the cost of the system, and then some suggestions for improving and perfecting are made. For the generation of non-diffraction beams, the passive methods are used most to convert other beams into corresponding non-diffraction beams by optical components. Due to the low damage threshold and high cost of optical components, the power, energy and beam quality of a non-diffracting beam will be limited. How to generate a high-power, high-beam quality non-diffracting beam will be a hot research spot. Diffractionless beams have attracted a great deal of interest due to their unique non-diffraction, transverse-accelerating (or self-bending) and self-healing property. Transverse-accelerating property refers to that non-diffraction beams propagate along a parabola trajectory. The diffractionless beams' propagation trajectory control method implemented by changing system parameters is simple and easily successful, but cannot reverse acceleration direction, and its controlling range is limited. The self-healing property means that the non-diffraction beam tends to reform during propagation in spite of severe perturbations imposed. Both the Airy beam and the Bessel beam exhibit self-healing properties during propagation. And non-diffraction beams have potential applications in many fields. In atmosphere, such as in optical communication, non-diffracting beam exhibits more resilience against perturbations. Finally, brief summary and outlook of non-diffraction beams playing important roles in future study, and their application prospects are presented. In addition to Airy beam and Bessel beam, for other non-diffraction beams due to the complexity of the beams themselves, by comparison, their applications are investigated very little, so the applications in Mathieu beam, cosine beam, and parabolic beam will be a hot research spot.

Elastic properties of a cellular structure with in-plane corrugated cosine beams

Cellular structure cores are potential candidates for support structures of flexible skin. The skin requires low in-plane and high out-of-plane stiffness of the support structure. To overcome these problems, a cellular structure with in-plane corrugated cosine beams having close-to-zero Poisson’s ratio to significantly reduce unnecessary stress and strain for one-dimensional morphing application was developed. The elastic properties were theoretically analyzed by energy methods, and verified by finite element analysis. Results show that better in-plane morphing and out-of-plane load-bearing capabilities can be obtained with larger height-to-length ratio, spacing-to-length ratio and vertical beam to cosine beam thickness ratio as well as smaller thickness-to-length ratio. Comparisons on properties with conventional accordion honeycomb were carried out. The results reveal that the cellular structure is of lower in-plane elastic modulus, which shows better in-plane property but weaker out-of-plane load-bearing capability. However, the out-of-plane load-bearing capability can be reinforced by increasing the height-to-length ratio and vertical beam to cosine beam thickness ratio.

Spatial scales of coherence of diffraction-free beams in a turbulent atmosphere

Coherent properties of diffraction-free optical beams propagating in a turbulent atmosphere are studied. The analysis is based on the solution of the equation for the second-order mutual coherence function of an optical radiation field. The behavior of the degree of coherence of the diffraction-free (cosine and fundamental Bessel) optical beams depending on the beam parameters and characteristics of the turbulent atmosphere is investigated. It turns out that the oscillating character of the degree of coherence of these beams is a fundamental property of diffraction-free beams, which is shown under weak fluctuations in a turbulent atmosphere. At high levels of fluctuations in a turbulent atmosphere, the degree of coherence of a diffraction-free cosine beam becomes closer to that of a plane wave, and of a diffraction-free fundamental Bessel beam, to a spherical wave. The analysis of two spatial scales of the degree of coherence of optical beams has shown that the integral scale of the degree of coherence for diffraction-free beams is a more representative characteristic than the coherence length; the former definitely correlates with optical radiation propagation conditions in a turbulent atmosphere.

Toward the optical "magic carpet": reducing the divergence of a light sheet below the diffraction limit.

In 3D, diffraction-free or Bessel beams are well known and have found applications in diverse fields. An analog in 2D, or pseudonondiffracting (PND) beams, is a nontrivial problem, and existing methods suffer from deficiencies. For example, Airy beams are not highly localized, some PND beams have significant side lobes, and a cosine beam has to be truncated by a very narrow aperture thus discarding most of the energy. We show, both theoretically and experimentally, that it is possible to generate a quasi-nondiffracting 2D light beam in a simple and efficient fashion. This is achieved by placing a mask consisting of a pair of double slits on a cylindrical lens. The applications include light sheet microscopy/optical sectioning and particle manipulation.

An Algorithm for Beam Propagation Method in Matrix Form

A new and efficient method for waveguide field calculation is proposed. In the proposed Fourier cosine beam propagation method, both dispersion and waveguide effects for each propagation interval are treated in a matrix form. Such a calculation method converts the conventional point-by-point analysis skill into a matrix-based one. By using the matrix method, the computing time required for calculating the field evolution is much less than that required by using the commonly used finite-difference beam propagation method. Two y-branches with, respectively, a rib-type and a channel-type cross sections are tested. The numerical results demonstrate the efficiency of the proposed method.

Generation of partially coherent diffraction-free fields with tunable geometry.

The synthesis of diffraction-free fields with different profiles is described. The synthesis is done by illuminating a screen containing a circular slit with a cosine beam. The treatment is equivalent to the modulation of the slit transfer characteristics and makes possible a tunable interference interaction of Bessel beams with noncommon axes. These results are generalized, and it is shown that coherent diffraction-free fields with arbitrary profiles can be expressed as the superposition of shifted zero-order Bessel beams and temporary parametric representations of the shifted functions. Diffraction-free fields with partially coherent features can be obtained. Experimental results are shown for each case.

Propagation properties of Hermite-cosine-Gaussian beams through a paraxial optical ABCD system with hard-edge aperture

Based on the generalized Huygens–Fresnel diffraction integral, a recurrence propagation equation of Hermite-cosine-Gaussian (HcoG) beams through a paraxial optical ABCD system with hard-edge aperture is derived, which permits us to obtain the analytical propagation expression for HcoG beams of any order. Furthermore, the closed-form propagation expressions for the Gaussian, Hermite–Gaussian, cosine (sine)-Gaussian, cosh (sinh) and cosine (sine) beams passing through a paraxial optical ABCD system with hard-edge aperture can be obtained by treating them as special cases of the analytical propagation expression for HcoG beams. The advantages of our analytical results are analyzed, and the applications are illustrated with numerical examples.

Truncation of a two-dimensional nondiffracting cos beam

The cosine (cos) beam is the two-dimensional counterpart of the three-dimensional nondiffracting beam, the Bessel beam. The propagation behavior of the truncated cos beam is similar to that of the truncated Bessel beam. The propagation of the apertured cos beams is studied. The pseudonondiffracting beam proposed recently by Rosen [Opt. Lett.20, 423 (1995)] can be obtained by the proper truncation of the cos beam. The temporal nondispersive pulse can be treated in a similar way, owing to the space–time analogy.