Abstract: We explore elastic wave focusing and enhanced energy harvesting by means of a 3D-printed Gradient-Index Phononic Crystal Lens (GRIN-PCL) bonded on a metallic host structure. The lens layer is fabricated by 3D printing a rectangular array of cylindrical nylon stubs with varying heights. The stub heights are designed to obtain a hyperbolic secant distribution of the refractive index to achieve the required phase velocity variation in space, hence the gradient-index lens behavior. Finite element simulations are performed on composite unit cells with various stub heights to obtain the lowest antisymmetric mode Lamb wave band diagrams, yielding a correlation between the stub height and refractive index. The elastic wave focusing performance of lenses with different design parameters (gradient coefficient and aperture size) is simulated numerically under plane wave excitation. It is observed that the focal points of the wider aperture lens designs have better consistency with the analytical beam trajectory results. Experiments are conducted using a PA2200 nylon lens bonded to an aluminum plate to demonstrate wave focusing and enhanced energy harvesting within the 3D-printed GRIN-PCL domain. The piezoelectric energy harvester at the focal region of the GRIN-PCL produces 3 times more power output than the baseline harvester at the same distance in the flat plate region. The results show that 3D printing can provide a simple and practical method for implementing phononic crystal concepts with minimal modification of the host structure.

Abstract: Three-dimensional (3D) gapless topological phases can be classified by the dimensionality of the band degeneracies, including zero-dimensional (0D) nodal points, one-dimensional (1D) nodal lines, and two-dimensional (2D) nodal surfaces. Both nodal points and nodal lines have been realized recently in photonics and acoustics. However, a nodal surface has never been observed in any classical-wave system. Here, we report on the experimental observation of a twofold symmetry-enforced nodal surface in a 3D chiral acoustic crystal. In particular, the demonstrated nodal surface carries a topological charge of 2, constituting the first realization of a higher-dimensional topologically-charged band degeneracy. Using direct acoustic field measurements, we observe the projected nodal surface and its Fermi-arc-like surface states and demonstrate topologically-induced robustness of the surface states against disorders. This discovery of a higher-dimensional topologically-charged band degeneracy paves the way toward further explorations of the physics and applications of new topological semimetal phases.

Abstract: In this paper, coding Huygens’ metasurface (CHM) is proposed for holographic imaging with enhanced quality. A weighted holographic algorithm is used to calculate the phase distribution at the interface and to design the CHM. Experimental demonstration performed in the microwave region validates holographic imaging with the ability to modulate energy distribution among focal points and improve image quality. By judiciously engineering both electric and magnetic dipolar resonators, the proposed digital Huygens’ meta-atom is able to provide a full transmission–phase covering the whole range of 2π together with a near-unity transmission efficiency. The proof-of-concept experiments show that holographic imaging quality can be indeed improved by using digital meta-atoms with several bits. Furthermore, the modulation of intensity distribution among focal points is experimentally realized by using the 3-bits CHM. The proposed CHM hologram shows great potential in a variety of application fields, such as programmable high-resolution imaging lenses, microscopy, data storage, information processing, and computer-generated holograms.

Abstract: High-power vortex beams have extensive applications in optical communication, nonlinear frequency conversion, and laser processing. To overcome a single beam’s power limitation, generating vortex beams, based on a phased beam array, is an intuitive idea that requires locking each beamlet’s phase to a specific different value. Conventionally, the intensity profiles of the focal plane (far field) are used for extracting the cost functions in active phase control systems. However, as for generating vortex beams, the cost function extraction method at the focal plane suffers because the same intensity profile of the beam array could correspond to different phase distributions in near field. Thus, the accurate phase control signals are difficult to obtain. In this paper, a new concept of extracting cost functions at the non-focal-plane is firstly presented and analyzed in detail by numerical simulation. This cost function extraction method is an efficient way of generating vortex beams with different topological charges, including second-order Bessel-Gaussian beams. The new concept could provide a valuable reference and contribute to the practical implementation of generating vortex beams by coherent beam combining technology.

Abstract: A new kind of beam, i.e., power-exponent helico-conical (PEHC) optical beams, has been proposed in this paper. The proposed beams possess a variety of interesting properties different from optical vortex beams. The intensities of the proposed optical beams at the focal plane are analyzed theoretically and experimentally. The far field mappings are also theoretically analyzed. The results demonstrate that the proposed beams have the ring-broken openings which can be adjusted by modifying the exponent n. The proposed beams can be useful for the extension applications of helico-conical optical beams, especially for optical trapping, guiding, and sorting.

Abstract: Thanks to significant advances in real-time terahertz imaging in terms of resolution and image quality, adapting and extending optical methods for 3D imaging at the millimeter scale is now promising. The shape-from-focus algorithm is a post-processing tool used in optical microscopy to reconstruct the external shape surface of a convex surface object. Images acquired at different distances from the object-side focal plane are implemented in this algorithm. We localize the best focus position in the stack of images for each pixel and then reconstruct the object in 3D due to the short depth of field. In this Letter, we propose an application of this algorithm in active and real-time terahertz imaging. We achieve the experimental reconstruction in 3D with a terahertz waves imaging system composed of a powerful source and a real-time terahertz camera.

Abstract: In this paper, the tight focusing of high-order cylindrical vector beams (beams with polarization singularity) was investigated. Using the Richards–Wolf formalism, there were obtained expressions for all projections of the electric and magnetic light fields with m -order polarization singularity in the focus of the aplanatic system. Also expressions for the longitudinal component of the Poynting vector were obtained. It was shown that these beams produce in the focal areas with the direction of the Poynting vector opposite to the direction of propagation of the beam. Moreover, the negative values could be comparable in absolute value with positive values; however, this strong inverse energy flow is obtained only while laser light is focused by a lens with high numerical aperture. Of particular interest is the case when the beam order is two ( m = 2). In this case, the region where the Poynting vector longitudinal projection is negative is located on the optical axis. If the order of the beam is more than two ( m > 2), than the reverse flow occurs near the optical axis and has a shape of a “tube.” Moreover, the width of the negative values region (the diameter of the “tube”) increases with increasing order of the beam, however, the absolute value of energy backflow decreases. Earlier, we reported on the observation of a spiral negative energy flow from the center of the focal plane of a focused vortex beam. In this paper, the negative propagation of a laminar near-axis energy flow is reported.

Abstract: Multi-photon scanning microscopy provides a robust tool for optical sectioning, which can be used to capture fast biological events such as blood flow, mitochondrial activity, and neuronal action potentials. For many studies, it is important to visualize several different focal planes at a rate akin to the biological event frequency. Typically, a microscope is equipped with mechanical elements to move either the sample or the objective lens to capture volumetric information, but these strategies are limited due to their slow speeds or inertial artifacts. To overcome this problem, remote focusing methods have been developed to shift the focal plane axially without physical movement of the sample or the microscope. Among these methods is liquid lens technology, which adjusts the focus of the lens by changing the wettability of the liquid and hence its curvature. Liquid lenses are inexpensive active optical elements that have the potential for fast multi-photon volumetric imaging, hence a promising and accessible approach for the study of biological systems with complex dynamics. Although remote focusing using liquid lens technology can be used for volumetric point scanning multi-photon microscopy, optical aberrations and the effects of high energy laser pulses have been concerns in its implementation. In this paper, we characterize a liquid lens and validate its use in relevant biological applications. We measured optical aberrations that are caused by the liquid lens, and calculated its response time, defocus hysteresis, and thermal response to a pulsed laser. We applied this method of remote focusing for imaging and measurement of multiple in-vivo specimens, including mesenchymal stem cell dynamics, mouse tibialis anterior muscle mitochondrial electrical potential fluctuations, and mouse brain neural activity. Our system produces 5 dimensional (x,y,z,λ,t) data sets at the speed of 4.2 volumes per second over volumes as large as 160 x 160 x 35 µm3.

Abstract: Several novel spin-selected dual-wavelength metalenses have been proposed and investigated based on the plasmonic metasurface consisting of two kinds of rotary rectangle gap nanoantennas (RGN), which are designed based on merging two or four polarity-inverse lenses corresponding to different wavelengths (765 and 1300 nm). The spin-selected dual-wavelength metalenses with two similar and two different vertical and lateral focal points have also been proposed respectively, which can focus two wavelengths with inverse spin states to arbitrary special positions. The three-dimensional metalens with four focal points have also been proposed, which can focus four beams with inverse spin states and different wavelengths to preset positions. Moreover, a spin-dependent achromatic metalens has also been proposed, which can focus left circularly polarized (LCP) incidence with different wavelengths to the same position. Our work opens up new avenues toward establishing novel spin-selected and wavelength-selected metadevices, and is significant for the development of spin-controlled photonics and particles manipulation. In addition, it provides a new idea for solving the problem of data transmission from optical fiber communication to visible light communication.

Abstract: In this letter, a near-field focused array antenna is applied to two-dimensional microwave imaging, which steers its focus on the designed focal plane by changing the operating frequency and by phase control in two directions, respectively. The imaging system is composed of this array and two microstrip antennas, as receiver and transmitters, respectively. Simulations and measurements have proved the feasibility of the image reconstruction approach. The proposed method has a high imaging speed due to fast electrical beam scan, and thanks to the frequency scan performance of the array in one dimension, it also shows a low-cost property against the fully phased method.

Abstract: Due to the high design freedom, metasurfaces are widely applied to realize miniaturized optical devices with high performance. Recently, assisted by optical design, monochromatic aberration–corrected lenses, composed of two metasurface layers, have been proposed for a well-focused light spot in the focal plane at large incident angles. However, the focus cannot be tuned in these structures. In this paper, based on the principle of the Moire lens, a wide-angle (±30∘) metalens with continuously tunable and monochromatic aberration–corrected focus that consists of two cascaded face-to-face metasurfaces is proposed. The focal length of the lens can be tuned by the mutual rotation of the metasurfaces. Simulation results show that the focal plane is changed to 5.34 µm when the rotation angle is increased by 0.4 rad at the incident wavelength of 810 nm. It is anticipated that the proposed metalens may have a good application prospect in integrated miniaturized imaging systems.

Abstract: In view of the optical detection requirements of wide-area and continuous surveillance of air targets, the detection ability of an infrared imaging system in geostationary orbit for aircraft plumes is studied. The point spread model of the subpixel imaging of the full chain, including the aircraft plume, the sea surface, the environmental atmosphere, the optical system, and the imaging detector is established. The detection ability of the typical imaging system in geostationary orbit is analyzed from the signal-to-noise ratio (SNR) and the detection range in combination with the effect of the point spread function (PSF) of the optical system. Meanwhile, the optimal coupling condition of the PSF to the spatial resolution is discussed. The imaging characteristics of the aircraft target on the focal plane of the infrared imaging system under different spatial sampling rates are simulated and verified. Research shows that the SNR of the system first increases, and then decreases gradually with an increase of the spatial sampling rate. The detectable range covered by the pixel footprint decreases as the detector size increases. When the detector size is 15, 20, and 30 μm, the target can be detected with a spatial resolution of 200-700, 300-700, and 400-600 m, respectively.

Abstract: We show that elongating a tightly focused field in the direction perpendicular to the optical axis is possible. We demonstrate our approach by specially shaping the Pancharatnam–Berry (PB) phase. Moreover, the analytical formulae required to calculate the strength vectors and energy flux of the three-dimensional electromagnetic fields near the focus of an aplanatic optical system are derived using the Richards and Wolf vectorial diffraction methods. Calculations reveal that the transverse enhancement is controllable and depend on the phase index in the PB phase, thereby giving rise to a focus with tunable length and subwavelength width in the focal plane.

Abstract: In this paper, we propose a systematic approach to automatically retrieve the first-order designs of three-component zoom systems with fixed spacing between focal points based on Particle Swarm Optimization (PSO) algorithm. In this method, equations are derived for the first-order design of a three-component zoom lens system in the framework of geometrical optics to decide its basic optical parameters. To realize the design, we construct the mathematical model of the special zoom system with two fixed foci based on Gaussian reduction. In the optimization phase, we introduce a new merit function as a performance metric to optimize the first-order design, considering maximum zoom ratio, total optical length and aberration term. The optimization is performed by iteratively improving a candidate solution under the specific merit function in the multi-dimensional parametric space. The proposed method is demonstrated through several examples, which cover almost all the common application scenarios. The results show that this method is a practical and powerful tool for automatically retrieving the optimal first-order design for complex optical systems.

Abstract: We introduce a new kind of partially coherent vortex beam with periodical coherence properties, named optical coherence vortex lattices (OCVLs). With the help of the generalized Collins formula, we explore the propagation properties of the intensity and the complex degree of coherence of OCVLs focused by a thin lens. Compared to conventional partially coherent vortex beam, OCVLs display extraordinary propagation properties, i.e., a Gaussian beam spot evolves into multiple beam spots (i.e., intensity lattices) in the focal plane (i.e., in the far field). The intensity lattices with solid or hollow beamlets can be formed through manipulating the coherence width in the source plane. We also find that the topological charge of the OCVLs can be determined from the distribution of its complex degree of coherence in the focal plane. Furthermore, we report experimental generation of OCVLs. The OCVLs will be useful for particle trapping and information transfer.

Abstract: One of the most important factors for improving the resolution of optical systems is to compensate for the aberrations (distortions) of the wave front. As a rule, whether special measuring devices (wavefront sensors) are used for such compensation or adaptive mirrors that perform iterative correction of the wavefront. However, often (for reasons of compactness or weight reduction), it is not possible to use the special equipment for measuring aberrations. To obtain certain information on the wave front, one can use the measured point spread function (PSF) or the intensity pattern in the focal plane. Methods of processing two PSFs (focal and nonfocal) with the help of neural networks are known. In this paper, we investigate the possibility of recognizing the wave front from a single intensity pattern in the focal plane. The technology of deep machine learning - convolutional neural network is chosen as the way for implementation. The idea of this technology lies in the alternation of convolutional and subsampling layers, for the purpose of efficient image recognition. Such approach will allow to optimize the process of compensation of optical system aberrations and to reduce the amount of required input data.

Abstract: Inserting an electrically tunable lens (ETL), such as liquid lens or tunable acoustic gradient lens, into a microscope can enable fast axial scanning, autofocusing, and extended depth of field. However, placing the ETL at different positions has different influences on image quality. Specially, in a wide-field microscope for measurement, the magnification has to be constant when introducing an ETL, otherwise it will affect measurement accuracy. To determine the best position of ETL, axial scanning range and magnification variation are quantitatively analyzed and discussed in finite and infinite microscopes through theoretical analysis, optical simulation, and experiment for four configurations: when ETL is placed at the back focal plane of objective, at the conjugate plane of objective's back focal plane between two relay lenses, or behind two relay lenses, and at imaging detector plane. The obtained results are as follows. When ETL is placed at the back focal plane, the system has a large scanning range, but the magnification varies because the back focal plane is inside the objective. When ETL is placed between two relay lenses, the magnification stays constant, but the scanning range is small. When ETL is placed behind two relay lenses, the magnification keeps invariant and the scanning range is large, but ETL and two relay lenses are inside the microscope and the system has to be customized. Finally, when ETL is placed at imaging detector plane, the magnification stays constant, but the scanning range is 0, which means the system has no axial scanning capability. RESEARCH HIGHLIGHTS: An electrically tunable lens (ETL) is introduced into a wide-field microscope for measurement. Axial scanning range and magnification variation are analyzed and discussed. Theoretical analysis, ZEMAX optical simulation and experiments are performed.

Abstract: Wavefront sensors encode phase information of an incoming wavefront into an intensity pattern that can be measured on a camera Several kinds of wavefront sensors (WFS) are used in astronomical adaptive optics Amongst them, Fourier-based wavefront sensors perform a filtering operation on the wavefront in the focal plane The most well known example of a WFS of this kind is the Zernike wavefront sensor, and the pyramid wavefront sensor (PWFS) also belongs to this class Based on this same principle, new WFSs can be proposed such as the n-faced pyramid (which ultimately becomes an axicone) or the flattened pyramid, depending on whether the image formation is incoherent or coherent In order to test such novel concepts, the LOOPS adaptive optics testbed hosted at the Laboratoire d'Astrophysique de Marseille has been upgraded by adding a Spatial Light Modulator (SLM) This device, placed in a focal plane produces high-definition phase masks that mimic otherwise bulk optic devices In this paper, we first present the optical design and upgrades made to the experimental setup of the LOOPS bench Then, we focus on the generation of the phase masks with the SLM and the implications of having such a device in a focal plane Finally, we present the first closed-loop results in either static or dynamic mode with different WFS applied on the SLM

Abstract: This study introduces and demonstrates the diffractive feature of a bi-segment spiral zone plate, so that each segment has its own width, topological charge, and radial phase shift. We show that the focusing behavior of this element depends strongly on these parameters. We demonstrate how these features can handle the focused intensity and structure of an incident plane beam. A variety of beam shapes and structures are generated at the focal plane. Theoretical and simulation results are verified by the corresponding experiments.

Abstract: Wide-angle optical functionality is crucial for implementation of advanced imaging and image projection devices. Conventionally, wide-angle operation is attained by complicated assembly of multiple optical elements. Recent advances in nanophotonics have led to metasurface lenses or metalenses, a new class of ultra-thin planar lenses utilizing subwavelength nanoantennas to gain full control of the phase, amplitude, and/or polarization of light. Here we present a novel metalens design capable of performing diffraction-limited focusing and imaging over an unprecedented > 170 degree angular field of view (FOV). The lens is monolithically integrated on a one-piece flat substrate and involves only a single layer of metasurface that corrects third-order Seidel aberrations including coma, astigmatism, and field curvature. The metalens further features a planar focal plane, which enables considerably simplified system architectures for applications in imaging and projection. We fabricated the metalens using Huygens meta-atoms operating at 5.2 micron wavelength and experimentally demonstrated aberration-free focusing and imaging over the entire FOV. The design concept is generic and can be readily adapted to different meta-atom geometries and wavelength ranges to meet diverse application demands.

Abstract: We prove that for closed rank 1 manifolds without focal points the equilibrium states are unique for Holder potentials satisfying the pressure gap condition. In addition, we provide a criterion for a continuous potential to satisfy the pressure gap condition. Moreover, we derive several ergodic properties of the unique equilibrium states including the equidistribution and the K-property.

Abstract: Propagation of an axially symmetrical beam through an apodizer comprising a circular serrated aperture and a spatial filter is considered on the basis of the parabolic equation solution. In part I, the equation is solved for uniform and Gaussian beams with a flat wavefront, which propagate from the circular serrated aperture to the spatial filter focal plane. By analyzing the field structure in the focal plane, the diameter of the spatial filter pinhole required for recovering the axial symmetry of the field at the spatial filter exit is determined as a function of the serrated aperture and spatial filter parameters.

Abstract: Nodal aberration theory is used to calculate the third-order aberrations that result in image blur for an unobscured modified 4f relay (2f1 + 2f2) formed by two tilted spherical mirrors for objects at infinity (infinite conjugate) and near the front focal plane of the first mirror (finite conjugate). The field-averaged wavefront variance containing only non-rotationally symmetric aberration coefficients is then proposed as an optimization metric. Analytical and ray tracing optimization are demonstrated through sample designs. The particular cases of in-plane and orthogonal folding of the optical axis ray are discussed, followed by an analysis of a modified 2f1 + 2f2 relay in which the distance of the first mirror to the object or pupil is allowed to vary for aberration correction. The sensitivity of the infinite conjugate 2f1 + 2f2 relay to the input marginal ray angle is also examined. Finally, the optimization of multiple conjugate systems through a weighted combination of wavefront variances is proposed.

Abstract: Field solutions for a conventional Veselago-Pendry (VP) flat lens with ϵ=−ϵ 0 and μ=−μ 0 can be derived based on transformation optics (TO) principles. The TO viewpoint makes it clear that perfect imaging by a VP lens is a consequence of multivalued nature of the particular coordinate transformation involved. This transformation is equivalent to a “space folding” whereby one point in the transformed domain (source point) is mapped to three different points in the physical domain (the original source point plus two focal points). In theory, a VP lens would enable the recovery of the entire range of spectral components, i.e. both propagating and evanescent fields, thus characterizing a “perfect lens”. Such lens, if lossess, is indeed “perfect” for monochromatic waves; however, for any realistic wave packet the space folding interpretation provided by TO makes it clear that a VP lens violates primitive causality constraints, which precludes any practical realization. Here, we utilize complex transformation optics (CTO) to derive generalized Veselago-Pendry (GVP) lenses without requiring a multivalued transformation. Unlike the conventional VP lens, the proposed lenses can fully recover the evanescent spectra under more general conditions that include the presence of (anisotropic) material loss/gain.

Abstract: This study focuses on improving the reconstruction process of the brightfield optical projection tomography (OPT). OPT is often described as the optical equivalent of X-ray computed tomography, but based on visible light. The detection optics used to collect light in OPT focus on a certain distance and induce blurring in those features out of focus. However, the conventionally used inverse Radon transform assumes an absolute focus throughout the propagation axis. In this study, we model the focusing properties of the detection by coupling Gaussian beam model (GBM) with the Radon transform. The GBM enables the construction of a projection operator that includes modeling of the blurring caused by the light beam. We also introduce the concept of a stretched GBM (SGBM) in which the Gaussian beam is scaled in order to avoid the modeling errors related to the determination of the focal plane. Furthermore, a thresholding approach is used to compress memory usage. We tested the GBM and SGBM approaches using simulated and experimental data in mono- and multifocal modes. When compared with the traditionally used filtered backprojection algorithm, the iteratively computed reconstructions, including the Gaussian models GBM and SGBM, provided smoother images with higher contrast.

Abstract: The STereo imaging Channel (STC) is the first push-frame stereo camera on board an European Space Agency (ESA) satellite, i.e., the ESA-Japan Aerospace eXploration Agency mission BepiColombo. It was launched in October 2018, and it will reach its target, Mercury, in 2025. The STC main aim is to provide the global three-dimensional reconstruction of the Mercury surface. STC, the stereo channel of spectrometer and imagers for Mercury Planetary Orbiter BepiColombo-Integrated Observatory System, is based on an original optical design that incorporates the advantages of a compact unique detector instrument and the convenience of a double direction acquisition system. In fact, STC operates in a push-frame imaging mode and its two optical sub-channels will converge the incoming light on a single focal plane assembly allowing to minimize mass and volume. The focal plane of the instrument is housing six different filters: two panchromatic filters in the range 600-800 nm and four broadband filters with central wavelengths in the range 420-920 nm. In this paper, the geometrical calibration of the instrument, including the optical setups used, will be described. The methods used to derive the focal lengths, the boresights, and the reference systems of the different filter models are presented, and the related distortion results are discussed. The STC off-axis configuration forced to develop a distortion map model based on the RFM (rational function model). In contrast to other existing models, which allow linear estimates, the RFM is not referred to specific lens geometry, but it is sufficiently general to model a variety of distortion types, as it will be demonstrated in this particular case.