Continuous Phase Profile Research Articles

Design of adjustable multifocal diffractive optical elements with an improved smooth phase profile by continuous variable curve with multi-subperiods method.

Multifocal diffractive optical elements (MDOEs), which produce arbitrary light distribution, are widely used in lightweight and compact optical systems. MDOEs that are combined with multiple functions tend to have complex step structures, limiting their applications. We propose a facile method named continuous variable curve with multi-subperiods (CVCMS) to design adjustable multifocal single-layer diffractive optical elements. Through the analysis, the model achieved arbitrary diffraction efficiency distribution with an improved smooth continuous phase profile in each diffractive ring while retaining the periodicity. To display the high design freedom of the method, we utilized this method to design and discuss a broadband multifocal intraocular lens (MIOL) focused on the optimization of far focal point. Finally, the method was compared with other multifocal design methods. The results show that the CVCMS method achieved adjustable multifocal design with better performance and smoother profile than other MDOE design techniques. The proposed model can be applied to multifocal ophthalmic lens designs.

Quadratic-Gradient Metasurface-Dome for Wide-Angle Beam-Steering Phased Array With Reduced Gain Loss at Broadside

The quest for increasing the scanning range of a phased array is a challenging task for antenna engineers, and its solution could lead to significant advances in different applicative scenarios, ranging from 5G and beyond 5G communications to radar and satellite systems. For this purpose, the use of a deflecting meta-dome is one of the most promising solutions recently proposed that, however, still presents some inherent limitations, such as the significant reduction of the broadside gain of the array, due to the diverging effect of the dome, as well as the complexity of the implementation due to the need of a continuous phase profile. In this framework, the paper aims at proposing some technical solutions for maximizing the meta-dome performance and relaxing the implementation complexity. In particular, by properly discretizing and engineering the phase profile along the dome and by taking into account the different angles of incidence onto the meta-cells, we show how it is possible designing realistic meta-domes with reduced insertion loss at broadside, improved steering capabilities, and a reduced profile. In addition, a complete design workflow for a realistic meta-dome based on cascaded metasurfaces is presented.

Terahertz passive amplification via temporal Talbot effect in metamaterial-based Bragg fibers

A fully passive terahertz (THz) pulse amplification device is proposed based on leveraging the temporal Talbot effect (TTE) on a highly dispersive silicon-based metamaterial Bragg fiber. To maximize the TTE passive gain, we introduce and explore three different strategies, denoted as coherent pulse addition (CPA), forward Talbot illuminator (FTAI), and backward Talbot illuminator (BTAI). The BTAI strategy allows additional degrees of freedom for controlling the output pulse shape. Moreover, by using a continuous phase profile, we overcome the hurdle of implementing discrete phase gratings in limited time response phase modulators. We explore different pulse shapes and chirped pulses with CPA, and different gain factors with both BTAI and FTAI. Numerical simulation results show a 5.8 dB gain for a 9.8 cm long fiber with the CPA method, a 9.9 dB gain with FTAI (1.37 cm long), and a 8.8 dB gain with BTAI (1.25 cm long). These results indicate the potential of the approaches presented here, which can be used as a springboard for further developments toward high gain passive amplification THz devices.

Multi beam scanning programmable metasurface using miniaturized unit cells for 5G applications

This paper proposes a programmable reflective metasurface with a miniaturized unit cell that actively controls the scattered waves for achieving steerable multibeam radiation in sub-6 GHz 5G communication systems. The design uses array theory to provide the required phase shifts for various multibeam radiation patterns. The reconfigurability of the metasurface phase profile is attained by voltage-controlled varactor diodes embedded in the structure. Then, different unit cell arrangements are employed to achieve multibeam functionality where Pianoboard and Chessboard configurations provide one and two-dimensional multi beams, respectively. It turns out steerable multibeam radiation is achieved by dynamically change the dimension of the super unit cells. The reliability of the results is verified through analytical and numerical approaches. Moreover, the comparisons show that the proposed unit cell has more miniaturized size rather than the conventional cells, resulting in a better approximation for the ideally continuous phase profile identified by the generalized Snell’s law.

Mathematical Operations of Transmissive Near Fields Controlled by Metasurface with Phase and Amplitude Modulations

AbstractMetasurfaces show great potential due to their powerful ability to manipulate electromagnetic waves as desired, which has been widely investigated in the microwave, terahertz, infrared, and visible regimes. Here, it is proposed to control near‐field distributions through use of a metasurface with both amplitude and phase modulations. A C‐shaped particle is designed to provide stable and continuous amplitude and phase profiles independently of transmitted waves by varying its opening and orientation angles. Benefiting from both amplitude and phase modulations on the metasurface, differentiation and integration on electric‐field distributions can be achieved by changing the arrangements of complex coefficients on the metasurface. Besides, the differential operation can be utilized to show the edges of predesigned electric‐field distributions. It is believed that the proposed method will accelerate the pace of metasurfaces towards many applications by engineering and operating the near‐field distributions.

Regional iterative optimization algorithm to reduce error caused by DOE binarization.

To reduce the manufacturing cost and the manufacturing time, the continuous phase profile of a diffractive optical element is usually quantized into two levels, which causes the degradation of optic performance. Based on the deep analysis on the existing binarization algorithms, the paper proposes an algorithm based on regional iterative optimization. The simulation results show that the proposed algorithm can achieve improvements on mean square error, average amplitude in the output area, and nonuniformity. The phase patterns created by different algorithms are fabricated on polyethylene glycol terephthalate substrates by maskless lithography technology. The image reconstructed by the proposed algorithm exhibits higher intensity, more accurate shape, and higher uniformity.

High‐Efficiency and Tunable Circular‐Polarization Beam Splitting with a Liquid‐Filled All‐Metallic Catenary Meta‐Mirror

AbstractCircular‐polarization beam splitting is one functionality of interest in polarization control. However, current splitters suffer from limitations in either efficiency or tunability. It is theoretically and experimentally demonstrated that a meta‐mirror composed of catenary‐shaped metallic gratings can efficiently deflect left‐handed and right‐handed circularly polarized waves in opposite directions with power efficiency of over 90%. This ultrahigh efficiency is attributed to the nearly perfect polarization conversion and continuous phase profile of the metallic catenary structure. Furthermore, the meta‐mirror demonstrates high beam‐splitting tunability with ethanol injected into the catenary groove. By controlling ethanol depth, the working frequency for peak deflection can be continuously tuned from 10.5 to 8.5 GHz. It is believed that this approach can provide valuable guidance for efficient and dynamic control of electromagnetic waves for various applications.

A novel wavefront engineering approach for producing new classes of optical components with enhanced functionality

Scientists demonstrated highly efficient transmissive dielectric metasurfaces capable of forming a spatially continuous phase profile for complex wavefront engineering, enabling new classes of ultra-thin, high-performance optical components.

Impedance-matched dielectric metasurfaces for non-discrete wavefront engineering

Metasurfaces can manipulate optical wavefronts by locally shifting the phase of incident light with metallic or dielectric optical nanoresonators that are generally arranged on a lattice with subwavelength spacing. However, such conventional metasurfaces inevitably generate a spatially discrete multi-level phase profile due to the spacing of their building blocks. This directly leads to an efficiency reduction and thus limits their capability. Here, we propose and demonstrate highly efficient transmissive metasurfaces with the ability to form a continuous phase profile. The proposed strategy relies on the fact that high-index dielectric nanobeams with gradually modulated widths can be interpreted to be a virtually impedance-matched material with spatial variations of its refractive index. By highly utilizing such features, one-dimensionally continuous, arbitrary phase profiles can be created in a simple manner with the width profile design. Since spatial transmittance variations can be minimized due to the impedance matching feature, this approach provides a nearly ideal phase profile for spatial light modulation with phase-only filtering operations. We demonstrate that this approach has the capability to improve the performance in various metasurface-based optical components, including polarization-dependent, large-angle beam deflectors and versatile multi-beam splitters. Considering that designing optical phases even in deep-subwavelength regimes is critical for free-space optics, the proposed approach will enable new classes of optical components with complex wavefront engineering.

Multidimensional joint coupling: a case study visualisation approach to movement coordination and variability

A case study visualisation approach to examining the coordination and variability of multiple interacting segments is presented using a whole-body gymnastic skill as the task example. One elite male gymnast performed 10 trials of 10 longswings whilst three-dimensional locations of joint centres were tracked using a motion analysis system. Segment angles were used to define coupling between the arms and trunk, trunk and thighs and thighs and shanks. Rectified continuous relative phase profiles for each interacting couple for 80 longswings were produced. Graphical representations of coordination couplings are presented that include the traditional single coupling, followed by the relational dynamics of two couplings and finally three couplings simultaneously plotted. This method highlights the power of visualisation of movement dynamics and identifies properties of the global interacting segmental couplings that a more formal analysis may not reveal. Visualisation precedes and informs the appropriate qualitative and quantitative analysis of the dynamics.

A Generalized Circular Dammann Grating With Controllable Impulse Ring Profile

We present a type of generalized circular Dammann gratings (GCDGs) with controllable impulse ring profiles. Different from impulse rings generated by traditional circular Dammann gratings, the intensity profile of impulse rings can be tuned by redesigning the phase structure of GCDGs. Also, the physical picture behind this controllable impulse ring profile is given clearly. As examples, four one-order binary (0, $\pi $ ) GCDGs are designed and fabricated for generation of impulse rings with four different intensity profiles. In addition, GCDGs with continuous-phase profile are also demonstrated for generation of multiple concentric equal-intensity impulse rings with different intensity profiles. This type of impulse rings with tunable intensity profiles will enrich the function of CDGs, and it should be of high interest for its potential applications in various realms, such as structured pumping laser, novel optical manipulation, generation of dark perfect vortices, and optical testing and measurement.

High-performance geometric phase elements in silica glass

High-precision three-dimensional ultrafast laser direct nanostructuring of silica glass resulting in multi-layered space-variant dielectric metasurfaces embedded in volume is demonstrated. Continuous phase profiles of nearly any optical component are achieved solely by the means of geometric phase. Complex designs of half-wave retarders with 90% transmission at 532 nm and >95% transmission at >1 μm, including polarization gratings with efficiency nearing 90% and computer generated holograms with a phase gradient of ∼0.8π rad/μm, were fabricated. A vortex half-wave retarder generating a single beam optical vortex with a tunable orbital angular momentum of up to ±100ℏ is shown. The high damage threshold of silica elements enables the simultaneous optical manipulation of a large number of micro-objects using high-power laser beams. Thus, the continuous control of torque without altering the intensity distribution was implemented in optical trapping demonstration with a total of 5 W average power, which is otherwise impossible with alternate beam shaping devices. In principle, the direct-write technique can be extended to any transparent material that supports laser assisted nanostructuring and can be effectively exploited for the integration of printed optics into multi-functional optoelectronic systems.

Splitting light beam by meanderline with continuous phase profile

It has been successfully demonstrated can be widely used in nano-photonics applications owing to their flexible wavefront manipulation in a limited physical profile. However, how to improve the efficiency for the transmission light is still a challenge. We experimentally demonstrate that the sine-shaped metallic meanderline fabricated by focus ion beam technology converts circularly polarized (CP) light to its opposite handedness and sends them into different propagation directions depending on the polarization states in near-infrared and visible frequency regions. The beam splitting behavior is well characterized by a simple geometry relation, following the rule concluded from other works on the wavefront manipulation of metasurface with phase discontinuity. Importantly, the meanderline is demonstrated to be more efficient in realizing the same functions due to the suppressed high order diffractions resulted from the absence of interruption in phase profile. The theoretical efficiency reaches 67%. Particularly, potential improvements are feasible by changing or optimizing shape of the meanderline, offering high flexibility in applications for optical imaging, communications and other phase-relative techniques. Additionally, since the continuous phase provided by the meanderline can improve the sampling efficiency of the phase function, it is helpful in realizing high quality hologram.

Ultrafast Laser‐Induced Metasurfaces for Geometric Phase Manipulation

Direct-write femtosecond laser nanostructuring of 300 nanometer thick a-Si:H films results in space-variant functional metasurfaces with form birefringence of up to ne-no=–0.5. Engineering the orientation of local optical axis allows implementing continuous phase profiles of nearly any optical element including arrays of polarization micro-converters and micro lenses, polarization gratings and computer generated holograms with continuous phase gradients of ~1 rad/µm.

Scattering engineering in continuously shaped metasurface: An approach for electromagnetic illusion.

The control of electromagnetic waves scattering is critical in wireless communications and stealth technology. Discrete metasurfaces not only increase the design and fabrication complex but also cause difficulties in obtaining simultaneous electric and optical functionality. On the other hand, discontinuous phase profiles fostered by discrete systems inevitably introduce phase noises to the scattering fields. Here we propose the principle of a scattering-harness mechanism by utilizing continuous gradient phase stemming from the spin-orbit interaction via sinusoidal metallic strips. Furthermore, by adjusting the amplitude and period of the sinusoidal metallic strip, the scattering characteristics of the underneath object can be greatly changed and thus result in electromagnetic illusion. The proposal is validated by full-wave simulations and experiment characterization in microwave band. Our approach featured by continuous phase profile, polarization independent performance and facile implementation may find widespread applications in electromagnetic wave manipulation.

Thin-film Pancharatnam lens with low f-number and high quality.

We have made an ultra-thin (~2.26 µm) f/2.1 lens based on the Pancharatnam phase effect using the polarization holography alignment technique. This lens exhibits a continuous phase profile, high efficiency (>97%), and is switchable from having a positive focal length to a negative one by changing the handedness of input circularly polarized light. We analyzed its optical performance and simulated it as a gradient index lens for further comparison, and to discuss its bandwidth limitation. The conditions required for improving the performance and its low-cost fabrication method is discussed. Because of the nature of Pancharatnam devices and the demonstrated fabrication method, these results are applicable to a wide size range.

Coordination as a function of skill level in the gymnastics longswing

The purpose of this study was to investigate the nature of inter-joint coordination at different levels of skilled performance to: (1) distinguish learners who were successful versus unsuccessful in terms of their task performance; (2) investigate the pathways of change during the learning of a new coordination pattern and (3) examine how the learner’s coordination patterns relate to those of experts in the longswing gymnastics skill. Continuous relative phase of hip and shoulder joint motions was examined for longswings performed by two groups of novices, successful (n = 4) and unsuccessful (n = 4) over five practice sessions, and two expert gymnasts. Principal component analysis showed that during longswing positions where least continuous relative phase variability occurred for expert gymnasts, high variability distinguished the successful from the unsuccessful novice group. Continuous relative phase profiles of successful novices became more out-of-phase over practice and less similar to the closely in-phase coupling of the expert gymnasts. Collectively, the findings support the proposition that at the level in inter-joint coordination a technique emerges that facilitates successful performance but is not more like an expert’s movement coordination. This finding questions the appropriateness of inferring development towards a “gold champion” movement coordination.

From regular periodic micro-lens arrays to randomized continuous phase profiles

Abstract Illumination systems for various industrial applications, e.g., in semiconductor industries and medical treatment techniques, require a specific and well-adapted intensity distribution with maximum efficiency, best achievable accuracy, and highest flexibility in the selection of the target light field. Additionally, for particular applications, all these aspects have to be fulfilled simultaneously for different wavelengths. In most of these situations, the challenging optical specifications are accompanied by the requirement of a cost-efficient fabrication technique, suitable at least for batch or small series production. In the present contribution, we first retrace the development steps and performance progress of micro-optical-based beam shaping setups. Secondly, we discuss the possibilities resulting from a combination of both refractive and diffractive optical characteristics. Especially, we show that a well-adapted combination of refractive and diffractive properties in a single element allows us to create achromatic diffusers with exceptional flexibility and high conversion efficiency.

Complex-amplitude-based phase unwrapping method for digital holographic microscopy

Abstract A complex-amplitude-based phase unwrapping approach for digital holographic microscopy is proposed in this paper. A quality map is derived directly from the reconstructed complex amplitude distribution of object wave to evaluate noise influence and phase reliability in the wrapped phase image. Quality-guided phase unwrapping algorithm is then implemented with the quality map to retrieve continuous phase profile. Unwrapping errors caused by unreliable phase data are successfully suppressed. The effectiveness of this method is demonstrated with simulation and experimental results.

Inter-segmental coordination in progressions for the longswing on high bar

This study focused on identifying the most effective skill progression for developing the longswing on high bar in men's artistic gymnastics. Building on previous work by Irwin and Kerwin (2005), in which a method to rank progressions based on their angular kinematics was developed, this study aimed to use the method to quantify similarities in inter-segmental coordination between selected progressions and the longswing on high bar. Video images of four members of the UK men's national gymnastics squad performing three series of five longswings and eight progressions were recorded at 50 Hz. Two-dimensional direct linear transformation techniques were used to determine the real-world coordinates from the digitized data. Inter-segmental coordination of the hip and shoulder joints during the functional phases of the longswing was assessed using continuous relative phase. Similarity between the longswing and each progression was represented by a “specificity score”, which was also used to rank the progressions. Each progression's specificity score was calculated by combining a “difference score” (root mean squared difference between the continuous relative phase profiles of the longswing and the progression) and a “variability score” (standard deviation of the continuous relative phase profiles for each progression). The progressions that were most similar to the longswing included the looped bar longswing and layaway swing down (ranked 1st and 2nd), with specificity scores of 9% and 10% respectively. In contrast, the least similar progressions were the looped bar “no action” longswing (51%) and pendulum swing (63%) (ranked 7th and 8th). Establishing effective skill learning pathways is recognized as a key component of the coaching process and ranking progressions based on their specificity score provided a mechanism to identify progressions with similar inter-segmental coordination profiles to the key skill on the high bar, the longswing.