Nonlinear Shaping Research Articles

Universal Narrowband Wavefront Shaping with High Quality Factor Meta-Reflect-Arrays.

Optical metasurfaces offer unprecedented flexibility in light wave manipulation but suffer weak resonant enhancement. Tackling this problem, we experimentally unveil a new phase gradient metasurface platform made entirely from individually addressable high quality factor (high-Q) silicon meta-atoms. Composed of pairs of nearly identical nanoblocks, these meta-atoms support dipolar-guided-mode resonances that, due to the controlled suppression of radiation loss, serve as highly sensitive phase pixels when placed above a mirror. A key novelty of this platform lies in the vanishingly small structural perturbations needed to produce universal phase fronts. Having fabricated elements with Q-factor ∼380 and spaced by λ/1.2, we achieve strong beam steering, up to 59% efficient, to angles 32.3°, 25.3°, and 20.9°, with variations in nanoantenna volume fractions across the metasurfaces of ≤2.6%, instead of >50% required by traditional versions. Aside from extreme sensitivity, the metasurfaces exhibit near-field intensity enhancement over 1000×. Taken together, these properties represent an exciting prospect for dynamic and nonlinear wave shaping.

Sequential Three-Dimensional Nonlinear Photonic Structures for Efficient and Switchable Nonlinear Beam Shaping

Nonlinear beam shaping can be dynamically controlled by temperature or polarization to form switchable nonlinear structured beams, which constitute an unprecedented system for realizing optical encryption at new frequencies and high-dimensional nonclassical light sources. However, previous works were limited by a trade-off between the conversion efficiency and the modulation dimension of the beam. It is still technologically challenging to achieve efficient and switchable multidimensional nonlinear beam shaping. Here, we demonstrate switchable generation of nonlinear structured beams via three-dimensional (3D) nonlinear photonic crystals (NPCs) fabricated by femtosecond laser writing technique with considerable conversion efficiency. The 3D NPCs contain different sequential 3D arrays of spatially modulated χ(2) nonlinearity designed by computer-generated hologram (CGH) along the optical y-axis (LiNbO3 crystal). The output direction of the nonlinear beams can be changed by the carrier frequencies, while their efficiencies can be increased by the quasi-phase matching condition.

Effect of spatial variation of the duty cycle in transverse second-harmonic generation.

Transverse second-harmonic generation, in which the emission angles of the second harmonic are determined by the spatial modulation of the quadratic nonlinearity, has important applications in nonlinear optical imaging, holography, and beam shaping. Here we study the role of the local duty cycle of the nonlinearity on the light intensity distribution in transverse second-harmonic generation, taking the generation of perfect vortices in periodically poled ferroelectric crystal as an example. We show, theoretically and experimentally, that spatial variations of the nonlinearity modulation must be accompanied by the corresponding changes of the width of inverted ferroelectric domains, to ensure uniformity of the light intensity distribution in the generated second harmonic. This work provides a fundamental way to achieve high-quality transverse second-harmonic generation and, hence, opens more possibilities in applications based on harmonic generation and its control.

Massive MIMO Precoding and Spectral Shaping With Low Resolution Phase-Only DACs and Active Constellation Extension

Nonlinear precoding and pulse shaping are jointly considered in multi-user massive multiple-input multiple-output (MIMO) systems with low resolution D/A-converters (DACs) in terms of algorithmic approach as well as large system performance. Two design criteria are investigated: the mean squared error (MSE) with active constellation extension (ACE) and the symbol error rate (SER). Both formulations are solved based on a modified version of the generalized approximate message passing (GAMP) algorithm. Furthermore, theoretical performance results are derived based on the state evolution analysis of the GAMP algorithm. The MSE based technique is extended to jointly perform over-the-air (OTA) spectral shaping and precoding for frequency-selective channels, in which the spectral performance is characterized at the transmitter and at the receiver. Simulation and analytical results demonstrate that the MSE based approach yields the same performance as the SER based formulation in terms of uncoded SER. The analytical results provide good performance predictions up to medium SNR. Substantial improvements in detection, as well as spectral performance, are obtained from the proposed combined pulse shaping and precoding approach compared to standard linear methods.

Archetypes of images of nonlinear architecture: randomness or conscious assimilation

For the first time in art history the problem of the appeal of architects of the digital era to the reconstruction of images of objects of the organic world through nonlinear shaping is raised. The aim of the research is to establish the archetypal nature of the images of nonlinear architecture through the essence of the phenomenon of sporadicity and conscious choice. It is revealed on the basis of the author’s artistic and figurative concept, which represents architecture as a symbiosis of phenomenological, procedural (evolutionary) and reproduced existences. The methodological basis is provided by the scientific works of scientists in the field of art and architecture (F. Johnson, A. Vidler, P. Schumacher, I. Dobritsyna, I. Azizyan, E. Lapshina, E. Sokolova, A. Shamruk). Through the prism of retrospection and comparative analysis, the architects aspirations to imitate the objects of the surrounding reality in the forms and structures of structures are revealed. The author substantiates the premeditation and randomness in the modeling of images of nonlinear architecture as a result of synthetic architecture. It is concluded that in appealing to the prototypes of real reality, the architect of the digital age acted as the creator of the beautiful, designed in the image and likeness of nature.

Open-loop control of electrostatic levitation actuators to enhance the travel-range of optical switches

Command shaping is a driving technique for handling the large settling time of the high-Q-MEMS actuators. The strong nonlinearity due to the electrostatic actuation limits the linear operation range in cantilevered or torsional micro-mirrors where command shaping techniques can be applied for positioning. Experimental and simulation results of this research demonstrate the effectiveness of using electrostatic levitation to overcome the actuation nonlinearities and a significant increase in the operation range. The motivation for this research is that applying the nonlinear command shaping causes complexity in command manipulation and requires an accurate knowledge of the nonlinear terms involved in the system model. The large linear operation range generated by the levitating force allows using the practical simple command shaping methods for open-loop control.

Methodology for Shape Optimization of Magnetic Designs: Magnetic Spring Characteristic Tailored to Application Needs

Topology and shape optimization are still rarely applied to problems in electromagnetic design due to the computational complexity and limited commercial tooling, even though components such as electrical motors, magnetic springs or magnetic bearings could benefit from it, either to improve performance (reducing torque ripple and losses through shaping harmonic content in back electromotive force) or reduce the use of rare-earth materials. Magnetic springs are a fatigue free alternative to mechanical springs, where shape optimization can be exploited to a great degree—allowing for advanced non-linear stiffness characteristic shaping. We present the optimization methodology relying on a combination of several approaches for characteristic shaping of magnetic springs through either a modular design approach based on: (i) Fourier order decomposition; (ii) breaking conventional design symmetry; or (iii) free shaping of magnets through deviation from a nominal design using problem formulations such as spline and polynomials for material boundary definitions. Each of the parametrizations is formulated into a multi-objective optimization problem with both performance and material cost, and solved using gradient free optimization techniques (direct search, genetic algorithm). The methodology is employed on several benchmark problems—both academic and application inspired magnetic spring torque characteristic requirements. The resulting designs fit well with the requirements, with a relatively low computational cost. As such, the methodology presented is a promising candidate for other design problems in 2D shape optimization in electrical motor research and development.

Nonlinear wavefront engineering with metasurface decorated quartz crystal

Abstract In linear optical processes, compact and effective wavefront shaping techniques have been developed with the artificially engineered materials and devices in the past decades. Recently, wavefront shaping of light at newly generated frequencies was also demonstrated using nonlinear photonic crystals and metasurfaces. However, the nonlinear wave-shaping devices with both high nonlinear optical efficiency and high wave shaping efficiency are difficult to realize. To circumvent this constraint, we propose the idea of metasurface decorated optical crystal to take the best aspects of both traditional nonlinear crystals and photonic metasurfaces. In the proof-of-concept experiment, we show that a silicon nitride metasurface decorated quartz crystal can be used for the wavefront shaping of the second harmonic waves generated in quartz. With this crystal-metasurface hybrid platform, the nonlinear vortex beam generation and nonlinear holography were successfully demonstrated. The proposed methodology may have important applications in nonlinear structured light generation, super-resolution imaging, and optical information processing, etc.

3D Nanoprinting with Charged Aerosol Particles─An Overview

ConspectusThree-dimensional (3D) printing is a revolutionary technology allowing rapid, cost-effectively, and flexible design of desired 3D products. In this regard, various techniques for downscaling 3D printing have been developed based on several methodologies in the past decades to exploit the advantages of 3D printing at the micro/nanoscale. The development of 3D nanoprinting techniques has provided a method to design unique and sophisticated nanoscale 3D objects enabling functional applications that are thus far constrained with conventional planar nanomanufacturing processes such as photolithography and electron beam lithography. However, the versatile and practical realization of 3D nanoprinting in a broad science and engineering field remains challenging due to limitations such as feature size resolution, suitable materials, and design flexibility. Therefore, innovative 3D nanoprinting techniques are required to overcome current limitations. In this Account, we describe our achievements in developing 3D nanoprinting with charged aerosols relying on the physics behind counteracting electric fields. We introduce the generation of charged aerosols, the most feasible in the broad range of fundamental building blocks (mainly all types of metals and alloys, their oxides, polymers, and organics) for 3D nanoprinting. Moreover, charged aerosols can be processed at ambient conditions easily. The aerosols could be precisely controlled and delivered for the assembly, using electric fields of complicated configurations despite the Brownian diffusion and other chaotic processes. The converging electric fields are formed around openings by the interactions of two electric fields. One of the electric fields comes from a negatively biased substrate. In contrast, the counteracting electric field comes from the positive ions distributed on a prepatterned dielectric layer over the substrate. As a result, the positively charged aerosols are focused through these fields to grow with nanoscale resolution only in the openings of the layer. Furthermore, a growing structure itself could reconfigure the electric field, producing self-focusing nonlinear effects shaping the printed structure. By lifting the layer over the substrate and translating the latter according to a 3D motion program, we created charged aerosol jets that self-focus on the tips of the growing structure and could print diverse 3D forms. The aerosol jets are also capable of writing on the substrate. The 3D nanoprinting produced using the described approach enables the development of the intricate 3D nanostructures described in the Account in detail, including their material characterization and diverse applications. Finally, we concluded and outlined current challenges and future developments of the 3D nanoprinting with charged aerosol particles.

Nonlinear Wavefront Shaping and Imaging in Nonlinear Photonic Crystals with a Generalized Quasi-Multivalue-Encoding Method

Nonlinear Wavefront Shaping and Imaging in Nonlinear Photonic Crystals with a Generalized Quasi-Multivalue-Encoding Method

Deblending of Simultaneous-Source Seismic Data Using Bregman Iterative Shaping

Deblending plays an important role in preparing high-quality seismic data from modern blended simultaneous-source seismic data. The conventional methods become problematic when the random ambient noise becomes extremely strong and the inversion iteratively fits the random noise instead of the signal and blending interference. In this article, an improved method is proposed to separate blended seismic data. We treat the deblending problem as a regularization problem under the frame of compressed sensing (CS), and propose a new nonlinear Bregman iterative shaping (BIS) algorithm to solve the minimization problem. Based on the principle of CS, we transform the simultaneous-source data to the seislet-domain for inversion and separation, and verify the effectiveness and superiority of the proposed method by two theoretical model data and an actual marine streamer blended data. Compared with the traditional iterative shaping (TIS) algorithm, BIS adds data residuals to the observed data (the blended data) in each iteration, so that the error between the calculated data after each iteration and the main source signal in the known blended data is the smallest, and helps to recover the weaker information in the seismic data and obtain higher precision separation results. BIS uses a fixed soft threshold, which speeds up the convergence speed. In addition, BIS can effectively improve the separation accuracy when the given sparse domain threshold is not suitable.

Controlled modulation of optical energy in the high order Hermite-Gaussian laser modes

The multiple lobes of high order Hermite-Gaussian (HG) laser modes differ in terms of shape, size, and optical energy distribution. Here, we introduce a generic numerical method that redistributes optical energy among the lobes of high order HG modes such that all the identical low intense lobes become both moderate or high intense lobes and vice-versa, in a controlled manner. Further, the modes which consist of only two types of intensity distribution among its multiple lobes are transformed together into all high intense lobes. Furthermore, in some cases, moderate intense lobes together with high intense lobes become high intense lobes, and moderate intense lobes together with low intense lobes become high intense lobes. Such controlled modulation of optical energy may offer efficient and selective utilization of each lobe of HG modes in most applications like particle manipulation, optical lithography, and the method can be used in other fields like nonlinear frequency conversion and shaping ultrafast optical pulses.

Tensorial phase control in nonlinear meta-optics

Nonlinear metasurfaces have recently brought harmonic generation to subwavelength level, with spectral and polarization control unachievable in bulk crystals. Not only does nonlinear meta-optics enable the investigation of nonlinear physics at the nanoscale, but it also opens promising technological perspectives. To date, however, no full-phase control has been demonstrated on a harmonic field generated with a sufficient efficiency for most practical purposes. In this work, based on the χ ( 2 ) fully tensorial features of AlGaAs metasurfaces, we propose a robust method to generate 0 − 2 π phase-encoded second harmonic light for nonlinear wavefront shaping, experimentally demonstrating nonlinear beam steering and all-dielectric metalenses that generate and focus second harmonic beams to sub-wavelength spot sizes. Nonlinear generation with record efficiency and phase control are achieved in nanostructured arrays that are fully compatible with mature III-V semiconductor technology. This breakthrough paves the way for the development of ultrathin, free-space photonic devices for nonlinear imaging, including night vision.

Modelling self-similar parabolic pulses in optical fibres with a neural network

We expand our previous analysis of nonlinear pulse shaping in optical fibres using machine learning [Opt. Laser Technol., 131 (2020) 106439] to the case of pulse propagation in the presence of gain/loss, with a special focus on the generation of self-similar parabolic pulses. We use a supervised feedforward neural network paradigm to solve the direct and inverse problems relating to the pulse shaping, bypassing the need for direct numerical solution of the governing propagation model.

Enhanced Pulse Compression within Sign-Alternating Dispersion Waveguides

We show theoretically and numerically how to optimize sign-alternating dispersion waveguides for maximum nonlinear pulse compression, while leveraging the substantial increase in bandwidth-to-input peak power advantage of these structures. We find that the spectral phase can converge to a parabolic profile independent of uncompensated higher-order dispersion. The combination of an easy to compress phase spectrum, with low input power requirements, then makes sign-alternating dispersion a scheme for high-quality nonlinear pulse compression that does not require high powered lasers, which is beneficial for instance in integrated photonic circuits. We also show a new nonlinear compression regime and soliton shaping dynamic only seen in sign-alternating dispersion waveguides. Through an example SiN-based integrated waveguide, we show that the dynamic enables the attainment of compression to two optical cycles at a pulse energy of 100 pJ which surpasses the compression achieved using similar parameters for a current state-of-the-art SiN system.

Efficiency analysis of polynomial filtering algorithms in navigation data processing for a class of nonlinear discrete dynamical systems

A polynomial filtering algorithm is designed for estimating a Markov sequence based on linear measurements. The feature of the estimation problem is that the Markov sequence is described by a nonlinear shaping filter, which is a second-order polynomial with respect to the state vector components. The algorithm efficiency is illustrated by three examples of navigation data processing. It is shown that the polynomial filter provides accuracy close to the best potential one calculated using the particle filter. At the same time, the amount of computation required to implement this algorithm is much smaller than that for the particle filter. In addition, the polynomial filter provides a consistent calculated accuracy characteristic.

Three-dimensional nonlinear photonic crystal in naturally grown potassium\u2013tantalate\u2013niobate perovskite ferroelectrics

Since quasi-phase-matching of nonlinear optics was proposed in 1962, nonlinear photonic crystals were rapidly developed by ferroelectric domain inversion induced by electric or light poling. The three-dimensional (3D) periodical rotation of ferroelectric domains may add feasible modulation to the nonlinear coefficients and break the rigid requirements for the incident light and polarization direction in traditional quasi-phase-matching media. However, 3D rotating ferroelectric domains are difficult to fabricate by the direct external poling technique. Here, we show a natural potassium–tantalate–niobate (KTN) perovskite nonlinear photonic crystal with spontaneous Rubik’s cube-like domain structures near the Curie temperature of 40 °C. The KTN crystal contains 3D ferroelectric polarization distributions corresponding to the reconfigured second-order susceptibilities, which can provide rich reciprocal vectors to compensate for the phase mismatch along an arbitrary direction and polarization of incident light. Bragg diffraction and broadband second-harmonic generation are also presented. This natural nonlinear photonic crystal directly meets the 3D quasi-phase-matching condition without external poling and establishes a promising platform for all-optical nonlinear beam shaping and enables new optoelectronic applications for perovskite ferroelectrics.

Nonlinear beam shaping in periodical χ (2) fork gratings with structural defects

Nonlinear beam shaping provides an efficient way to control the phase and amplitude of optical waves while shifting their frequency. Periodical topological structures with a modulated second-order nonlinear optical coefficient (χ (2)) are commonly used to generate special optical beams at new frequencies, e.g. the second harmonic vortices. In this paper, we theoretically study the influence of structural imperfection on nonlinear beam shaping and demonstrate how to utilize these imperfections for second harmonic generation with controlled orbital angular momentums. The results indicate that the studied nonlinear beam-shaping process has excellent tolerance to structural defects, and introducing designed defects of different scales and shapes constitutes a flexible approach for controlling the orbital angular momentum of light at new frequencies. As a proof of concept example, the nested χ (2) structures are designed for generating optical vortices with predesigned topological charges along different directions. In addition, the performance of the nonlinear generation of vortex beams with a fundamental beam shifted from the center of the fork grating is also discussed. The study opens up new prospects for the optimization of nonlinear χ (2) structures for special beam generation at new frequencies.

The generation of non-conventional beam in a nonlinear electro-optic photonic crystal

We theoretically report the generation of a frequency-doubling Bessel-like beam in a nonlinear electro-optic photonic crystal. For nonlinear beam shaping in a sample, the entire crystal is equivalent to a series of positive and negative micro-axicons in tandem in the interactions where duty cycle is of great importance. Despite the inevitable domain deviations introduced by the poling, it has little influence on the general modulation peculiarities if the randomness is slight. Moreover, the generated nonlinear Bessel beam can be dynamically manipulated via fine tuning of the applied voltage distribution. We believe that, such a scheme to generate a non-conventional beam is efficient and compact, which offers people a feasible way to perform frequency conversion and wavefront manipulation simultaneously to manufacture nonlinear spatial light modulator that is flexible for beam-shaping of various beam shapes desired.

Nonlinear Beam Shaping with Binary Phase Modulation on Patterned WS2 Monolayer

The capability of controlling the phase of the nonlinear polarization of media is vital for nonlinear optical beam shaping. Achieving this control over nonlinear phase manipulation on the nanoscale...