Subwavelength Geometry Research Articles

Plasticity in nonlinear elastic metamaterials: Low-order dynamic modeling

Nonlinear elastic metamaterials have been shown to admit a variety of rich, dynamical features that can be leveraged to tailor the propagation of mechanical waves. Since these materials derive their properties from intricate, subwavelength geometries, direct numerical simulations are often prohibitively expensive at scales of interest. To overcome this limitation, reduced-order models, typically in the form of effective continua or discrete lattices that capture the essential features of the material at sufficiently long wavelengths, have been developed. While many prior studies have implemented these models successfully, the vast majority have considered only recoverable elastic deformations with linear damping and neglected history-dependent effects, such as plasticity and friction. In this presentation, we introduce an effective lattice modeling framework for nonlinear elastic metamaterials undergoing plastic deformation. Due to the history-dependent nature of plasticity, this framework generally yields a system of differential-algebraic equations whose computational cost is significantly greater than a purely elastic system of similar size. We apply the method to several examples of interest and explore means to obtain phenomenological elastic-plastic models for general material architectures.

Discrete element models for elasto-plastic wave propagation in nonlinear architected materials

Nonlinear architected materials are known to exhibit a plethora of dynamic phenomena that enhance our capacity to manipulate elastic waves. Since these properties stem from complex, subwavelength geometry, dynamic simulations at high resolutions are often intractable at scales of interest. Therefore, prior studies have turned to effective medium models that capture essential properties in the long-wavelength limit. One class of such models is a periodic structure composed of discrete mass, spring, and damper elements, whose constitutive relationships are computed to match behaviors observed in experiments or fine-scale simulations of representative volume elements. While models of this type have been implemented successfully in many cases, the majority of literature has been focused on recoverable deformation, possibly including linear damping. However, history-dependent effects, such as friction and plasticity, have been much less explored. In this work, we develop a discrete element modeling framework for nonlinear architected materials undergoing plastic deformation. Due to the history- and rate-dependent characteristics of plasticity, the framework generally yields a system of differential-algebraic equations whose computational cost is significantly greater than an elastic system of comparable size. We demonstrate the method using several examples from the literature and explore means to obtain phenomenological plasticity models for general geometries.

Detecting acoustic chirality with matched metamaterial vortex wave antennas.

Acoustic communications often have limited data rates because of the intrinsically low frequencies. Exploring new spatial modes to increase data bandwidth at fixed frequency is a possible solution to this problem. Here, we demonstrate acoustic wave chirality transmission between two reciprocal metamaterial vortex wave antennas, generating and sensing transmitted acoustic wave chirality through the sub-wavelength geometry of the system. By adding an acoustic leaky wave surface to a ring resonator waveguide, acoustic vortex waves with positive or negative integer mode chirality are independently radiated and detected using a small number of microphones. Through computational simulation and experimental verification, using three-dimensional printed waveguides, we show that the vortex mode chirality can be transferred between two opposing acoustic vortex wave antennas across a small unguided air gap. We also show that emission into an external waveguide can provide long distance data transmission. This demonstrates the first use of metamaterial vortex wave antennas as chiral, mode multi-channel data transceivers.

Meta-interface textures for increased frictional damping in elastic structures

The unique behavior of acoustic and elastic metamaterials results from engineered subwavelength material composition and geometry. Though there has been a profusion of metamaterial research over the last two decades, relatively little focus has been on the dissipation of vibro-acoustic energy. Most research on metamaterials for acoustic damping have focused on viscous or viscoelastic effects [1]. However, the design of interfaces within materials or at connecting surfaces between elastic structures to amplify micro-friction events due to the relative motion of contacting surfaces is of interest for the reduction of vibro-acoustic energy. Dissipation due to friction is best represented as a nonlinear constitutive response. Here, we report on the use of friction via meta-interface textures to create interfaces with elevated damping, leading to increased macroscopic dissipation. We employ the five-parameter Bouc-Wen model to describe the complex behavior at these interfaces and study the influence of subwavelength interface texture on the parameters of the friction model. This increased dissipation from this approach can be used to reduce structural vibrations and the transmission of acoustical energy in structural components. [1] C. L. Bacquet et al., “Metadamping: Dissipation emergence in elastic metamaterials.” Adv. App. Mech. 51, 115i–164, (2018).

Self-consistent Maxwell–Bloch model for high-order harmonic generation in nanostructured semiconductors

In pursuit of efficient high-order harmonic conversion in semiconductor devices, modeling insights into the complex interplay among ultrafast microscopic electron–hole dynamics, nonlinear pulse propagation, and field confinement in nanostructured materials are urgently needed. Here, a self-consistent approach coupling semiconductor Bloch and Maxwell equations is applied to compute transmission and reflection high-order harmonic spectra for finite slab and sub-wavelength nanoparticle geometries. An increase in the generated high harmonics by several orders of magnitude is predicted for gallium arsenide nanoparticles with a size maximizing the magnetic dipole resonance. Serving as a conceptual and predictive tool for ultrafast spatiotemporal nonlinear optical responses of nanostructures with arbitrary geometry, our approach is anticipated to deliver new strategies for optimal harmonic manipulation in semiconductor metadevices.

Spatiotemporal isotropic-to-anisotropic meta-atoms

Metamaterials and metasurfaces are designed by spatially arranging (periodically or non-periodically) subwavelength geometries, allowing a tailored manipulation of the electromagnetic response of matter. Here, we exploit temporal variations of permittivity inside subwavelength geometries to propose the concept of spatiotemporal meta-atoms having time-dependent properties. We exploit isotropic-to-anisotropic temporal boundaries within spatially subwavelength regions where their permittivity is rapidly changed in time. In so doing, it is shown how resulting scattered waves travel in directions that are different from the direction of the impinging wave, and depend on the values of the chosen anisotropic permittivity tensor. To provide a full physical insight of their performance, multiple scenarios are studied numerically such as the effect of using different values of permittivity tensor, different geometries of the spatiotemporal meta-atom and time duration of the induced isotropic-to-anisotropic temporal boundary. The intrinsic asymmetric response of the proposed spatiotemporal meta-atoms is also studied demonstrating, both theoretically and numerically, its potential for an at-will manipulation of scattered waves in real time. These results may open new paradigms for controlling wave–matter interactions and may pave the way for the next generation of metamaterials and metasurfaces by unleashing their potential using four-dimensional unit cells.

A review of silicon subwavelength gratings: building break-through devices with anisotropic metamaterials

Abstract Silicon photonics is playing a key role in areas as diverse as high-speed optical communications, neural networks, supercomputing, quantum photonics, and sensing, which demand the development of highly efficient and compact light-processing devices. The lithographic segmentation of silicon waveguides at the subwavelength scale enables the synthesis of artificial materials that significantly expand the design space in silicon photonics. The optical properties of these metamaterials can be controlled by a judicious design of the subwavelength grating geometry, enhancing the performance of nanostructured devices without jeopardizing ease of fabrication and dense integration. Recently, the anisotropic nature of subwavelength gratings has begun to be exploited, yielding unprecedented capabilities and performance such as ultrabroadband behavior, engineered modal confinement, and sophisticated polarization management. Here we provide a comprehensive review of the field of subwavelength metamaterials and their applications in silicon photonics. We first provide an in-depth analysis of how the subwavelength geometry synthesizes the metamaterial and give insight into how properties like refractive index or anisotropy can be tailored. The latest applications are then reviewed in detail, with a clear focus on how subwavelength structures improve device performance. Finally, we illustrate the design of two ground-breaking devices in more detail and discuss the prospects of subwavelength gratings as a tool for the advancement of silicon photonics.

Inverse Design for Silicon Photonics: From Iterative Optimization Algorithms to Deep Neural Networks

Silicon photonics is a low-cost and versatile platform for various applications. For design of silicon photonic devices, the light-material interaction within its complex subwavelength geometry is difficult to investigate analytically and therefore numerical simulations are majorly adopted. To make the design process more time-efficient and to improve the device performance to its physical limits, various methods have been proposed over the past few years to manipulate the geometries of silicon platform for specific applications. In this review paper, we summarize the design methodologies for silicon photonics including iterative optimization algorithms and deep neural networks. In case of iterative optimization methods, we discuss them in different scenarios in the sequence of increased degrees of freedom: empirical structure, QR-code like structure and irregular structure. We also review inverse design approaches assisted by deep neural networks, which generate multiple devices with similar structure much faster than iterative optimization methods and are thus suitable in situations where piles of optical components are needed. Finally, the applications of inverse design methodology in optical neural networks are also discussed. This review intends to provide the readers with the suggestion for the most suitable design methodology for a specific scenario.

Spectral dependence of subwavelength slit geometry

For two decades, extraordinary optical transmission (EOT) has amplified exploration into subwavelength systems. Researchers have previously suggested exploiting the spectrally selective electromagnetic field confinement of subwavelength slits for multispectral detectors. Utilizing the finite-difference frequency domain (FDFD) method, we examine electromagnetic field confinement in both 2-dimensional and 3-dimensional scenarios from 2.5 to 6 microns, i.e. midwave infrared (MWIR). We explore the trade space of deep subwavelength slits and its impact on resonant enhancement of the electromagnetic field. This builds fundamental understanding of the coupling mechanisms allowing for prediction of resonant spectral behavior based on slit geometry and material properties.

Loss in acoustic metasurfaces: a blessing in disguise

From being an unfavorable consequence to finding itself as the intended imaginary part of a non-Hermitian system, loss has truly emerged as more of a friend than a foe in the context of acoustic metasurfaces. With the promising features of sub-wavelength geometries and the rapid advances in manufacturing techniques that can enable their realization, loss becomes a central topic of discussion. Further, the capability of introducing and tailoring loss allows it to serve as a new degree of freedom in passive wavefront shaping devices. In this review, the authors look back at the recent progress in the field of lossy acoustic metasurfaces. The background behind loss in deep sub-wavelength geometries and the instinctive responses to treat them and exploit them are overviewed, followed by more recent works that embrace and tailor their behavior for unconventional applications. The forthcoming years for acoustic metasurfaces thus hold several promising avenues for exploration, with loss as the protagonist.

Bismuth plasmonics for extraordinary light absorption in deep sub-wavelength geometries.

In this Letter, we demonstrate an ultra-broadband metamaterial absorber of unrivaled bandwidth (BW) using extraordinary optical response of bismuth (Bi), which is the material selected through our novel analysis. Based on our theoretical model, we investigate the maximum metal-insulator-metal (MIM) cavity BW, achievable by any metal with known n-k data. We show that an ideal metal in such structures should have a positive real permittivity part in the near-infrared (NIR) regime. Contrary to noble and lossy metals utilized by most research groups in the field, this requirement is satisfied only by Bi, whose data greatly adhere to the ideal material properties predicted by our analysis. A Bi nanodisc-based MIM resonator with an absorption above 0.9 in an ultra-broadband range of 800 nm-2390 nm is designed, fabricated, and characterized. To the best of our knowledge, this is the broadest absorption BW reported for a MIM cavity in the NIR with its upper-to-lower absorption edge ratio exceeding best contenders by more than 150%. According to the findings in this Letter, the use of proper materials and dimensions will lead to realization of deep sub-wavelength efficient optical devices.

High-Index Dielectric Metasurfaces Performing Mathematical Operations.

Image processing and edge detection are at the core of several newly emerging technologies, such as augmented reality, autonomous driving, and more generally object recognition. Image processing is typically performed digitally using integrated electronic circuits and algorithms, implying fundamental size and speed limitations, as well as significant power needs. On the other hand, it can also be performed in a low-power analog fashion using Fourier optics, requiring, however, bulky optical components. Here, we introduce dielectric metasurfaces that perform optical image edge detection in the analog domain using a subwavelength geometry that can be readily integrated with detectors. The metasurface is composed of a suitably engineered array of nanobeams designed to perform either first- or second-order spatial differentiation. We experimentally demonstrate the second-derivative operation on an input image, showing the potential of all-optical edge detection using a silicon metasurface geometry working at a numerical aperture as large as 0.35.

Effects of metal 3-D printing processes on acoustic metamaterial elements

Acoustic metamaterial properties derive from inherently complex, sub-wavelength geometries which aim to control the propagation of sound and elastic waves. The material properties of the unit cell element, the meta-atom, are important when considering either resonant response, or when the transport medium is a high density fluid, such as water. For water applications, this typically means using metals in the design. Metal additive manufacturing (AM) is a logical approach to achieve the needed design complexity. The most common approach in metal AM is selective laser melting. This approach utilizes a high-power laser beam to locally melt powder into a solid. 3D geometries are built through layer-by-layer melting of material. This approach to fabrication incorporates thermodynamic complexities such as extreme temperature gradients, simultaneous multiple material phases, gradient driven convection, rapid solidification, and occasional void formation. We will outline the complications that arise when using this technology to build one of the simplest acoustic meta-atoms: a thin disk. We show that thermal stresses can thermally warp the geometry, and microstructural heterogeneities can locally change material properties. These effects alter both the AM membrane’s macroscale (resonance) and microscale (crystal structure), significantly impacting the acoustic response. [Work Sponsored by the Office Of Naval Research.]

Scanning Laser Lithography With Constrained Quadratic Exposure Optimization

Scanning laser lithography is a maskless lithography method for selectively exposing features on a film of photoresist. A set of exposure positions and beam energies are required to optimally reproduce the desired feature pattern. The task of determining the exposure energies is inherently nonlinear due to the photoresist model and the requirement for only positive energy. In this brief, a nonlinear programming approach is employed to find an optimal exposure profile that minimizes the feature error and total exposure energy. This method is demonstrated experimentally to create a feature with subwavelength geometry.

Pure magnetic-quadrupole scattering and efficient second-harmonic generation from plasmon-dielectric hybrid nano-antennas

We theoretically demonstrate that pure magnetic quadrupole (MQ) scattering is achieved via the excitation of anapole modes and Fano resonance in noble metal (Au or Ag) and high refractive index dielectric (AlGaAs) hybrid nano-antennas. In Au-AlGaAs hybrid nano-antennas, electric anapole and magnetic anapole modes are observed, leading to the suppressions of electric and magnetic dipoles. Introducing gain material to AlGaAs nanodisk to increase the strength of electric quadrupole (EQ) Fano resonance leads to the suppression of EQ scattering. Then, ideal MQ scattering is achieved at the wavelength of total scattering cross-section dip. The increase of signal-to-noise ratio of MQ results in the great enhancement of near-field inside AlGaAs nanodisk. Additionally, the strong MQ resonance exhibits great capability for boosting second-harmonic generation by proper mode matching. These findings achieved in subwavelength geometries have important implications for functional metamaterials and nonlinear photonic nanodevices.

Evaluation of metamaterial unit cell analysis techniques

The field of acoustic metamaterials has produced novel materials in a wide variety of applications. An important step in designing a metamaterial is unit cell analysis with subwavelength geometry. There are several techniques used for unit cell analysis when designing acoustic properties of interest for metamaterial applications. Such techniques include, but are not limited to, band diagrams, effective material properties, or half-space homogenization. This talk discusses the challenges and tradeoffs between analysis techniques and types of structures that lend to one method or another. Unit cell analysis methods will be evaluated to perform trade space exploration, including validation and parametric studies for metamaterial design.

Non-reciprocity in mechanically modulated elastic metamaterials with geometric asymmetry

Elastic metamaterials with time- and space-dependent effective material properties have received great attention as a means to generate non-reciprocal wave propagation in acoustic and elastic media. These materials have promise for applications such as acoustic communication devices with increased data throughput and improved vibration isolation components. One means to modulate the material properties of a heterogeneous medium is via nonlinear mechanical deformation on time scales that are slow compared to propagating waves. This approach has been explored by the authors using the finite element method (FEM) to demonstrate non-reciprocal elastic wave propagation in negative stiffness honeycombs with a time- and space-varying external pre-strain [Goldsberry et al., JASA 144, 1763 (2018)]. One benefit of FEM is that it can be used to study the degree of non-reciprocity when varying sub-wavelength geometry or geometric modulations that are difficult or impossible to represent using analytical models. The present work employs FEM to investigate non-reciprocity in elastic lattices consisting of unit cells with varied geometric asymmetry and more general forms of mechanical modulation. [Work supported by National Science Foundation EFRI under Award No. 1641078.]

Subwavelength engineering and asymmetry: two efficient tools for sub-nanometer-bandwidth silicon Bragg filters.

Bragg filters stand as key building blocks of the silicon-on-insulator (SOI) photonics platform, allowing the implementation of advanced on-chip signal manipulation. However, achieving narrowband Bragg filters with large rejection levels is often hindered by fabrication constraints and imperfections. Here, we show that the combination of single-side corrugation asymmetry and subwavelength engineering provides a narrowband response with large corrugations, overcoming minimum feature size constraints of conventional Si Bragg filters. We comprehensively study the impact of the corrugation asymmetry in conventional and subwavelength single-etched SOI Bragg filters, showing their potential for bandwidth reduction. Finally, we experimentally demonstrate novel subwavelength geometry based on shifted corrugation teeth, achieving null-to-null bandwidths and rejections of 0.8nm and 40dB for the symmetric configuration and 0.6nm and 15dB for the asymmetric case.

Non-reciprocal wave phenomena through pump-signal wave interaction in discrete systems with asymmetric subwavelength geometry

Acoustic non-reciprocity has been shown to enable a plethora of effects analogous to phenomena seen in quantum physics and electromagnetics, such as immunity from back-scattering, unidirectional band gaps, and topologically protected states, which could lead to the design of direction-dependent acoustic devices. One class of material that holds promise as a means to achieve acoustic non-reciprocity is the “Willis medium,” which exhibits strain-momentum coupling owing to asymmetry and non-local effects in the material microstructure. This work considers a method for obtaining non-reciprocal elastic wave propagation in a system with sub-wavelength asymmetry inspired by asymmetric Willis microstructures. Non-reciprocity is achieved through application of a slowly-varying pump wave that acts as a spatio-temporal modulation of the material, which is modeled as a discrete system with geometric nonlinearity. The modulation generates momentum bias for a fast-varying signal wave with pump-signal interaction enabled by weak nonlinearity associated with the variation of subwavelength asymmetric geometry. It is shown that momentum bias may be generated with a pump wave acting transverse to the direction of propagation, which may facilitate experimental realizations. [This work was supported by the National Science Foundation.]

All-Dielectric Meta-Holograms with Holographic Images Transforming Longitudinally

Metasurfaces are unique subwavelength geometries capable of engineering electromagnetic waves at will, delivering new opportunities for holography. Most previous meta-holograms, so-called phase-only meta-holograms, modulate only the amplitude distribution of a virtual object and require optimizing techniques to improve the image quality. However, the phase distribution of the reconstructed image is usually overlooked in previous studies, leading to inevitable information loss. Here, we demonstrate all-dielectric meta-holograms that allow tailoring of both the phase and amplitude distributions of virtual objects. Several longitudinal manipulations of the holographic images are theoretically and experimentally demonstrated, including shifting, stretching, and rotating, enabling a large depth of focus. Furthermore, a new meta-hologram with a three-dimensional holographic design method is demonstrated with an even enhanced depth of focus. The proposed meta-holograms offer more freedom in holographic design an...