Data-Driven Design for Metamaterials and Multiscale Systems: A Review

Metamaterials are artificial materials designed to exhibit effective material parameters that go beyond those found in nature. Composed of unit cells with rich designability that are assembled into multiscale systems, they hold great promise for realizing next-generation devices with exceptional, often exotic, functionalities. However, the vast design space and intricate structure-property relationships pose significant challenges in their design. A compelling paradigm that could bring the full potential of metamaterials to fruition is emerging: data-driven design. This review provides a holistic overview of this rapidly evolving field, emphasizing the general methodology instead of specific domains and deployment contexts. Existing research is organized into data-driven modules, encompassing data acquisition, machine learning-based unit cell design, and data-driven multiscale optimization. The approaches are further categorized within each module based on shared principles, analyze and compare strengths and applicability, explore connections between different modules, and identify open research questions and opportunities.

Emission Enhancement of Ge/Si Quantum Dots in Hybrid Structures with Subwavelength Lattice of Al Nanodisks

The effects of resonance interaction of plasmonic and photonic modes in hybrid metal-dielectric structures with square Al nanodisk lattices coupled with a Si waveguide layer were investigated using micro-photoluminescence (micro-PL) spectroscopy. As radiation sources, GeSi quantum dots were embedded in the waveguide. A set of narrow PL peaks superimposed on the broad bands were observed in the range of quantum dot emissions. At optimal parameters of Al nanodisks lattices, almost one order increasing of PL intensity was obtained. The experimental PL spectra are in good agreement with results of theoretical calculations. The realization of high-quality bound states in the continuum was confirmed by a comparative analysis of the experimental spectra and theoretical dispersion dependences. The results demonstrated the perspectives of these type structures for a flat band realization and supporting the slow light.

Nanostructured surface plasmon resonance sensors: Toward narrow linewidths

Surface plasmon resonance sensors have found wide applications in optical sensing field due to their excellent sensitivity to the slight refractive index change of surrounding medium. However, the intrinsically high optical losses in metals make it nontrivial to obtain narrow resonance spectra, which greatly limits the performance of surface plasmon resonance sensors. This review first introduces the influence factors of plasmon linewidths of metallic nanostructures. Then, various approaches to achieve narrow resonance linewidths are summarized, including the fabrication of nanostructured surface plasmon resonance sensors supporting surface lattice resonance/plasmonic Fano resonance or coupling with a photonic cavity, the preparation of surface plasmon resonance sensors with ultra-narrow resonators, as well as strategies such as platform-induced modification, alternating different dielectric layers, and the coupling with whispering-gallery-modes. Lastly, the applications and some existing challenges of surface plasmon resonance sensors are discussed. This review aims to provide guidance for the further development of nanostructured surface plasmon resonance sensors.

Artificial Neural Network Modelling for Optimizing the Optical Parameters of Plasmonic Paired Nanostructures

The Artificial Neural Network (ANN) has become an attractive approach in Machine Learning (ML) to analyze a complex data-driven problem. Due to its time efficient findings, it has became popular in many scientific fields such as physics, optics, and material science. This paper presents a new approach to design and optimize the electromagnetic plasmonic nanostructures using a computationally efficient method based on the ANN. In this work, the nanostructures have been simulated by using a Finite Element Method (FEM), then Artificial Intelligence (AI) is used for making predictions of associated sensitivity (S), Full Width Half Maximum (FWHM), Figure of Merit (FOM), and Plasmonic Wavelength (PW) for different paired nanostructures. At first, the computational model is developed by using a Finite Element Method (FEM) to prepare the dataset. The input parameters were considered as the Major axis, a, the Minor axis, b, and the separation gap, g, which have been used to calculate the corresponding sensitivity (nm/RIU), FWHM (nm), FOM, and plasmonic wavelength (nm) to prepare the dataset. Secondly, the neural network has been designed where the number of hidden layers and neurons were optimized as part of a comprehensive analysis to improve the efficiency of ML model. After successfully optimizing the neural network, this model is used to make predictions for specific inputs and its corresponding outputs. This article also compares the error between the predicted and simulated results. This approach outperforms the direct numerical simulation methods for predicting output for various input device parameters.

Near-Infrared Photoresponse in Ge/Si Quantum Dots Enhanced by Photon-Trapping Hole Arrays

Group-IV photonic devices that contain Si and Ge are very attractive due to their compatibility with integrated silicon photonics platforms. Despite the recent progress in fabrication of Ge/Si quantum dot (QD) photodetectors, their low quantum efficiency still remains a major challenge and different approaches to improve the QD photoresponse are under investigation. In this paper, we report on the fabrication and optical characterization of Ge/Si QD pin photodiodes integrated with photon-trapping microstructures for near-infrared photodetection. The photon traps represent vertical holes having 2D periodicity with a feature size of about 1 μm on the diode surface, which significantly increase the normal incidence light absorption of Ge/Si QDs due to generation of lateral optical modes in the wide telecommunication wavelength range. For a hole array periodicity of 1700 nm and hole diameter of 1130 nm, the responsivity of the photon-trapping device is found to be enhanced by about 25 times at λ=1.2 μm and by 34 times at λ≈1.6 μm relative to a bare detector without holes. These results make the micro/nanohole Ge/Si QD photodiodes promising to cover the operation wavelength range from the telecom O-band (1260–1360 nm) up to the L-band (1565–1625 nm).

Deep Learning Meets Nanophotonics: A Generalized Accurate Predictor for Near Fields and Far Fields of Arbitrary 3D Nanostructures

Deep artificial neural networks are powerful tools with many possible applications in nanophotonics. Here, we demonstrate how a deep neural network can be used as a fast, general purpose predictor of the full near-field and far-field response of plasmonic and dielectric nanostructures. A trained neural network is shown to infer the internal fields of arbitrary three-dimensional nanostructures many orders of magnitude faster compared to conventional numerical simulations. Secondary physical quantities are derived from the deep learning predictions and faithfully reproduce a wide variety of physical effects without requiring specific training. We discuss the strengths and limitations of the neural network approach using a number of model studies of single particles and their near-field interactions. Our approach paves the way for fast, yet universal, methods for design and analysis of nanophotonic systems.

Benchmarking of software tools for the characterization of nanoparticles

Although many commercially available electromagnetic tools are conveniently used in RF and microwave applications, only a few of them provide the capability to analyze the optical response of nanometric radiators and scatterers. The assessment of their performance in the visible to near ultraviolet part of the electromagnetic (EM) spectrum becomes more and more important, considering the exponential rise of nanoscale systems. Since the accuracy of these numerical tools has not been fully investigated in literature, in this paper we essentially demonstrate a comparative study of the most widely used EM field solvers in the area of nano-plasmonics: COMSOL, CST and Lumerical. This is done through the investigation of the near and far field characteristics of basic canonical nanoparticles such as spheres, shells, cubes and cuboids, varying their sizes and constituting materials. The benchmarking results clearly show that at this moment not all EM field solvers offer the same accuracy.

Photovoltaic Ge/SiGe quantum dot mid-infrared photodetector enhanced by surface plasmons

We report the fabrication and characterization of a multilayer Ge quantum dot detector grown on Si_1-xGex virtual substrate (x = 0.18) for photovoltaic mid-wave infrared photodetection. Detector displays an over 100% photovoltaic response enhancement as compared to a conventional Ge/Si device due to smaller hole effective mass in the SiGe barriers. A further enhancement in sensitivity is achieved by excitation of surface plasmon polariton waves in a Ge/SiGe photodetector coupled with a two-dimensional plasmonic structure. The plasmonic resonance induced photocurrent enhancement is found to be larger when the incident infrared light illuminates the detector from its substrate side. At zero bias and 90 K, the responsivity of 40 mA/W and peak detectivity of 1.4 × 10¹¹ cm·Hz^1/2/W are determined at a wavelength of 4 µm.

A fast and high-order accurate surface perturbation method for nanoplasmonic simulations: basic concepts, analytic continuation and applications

In this paper we demonstrate that rigorous high-order perturbation of surfaces (HOPS) methods coupled with analytic continuation mechanisms are particularly well-suited for the assessment and design of nanoscale devices (e.g., biosensors) that operate based on surface plasmon resonances generated through the interaction of light with a periodic (metallic) grating. In this connection we explain that the characteristics of the latter are perfectly aligned with the optimal domain of applicability of HOPS schemes, as these procedures can be shown to be the methods of choice for low to moderate wavelengths of radiation and grating roughness that is representable by a few (e.g., tens of) Fourier coefficients. We argue that, in this context, the method can, for instance, produce full and precise reflectivity maps in computational times that are orders of magnitude faster than those of alternative numerical schemes (e.g., the popular "C-method," finite differences, integral equations or finite elements). In this initial study we concentrate on the description of the basic principles that underlie the solution scheme, including those that relate to analytic continuation procedures. Within this framework, we explain how, in spite of conventional wisdom to the contrary, the resulting perturbative techniques can provide a most valuable tool for practical investigations in plasmonics. We demonstrate this with some examples that have been previously discussed in the literature (including treatments of the reflectivity and band gap structure of some simple geometries) and extend this to demonstrate the wider applicability of the proposed approach.

Engineering metallic nanostructures for plasmonics and nanophotonics

Metallic nanostructures now play an important role in many applications. In particular, for the emerging fields of plasmonics and nanophotonics, the ability to engineer metals on nanometric scales allows the development of new devices and the study of exciting physics. This review focuses on top-down nanofabrication techniques for engineering metallic nanostructures, along with computational and experimental characterization techniques. A variety of current and emerging applications are also covered.

3-dimensional eigenmodal analysis of plasmonic nanostructures

We introduce a 3-dimensional electromagnetic eigenmodal algorithm for the theoretical analysis of resonating nano-optical structures. The method, a variant of the Jacobi-Davidson algorithm, solves the electric field vector wave, or curl-curl, equation for the electromagnetic eigenmodes of resonant optical structures with a finite element method. In particular, the method includes transparent boundary conditions that enable the analysis of resonating structures in unbounded space. We demonstrate the performance of the method. First, we calculate the modes of several dielectric resonator antennas and compare them to theoretically determined results. Second, we calculate the modes of a nano-cuboid and compare them to theoretically determined results. Third, we numerically analyze spherical nanoparticles and compare the result to the theoretical Mie solution. Fourth, we analyze optical dipole antenna configurations in order to assess the method's capability for solving technologically relevant problems.

Numerical analysis of a SNOM tip based on a partially cladded optical fiber

A Scanning Nearfield Optical Microscope (SNOM) tip with partial metallic cladding is presented. For its design, a very demanding 2D eigenvalue analysis of an optical waveguide with material and radiation losses is carried out by the Multiple Multipole Program (MMP) and by the Finite Element Method (FEM). These simulations require some special tricks that are outlined. The computed 2D MMP and FEM results are compared and discussed. This 2D analysis is followed by a full 3D FEM analysis of the SNOM tip. The obtained 3D results confirm the corresponding 2D predictions. Important conclusions regarding the guiding capabilities of the chosen structure and the efficiency of the applied numerical methods are presented.

Sensoric potential of gold-silver core-shell nanoparticles

The sensitivities of five different core-shell nanostructures were investigated towards changes in the refractive index of the surrounding medium. The shift of the localized surface plasmon resonance (LSPR) maximum served as a measure of the (respective) sensitivity. Thus, gold-silver core-shell nanoparticles (NPs) were prepared with different shell thicknesses in a two-step chemical process without the use of any (possibly disturbing) surfactants. The measurements were supported by ultramicroscopic images in order to size the resulting core-shell structures. When compared to sensitivities of nanostructures reported in the literature with those of the (roughly spherical) gold-silver core-shell NPs, the latter showed comparable (or even higher) sensitivities than gold nanorods. The experimental finding is supported by theoretical calculation of optical properties of such core-shell NP. Extinction spectra of ideal spherical and deformed core-shell NPs with various core/shell sizes were calculated, and the presence of an optimal silver shell thickness with increased sensitivity was confirmed. This effect is explained by the existence of two overlapping plasmon bands in the NP, which change their relative intensity upon change of refractive index. Results of this research show a possibility of improving LSPR sensor by adding an extra metallic layer of certain thickness.

Investigation of plasmon resonances in metal films with nanohole arrays for biosensing applications

Biosensing with nanoholes is one of the most promising applications of nanoplasmonic devices. The sensor properties, however, are complex due to coupled resonances through propagating and localized surface plasmons. This Full Paper demonstrates experimental and simulation studies on different plasmonic hole systems, namely various patterns of circular holes in gold films. In contrast to most previous work, here, the challenging situation of optically thin films is considered. The refractive-index-sensing properties, such as sensitive locations in the nanostructure and sensitive spectral features, are investigated. The multiple multipole program provides the complete field distribution in the nanostructure for different wavelengths. It is shown that the spectral feature most sensitive to refractive-index changes is the extinction minimum, rather than the maximum. The results are consistent with theory for perfect electrical conductors. The spectral response is investigated for molecular adsorption at different positions inside or outside a hole. Furthermore, the optical properties of nanohole arrays with long-range and short-range order are compared and found to demonstrate remarkable similarities. Our results help to predict the resonance wavelengths of nanoholes with arbitrary patterns, including short-range order. The results presented here are highly important since they extend and challenge several aspects of the current understanding of plasmon resonances in nanohole arrays. These theoretical models, simulation results, and experimental data together help provide the understanding necessary for the development of efficient biomolecular analysis tools based on metallic nanoholes.

Shape-dependent sensitivity of single plasmonic nanoparticles for biosensing

Shape-dependent sensitivity of localized surface plasmon-based biosensing was investigated by combining single-particle protein-sensing and multiple multipole program simulation. Significantly higher sensitivity was observed for tetrahedral particles than spherical ones, which was revealed by careful structural analysis of individually measured particles. The simulation of the corresponding particles with layered protein adsorption model showed consistent optical property and sensitivity, which were explained in terms of the field enhancement at the pointing edges.