Analytical realization of complex thermal meta-devices.

Fourier's law dictates that heat flows from warm to cold. Nevertheless, devices can be tailored to cloak obstacles or even reverse the heat flow. Mathematical transformation yields closed-form equations for graded, highly anisotropic thermal metamaterial distributions needed for obtaining such functionalities. For simple geometries, devices can be realized by regular conductor distributions; however, for complex geometries, physical realizations have so far been challenging, and sub-optimal solutions have been obtained by expensive numerical approaches. Here we suggest a straightforward and highly efficient analytical de-homogenization approach that uses optimal multi-rank laminates to provide closed-form solutions for any imaginable thermal manipulation device. We create thermal cloaks, rotators, and concentrators in complex domains with close-to-optimal performance and esthetic elegance. The devices are fabricated using metal 3D printing, and their omnidirectional thermal functionalities are investigated numerically and validated experimentally. The analytical approach enables next-generation free-form thermal meta-devices with efficient synthesis, near-optimal performance, and concise patterns.

Impact of figures of merit in photonic inverse design.

The rates of optical processes, such as two-photon absorption and spontaneous photon emission, are strongly dependent on the environment in which they take place, easily varying by orders of magnitude between different settings. Using topology optimization, we design a set of compact wavelength-sized devices, to study the effect of optimizing geometries for enhancing processes that depend differently on the field in the device volume, characterized by different figures of merit. We find that significantly different field distributions lead to maximization of the different processes, and - by extension - that the optimal device geometry is highly dependent on the targeted process, with more than an order of magnitude performance difference between optimized devices. This demonstrates that a univeral measure of field confinement is meaningless when evaluting device performance, and stresses the importance of directly targeting the appropriate metric when designing photonic components for optimal performance.

On the trade-off between mode volume and quality factor in dielectric nanocavities optimized for Purcell enhancement.

This study explores the effect of geometric limitations on the achievable Purcell factor for single emitters in dielectric structures by employing topology optimization as an inverse design tool to maximize the local density of states. Nanobeams of different lengths with varying fixed central bridge widths are considered to investigate the impact of footprint and geometric length-scale. In single-mode photonic cavities, the Purcell factor is known to be proportional to the ratio of the quality factor Q to the effective mode volume V. Analysis of the optimized nanocavities shows a trade-off between quality factor and mode volume as a function of geometric limitations. Crucially, the design exhibiting the largest Purcell enhancement does not have the highest Q nor the lowest V found in the design pool. On the contrary, it is found that Q consistently drops along with decreasing V as the minimum allowed geometric length-scale decreases while the Purcell factor increases. Finally, the study provides insight into the importance of Q and V for enhancing the Purcell factor under geometric limitations.

Nanometer-scale photon confinement in topology-optimized dielectric cavities.

Nanotechnology enables in principle a precise mapping from design to device but relied so far on human intuition and simple optimizations. In nanophotonics, a central question is how to make devices in which the light-matter interaction strength is limited only by materials and nanofabrication. Here, we integrate measured fabrication constraints into topology optimization, aiming for the strongest possible light-matter interaction in a compact silicon membrane, demonstrating an unprecedented photonic nanocavity with a mode volume of V ~ 3 × 10-4 λ3, quality factor Q ~ 1100, and footprint 4 λ2 for telecom photons with a λ ~ 1550 nm wavelength. We fabricate the cavity, which confines photons inside 8 nm silicon bridges with ultra-high aspect ratios of 30 and use near-field optical measurements to perform the first experimental demonstration of photon confinement to a single hotspot well below the diffraction limit in dielectrics. Our framework intertwines topology optimization with fabrication and thereby initiates a new paradigm of high-performance additive and subtractive manufacturing.

Digital synthesis of free-form multimaterial structures for realization of arbitrary programmed mechanical responses.

SignificanceCreating structures to realize function-oriented mechanical responses is desired for many applications. Yet, the use of a single material phase and heuristics-based designs may fail to attain specific target behaviors. Here, through a deterministic algorithmic procedure, multiple materials with dissimilar properties are intelligently synthesized into composite structures to achieve arbitrary prescribed responses. Created structures possess unconventional geometry and seamless integration of multiple materials. Despite geometric complexity and varied material phases, these structures are fabricated by multimaterial manufacturing, and tested to demonstrate that wide-ranging nonlinear responses are physically and accurately realized. Upon heteroassembly, resulting structures provide architectures that exhibit highly complex yet navigable responses. The proposed strategy can benefit the design of function-oriented nonlinear mechanical devices, such as actuators and energy absorbers.

Ultra-coherent nanomechanical resonators based on inverse design.

Engineered micro- and nanomechanical resonators with ultra-low dissipation constitute a promising platform for various quantum technologies and foundational research. Traditionally, the improvement of the resonator's performance through nanomechanical structural engineering has been driven by human intuition and insight. Such an approach is inefficient and leaves aside a plethora of unexplored mechanical designs that potentially achieve better performance. Here, we use a computer-aided inverse design approach known as topology optimization to structurally design mechanical resonators with optimized performance of the fundamental mechanical mode. Using the outcomes of this approach, we fabricate and characterize ultra-coherent nanomechanical resonators with, to the best of our knowledge, record-high Q ⋅ f products for their fundamental mode (where Q is the quality factor and f is the frequency). The proposed approach - which can also be used to improve phononic crystals and coupled-mode resonators - opens up a new paradigm for designing ultra-coherent micro- and nanomechanical resonators, enabling e.g. novel experiments in fundamental physics and extreme sensing.

Closing the gap towards super-long suspension bridges using computational morphogenesis.

Girder design for suspension bridges has remained largely unchanged for the past 60 years. However, for future super-long bridges, aiming at record-breaking spans beyond 3 km, the girder weight is a limiting factor. Here we report on a design concept, inspired by computational morphogenesis procedures, demonstrating possible weight savings in excess of 28 percent while maintaining manufacturability. Although morphogenesis procedures are rarely used in civil engineering, often due to complicated designs, we demonstrate that even a crude extraction of the main features of the optimized design, followed by a simple parametric optimization, results in hitherto unseen weight reductions. We expect that further studies of the proposed design, as well as applications to other structures, will lead to even greater weight savings and reductions in carbon footprint in a construction industry, currently responsible for 39 percent of the world's CO2 emissions.

Inverse design of nanoparticles for enhanced Raman scattering.

We show that topology optimization (TO) of metallic resonators can lead to ∼102 × improvement in surface-enhanced Raman scattering (SERS) efficiency compared to traditional resonant structures such as bowtie antennas. TO inverse design leads to surprising structures very different from conventional designs, which simultaneously optimize focusing of the incident wave and emission from the Raman dipole. We consider isolated metallic particles as well as more complicated configurations such as periodic surfaces or resonators coupled to dielectric waveguides, and the benefits of TO are even greater in the latter case. Our results are motivated by recent rigorous upper bounds to Raman scattering enhancement, and shed light on the extent to which these bounds are achievable.

Topological Insulators by Topology Optimization.

An acoustic topological insulator (TI) is synthesized using topology optimization, a free material inverse design method. The TI appears spontaneously from the optimization process without imposing explicit requirements on the existence of pseudospin-1/2 states at the TI interface edge, or the Chern number of the topological phases. The resulting TI is passive, consisting of acoustically hard members placed in an air background and has an operational bandwidth of ≈12.5% showing high transmission. Further analysis demonstrates confinement of more than 99% of the total field intensity in the TI within at most six lattice constants from the TI interface. The proposed design hereby outperforms a reference from recent literature regarding energy transmission, field confinement, and operational bandwidth.

Field-enhancing photonic devices utilizing waveguide coupling and plasmonics - a selection rule for optimization-based design.

This paper describes a systematic design study of periodic gold-nanostrip arrays placed on a thin film aimed at enhancing the electric field inside the film when irradiated by light. Based on the study, a "selection rule" is proposed, which provides optimization-based design methods with an a priori choice between field-enhancement dominated by coupling to guided modes, by plasmonic near-field enhancement or by a mix hereof. An appropriate choice of wavelength and grating period is shown to selectively suppress or include waveguiding effects for the optimized designs. The validity of the selection rule is demonstrated through a numerical topology optimization study in which gold nanostrips are optimized for electric-field enhancement in an erbium-doped TiO2 thin film, targeting increased spectral upconversion in the erbium ions. The obtained designs exhibit waveguide excitation within the predicted intervals and, for light polarized perpendicularly to the strips, plasmonic response outside.

Benchmarking five numerical simulation techniques for computing resonance wavelengths and quality factors in photonic crystal membrane line defect cavities.

We present numerical studies of two photonic crystal membrane microcavities, a short line-defect cavity with a relatively low quality (Q) factor and a longer cavity with a high Q. We use five state-of-the-art numerical simulation techniques to compute the cavity Q factor and the resonance wavelength λ for the fundamental cavity mode in both structures. For each method, the relevant computational parameters are systematically varied to estimate the computational uncertainty. We show that some methods are more suitable than others for treating these challenging geometries.

Infill Optimization for Additive Manufacturing-Approaching Bone-Like Porous Structures.

Porous structures such as trabecular bone are widely seen in nature. These structures are lightweight and exhibit strong mechanical properties. In this paper, we present a method to generate bone-like porous structures as lightweight infill for additive manufacturing. Our method builds upon and extends voxel-wise topology optimization. In particular, for the purpose of generating sparse yet stable structures distributed in the interior of a given shape, we propose upper bounds on the localized material volume in the proximity of each voxel in the design domain. We then aggregate the local per-voxel constraints by their p-norm into an equivalent global constraint, in order to facilitate an efficient optimization process. Implemented on a high-resolution topology optimization framework, our results demonstrate mechanically optimized, detailed porous structures which mimic those found in nature. We further show variants of the optimized structures subject to different design specifications, and we analyze the optimality and robustness of the obtained structures.

Giga-voxel computational morphogenesis for structural design.

In the design of industrial products ranging from hearing aids to automobiles and aeroplanes, material is distributed so as to maximize the performance and minimize the cost. Historically, human intuition and insight have driven the evolution of mechanical design, recently assisted by computer-aided design approaches. The computer-aided approach known as topology optimization enables unrestricted design freedom and shows great promise with regard to weight savings, but its applicability has so far been limited to the design of single components or simple structures, owing to the resolution limits of current optimization methods. Here we report a computational morphogenesis tool, implemented on a supercomputer, that produces designs with giga-voxel resolution-more than two orders of magnitude higher than previously reported. Such resolution provides insights into the optimal distribution of material within a structure that were hitherto unachievable owing to the challenges of scaling up existing modelling and optimization frameworks. As an example, we apply the tool to the design of the internal structure of a full-scale aeroplane wing. The optimized full-wing design has unprecedented structural detail at length scales ranging from tens of metres to millimetres and, intriguingly, shows remarkable similarity to naturally occurring bone structures in, for example, bird beaks. We estimate that our optimized design corresponds to a reduction in mass of 2-5 per cent compared to currently used aeroplane wing designs, which translates into a reduction in fuel consumption of about 40-200 tonnes per year per aeroplane. Our morphogenesis process is generally applicable, not only to mechanical design, but also to flow systems, antennas, nano-optics and micro-systems.

Reproducing the hierarchy of disorder for Morpho-inspired, broad-angle color reflection.

The scales of Morpho butterflies are covered with intricate, hierarchical ridge structures that produce a bright, blue reflection that remains stable across wide viewing angles. This effect has been researched extensively, and much understanding has been achieved using modeling that has focused on the positional disorder among the identical, multilayered ridges as the critical factor for producing angular independent color. Realizing such positional disorder of identical nanostructures is difficult, which in turn has limited experimental verification of different physical mechanisms that have been proposed. In this paper, we suggest an alternative model of inter-structural disorder that can achieve the same broad-angle color reflection, and is applicable to wafer-scale fabrication using conventional thin film technologies. Fabrication of a thin film that produces pure, stable blue across a viewing angle of more than 120 ° is demonstrated, together with a robust, conformal color coating.

Topology optimized mode multiplexing in silicon-on-insulator photonic wire waveguides.

We design and experimentally verify a topology optimized low-loss and broadband two-mode (de-)multiplexer, which is (de-)multiplexing the fundamental and the first-order transverse-electric modes in a silicon photonic wire. The device has a footprint of 2.6 µm x 4.22 µm and exhibits a loss <1.2 dB in a 100 nm bandwidth measured around 1570 nm. The measured cross talk is <-12 dB and the extinction ratio is >14 dB in the C-band. Furthermore, we demonstrate that the design method can be expanded to include more modes, in this case including also the second order transverse-electric mode, while maintaining functionality.

Topology Optimized Architectures with Programmable Poisson's Ratio over Large Deformations.

Topology optimized architectures are designed and printed with programmable Poisson's ratios ranging from -0.8 to 0.8 over large deformations of 20% or more.

Experimental validation of a topology optimized acoustic cavity.

This paper presents the experimental validation of an acoustic cavity designed using topology optimization with the goal of minimizing the sound pressure locally for monochromatic excitation. The presented results show good agreement between simulations and measurements. The effect of damping, errors in the production of the cavity, and variations in operating frequency is discussed and the importance of taking these factors into account in the modeling process is highlighted.

Topology optimization for optical projection lithography with manufacturing uncertainties.

This article presents a topology optimization approach for micro- and nano-devices fabricated by optical projection lithography. Incorporating the photolithography process and the manufacturing uncertainties into the topology optimization process results in a binary mask that can be sent directly to manufacturing without additional optical proximity correction (OPC). The performance of the optimized device is robust toward the considered process variations. With the proposed unified approach, the design for photolithography is achieved by considering the optimal device performance and manufacturability at the same time. Only one optimization problem is solved instead of two as in the conventional separate procedures by (1) blueprint design and (2) OPC. A micro-gripper design example is presented to demonstrate the potential of this approach.

Topology optimized mode conversion in a photonic crystal waveguide fabricated in silicon-on-insulator material.

We have designed and for the first time experimentally verified a topology optimized mode converter with a footprint of ~6.3 µm × ~3.6 µm which converts the fundamental even mode to the higher order odd mode of a dispersion engineered photonic crystal waveguide. 2D and 3D topology optimization is utilized and both schemes result in designs theoretically showing an extinction ratio larger than 21 dB. The 3D optimized design has an experimentally estimated insertion loss lower than ~2 dB in an ~43 nm bandwidth. The mode conversion is experimentally confirmed in this wavelength range by recording mode profiles using vertical grating couplers and an infrared camera. The experimentally determined extinction ratio is > 12 dB and is believed to be limited by the spatial resolution of our setup.

Fundamental limitations to gain enhancement in periodic media and waveguides.

A common strategy to compensate for losses in optical nanostructures is to add gain material in the system. By exploiting slow-light effects it is expected that the gain may be enhanced beyond its bulk value. Here we show that this route cannot be followed uncritically: inclusion of gain inevitably modifies the underlying dispersion law, and thereby may degrade the slow-light properties underlying the device operation and the anticipated gain enhancement itself. This degradation is generic; we demonstrate it for three different systems of current interest (coupled-resonator optical waveguides, Bragg stacks, and photonic crystal waveguides). Nevertheless, a small amount of added gain may be beneficial.