Topology optimization of freeform large-area metasurfaces

We demonstrate optimization of optical metasurfaces over $10^5$--$10^6$ degrees of freedom in two and three dimensions, 100--1000+ wavelengths ($\lambda$) in diameter, with 100+ parameters per $\lambda^2$. In particular, we show how topology optimization, with one degree of freedom per high-resolution "pixel," can be extended to large areas with the help of a locally periodic approximation that was previously only used for a few parameters per $\lambda^2$. In this way, we can computationally discover completely unexpected metasurface designs for challenging multi-frequency, multi-angle problems, including designs for fully coupled multi-layer structures with arbitrary per-layer patterns. Unlike typical metasurface designs based on subwavelength unit cells, our approach can discover both sub- and supra-wavelength patterns and can obtain both the near and far fields

Sideways adiabaticity: Beyond ray optics for slowly varying metasurfaces

Optical metasurfaces (subwavelength-patterned surfaces typically described by variable effective surface impedances) are typically modeled by an approximation akin to ray optics: the reflection or transmission of an incident wave at each point of the surface is computed as if the surface were "locally uniform", and then the total field is obtained by summing all of these local scattered fields via a Huygens principle. (Similar approximations are found in scalar diffraction theory and in ray optics for curved surfaces.) In this paper, we develop a precise theory of such approximations for variable-impedance surfaces. Not only do we obtain a type of adiabatic theorem showing that the "zeroth-order" locally uniform approximation converges in the limit as the surface varies more and more slowly, including a way to quantify the rate of convergence, but we also obtain an infinite series of higher-order corrections. These corrections, which can be computed to any desired order by performing integral operations on the surface fields, allow rapidly varying surfaces to be modeled with arbitrary accuracy, and also allow one to validate designs based on the zeroth-order approximation (which is often surprisingly accurate) without resorting to expensive brute-force Maxwell solvers. We show that our formulation works arbitrarily close to the surface, and can even compute coupling to guided modes, whereas in the far-field limit our zeroth-order result simplifies to an expression similar to what has been used by other authors

Efficient inverse design of large-area metasurfaces for incoherent light

Incoherent light is ubiquitous, yet designing optical devices that can handle its random nature is very challenging, since directly averaging over many incoherent incident beams can require a huge number of scattering calculations. We show how to instead solve this problem with a reciprocity technique which leads to three orders of magnitude speedup: one Maxwell solve (using any numerical technique) instead of thousands. This improvement enables us to perform efficient inverse design, large scale optimization of the metasurface for applications such as light collimators and concentrators. We show the impact of the angular distribution of incident light on the resulting performance, and show especially promising designs for the case of "annular" beams distributed only over nonzero angles

Physics-enhanced deep surrogates for PDEs

We present a ''physics-enhanced deep-surrogate'' (''PEDS'') approach towards developing fast surrogate models for complex physical systems, which is described by partial differential equations (PDEs) and similar models. Specifically, a unique combination of a low-fidelity, explainable physics simulator and a neural network generator is proposed, which is trained end-to-end to globally match the output of an expensive high-fidelity numerical solver. We consider low-fidelity models derived from coarser discretizations and/or by simplifying the physical equations, which are several orders of magnitude faster than a high-fidelity ''brute-force'' PDE solver. The neural network generates an approximate input, which is adaptively mixed with a downsampled guess and fed into the low-fidelity simulator. In this way, by incorporating the limited physical knowledge from the differentiable low-fidelity model ''layer'', we ensure that the conservation laws and symmetries governing the system are respected by the design of our hybrid system. Experiments on three test problems -- diffusion, reaction-diffusion, and electromagnetic scattering models -- show that a PEDS surrogate can be up to 3$\times$ more accurate than a ''black-box'' neural network with limited data ($\approx 10^3$ training points), and reduces the data needed by at least a factor of 100 for a target error of $5\%$, comparable to fabrication uncertainty. PEDS even appears to learn with a steeper asymptotic power law than black-box surrogates. In summary, PEDS provides a general, data-driven strategy to bridge the gap between a vast array of simplified physical models with corresponding brute-force numerical solvers, offering accuracy, speed, data efficiency, as well as physical insights into the process

Physics-informed neural networks with hard constraints for inverse design

Inverse design arises in a variety of areas in engineering such as acoustic, mechanics, thermal/electronic transport, electromagnetism, and optics. Topology optimization is a major form of inverse design, where we optimize a designed geometry to achieve targeted properties and the geometry is parameterized by a density function. This optimization is challenging, because it has a very high dimensionality and is usually constrained by partial differential equations (PDEs) and additional inequalities. Here, we propose a new deep learning method -- physics-informed neural networks with hard constraints (hPINNs) -- for solving topology optimization. hPINN leverages the recent development of PINNs for solving PDEs, and thus does not rely on any numerical PDE solver. However, all the constraints in PINNs are soft constraints, and hence we impose hard constraints by using the penalty method and the augmented Lagrangian method. We demonstrate the effectiveness of hPINN for a holography problem in optics and a fluid problem of Stokes flow. We achieve the same objective as conventional PDE-constrained optimization methods based on adjoint methods and numerical PDE solvers, but find that the design obtained from hPINN is often simpler and smoother for problems whose solution is not unique. Moreover, the implementation of inverse design with hPINN can be easier than that of conventional methods

Seismicity induced during the development of the Rittershoffen geothermal field, France

The development of the Rittershoffen deep geothermal field (Alsace, Upper Rhine Graben) between 2012 and 2014 induced unfelt seismicity with a local magnitude of less than 1.6. This seismicity occurred during two types of operations: (1) mud losses in the Muschelkalk formation during the drilling of both wells of the doublet and (2) thermal and hydraulic stimulations of the GRT-1 well. Seismicity was also observed 4 days after the main hydraulic stimulation, although no specific operation was performed. During chemical stimulation, however, no induced seismicity was detected. In the context of all field development operations and their injection parameters (flow rates, overpressures, volumes), we detail the occurrence or lack of seismicity, its magnitude distribution and its spatial distribution. The observations suggest the presence of the rock stress memory effect (Kaiser effect) of the geothermal reservoir as well as uncritically stressed zones connected to the GRT-1 well and/or rock cohesion. A reduction of the seismic rate concurrent with an increase of injectivity was noticed as well as the reactivation of a couple of faults, including the Rittershoffen fault, which was targeted by the wells. These results are derived from the homogeneous and consistent catalogue of more than 1300 local earthquakes that is provided. This reference catalogue is based on a standard detection method, whose output was manually verified and improved. The given absolute locations have been computed in a calibrated, geologically realistic 3D velocity model. Our work builds on previous analyses addressing the seismicity induced by the GRT-1 hydraulic stimulation and places the results into a historical context, thus considering the full dynamics of the observed phenomena. This paper also complements existing descriptions of the hydrothermal characteristics of the deep reservoir by providing insights separate from the wells

Inverse design of large-area metasurfaces

We present a computational framework for efficient optimization-based "inverse design" of large-area "metasurfaces" (subwavelength-patterned surfaces) for applications such as multi-wavelength and multi-angle optimizations, and demultiplexers. To optimize surfaces that can be thousands of wavelengths in diameter, with thousands (or millions) of parameters, the key is a fast approximate solver for the scattered field. We employ a "locally periodic" approximation in which the scattering problem is approximated by a composition of periodic scattering problems from each unit cell of the surface, and validate it against brute-force Maxwell solutions. This is an extension of ideas in previous metasurface designs, but with greatly increased flexibility, e.g. to automatically balance tradeoffs between multiple frequencies, or to optimize a photonic device given only partial information about the desired field. Our approach even extends beyond the metasurface regime to non-subwavelength structures where additional diffracted orders must be included (but the period is not large enough to apply scalar diffraction theory).Comment: 18 pages, 8 figure

Neutralizing Aptamers from Whole-Cell SELEX Inhibit the RET Receptor Tyrosine Kinase

Targeting large transmembrane molecules, including receptor tyrosine kinases, is a major pharmacological challenge. Specific oligonucleotide ligands (aptamers) can be generated for a variety of targets through the iterative evolution of a random pool of sequences (SELEX). Nuclease-resistant aptamers that recognize the human receptor tyrosine kinase RET were obtained using RET-expressing cells as targets in a modified SELEX procedure. Remarkably, one of these aptamers blocked RET-dependent intracellular signaling pathways by interfering with receptor dimerization when the latter was induced by the physiological ligand or by an activating mutation. This strategy is generally applicable to transmembrane receptors and opens the way to targeting other members of this class of proteins that are of major biomedical importance