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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.

Periodic wavelength-scale surface patterns have long been used in the context of lasing and spontaneous emission to enhance emission by light trapping (distributed Bragg resonances). Buried within these well-known devices, however, are theoretical mysteries that are still being unravelled. A periodic surface grating actually creates a continuum of resonant modes, so what determines which single mode (if any) lases? Technically, what determines the stability of a periodic lasing mode: is it only the finite size of a surface that allows single-mode lasing, or can it arise for arbitrarily large structures? More generally, if one continuously deforms an unpatterned surface to maximize light emission, how is the symmetry broken and what optimal structures arise? We address these questions by combining new computational techniques for modeling and large-scale optimization of incoherent emission and lasing with new analytical results arising from perturbation and stability theory.

Optical nanocavities confine and store light, which is essential to increase the interaction between photons and electrons in semiconductor devices, enabling, e.g., lasers and emerging quantum technologies. While temporal confinement has improved by orders of magnitude over the past decades, spatial confinement inside dielectrics was until recently believed to be bounded at the diffraction limit. The conception of dielectric bowtie cavities (DBCs) shows a path to photon confinement inside semiconductors with mode volumes bound only by the constraints of materials and nanofabrication, but theory was so far misguided by inconsistent definitions of the mode volume and experimental progress has been impeded by steep nanofabrication requirements. Here we demonstrate nanometer-scale photon confinement inside 8 nm silicon DBCs with an aspect ratio of 30, inversely designed by fabrication-constrained topology optimization. Our cavities are defined within a compact device footprint of 4 lambda^2 and exhibit mode volumes down to V = 3E-4 lambda^3 with wavelengths in the lambda = 1550 nm telecom band. This corresponds to field localization deep below the diffraction limit in a single hotspot inside the dielectric. A crucial insight underpinning our work is the identification of the critical role of lightning-rod effects at the surface. They invalidate the common definition of the mode volume, which is prone to gauge meretricious surface effects or numerical artefacts rather than robust confinement inside the dielectric. We use near-field optical measurements to corroborate the photon confinement to a single nanometer-scale hotspot. Our work enables new CMOS-compatible device concepts ranging from few- and single-photon nonlinearities over electronics-photonics integration to biosensing.

We demonstrate new axisymmetric inverse-design techniques that can solve problems radically different from traditional lenses, including \emph{reconfigurable} lenses (that shift a multi-frequency focal spot in response to refractive-index changes) and {\emph{widely separated}} multi-wavelength lenses ($\lambda = 1\,\mu$m and $10\,\mu$m). We also present experimental validation for an axisymmetric inverse-designed monochrome lens in the near-infrared fabricated via two-photon polymerization. Axisymmetry allows fullwave Maxwell solvers to be scaled up to structures hundreds or even thousands of wavelengths in diameter before requiring domain-decomposition approximations, while multilayer topology optimization with $\sim 10^5$ degrees of freedom can tackle challenging design problems even when restricted to axisymmetric structures., Comment: 13 pages, 6 figures

We previously introduced a preconditioner that has proven effective for h p -FEM discretizations of various challenging elliptic and hyperbolic problems. The construction is inspired by standard nested dissection, and relies on the assumption that the Schur complements can be approximated, to high precision, by Hierarchically-Semi-Separable matrices. The preconditioner is built as an approximate L D M t factorization through a divide-and-conquer approach. This implies an enhanced flexibility which allows to handle unstructured geometric meshes, anisotropies, and discontinuities. We build on our previous numerical experiments and develop a preconditioner-update strategy that allows us to handle matrix sequences arising from problems with slowly-varying coefficients. We investigate the performance of the preconditioner along with the update strategy in context of topology optimization of an acoustic cavity.

This paper corrects an error in the software provided with J. Opt. Soc. Am. B 38, 510 (2021)JOBPDE0740-322410.1364/JOSAB.405955.

Upconversion of sub-band-gap photons constitutes a promising way for improving the efficiency of silicon-based solar cells beyond the Shockley-Queisser limit. 1500 to 980 nm upconversion by trivalent erbium ions is well-suited for this purpose, but the small absorption cross section hinders real-world applications. We employ tailored gold nanostructures to vastly improve the upconversion efficiency in erbium-doped TiO$_2$ thin films. The nanostructures are found using topology optimization and parameter optimization and fabricated by electron beam lithography. In qualitative agreement with a theoretical model, the samples show substantial electric-field enhancements inside the upconverting films for excitation at 1500 nm for both s- and p-polarization under a wide range of incidence angles and excitation intensities. An unprecedented upconversion enhancement of 913(51) is observed at an excitation intensity of 1.7 Wcm$^{-2}$. We derive a semi-empirical expression for the photonically enhanced upconversion efficiency, valid for all excitation intensities. This allows us to determine the upconversion properties needed to achieve significant improvements in real-world solar-cell devices through photonic-enhanced upconversion., Comment: 9 pages (main text), 4 figures, 1 supporting information of 15 pages

We show that topology optimization (TO) of metallic resonators can lead to $\sim 10^2\times$ 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., Comment: 19 pages

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 requirements on the existence of pseudo spin-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 $\approx$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., 6 pages, 5 figures

Resonance and wave-propagation problems are known to be highly sensitive towards parameter variations. This paper discusses topology optimization formulations for creating designs that perform robustly under spatial variations for acoustic cavity problems. For several structural problems, robust topology optimization methods have already proven their worth. However, it is shown that direct application of such methods is not suitable for the acoustic problem under consideration. A new double filter approach is suggested which makes robust optimization for spatial variations possible. Its effect and limitations are discussed. In addition, a known explicit penalization approach is considered for comparison. For near-uniform spatial variations it is shown that highly robust designs can be obtained using the double filter approach. It is finally demonstrated that taking non-uniform variations into account further improves the robustness of the designs.

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.

Measuring the Green’s function over the entire volume of a room would typically require an unfeasible number of measurements, due to requirements on spatial sampling. To alleviate the need for excessive measurements, sparse reconstruction methods can be employed, as they make it possible to reconstruct a seemingly undersampled signal. The present study proposes a method for acquiring experimentally the Green’s function in a room by measuring directly the mode shapes of the room, based on the conception that any mode can be expanded into a number of propagating waves. If the modes are described in the wavenumber domain (as a plane-wave expansion), sparse reconstruction methods can be employed, under the implicit assumption that each mode shape is represented as the superposition of a small number of plane waves. In addition, it is assumed that the medium is source-free and homogeneous. The methodology is examined numerically and verified experimentally, based on measurements in a lightly damped rectangular room.

This letter presents a topology optimization study of metal nanostructures optimized for electric-field enhancement in the infrared spectrum. Coupling of such nanostructures with suitable ions allows for an increased photon-upconversion yield, with one application being an increased solar-cell efficiency by exploiting the long-wavelength part of the solar spectrum. In this work, topology optimization is used to design a periodic array of two-dimensional gold nanostrips for electric-field enhancements in a thin film doped with upconverting erbium ions. The infrared absorption band of erbium is utilized by simultaneously optimizing for two polarizations, up to three wavelengths, and three incident angles. Geometric robustness towards manufacturing variations is implemented considering three different design realizations simultaneously in the optimization. The polarization-averaged field enhancement for each design is evaluated over an 80 nm wavelength range and a ±15-degree incident angle span. The highest polarization-averaged field enhancement is 42.2 varying by maximally 2% under ±5 nm near-uniform design perturbations at three different wavelengths (1480 nm, 1520 nm, and 1560 nm). The proposed method is generally applicable to many optical systems and is therefore not limited to enhancing photon upconversion.

Various scatterers such as rough surfaces or nanostructures are typically used to enhance the low efficiency of Raman spectroscopy (surface-enhanced Raman scattering). In this work, we find fundamental upper bounds on the Raman enhancement for arbitrary-shaped scatterers, depending only on its material constants and the separation distance from the molecule. According to our metric, silver is optimal in visible wavelengths while aluminum is better in the near-UV region. Our general analytical bound scales as the volume of the scatterer and the inverse sixth power of the distance to the active molecule. For periodic scatterers, a second bound with surface-area scaling is presented. Simple geometries such as spheres and bowties are shown to fall short of the bounds. However, using topology optimization based inverse design, we obtain surprising structures maximizing the Raman enhancement. These optimization results shed light to what extent our bounds are achievable.

We consider the design of individual and periodic arrangements of metal or semiconductor nanoparticles for localized electromagnetic field enhancement utilizing a topology optimization based numerical framework as the design tool. We aim at maximizing a function of the electromagnetic field amplitude in a region of space through the introduction of nanoparticles in and/or near the region.

We design, fabricate, and characterize an ultracompact (2) photonic nanocavity in silicon with a deep subwavelength mode volume, which enables strongly enhanced light-matter interaction for applications in nanolasers and nonlinear nanophotonics.