arXiv subjects

Rasmus E. Christiansen

Publications and source records attributed to Rasmus E. Christiansen.

16 recordsLinked to original sources

arXiv2026

Topology-optimized distributed 3d anisotropic Raman emission

Topology optimization (TO) of 3D surface-enhanced Raman scattering (SERS) substrates faces challenges in managing field singularities and modeling orientation-averaged anisotropic molecules. We present 3D TO for manufacturable SERS substrates that maximize spatially averaged signals from randomly oriented, anisotropic molecules in both elastic and inelastic scattering. A new trace formulation provides a closed-form rotational average of anisotropic Raman tensors, which are not equivalent to isotropic molecules because of tensor nonlinearity. Optimized silver and Si3N4 devices show that lengthscale constraints are sufficient to suppress designs that rely on unphysical mathematical field divergences at sharp corners. Metallic designs deliver broadband enhancement and remain robust to typical Raman shifts, whereas dielectric designs yield narrower, quality-factor-limited gains that are inferior to metallic designs for quality factors below about 500. Our approach readily incorporates additional physics, such as a nonlinear damage model. Together, these results provide a practical route to improved manufacturable SERS substrates and extend naturally to other distributed-emitter design problems.

physics.optics↗

arXiv2026

Orders-of-magnitude reduction in photonic mode volume by nano-sculpting

Achieving strong light-matter interaction is important for studying and exploiting several physics phenomena. The light-matter interaction strength depends on the optical field intensity in the interaction region, often measured by the Purcell factor, which for a single emitter is proportional to the spectral confinement, quantified by the cavity quality factor $Q$, and inversely proportional to the spatial localization of light, quantified by the optical model volume $V$, $F \propto \frac{Q}{V}$. While plasmonic (metallic) devices can support extreme spatial light confinement, ohmic losses reduce the cavity lifetime, thereby limiting the achievable spectral confinement. It is therefore of both practical and fundamental interest to explore the potential for achieving extreme spatial light confinement in (near) loss-less dielectric environments. Employing topology optimization we explore the limits of spatial light confinement in dielectric environments when allowing for three-dimensional sculpted dielectric nanostructures. Here we discover structures supporting optical modes that are concentrated in material (air) with mode volumes that are three (four) orders of magnitude below the so-called diffraction limit, $V_{\textbf{r}_0} \approx 4 \cdot 10^{-4} \left[λ/(2 n)\right]^3 \left( V_{\textbf{r}_0} \approx 3 \cdot 10^{-5} \left[λ/2\right]^3\right)$. Remarkably, we further discover that encapsulating the nanostructure by ellipsoidal shells enables seemingly unbounded enhancement of the mode quality factor ($Q > 10^8$ demonstrated numerically) leading to theoretical Purcell factor enhancement above $10^{11}$. It is established how $V_{\textbf{r}_0}$ and $Q$ depend on the choice of material platform, device volume, minimum feature size and the number of shells. Finally a study of sensitivity towards geometric variations is presented, revealing robust behaviour.

physics.optics↗

arXiv2024

On performance bounds for topology optimization

Topology optimization has matured to become a powerful engineering design tool that is capable of designing extraordinary structures and materials taking into account various physical phenomena. Despite the method's great advancements in recent years, several unanswered questions remain. This paper takes a step towards answering one of the larger questions, namely: How far from the global optimum is a given topology optimized design? Typically this is a hard question to answer, as almost all interesting topology optimization problems are non-convex. Unfortunately, this non-convexity implies that local minima may plague the design space, resulting in optimizers ending up in suboptimal designs. In this work, we investigate performance bounds for topology optimization via a computational framework that utilizes Lagrange duality theory. This approach provides a viable measure of how \say{close} a given design is to the global optimum for a subset of optimization formulations. The method's capabilities are exemplified via several numerical examples, including the design of mode converters and resonating plates.

cs.CE↗

arXiv2024

Morphogenesis of sound creates acoustic rainbows

Sound is an essential sensing element for many organisms in nature, and multiple species have evolved organic structures that create complex acoustic scattering and dispersion phenomena to emit and perceive sound unambiguously. To date, it has not proven possible to design artificial scattering structures that rival the performance of those found in organic structures. Contrarily, most sound manipulation relies on active transduction in fluid media rather than relying on passive scattering principles, as are often found in nature. In this work, we utilize computational morphogenesis to synthesize complex energy-efficient wavelength-sized single-material scattering structures that passively decompose radiated sound into its spatio-spectral components. Specifically, we tailor an acoustic rainbow structure with "above unity" efficiency and an acoustic wavelength-splitter. Our work paves the way for a new frontier in sound-field engineering, with potential applications in transduction, bionics, energy harvesting, communications and sensing.

cs.SD↗

arXiv2022

Trace formulation for photonic inverse design with incoherent sources

Spatially incoherent light sources, such as spontaneously emitting atoms, naively require Maxwell's equations to be solved many times to obtain the total emission, which becomes computationally intractable in conjunction with large-scale optimization (inverse design). We present a trace formulation of incoherent emission that can be efficiently combined with inverse design, even for topology optimization over thousands of design degrees of freedom. Our formulation includes previous reciprocity-based approaches, limited to a few output channels (e.g. normal emission), as special cases, but generalizes to a continuum of emission directions by exploiting the low-rank structure of emission problems. We present several examples of incoherent-emission topology optimization, including tailoring the geometry of fluorescent particles, a periodically emitting surface, and a structure emitting into a waveguide mode, as well as discussing future applications to problems such as Raman sensing and cathodoluminescence.

physics.optics↗

arXiv2022

Designing Structures that Maximize Spatially Averaged Surface-Enhanced Raman Spectra

We present a general framework for inverse design of nanopatterned surfaces that maximize spatially averaged surface-enhanced Raman (SERS) spectra from molecules distributed randomly throughout a material or fluid, building upon a recently proposed trace formulation for optimizing incoherent emission. This leads to radically different designs than optimizing SERS emission at a single known location, as we illustrate using several 2D design problems addressing effects of hot-spot density, angular selectivity, and nonlinear damage. We obtain optimized structures that perform about 4 times better than coating with optimized spheres or bowtie structures and about 20 times better when the nonlinear damage effects are included.

physics.optics↗

arXiv2021

Towards 3D-Printed Inverse-Designed Metaoptics

Optical metasurfaces have been heralded as the platform to integrate multiple functionalities in a compact form-factor, potentially replacing bulky components. A central stepping stone towards realizing this promise is the demonstration of multifunctionality under several constraints (e.g. at multiple incident wavelengths and/or angles) in a single device -- an achievement being hampered by design limitations inherent to single-layer planar geometries. Here, we propose a general framework for the inverse design of volumetric 3D metaoptics via topology optimization, showing that even few-wavelength thick devices can achieve high-efficiency multifunctionality. We embody our framework in multiple closely-spaced patterned layers of a low-index polymer. We experimentally demonstrate our approach with an inverse-designed 3d-printed light concentrator working at five different non-paraxial angles of incidence. Our framework paves the way towards realizing multifunctional ultra-compact 3D nanophotonic devices.

physics.optics↗

arXiv2021

Compact 200 line MATLAB code for inverse design in photonics by topology optimization: tutorial

We provide a compact 200 line MATLAB code demonstrating how topology optimization (TopOpt) as an inverse design tool may be used in photonics, targeting the design of two-dimensional dielectric metalenses and a metallic reflector as examples. The physics model is solved using the finite element method, and the code utilizes MATLAB's fmincon algorithm to solve the optimization problem. In addition to presenting the code itself, we briefly discuss a number of extensions and provide the code required to implement some of these. Finally, we demonstrate the superiority of using a gradient-based method compared to a genetic-algorithm-based method (using MATLAB's ga algorithm) for solving inverse design problems in photonics. The MATLAB software is freely available in the paper and may be downloaded from https://www.topopt.mek.dtu.dk.

cs.MS↗

arXiv2021

Inverse design in photonics by topology optimization: tutorial

Topology optimization methods for inverse design of nano-photonic systems have recently become extremely popular and are presented in various forms and under various names. Approaches comprise gradient and non-gradient based algorithms combined with more or less systematic ways to improve convergence, discreteness of solutions and satisfaction of manufacturing constraints. We here provide a tutorial for the systematic and efficient design of nano-photonic structures by Topology Optimization (TopOpt). The implementation is based on the advanced and systematic approaches developed in TopOpt for structural optimization during the last three decades. The tutorial presents a step-by-step guide for deriving the continuous constrained optimization problem forming the foundation of the Topology Optimization method, using a cylindrical metalens design problem as an example. It demonstrates the effect and necessity of applying a number of auxiliary tools in the design process in order to ensure good numerical modelling practice and to achieve physically realisable designs. Application examples also include an optical demultiplexer.

physics.optics↗

arXiv2021

Topology Optimization of Surface-enhanced Raman Scattering Substrates

Surface-enhanced Raman spectroscopy is a powerful and versatile sensing method with a detection limit down to the single molecule level. In this article, we demonstrate how topology optimization (TopOpt) can be used for designing surface enhanced Raman scattering (SERS) substrates adhering to realistic fabrication constraints. As an example, we experimentally demonstrated a SERS enhancement factor of 5*10e4 for the 604 cm-1 Raman line of rhodamine 6G using metal nanostructures with a critical dimension of 20 nm. We then show that, by relaxing the fabrication constraints, TopOpt may be used to design SERS substrates with orders of magnitude larger enhancement factor. The results validate topology optimization as an effective method for engineering nanostructures with optimal performance and fabrication tolerance.

cond-mat.mes-hall↗

arXiv2020

Computational inverse design for ultra-compact single-piece metalenses free of chromatic and angular aberration

We present full-Maxwell topology-optimization design of a single-piece multlayer metalens, about 10 wavelengths~$λ$ in thickness, that simultaneously focuses over a $60^\circ$ angular range and a 23\% spectral bandwidth without suffering chromatic or angular aberration, a "plan-achromat." At all angles and frequencies it achieves diffraction-limited focusing (Strehl ratio $> 0.8$) and absolute focusing efficiency $> 50$\%. Both 2D and 3D axi-symmetric designs are presented, optimized over $\sim 10^5$ degrees of freedom. We also demonstrate shortening the lens-to-sensor distance while producing the same image as for a longer "virtual" focal length and maintaining plan-achromaticity. These proof-of-concept designs demonstrate the ultra-compact multi-functionality that can be achieved by exploiting the full wave physics of subwavelength designs, and motivate future work on design and fabrication of multi-layer meta-optics.

physics.optics↗

arXiv2020

Fullwave Maxwell inverse design of axisymmetric, tunable, and multi-scale multi-wavelength metalenses

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 ($λ= 1\,μ$m and $10\,μ$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.

physics.optics↗

arXiv2019

Inverse Design of Nanoparticles for Enhanced Raman Scattering

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.

physics.optics↗

arXiv2019

Strongly enhanced upconversion in trivalent erbium ions by tailored gold nanostructures: toward high-efficient silicon-based photovoltaics

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.

physics.app-ph↗

arXiv2019

Designing Photonic Topological Insulators with Quantum-Spin-Hall Edge States using Topology Optimization

Designing photonic topological insulators is highly non-trivial because it requires inversion of band symmetries around the band gap, which was so far done using intuition combined with meticulous trial and error. Here we take a completely different approach: we consider the design of photonic topological insulators as an inverse design problem and use topology optimization to maximize the transmission through an edge mode with a sharp bend. Two design domains composed of two different, but initially identical, C$_\text{6v}$-symmetric unit cells define the geometrical design problem. Remarkably, the optimization results in a photonic topological insulator reminiscent of the shrink-and-grow approach to quantum-spin-Hall photonic topological insulators but with notable differences in the topology of the crystal as well as qualitatively different band structures and with significantly improved performance as gauged by the band-gap sizes, which are at least 50 \% larger than previous designs. Furthermore, we find a directional beta factor exceeding 99 \%, and very low losses for sharp bends. Our approach allows for the introduction of fabrication limitations by design and opens an avenue towards designing PTIs with hitherto unexplored symmetry constraints.

cond-mat.mes-hall↗

arXiv2019

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 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.

cond-mat.mes-hall↗