arXiv subjects

Owen D. Miller

Publications and source records attributed to Owen D. Miller.

At least 37 records · Page 2Linked to original sources

arXiv2023

Many Physical Design Problems are Sparse QCQPs

Physical design refers to mathematical optimization of a desired objective (e.g. strong light--matter interactions, or complete quantum state transfer) subject to the governing dynamical equations, such as Maxwell's or Schrodinger's differential equations. Computing an optimal design is challenging: generically, these problems are highly nonconvex and finding global optima is NP hard. Here we show that for linear-differential-equation dynamics (as in linear electromagnetism, elasticity, quantum mechanics, etc.), the physical-design optimization problem can be transformed to a sparse-matrix, quadratically constrained quadratic program (QCQP). Sparse QCQPs can be tackled with convex optimization techniques (such as semidefinite programming) that have thrived for identifying global bounds and high-performance designs in other areas of science and engineering, but seemed inapplicable to the design problems of wave physics. We apply our formulation to prototypical photonic design problems, showing the possibility to compute fundamental limits for large-area metasurfaces, as well as the identification of designs approaching global optimality. Looking forward, our approach highlights the promise of developing bespoke algorithms tailored to specific physical design problems.

physics.optics↗

arXiv2022

Inverse Design of High-NA Metalens for Maskless Lithography

We demonstrate an axisymmetric inverse-designed metalens to improve the performance of zone-plate-array lithography (ZPAL), one of the maskless lithography approaches, that offer a new paradigm for nanoscale research and industry. First, we derive a computational upper bound for a unit-cell-based axisymmetric metalens. Then, we demonstrate a fabrication-compatible inverse-designed metalens with 85.50\% transmission normalized focusing efficiency at 0.6 numerical aperture at 405nm wavelength; a higher efficiency than a theoretical gradient index lens design (79.98\%). We also demonstrate experimental validation for our axisymmetric inverse-designed metalens via electron beam lithography. Metalens-based maskless lithography may open a new way of achieving low-cost, large-area nanofabrication.

physics.optics↗

arXiv2022

All electromagnetic scattering bodies are matrix-valued oscillators

In this article, we introduce a new viewpoint on electromagnetic scattering. Tailoring spectral electromagnetic response underpins important applications ranging from sensing to energy conversion, and is flourishing with new ideas from non-Hermitian physics. There exist excellent theoretical tools for modeling such responses, particularly coupled-mode theories and quasinormal-mode expansions. Yet these approaches offer little insight into the outer limits of what is possible when broadband light interacts with any designable nanophotonic pattern. We show that a special scattering matrix, the "$\mathbb{T}$" matrix, can always be decomposed into a set of fictitious Drude--Lorentz oscillators with matrix-valued (spatially nonlocal) coefficients. For any application and any scatterer, the only designable degrees of freedom are these matrix coefficients, implying strong constraints on lineshapes and response functions that had previously been "hidden." To demonstrate the power of this approach, we apply it to near-field radiative heat transfer, where there has been a long-standing gap between the best known designs and theoretical limits to maximum energy exchange. Our new framework identifies upper bounds that come quite close to the current state-of-the-art, and explains why unconventional plasmonic materials should be superior to conventional plasmonic materials. More generally, this approach can be seamlessly applied to high-interest applications across nanophotonics -- including for metasurfaces, imaging, and photovoltaics -- and may be generalizable to unique challenges that arise in acoustic and/or quantum scattering theory.

physics.optics↗

arXiv2022

Bounds on the Coupling Strengths of Communication Channels and Their Information Capacities

The concept of optimal communication channels shapes our understanding of wave-based communication. Its analysis, however, always pertains to specific communication-domain geometries, without a general theory of scaling laws or fundamental limits. In this article, we derive shape-independent bounds on the coupling strengths and information capacities of optimal communication channels for any two domains that can be separated by a spherical surface. Previous computational experiments have always observed rapid, exponential decay of coupling strengths, but our bounds predict a much slower, sub-exponential optimal decay, and specific source/receiver distributions that can achieve such performance. Our bounds show that domain sizes and configurations, and not domain shapes, are the keys to maximizing the number of non-trivial communication channels and total information capacities. Applicable to general wireless and optical communication systems, our bounds reveal fundamental limits to what is possible through engineering the communication domains of electromagnetic waves.

cs.IT↗

arXiv2021

Fundamental limits to multi-functional and tunable nanophotonic response

Tunable and multi-functional nanophotonic devices are used for applications from beam steering to sensing. Yet little is understood about fundamental limits to their functionality. The difficulty lies with the fact that it is a single structure that must exhibit optimal response over multiple scenarios. In this article, we present a general theoretical framework for understanding and computing fundamental limits to multi-functional nanophotonic response. Building from rapid recent advances in bounds to light-matter interactions, we show that after rewriting the design problems in terms of polarization fields, the introduction of suitable cross-correlation constraints imposes the crucial "single-structure" criteria. We demonstrate the utility of this approach for two applications: reflectivity contrast for optical sensing, and maximum efficiency for optical beam switching. Our approach generalizes to any active or multi-functional design in linear optics.

physics.optics↗

arXiv2021

Conservation-law-based global bounds to quantum optimal control

Active control of quantum systems enables diverse applications ranging from quantum computation to manipulation of molecular processes. Maximum speeds and related bounds have been identified from uncertainty principles and related inequalities, but such bounds utilize only coarse system information, and loosen significantly in the presence of constraints and complex interaction dynamics. We show that an integral-equation-based formulation of conservation laws in quantum dynamics leads to a systematic framework for identifying fundamental limits to any quantum control scenario. We demonstrate the utility of our bounds in three scenarios -- three-level driving, decoherence suppression, and maximum-fidelity gate implementations -- and show that in each case our bounds are tight or nearly so. Global bounds complement local-optimization-based designs, illuminating performance levels that may be possible as well as those that cannot be surpassed.

quant-ph↗

arXiv2021

High-NA optical edge detection via optimized multilayer films

There has been a significant effort to design nanophotonic structures that process images at the speed of light. A prototypical example is in edge detection, where photonic-crystal-, metasurface-, and plasmon-based designs have been proposed and in some cases experimentally demonstrated. In this work, we show that multilayer optical interference coatings can achieve visible-frequency edge detection in transmission with high numerical aperture, two-dimensional image formation, and straightforward fabrication techniques, unique among all nanophotonic approaches. We show that the conventional Laplacian-based transmission spectrum may not be ideal once the scattering physics of real designs is considered, and show that better performance can be attained with alternative spatial filter functions. Our designs, comprising alternating layers of Si and SiO$_2$ with total thicknesses of only $\approx 1{\rmμm}$, demonstrate the possibility for optimized multilayer films to achieve state-of-the-art edge detection, and, more broadly, analog optical implementations of linear operators.

physics.optics↗

arXiv2021

Towards Maximum Optical Efficiency of Ensembles of Colloidal Nanorods

Experimental and theoretical studies of colloidal nanoparticles have primarily focused on accurate characterization and simulation of observable characteristics, such as resonant wavelength. In this Letter, we tackle the optimal design of colloidal-nanoparticle ensembles: what is the largest possible optical response, which designs might achieve them, and can such response be experimentally demonstrated? We combine theory and experiment to answer each of these questions. We derive general bounds on the maximum cross-sections per volume, and we apply an analytical antenna model to show that resonant nanorods should nearly achieve such bounds. We use a modified seed-mediated synthesis approach to synthesize ensembles of gold nanorods with small polydispersity, i.e., small variations in size and aspect ratio. Polydispersity is the key determinant of how closely such ensembles can approach their respective bounds yet is difficult to characterize experimentally without near-field measurements. We show that a certain "extinction metric," connecting extinction cross-section per volume with the radiative efficiencies of the nanoparticles, offers a quantitative prediction of polydispersity via quantities that can be rapidly measured with far-field characterization tools. Our predictions apply generally across all plasmonic materials and offers a roadmap to the largest possible optical response of nanoparticle ensembles.

physics.optics↗

arXiv2021

Fundamental limits to the refractive index of transparent optical materials

Increasing the refractive index available for optical and nanophotonic systems opens new vistas for design: for applications ranging from broadband metalenses to ultrathin photovoltaics to high-quality-factor resonators, higher index directly leads to better devices with greater functionality. Although standard transparent materials have been limited to refractive indices smaller than 3 in the visible, recent metamaterials designs have achieved refractive indices above 5, accompanied by high losses, and near the phase transition of a ferroelectric perovskite a broadband index above 26 has been claimed. In this work, we derive fundamental limits to the refractive index of any material, given only the underlying electron density and either the maximum allowable dispersion or the minimum bandwidth of interest. The Kramers--Kronig relations provide a representation for any passive (and thereby causal) material, and a well-known sum rule constrains the possible distribution of oscillator strengths. In the realm of small to modest dispersion, our bounds are closely approached and not surpassed by a wide range of natural materials, showing that nature has already nearly reached a Pareto frontier for refractive index and dispersion. Surprisingly, our bound shows a cube-root dependence on electron density, meaning that a refractive index of 26 over all visible frequencies is likely impossible. Conversely, for narrow-bandwidth applications, nature does not provide the highly dispersive, high-index materials that our bounds suggest should be possible. We use the theory of composites to identify metal-based metamaterials that can exhibit small losses and sizeable increases in refractive index over the current best materials.

physics.optics↗

arXiv2020

Computational bounds to light-matter interactions via local conservation laws

We develop a computational framework for identifying bounds to light-matter interactions, originating from polarization-current-based formulations of local conservation laws embedded in Maxwell's equations. We propose an iterative method for imposing only the maximally violated constraints, enabling rapid convergence to global bounds. Our framework can identify bounds to the minimum size of any scatterer that encodes a specific linear operator, given only its material properties, as we demonstrate for the optical computation of a discrete Fourier transform. It further resolves bounds on far-field scattering properties over any arbitrary bandwidth, where previous bounds diverge.

physics.optics↗

arXiv2020

Maximal single-frequency electromagnetic response

Modern nanophotonic and meta-optical devices utilize a tremendous number of structural degrees of freedom to enhance light--matter interactions. A fundamental question is how large such enhancements can be. We develop an analytical framework to derive upper bounds to single-frequency electromagnetic response, across near- and far-field regimes, for any materials, naturally incorporating the tandem effects of material- and radiation-induced losses. Our framework relies on a power-conservation law for the polarization fields induced in any scatterer. It unifies previous theories on optical scattering bounds and reveals new insight for optimal nanophotonic design, with applications including far-field scattering, near-field local-density-of-states engineering, optimal wavefront shaping, and the design of perfect absorbers. Our bounds predict strikingly large minimal thicknesses for arbitrarily patterned perfect absorbers, ranging from 50--100 nm for typical materials at visible wavelengths to micrometer-scale thicknesses for polar dielectrics at infrared wavelengths. We use inverse design to discover metasurface structures approaching the minimum-thickness perfect-absorber bounds.

physics.optics↗

arXiv2020

Quasinormal Coupled Mode Theory

Coupled mode theory (CMT) is a powerful framework for decomposing interactions between electromagnetic waves and scattering bodies into resonances and their couplings with power-carrying channels. It has widespread use in few-resonance, weakly coupled resonator systems across nanophotonics, but cannot be applied to the complex scatterers of emerging importance. We use quasinormal modes to develop an exact, ab initio generalized coupled mode theory from Maxwell's equations. This quasinormal coupled mode theory, which we denote "QCMT", enables a direct, mode-based construction of scattering matrices without resorting to external solvers or data. We consider canonical scattering bodies, for which we show that a CMT model will necessarily be highly inaccurate, whereas QCMT exhibits near-perfect accuracy.

physics.optics↗

arXiv2020

Minimum Dielectric-Resonator Mode Volumes

We show that global lower bounds to the mode volume of a dielectric resonator can be computed via Lagrangian duality. State-of-the-art designs rely on sharp tips, but such structures appear to be highly sub-optimal at nanometer-scale feature sizes, and we demonstrate that computational inverse design offers orders-of-magnitude possible improvements. Our bound can be applied for geometries that are simultaneously resonant at multiple frequencies, for high-efficiency nonlinear-optics applications, and we identify the unavoidable penalties that must accompany such multiresonant structures.

physics.optics↗

arXiv2020

Approaching the upper limits of the local density of states via optimized metallic cavities

By computational optimization of air-void cavities in metallic substrates, we show that the local density of states (LDOS) can reach within a factor of $\approx 10$ of recent theoretical upper limits, and within a factor $\approx 4$ for the single-polarization LDOS, demonstrating that the theoretical limits are nearly attainable. Optimizing the total LDOS results in a spontaneous symmetry breaking where it is preferable to couple to a specific polarization. Moreover, simple shapes such as optimized cylinders attain nearly the performance of complicated many-parameter optima, suggesting that only one or two key parameters matter in order to approach the theoretical LDOS bounds for metallic resonators.

physics.optics↗

arXiv2020

Optimal materials for maximum near-field radiative heat transfer

We consider the space of all causal bulk materials, 2D materials, and metamaterials for maximum near-field radiative heat transfer (RHT). Causality constrains the bandwidth over which plasmonic response can occur, explaining two key traits in ideal materials: small background permittivities (minimal high-energy transitions in 2D materials), and Drude-like free-carrier response, which together optimally yield 10X enhancements beyond the theoretical state-of-the-art. We identify transparent conducting oxides, III-Nitrides, and graphene as materials that should offer nearly ideal near-field RHT rates, if doped to exhibit plasmonic resonances at what we term "near-field Wien frequencies." Deep-subwavelength patterning can provide marginal further gains, at the expense of extremely small feature sizes. Optimal materials have moderate loss rates and plasmonic response at 19 μm for 300K temperature, suggesting a new opportunity for plasmonics at mid- to far-infrared wavelengths, with low carrier concentrations and no requirement to minimize loss.

physics.optics↗

arXiv2020

Optical Materials for Maximal Nanophotonic Response

This article reviews the material properties that enable maximum optical response. We highlight theoretical results that enable shape-independent quantification of material "figures of merit," ranging from classical sum rules to more recent single-frequency scattering bounds. A key delineation at optical frequencies is between polaritonic materials that support highly subwavelength resonances and dielectric materials that can have vanishingly small loss rates. We discuss the key metrics that enable comparisons both within these material classes and between them. We discuss analogous metrics for 2D materials, and point to applications for which rigorous comparison can be made between bulk- and 2D-material approaches. The various results highlight the synergy between materials discovery and theoretical nanophotonic bounds, and point to opportunities in achieving new extremes in light--matter interactions.

physics.optics↗

arXiv2019

Maximal Free-Space Concentration of Electromagnetic Waves

We derive upper bounds to free-space concentration of electromagnetic waves, mapping out the limits to maximum intensity for any spot size and optical beam-shaping device. For sub-diffraction-limited optical beams, our bounds suggest the possibility for orders-of-magnitude intensity enhancements compared to existing demonstrations, and we use inverse design to discover metasurfaces operating near these new limits. We also demonstrate that our bounds may surprisingly describe maximum concentration defined by a wide variety of metrics. Our bounds require no assumptions about symmetry, scalar waves, or weak scattering, instead relying primarily on the transformation of a quadratic program via orthogonal-projection methods. The bounds and inverse-designed structures presented here can be useful for applications from imaging to 3D printing.

physics.optics↗

arXiv2019

Tunable metasurface inverse design for 80% switching efficiencies and 144$^\circ$ angular steering

Tunable metasurfaces have demonstrated the potential for dramatically enhanced functionality for applications including sensing, ranging and imaging. Liquid crystals (LCs) have fast switching speeds, low cost, and mature technological development, offering a versatile platform for electrical tunability. However, to date, electrically tunable metasurfaces are typically designed at a single operational state using physical intuition, without controlling alternate states and thus leading to limited switching efficiencies ($<30\%$) and small angular steering ($<$25$^\circ$). Here, we use large-scale computational 'inverse design' to discover high-performance designs through adjoint-based local-optimization design iterations within a global-optimization search. We study and explain the physics of these devices, which heavily rely on sophisticated resonator design to fully utilize the very small permittivity change incurred by switching the liquid-crystal voltage. The optimal devices show tunable steering angles ranging from 12$^\circ$ to 144$^\circ$ and switching efficiencies above 80%, exhibiting 6X angular improvements and 6X efficiency improvements compared to the current state-of-the-art.

physics.optics↗