arXiv subjects

Pengning Chao

Publications and source records attributed to Pengning Chao.

At least 19 recordsLinked to original sources

arXiv2026

Optically Incoherent Photonic Mutual Information

While traditional evaluations of optical information transfer rely on disjointed abstractions to bridge electromagnetic propagation, coherence, and communication theory, we introduce an end-to-end framework that directly connects rigorous subwavelength wave physics to Shannon mutual information. By lifting the Maxwell current-to-field Green's function to propagate second-order field correlations (the mutual intensity), we establish a unified linear channel model that encapsulates coherent communication, phase retrieval, and incoherent imaging. Applying this framework, we demonstrate that the mutual-information-optimized photonic front end is dictated jointly by available spatial degrees of freedom, source statistics, and detection laws. For coherent sources measured by square-law detectors, we identify a structural transition: when detectors outnumber sources, topology-optimized front ends shift from point-focusing to interferometric mixing. This mixing leverages interference cross terms to make relative source phases information-bearing, yielding mutual information that surpasses the point-focusing amplitude-only baseline. Conversely, for spatially incoherent sources, the channel reduces to the Hadamard square of the Green's function. In this regime, under an isotropic source covariance, we prove that point-focusing uniquely maximizes the mutual information at fixed Frobenius norm. Under source correlations, the optimized front ends instead favor optical mixing. Finally, we derive closed-form upper bounds on achievable incoherent mutual information, governed entirely by the coherent singular values of the underlying electromagnetic operator. Potential applications include near-field microscopy, direct-detection optical datalinks, reference-free phase retrieval, fluorescence and thermal imaging, and structure-agnostic benchmarks for end-to-end-designed computational imagers.

physics.optics↗

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↗

arXiv2025

Eigenvalue-accelerated LDOS optimization of high-Q optical resonances

We demonstrate a new method that yields orders-of-magnitude acceleration in inverse design (e.g. topology optimization) of high-$Q$ resonant cavities to maximize the local density of states (LDOS), and which is also applicable to other resonant-response metrics. The key idea is that, once conventional LDOS optimization has identified a strong resonance, subsequent optimizations can exploit a fast shift-invert eigensolver to ensure that the LDOS remains centered at the resonance peak. We show that this eliminates ill-conditioning at sharp resonances that otherwise dramatically slows LDOS (and similar) optimization for $Q \gg 100$. Our method is demonstrated by design of $Q > 10^6$ resonant cavities in 1d and 2d dielectric systems.

physics.optics↗

arXiv2025

Indexed singular value bounds on scattering operators: How many channels can a photonic device support?

Spectral properties of scattering operators, and their dependence on geometry, are of crucial importance to photonic design, enabling low-rank approximations and improved understanding of achievable power and information transfer. Here, we develop a method to bound indexed singular values (channel amplitudes) of the Green operator, $W$-operator, and proposed $P$-operator, for arbitrarily structured linear media. The approach yields computable upper bounds on the $n^{th}$ singular value, for any given $n$, that capture the complexity of multi-channel tradeoffs and competing scattering effects. As illustrations of the framework, channel bounds are provided for multi-wavelength three-dimensional ``mediating'' volumes (up to $64\,\lambda^3$, mimicking communication waveguide-like and metasurface-like configurations), power transfer between $9\,\lambda^3$ source and receiver volumes, and applied to elucidate the performance of a planewave angle discrimination problem (bounding the smallest singular value, or condition number, of a fixed input space). In addition to these exemplary uses, the approach is directly applicable to bounds on information theoretic objectives such as Shannon capacity and Fisher information, as well as computational guarantees, such as error limits for reduced-order models.

physics.optics↗

arXiv2025

Inferring Structure via Duality for Photonic Inverse Design

Led by a result derived from Sion's minimax theorem concerning constraint violation in quadratically constrained quadratic programs (QCQPs) with at least one constraint bounding the possible solution magnitude, we propose a heuristic scheme for photonic inverse design unifying core ideas from adjoint optimization and convex relaxation bounds. Specifically, through a series of alterations to the underlying constraints and objective, the QCQP associated with a given design problem is gradually transformed so that it becomes strongly dual. Once equivalence between primal and dual programs is achieved, a material geometry is inferred from the solution of the modified QCQP. This inferred structure, due to the complementary relationship between the dual and primal programs, encodes overarching features of the optimization landscape that are otherwise difficult to synthesize, and provides a means of initializing secondary optimization methods informed by the global problem context. An exploratory implementation of the framework, presented in a partner manuscript, is found to achieve dramatic improvements for the exemplary photonic design task of enhancing the amount of power extracted from a dipole source near the boundary of a structured material region -- roughly an order of magnitude compared to randomly initialized adjoint-based topology optimization for areas surpassing $10~\lambda^{2}$.

math.OC↗

arXiv2025

Bounds as blueprints: towards optimal and accelerated photonic inverse design

Our ability to structure materials at the nanoscale has, and continues to, enable key advances in optical control. In pursuit of optimal photonic designs, substantial progress has been made on two complementary fronts: bottom-up structural optimizations (inverse design) discover complex high-performing structures but offer no guarantees of optimality; top-down field optimizations (convex relaxations) reveal fundamental performance limits but offer no guarantees that structures meeting the limits exist. We bridge the gap between these two parallel paradigms by introducing a ``verlan'' initialization method that exploits the encoded local and global wave information in duality-based convex relaxations to guide inverse design towards better-performing structures. We illustrate this technique via the challenging problem of Purcell enhancement, maximizing the power extracted from a small emitter in the vicinity of a photonic structure, where ill-conditioning and the presence of competing local maxima lead to sub-optimal designs for adjoint optimization. Structures discovered by our verlan method outperform standard (random) initializations by close to an order of magnitude and approach fundamental performance limits within a factor of two, highlighting the possibility of accessing significant untapped performance improvements.

physics.optics↗

arXiv2025

Sum-of-Squares Bounds on Surface-Enhanced Raman Scattering

Surface-enhanced Raman scattering (SERS) is a critical tool for chemical sensing and spectroscopy, and a key question is how to optimally design nanostructures for maximizing SERS. We present fundamental limits on spatially-averaged SERS via periodic metasurfaces, derived using sum-of-squares (SOS) programming. This work represents the first use of SOS techniques to optics, overcoming difficulties that prior bounding techniques have with regards to non-linear photonic processes with higher order figures of merit. Our bounds on the $\int \lVert \mathbf{E} \rVert^4 \text{d} \mathbf{r}$ SERS enhancement factor for 2D examples demonstrate remarkable tightness when compared with inverse-designed dielectric and metallic structures for both electrical field out-of-plane ($E_z$) and in-plane ($H_z$) polarizations. We show that delocalized high-Q guided modes can achieve significant, theoretically diverging SERS enhancement even in the presence of material loss. For metallic structures, we demonstrate a fundamental performance limitation for $E_z$ polarized drive fields due to surface plasmon excitation restrictions. By varying the separation between Raman-active molecules and the metasurface design region, we also find material-dependent bounds on the maximum strength of field singularities. Our results offer insights into optimal metasurface design strategies for enhancing light-matter interactions, and our methodology may be adapted to the study of other nonlinear photonics design problems.

physics.optics↗

arXiv2024

Maximum Shannon Capacity of Photonic Structures

Information transfer through electromagnetic waves is an important problem that touches a variety of technologically relevant applications, including computing and telecommunications. Prior attempts to establish limits on optical information transfer have treated waves propagating through known photonic structures (including vacuum). In this article, we address fundamental questions concerning optimal information transfer in photonic devices. Combining information theory, wave scattering, and optimization theory, we formulate bounds on the maximum Shannon capacity that may be achieved by structuring senders, receivers, and their environment. Allowing for arbitrary structuring leads to a non-convex problem that is significantly more difficult than its fixed structure counterpart, which is convex and satisfies a known "water-filling" solution. We derive a geometry-agnostic convex relaxation of the problem that elucidates fundamental physics and scaling behavior of Shannon capacity with respect to device parameters and the importance of structuring for enhancing capacity. We also show that in regimes where communication is dominated by power insertion requirements, bounding Shannon capacity maps to a biconvex optimization problem in the basis of singular vectors of the Green's function. This problem admits analytical solutions that give physically intuitive interpretations of channel and power allocation and reveals how Shannon capacity varies with signal-to-noise ratio. Proof of concept numerical examples show that bounds are within an order of magnitude of achievable device performance and successfully predict the scaling of performance with channel noise. The presented methodologies have implications for the optimization of antennas, integrated photonic devices, metasurface kernels, MIMO space-division multiplexers, and waveguides to maximize communication efficiency and bit-rates.

physics.optics↗

arXiv2024

Limitations on bandwidth-integrated passive cloaking

We present a general framework for the computation of structure-agnostic bounds on the performance of passive cloaks over a nonzero bandwidth. We apply this framework in 2D to the canonical scenario of cloaking a circular object. We find that perfect cloaking using a finite-sized isotropic cloak is impossible over any bandwidth, with the bounds scaling linearly with the bandwidth before saturating due to the finite size of the cloak and the presence of material loss. The bounds also exhibit linear scaling with material loss in the cloak and linear scaling with the inverse of the radial thickness of the design region before saturation due to finite-size effects or the presence of material loss. The formulation could readily find applications in the development of cloaking devices, setting expectations and benchmarks for optimal performance.

physics.optics↗

arXiv2024

Physical limits on Raman scattering: the critical role of pump and signal co-design

We present a method for deriving limits on Raman scattering in structured media and exploit it to constrain the maximum Raman signal resulting from a planewave incident on either a single Raman molecule in the vicinity of a structured medium or a designable Raman medium. Results pertaining to metallic and dielectric structures illustrate the importance of accounting for the nonlinear interplay between pump and signal fields, showing that treating the pump-focusing and signal-extraction processes separately, as in prior work, leads to unrealistic enhancements. The formulation could readily find applications in further enhancing surface-enhanced Raman scattering (SERS) spectroscopy and Raman-assisted lasing.

physics.optics↗

arXiv2023

Suppressing electromagnetic local density of states via slow light in lossy quasi-1d gratings

We propose a spectral-averaging procedure that enables computation of bandwidth-integrated local density of states (LDOS) from a single scattering calculation, and exploit it to investigate the minimum extinction achievable from dipolar sources over finite bandwidths in structured media. Structure-agnostic extinction bounds are derived, providing analytical insights into scaling laws and fundamental design tradeoffs with implications to bandwidth and material selection. We find that perfect LDOS suppression over a finite bandwidth $\Delta\omega$ is impossible. Inspired by limits which predict nontrivial $\sqrt{\Delta\omega}$ scaling in systems with material dissipation, we show that pseudogap edge states of quasi-1d bullseye gratings can -- by simultaneously minimizing material absorption and radiation -- yield arbitrarily close to perfect LDOS suppression in the limit of vanishing bandwidth.

physics.optics↗

arXiv2023

Fundamental limits on $χ^{(2)}$ second harmonic generation

Recent advances in fundamental performance limits for power quantities based on Lagrange duality are proving to be a powerful theoretical tool for understanding electromagnetic wave phenomena. To date, however, in any approach seeking to enforce a high degree of physical reality, the linearity of the wave equation plays a critical role. In this manuscript, we generalize the current quadratically constrained quadratic program framework for evaluating linear photonics limits to incorporate nonlinear processes under the undepleted pump approximation. Via the exemplary objective of enhancing second harmonic generation in a (free-form) wavelength-scale structure, we illustrate a model constraint scheme that can be used in conjunction with standard convex relaxations to bound performance in the presence of nonlinear dynamics. Representative bounds are found to anticipate features observed in optimized structures discovered via computational inverse design. The formulation can be straightforwardly modified to treat other frequency-conversion processes, including Raman scattering and four-wave mixing.

physics.optics↗

arXiv2023

Can photonic heterostructures provably outperform single-material geometries?

Recent advances in photonic optimization have enabled calculation of performance bounds for a wide range of electromagnetic objectives, albeit restricted to single-material systems. Motivated by growing theoretical interest and fabrication advances, we present a framework to bound the performance of photonic heterostructures and apply it to investigate maximum absorption characteristics of multilayer films and compact, free-form multi-material scatterers. Limits predict trends seen in topology-optimized geometries -- often coming within factors of two of specific designs -- and may be exploited in conjunction with inverse designs to predict when heterostructures are expected to outperform their optimal single-material counterparts.

physics.optics↗

arXiv2022

Maximum Electromagnetic Local Density of States via Material Structuring

The electromagnetic local density of states (LDOS) is crucial to many aspects of photonics engineering, from enhancing emission of photon sources to radiative heat transfer and photovoltaics. We present a framework for evaluating upper bounds on LDOS in structured media that can handle arbitrary bandwidths and accounts for critical wave scattering effects with no heuristic approximations. The bounds are solely determined by the bandwidth, material susceptibility, and device footprint, with no assumptions on geometry. We derive an analytical expression for the maximum LDOS consistent with the conservation of energy across the entire design domain, which upon benchmarking with topology-optimized structures is shown to be nearly tight for large devices. Novel scaling laws for maximum LDOS enhancement are found: the bounds saturate to a finite value with increasing susceptibility and scale as the quartic root of the bandwidth for semi-infinite structures made of lossy materials, with direct implications on material selection and design applications.

physics.optics↗

arXiv2022

Trace Expressions and Associated Limits for Non-Equilibrium Casimir Torque

We exploit fluctuational electrodynamics to present trace expressions for the torque experienced by arbitrary objects in a passive, non-absorbing, rotationally invariant background environment. Specializing to a single object, this formalism, together with recently developed techniques for calculating bounds via Lagrange duality, is then used to derive limits on the maximum Casimir torque that a single object with an isotropic electric susceptibility can experience when out of equilibrium with its surrounding environment. The maximum torque achievable at any wavelength is shown to scale in proportion to body volumes in both subwavelength (quasistatics) and macroscopic (ray optics) settings, and come within an order of magnitude of achievable torques on topology optimized bodies. Finally, we discuss how to extend the formalism to multiple bodies, deriving expressions for the torque experienced by two subwavelength particles in proximity to one another.

physics.optics↗

arXiv2022

On Sion's Minimax Theorem, Compact QCQPs, and Wave Scattering Optimization

In these notes, we examine certain implications of Sion's minimax theorem for compact quadratically constrained quadratic programs (QCQPs), particularly QCQPs arising in the context of optimizing wave scattering, in relation to Lagrangian duality. The discussion puts forward an alternative "dual" understanding of optimization for wave phenomena that anticipates the realization of algorithmic (inverse design) methods attaining a guaranteed degree of global optimality for common figures of merit appearing in applied photonics, acoustics, and quantum mechanics.

math.OC↗

arXiv2021

Physical limits on electromagnetic response

Photonic devices play an increasingly important role in advancing physics and engineering, and while improvements in nanofabrication and computational methods have driven dramatic progress in expanding the range of achievable optical characteristics, they have also greatly increased design complexity. These developments have led to heightened relevance for the study of fundamental limits on optical response. Here, we review recent progress in our understanding of these limits with special focus on an emerging theoretical framework that combines computational optimization with conservation laws to yield physical limits capturing all relevant wave effects. Results pertaining to canonical electromagnetic problems such as thermal emission, scattering cross sections, Purcell enhancement, and power routing are presented. Finally, we identify areas for additional research, including conceptual extensions and efficient numerical schemes for handling large-scale problems.

physics.optics↗

arXiv2021

$\mathbb{T}$-Operator Limits on Optical Communication: Metaoptics, Computation, and Input-Output Transformations

We present an optimization framework based on Lagrange duality and the scattering $\mathbb{T}$ operator of electromagnetism to construct limits on the possible features that may be imparted to a collection of output fields from a collection of input fields, i.e., constraints on achievable optical transformations and the characteristics of structured materials as communication channels. Implications of these bounds on the performance of representative optical devices having multi-wavelength or multiport functionalities are examined in the context of electromagnetic shielding, focusing, near-field resolution, and linear computing.

physics.optics↗