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We derive a mesoscopic theory of the Josephson junction from non-relativistic scalar electrodynamics. Our theory reproduces the Josephson relations with the canonical current phase relation acquiring a weak second harmonic term, and it improves the standard lumped-element descriptions employed in circuit quantum electrodynamics by providing spatial resolution of the superconducting order parameter and electromagnetic field. By providing an ab initio derivation of the charge qubit Hamiltonian that relates traditionally free qubit parameters to geometric and material properties, we progress toward the quantum engineering of superconducting circuits at the subnanometer scale.

Nonlinear metasurfaces offer a new paradigm to realize optical nonlinear devices with new and unparalleled behavior compared to nonlinear crystals, due to the interplay between photonic resonances and materials properties. The complicated interdependency between efficiency and emission directionality of the nonlinear optical signal on the existence, localization, and lifetimes of photonic resonances, as well as on the nonlinear susceptibility, makes it extremely difficult to design optimal metasurfaces using conventional materials and geometries. Inverse design using topology optimization is a powerful design tool for photonic structures, but traditional approaches developed for linear photonics are not suitable for such high dimensional nonlinear problems. Here, we use a topology optimization approach to inverse-design a fabrication-robust nonlinear metasurface that includes quantum-engineered resonant nonlinearities in semiconductor heterostructures for efficient and directional second harmonic generation. Furthermore, we also demonstrate that under practical constraints, among all the parameters, the nonlinear modal overlap emerges as the dominant parameter that enhances conversion efficiency, a finding that contrasts with intuition-driven studies that often emphasize Purcell enhancement. Our results open new opportunities for optimizing nonlinear processes in nanophotonic structures for novel light sources, quantum information applications, and communication.

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., Comment: Alessio Amaolo and Pengning Chao contributed equally to this work. 19 pages, 3 figures

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.

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., Comment: 12 pages, 4 figures

We exploit fluctuational electrodynamics to present trace expressions for the torque experienced by arbitrary objects in a passive, nonabsorbing, rotationally invariant background environment. We present trace expressions for equilibrium Casimir torque which complement recently derived nonequilibrium torque expressions and explicate their relation to the Casimir free energy. We then use the derived trace expressions to calculate, via Lagrange duality, semianalytic structure-agnostic bounds on the Casimir torque between an anisotropic (reciprocal or nonreciprocal) dipolar particle and a macroscopic body composed of a local isotropic electric susceptibility, separated by vacuum.

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.

The NV$^-$ color center in diamond has been extensively investigated for quantum sensing, computation, and communication applications. Nonetheless, charge-state decay from the NV$^-$ to its neutral counterpart the NV$^0$ detrimentally affects the robustness of the NV$^-$ center and remains to be fully overcome. In this work, we provide an $ab~initio$ formalism for accurately estimating the rate of charge-state decay of color centers in wide-bandgap semiconductors. Our formalism employs density functional theory calculations in the context of thermal equilibrium. We illustrate the method using the transition of NV$^-$ to NV$^0$ in the presence of substitutional N [see Z. Yuan $et~al$., PRR 2, 033263 (2020)].

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., Comment: 10 pages, 4 figures

By applying a hydrodynamic representation of non-relativistic scalar electrodynamics to the superconducting order parameter, we predict a negative (attractive) pressure between planar superconducting bodies. For conventional superconductors with London penetration depth $\lambda_\text{L} \approx 100 \text{ nm}$, the pressure reaches tens of $\text{N/mm}^2$ at angstrom separations. The resulting surface energies are in better agreement with experimental values than those predicted by the Hartree-Fock theory, and the emergent electric-field screening length is comparable to that of the Thomas-Fermi theory. The model circumvents the bulk limitations of the Bardeen-Cooper-Schrieffer and Ginzburg-Landau theories to the analysis of superconducting quantum devices., Comment: 8 pages, 1 figure

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., Comment: 12 pages, 5 figures

Charge traps in the semiconductor bulk (bulk charge traps) make it difficult to predict the electric field within wide-bandgap semiconductors. The issue is the daunting number of bulk charge-trap candidates which means the treatment of bulk charge traps is generally qualitative or uses generalized models that do not consider the trap's particular electronic structure. The electric field within a wide-bandgap semiconductor is nonetheless a crucial quantity in determining the operation of semiconductor devices and the performance of solid-state single-photon emitters embedded within the semiconductor devices. In this work we accurately compute the average electric field measured at the location of N$V^-$ charged defects for the substitutional N (N$_\text{C}$) concentration of $n_{\text{N}_\text{C}} \approx 1.41\times10^{18}$ cm$^{-3}$ for the commonly used oxygen-terminated diamond (see [D. A. Broadway $et$ $al$., Nature Electronics 1, 502 (2018)]). We achieve this result by evaluating the leading-order contribution to the electric field far away from the surface, which comes from the N$_\text{C}$ defects that induce the ionization of the N$V^-$. Our results use density-functional theory (DFT) and the principle of band bending. Our work has the potential to aid both in the prediction of the functioning of semiconductor devices and in the prediction and correction of the spectral diffusion that often plagues the optical frequencies of solid-state single-photon emitters upon repeated photoexcitation measurements. Our results for the timescales involved in thermally driven charge transfer also have the potential to aid in investigations of charge dynamics.

The process of thermalization in many-body systems is driven by complex interactions among sub-systems and with the surrounding environment. Here we lay the theoretical foundations for the active control of local thermal states in arbitrary non-reciprocal systems close to their equilibrium state. In particular we describe how to (i) force some part of the system to evolve according to a prescribed law during the relaxation process (i.e. thermal targeting probem), (ii) insulate some elements from the rest of the system or (iii) synchronize their evolution during the relaxation process. We also derive the general conditions a system must fulfill in order that some parts relax toward a minimal temperature with a minimum energetic cost or relax toward a prescribed temperature with a minimum time. Finally, we consider several representative examples in the context of systems exchanging heat radiatively.

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.

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., Comment: 22 pages, 8 figures

We show that an isotropic dipolar particle in the vicinity of a substrate made of nonreciprocal plasmonic materials can experience a lateral Casimir force and torque when the particle's temperature differs from that of the slab and the environment. We connect the existence of the lateral force to the asymmetric dispersion of nonreciprocal surface polaritons and the existence of the lateral torque to the spin-momentum locking of such surface waves. Using the formalism of fluctuational electrodynamics, we show that the features of lateral force and torque should be experimentally observable using a substrate of doped Indium Antimonide (InSb) placed in an external magnetic field, and for a variety of dielectric particles. Interestingly, we also find that the directions of the lateral force and the torque depend on the constituent materials of the particles, which suggests a sorting mechanism based on lateral nonequilibrium Casimir physics.

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., Comment: 23 pages, 1 figure

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.

We show how the central equality of scattering theory, the definition of the $\mathbb{T}$ operator, can be used to generate hierarchies of mean-field constraints that act as natural complements to the standard electromagnetic design problem of optimizing some objective with respect to structural degrees of freedom. Proof-of-concept application to the problem of maximizing radiative Purcell enhancement for a dipolar current source in the vicinity of a structured medium, an effect central to many sensing and quantum technologies, yields performance bounds that are frequently more than an order of magnitude tighter than all current frameworks, highlighting the irreality of these models in the presence of differing domain and field-localization length scales. Closely related to domain decomposition and multi-grid methods, similar constructions are possible in any branch of wave physics, paving the way for systematic evaluations of fundamental limits beyond electromagnetism.

Solid-state defect qubit systems with spin-photon interfaces show great promise for quantum information and metrology applications. Photon collection efficiency, however, presents a major challenge for defect qubits in high refractive index host materials. Inverse-design optimization of photonic devices enables unprecedented flexibility in tailoring critical parameters of a spin-photon interface including spectral response, photon polarization and collection mode. Further, the design process can incorporate additional constraints, such as fabrication tolerance and material processing limitations. Here we design and demonstrate a compact hybrid gallium phosphide on diamond inverse-design planar dielectric structure coupled to single near-surface nitrogen-vacancy centers formed by implantation and annealing. We observe device operation near the theoretical limit and measure up to a 14-fold broadband enhancement in photon extraction efficiency. We expect that such inverse-designed devices will enable realization of scalable arrays of single-photon emitters, rapid characterization of new quantum emitters, sensing and efficient heralded entanglement schemes.

Many-body physics aims to understand emergent properties of systems made of many interacting objects. This article reviews recent progress on the topic of radiative heat transfer in many-body systems consisting of thermal emitters interacting in the near-field regime. Near-field radiative heat transfer is a rapidly emerging field of research in which the cooperative behavior of emitters gives rise to peculiar effects which can be exploited to control heat flow at the nanoscale. Using an extension of the standard Polder and van Hove stochastic formalism to deal with thermally generated fields in $N$-body systems, along with their mutual interactions through multiple scattering, a generalized Landauer-like theory is derived to describe heat exchange mediated by thermal photons in arbitrary reciprocal and non-reciprocal multi-terminal systems. In this review, we use this formalism to address both transport and dynamics in these systems from a unified perspective. Our discussion covers: (i) the description of non-additivity of heat flux and its related effects, including fundamental limits as well as the role of nanostructuring and material choice, (ii) the study of equilibrium states and multistable states, (iii) the relaxation dynamics (thermalization) toward local and global equilibria, (iv) the analysis of heat transport regimes in ordered and disordered systems comprised of a large number of objects, density and range of interactions, and (v) the description of thermomagnetic effects in magneto-optical systems and heat transport mechanisms in non-Hermitian many-body systems. We conclude this review by listing outstanding challenges and promising future research directions., Comment: 54 pages, 45 figures

Recent experimental advances probing coherent phonon and electron transport in nanoscale devices at contact have motivated theoretical channel-based analyses of conduction based on the nonequilibrium Green's function formalism. The transmission through each channel has been known to be bounded above by unity, yet actual transmissions in typical systems often fall far below these limits. Building upon recently derived radiative heat transfer limits and a unified formalism characterizing heat transport for arbitrary bosonic systems in the linear regime, we propose new bounds on conductive heat transfer. In particular, we demonstrate that our limits are typically far tighter than the Landauer limits per channel and are close to actual transmission eigenvalues by examining a model of phonon conduction in a 1-dimensional chain. Our limits have ramifications for designing molecular junctions to optimize conduction., Comment: 10 pages, 2 figures, 2 appendices

We present a general nonequilibrium Green's function formalism for modeling heat transfer in systems characterized by linear response that establishes the formal algebraic relationships between phonon and radiative conduction, and reveals how upper bounds for the former can also be applied to the latter. We also propose an extension of this formalism to treat systems susceptible to the interplay of conductive and radiative heat transfer, which becomes relevant in atomic systems and at nanometric and smaller separations where theoretical descriptions which treat each phenomenon separately may be insufficient. We illustrate the need for such coupled descriptions by providing predictions for a low-dimensional system of carbyne wires in which the total heat transfer can differ from the sum of its radiative and conductive contributions. Our framework has ramifications for understanding heat transfer between large bodies that may approach direct contact with each other or that may be coupled by atomic, molecular, or interfacial film junctions., Comment: 16 pages, 2 figures, 1 table, 2 appendices

We present an approach to describing fluctuational electrodynamic (FED) interactions, particularly van der Waals (vdW) interactions as well as radiative heat transfer (RHT), between material bodies of vastly different length scales, allowing for going between atomistic and continuum treatments of the response of each of these bodies as desired. Any local continuum description of electromagnetic (EM) response is compatible with our approach, while atomistic descriptions in our approach are based on effective electronic and nuclear oscillator degrees of freedom, encapsulating dissipation, short-range electronic correlations, and collective nuclear vibrations (phonons). While our previous works using this approach have focused on presenting novel results, this work focuses on the derivations underlying these methods. First, we show how the distinction between "atomic" and "macroscopic" bodies is ultimately somewhat arbitrary, as formulas for vdW free energies and RHT look very similar regardless of how the distinction is drawn. Next, we demonstrate that the atomistic description of material response in our approach yields EM interaction matrix elements which are expressed in terms of analytical formulas for compact bodies or semianalytical formulas based on Ewald summation for periodic media; we use this to compute vdW interaction free energies as well as RHT powers among small biological molecules in the presence of a metallic plate as well as between parallel graphene sheets in vacuum, showing strong deviations from conventional macroscopic theories due to the confluence of geometry, phonons, and EM retardation effects. Finally, we propose formulas for efficient computation of FED interactions among material bodies in which those that are treated atomistically as well as those treated through continuum methods may have arbitrary shapes, extending previous surface-integral techniques., Comment: 25 pages, 5 figures, 2 appendices

We present a method based on the scattering $\mathbb{T}$ operator, and conservation of net real and reactive power, to provide physical bounds on any electromagnetic design objective that can be framed as a net radiative emission, scattering or absorption process. Application of this approach to planewave scattering from an arbitrarily shaped, compact body of homogeneous electric susceptibility $\chi$ is found to predictively quantify and differentiate the relative performance of dielectric and metallic materials across all optical length scales. When the size of a device is restricted to be much smaller than the wavelength (a subwavelength cavity, antenna, nanoparticle, etc.), the maximum cross section enhancement that may be achieved via material structuring is found to be much weaker than prior predictions: the response of strong metals ($\mathrm{Re}[\chi] < 0$) exhibits a diluted (homogenized) effective medium scaling $\propto |\chi| / \mathrm{Im}[\chi]$; below a threshold size inversely proportional to the index of refraction (consistent with the half-wavelength resonance condition), the maximum cross section enhancement possible with dielectrics ($\mathrm{Re}[\chi] > 0$) shows the same material dependence as Rayleigh scattering. In the limit of a bounding volume much larger than the wavelength in all dimensions, achievable scattering interactions asymptote to the geometric area, as predicted by ray optics. For representative metal and dielectric materials, geometries capable of scattering power from an incident plane wave within an order of magnitude (typically a factor of two) of the bound are discovered by inverse design. The basis of the method rests entirely on scattering theory, and can thus likely be applied to acoustics, quantum mechanics, and other wave physics.

We derive upper and lower bounds on the Casimir--Polder force between an anisotropic dipolar body and a macroscopic body separated by vacuum via algebraic properties of Maxwell's equations. These bounds require only a coarse characterization of the system---the material composition of the macroscopic object, the polarizability of the dipole, and any convenient partition between the two objects---to encompass all structuring possibilities. We find that the attractive Casimir--Polder force between a polarizable dipole and a uniform planar semi-infinite bulk medium always comes within 10% of the lower bound, implying that nanostructuring is of limited use for increasing attraction. In contrast, the possibility of repulsion is observed even for isotropic dipoles, and is routinely found to be several orders of magnitude larger than any known design, including recently predicted geometries involving conductors with sharp edges. Our results have ramifications for the design of surfaces to trap, suspend, or adsorb ultracold gases., Comment: 6 pages, 3 figures

Nearly all thermal radiation phenomena involving materials with linear response can be accurately described via semi-classical theories of light. Here, we go beyond these traditional paradigms to study a nonlinear system which, as we show, necessarily requires quantum theory of damping. Specifically, we analyze thermal radiation from a resonant system containing a $\chi^{(2)}$ nonlinear medium and supporting resonances at frequencies $\omega_1$ and $\omega_2\approx 2\omega_1$, where both resonators are driven only by intrinsic thermal fluctuations. Within our quantum formalism, we reveal new possibilities for shaping the thermal radiation. We show that the resonantly enhanced nonlinear interaction allows frequency-selective enhancement of thermal emission through upconversion, surpassing the well-known blackbody limits associated with linear media. Surprisingly, we also find that the emitted thermal light exhibits non-trivial statistics ($g^{(2)}(0) \neq 2$) and biphoton intensity correlations (at two distinct frequencies). We highlight that these features can be observed in the near future by heating a properly designed nonlinear system, without the need for any external signal. Our work motivates new interdisciplinary inquiries combining the fields of nonlinear photonics, quantum optics and thermal science.

We derive fundamental per-channel bounds on angle-integrated absorption and thermal radiation for arbitrary bodies---for any given material susceptibility and bounding region---that simultaneously encode both the per-volume limit on polarization set by passivity and geometric constraints on radiative efficiencies set by finite object sizes through the scattering $\mathbb{T}$-operator. We then analyze these bounds in two practical settings, comparing against prior limits as well as near optimal structures discovered through topology optimization. Principally, we show that the bounds properly capture the physically observed transition from the volume scaling of absorptivity seen in deeply subwavelength objects (nanoparticle radius or thin film thickness) to the area scaling of absorptivity seen in ray optics (blackbody limits)., Comment: 9 pages including appendices, 2 figures, 1 table

Near-field radiative heat transfer between bodies at the nanoscale can surpass blackbody limits on thermal radiation by orders of magnitude due to contributions from evanescent electromagnetic fields, which carry no energy to the far-field. Thus far, principles guiding explorations of larger heat transfer beyond planar structures have assumed utility in surface nanostructuring, which can enhance the density of states, and further assumed that such design paradigms can approach Landauer limits, in analogy to conduction. We derive fundamental shape-independent limits to radiative heat transfer, applicable in near- through far-field regimes, that incorporate material and geometric constraints such as intrinsic dissipation and finite object sizes, and show that these preclude reaching the Landauer limits in all but a few restrictive scenarios. Additionally, we show that the interplay of material response and electromagnetic scattering among proximate bodies means that bodies which maximize radiative heat transfer actually maximize scattering rather than absorption. Finally, we compare our new bounds to existing Landauer limits, as well as limits involving bodies maximizing far-field absorption, and show that these lead to overly optimistic predictions. Our results have ramifications for the ultimate performance of thermophotovoltaics and nanoscale cooling, as well as related incandescent and luminescent devices., Comment: 12 pages including appendices, 1 figure; SM and PSV contributed equally

In a complementary article, we exploited algebraic properties of Maxwell's equations and fundamental principles such as electromagnetic reciprocity and passivity, to derive fundamental limits to radiative heat transfer applicable in near- through far-field regimes. The limits depend on the choice of material susceptibilities and bounding surfaces enclosing arbitrarily shaped objects. In this article, we apply these bounds to two different geometric configurations of interest, namely dipolar particles or extended structures of infinite area in the near field of one another, and compare these predictions to prior limits. We find that while near-field radiative heat transfer between dipolar particles can saturate purely geometric "Landauer" limits, bounds on extended structures cannot, instead growing much more slowly with respect to a material response figure of merit, an "inverse resistivity" for metals, due to the deleterious effects of multiple scattering; nanostructuring is unable to overcome these limits, which can be practically reached by planar media at the surface polariton condition.

One of the central problems in animal and plant developmental biology is deciphering how chemical and mechanical signals interact within a tissue to produce organs of defined size, shape and function. Cell walls in plants impose a unique constraint on cell expansion since cells are under turgor pressure and do not move relative to one another. Cell wall extensibility and constantly changing distribution of stress on the wall are mechanical properties that vary between individual cells and contribute to rates of expansion and orientation of cell division. How exactly cell wall mechanical properties influence cell behavior is still largely unknown. To address this problem, a novel, subcellular element computational model of growth of stem cells within the multilayered shoot apical meristem (SAM) of Arabidopsis thaliana is developed and calibrated using experimental data. Novel features of the model include separate, detailed descriptions of cell wall extensibility and mechanical stiffness, deformation of the middle lamella and increase in cytoplasmic pressure generating internal turgor pressure. The model is used to test novel hypothesized mechanisms of formation of the shape and structure of the growing, multilayered SAM based on WUS concentration of individual cells controlling cell growth rates and layer dependent anisotropic mechanical properties of subcellular components of individual cells determining anisotropic cell expansion directions. Model simulations also provide a detailed prediction of distribution of stresses in the growing tissue which can be tested in future experiments.

Second harmonic conversion from 1550~nm to 775~nm with an efficiency of 400% W$^{-1}$ is demonstrated in a gallium phosphide (GaP) on oxide integrated photonic platform. The platform consists of doubly-resonant, phase-matched ring resonators with quality factors $Q \sim 10^4$, low mode volumes $V \sim 30 (\lambda/n)^3$, and high nonlinear mode overlaps. Measurements and simulations indicate that conversion efficiencies can be increased by a factor of 20 by improving the waveguide-cavity coupling to achieve critical coupling in current devices., Comment: 13 pages, 6 figures

Van der Waals (vdW) and Casimir interactions depend crucially on material properties and geometry, especially at molecular scales, and temperature can produce noticeable relative shifts in interaction characteristics. Despite this, common treatments of these interactions ignore electromagnetic retardation, atomism, or contributions of collective mechanical vibrations (phonons) to the infrared response, which can interplay with temperature in nontrivial ways. We present a theoretical framework for computing electromagnetic interactions among molecular structures, accounting for their geometry, electronic delocalization, short-range interatomic correlations, dissipation, and phonons at atomic scales, along with long-range electromagnetic interactions among themselves or in the vicinity of continuous macroscopic bodies. We find that in carbon allotropes, particularly fullerenes, carbyne wires, and graphene sheets, phonons can couple strongly with long-range electromagnetic fields, especially at mesoscopic scales (nanometers), to create delocalized phonon polaritons that significantly modify the infrared molecular response. These polaritons especially depend on the molecular dimensionality and dissipation, and in turn affect the vdW interaction free energies of these bodies above a macroscopic gold surface, producing nonmonotonic power laws and nontrivial temperature variations at nanometer separations that are within the reach of current Casimir force experiments., Comment: 11 pages, 4 figures (3 single-column, 1 double-column), 2 appendices

We study a cavity-QED setup consisting of a two-level system coupled to a single cavity mode with two-photon relaxation. The system dynamics is modeled via a Lindblad master equation consisting of the Rabi Hamiltonian and a two-photon dissipator. We show that an even-photon relaxation preserves the $Z_2$ symmetry of the Rabi model, and provide a framework to study the corresponding non-Hermitian dynamics in the number-parity basis. We discuss the role of different terms in the two-photon dissipator and show how one can extend existing results for the closed Rabi spectrum to the open case. Furthermore, we characterize the role of the $Z_2$ symmetry in the excitation-relaxation dynamics of the system as a function of light-matter coupling. Importantly, we observe that initial states with even-odd parity manifest qualitatively distinct transient and steady state behaviors, contrary to the Hermitian dynamics that is only sensitive to whether the initial state is parity-invariant. Moreover, the parity-sensitive dynamical behavior is not a creature of ultrastrong coupling and is present even at weak coupling values., Comment: 14 pages, 8 figures and 1 table

Thermal radiative phenomena can be strongly influenced by the coupling of phonons and long-range electromagnetic fields at infrared frequencies. Typically employed macroscopic descriptions of thermal fluctuations tend to ignore atomistic effects that become relevant at nanometric scales, whereas purely microscopic treatments ignore long-range, geometry-dependent electromagnetic effects. We describe a mesoscopic framework for modeling thermal fluctuation phenomena among molecules in the vicinity of macroscopic bodies, conjoining atomistic treatments of electronic and vibrational fluctuations obtained from ab-initio density functional theory in the former with continuum descriptions of electromagnetic scattering in the latter. The interplay of these effects becomes particularly important at mesoscopic scales, where phonon polaritons can be strongly influenced by the finite sizes, shapes, and non-local/many-body response of the bodies to electromagnetic fluctuations. We show that even in small but especially in elongated low-dimensional molecular systems, such effects can modify thermal emission and heat transfer by orders of magnitude and produce qualitatively different behavior compared to predictions based on local, dipolar, or pairwise approximations valid only in dilute media., Comment: 7 pages, 2 figures, includes supplement as appendix

Efficient coupling between on-chip sources and cavities plays a key role in silicon photonics. However, despite the importance of this basic functionality, there are few systematic design tools to simultaneously control coupling between multiple modes in a compact resonator and a single waveguide. Here, we propose a large-scale adjoint optimization approach to produce wavelength-scale waveguide--cavity couplers operating over tunable and broad frequency bands. We numerically demonstrate couplers discovered by this method that can achieve critical, or nearly critical, coupling between multi-ring cavities and a single waveguide at up to six widely separated wavelengths spanning the $560$--$1500$~nm range of interest for on-chip nonlinear optical devices., Comment: 5 pages, 3 figures

The super-Planckian features of radiative heat transfer in the near-field are known to depend strongly on both material and geometric design properties. However, the relative importance and interplay of these two facets, and the degree to which they can be used to ultimately control energy flow, remains an open question. Recently derived bounds suggest that enhancements as large as $|\chi|^4 \lambda^{2} / \left(\left(4\pi\right)^{2} \Im\left[\chi\right]^{2} d^{2}\right)$ are possible between extended structures (compared to blackbody); but neither geometries reaching this bound, nor designs revealing the predicted material ($\chi$) scaling, have been previously reported. Here, exploiting inverse techniques, in combination with fast computational approaches enabled by the low-rank properties of elliptic operators for disjoint bodies, we investigate this relation between material and geometry on an enlarged space structures. Crucially, we find that the material proportionality given above does indeed emerge in realistic structures. In reaching this result, we also show that (in two dimensions) lossy metals such as tungsten, typically considered to be poor candidate materials for strongly enhancing heat transfer in the near infrared, can be structured to selectively realize flux rates that come within $50\%$ of those exhibited by an ideal pair of resonant lossless metals for separations as small as $2\%$ of a tunable design wavelength., Comment: 6 pages, 2 figures

Recent advancements in computational inverse design have begun to reshape the landscape of structures and techniques available to nanophotonics. Here, we outline a cross section of key developments at the intersection of these two fields: moving from a recap of foundational results to motivation of emerging applications in nonlinear, topological, near-field and on-chip optics., Comment: 13 pages, 6 figures

We modify and extend a recently proposed four-wave mixing scheme [Opt. Express 25 (19),23164 (2017)] for achieving near-field thermal upconversion and energy transfer, to demonstrate efficient thermal refrigeration at low intensities $\sim 10^{-9}$W/m$^2$ over a wide range of gap sizes (from tens to hundreds of nanometers) and operational temperatures (from tens to hundreds of Kelvins). We further exploit the scheme to achieve magnitude and directional tunability of near-field heat exchange between bodies held at different temperatures.

Typically, photonic waveguides designed for nonlinear frequency conversion rely on intuitive and established principles, including index guiding and band gap engineering, and are based on simple shapes with high degrees of symmetry. We show that recently developed inverse-design techniques can be applied to discover new kinds of microstructured fibers and metasurfaces designed to achieve large nonlinear frequency conversion efficiencies. As a proof of principle, we demonstrate complex, wavelengthscale chalcogenide glass fibers and gallium phosphide metasurfaces exhibiting some of the largest nonlinear conversion efficiencies predicted thus far. Such enhancements arise because, in addition to enabling a great degree of tunability in the choice of design wavelengths, these optimization tools ensure both frequency- and phase-matching in addition to large nonlinear overlap factors, potentially orders of magnitude larger than those obtained in hand-designed structures.

We present new theoretical tools, based on fluctuational electrodynamics and the integral-equation approach to computational electromagnetism, for numerical modeling of forces and torques on bodies of complex shapes and materials due to emission of thermal radiation out of thermal equilibrium. This extends our recently-developed fluctuating-surface-current (FSC) and fluctuating-volume-current (FVC) techniques for radiative heat transfer to the computation of non-equilibrium fluctuation-induced forces and torques; as we show, the extension is non-trivial due to the greater computational cost of modeling radiative momentum transfer, including new singularities that must be carefully neutralized. We introduce a new analytical cancellation technique that addresses these challenges and allows, for the first time, accurate and efficient prediction of non-equilibrium forces and torques on bodies of essentially arbitrary shapes---including asymmetric and chiral particles---and complex material properties, including continuously-varying and anisotropic dielectrics. We validate our approach by showing that it reproduces known results, then present new numerical predictions of non-equilibrium self-propulsion, self-rotation, and momentum-transfer phenomena in complex geometries that would be difficult or impossible to study with existing methods. Our findings indicate that the fluctuation-induced dynamics of micron-size room-temperature bodies in cold environments involve microscopic length scales but macroscopic time scales, with typical linear and angular velocities on the order of microns/second and radians/second; For a micron-scale gear driven by thermal radiation from a nearby chiral emitter, we find a strong and non-monotonic dependence of the magnitude and even the \textit{sign} of the induced torque on the temperature of the emitter., Comment: 18 pages, 9 figures

We propose a general topology optimization framework for metasurface inverse design that can automatically discover highly complex multi-layered meta-structures with increased functionalities. In particular, we present topology-optimized multi-layered geometries exhibiting angular phase control, including a single-piece nanophotonic metalens with angular aberration correction as well as an angle-convergent metalens that focuses light onto the same focal spot regardless of the angle of incidence.

We derive analytical formulas quantifying radiative emission from subwavelength emitters embedded in triply resonant nonlinear $\chi^{(2)}$ cavities supporting exceptional points (EP) made of dark and leaky modes. We show that the up-converted radiation rate in such a system can be greatly enhanced---by up to two orders of magnitude---compared to typical Purcell factors achievable in non-degenerate cavities, for both monochromatic and broadband emitters. We provide a proof-of-concept demonstration by studying an inverse-designed 2D photonic-crystal slab that supports an EP formed out of a Dirac cone at the emission frequency and a phase-matched, leaky-mode resonance at the second harmonic frequency.

Radiative heat-transport mediated by near-field interactions is known to be superdiffusive in dilute, many-body systems. In this Letter we use a generalized Landauer theory of radiative heat transfer in many-body planar systems to demonstrate a nonmonotonic transition from superdiffusive to ballistic transport in dense systems. We show that such a transition is associated to a change of the polarization of dominant modes, leading to dramatically different thermal relaxation dynamics spanning over three orders of magnitude. This result could have important consequences on thermal management at nanoscale of many-body systems., Comment: 5 pages, 4 figures

We present a scheme for achieving thermal bistability based on the selective coupling of three optical resonances. This approach requires one of the resonant frequencies to be temperature dependent, which can occur in materials exhibiting strong thermo-optic effects. For illustration, we explore thermal bistability in two different passive systems, involving either a periodic array of Si ring resonators or parallel GaAs thin films separated by vacuum and exchanging heat in the near field. Such a scheme could prove useful for thermal memory devices operating with transition times $\lesssim$ hundreds of milliseconds.