Measurement of Near-Field Radiative Heat Transfer at Deep Sub-Wavelength Distances using Nanomechanical Resonators.

Near-field radiative heat transfer (NFRHT) measurements often rely on custom microdevices that can be difficult to reproduce after their original demonstration. Here we study NFRHT using plain silicon nitride (SiN) membrane nanomechanical resonators─a widely available substrate used in applications such as electron microscopy and optomechanics─and on which other materials can easily be deposited. We report measurements down to a minimal distance of 180 nm between a large radius of curvature (15.5 mm) glass radiator and a SiN membrane resonator. At such deep sub-wavelength distance, heat transfer is dominated by surface polariton resonances over a (0.25 mm)2 effective area, which is comparable to plane-plane experiments employing custom microfabricated devices. We also discuss how measurements using nanomechanical resonators create opportunities for simultaneously measuring near-field radiative heat transfer and thermal radiation forces (e.g., thermal corrections to Casimir forces).

Fundamental limits on radiative 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.

Quantum nonlinear mixing of thermal photons to surpass the blackbody limit.

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 that, as we show, requires quantum theory of damping. Specifically, we analyze thermal radiation from a resonant system containing a χ(2) nonlinear medium and supporting resonances at frequencies ω1 and ω2 ≈ 2ω1, 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) ≠ ~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.

Fundamental Limits to Radiative Heat Transfer: The Limited Role of Nanostructuring in the Near-Field.

In a previous Letter, we derived fundamental limits to radiative heat transfer applicable in near- through far-field regimes, based on the choice of material susceptibilities and bounding surfaces enclosing arbitrarily shaped objects; the limits exploit algebraic properties of Maxwell's equations and fundamental principles such as electromagnetic reciprocity and passivity. In this Letter, 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. 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 very slowly with respect to a material response figure of merit (an "inverse resistivity" for metals) due to the deleterious effects of multiple scattering between bodies. While nanostructuring can produce infrared resonances, it is generally unable to further enhance the resonant energy transfer spectrum beyond what is practically achieved by planar media at the surface polariton condition.

Quantum Rabi Model with Two-Photon Relaxation.

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 or not 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.

T Operator Bounds on Angle-Integrated Absorption and Thermal Radiation for Arbitrary Objects.

We derive fundamental per-channel bounds on angle-integrated absorption and thermal radiation for arbitrarily structured 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 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).

Inverse design of compact multimode cavity couplers.

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.

400%/W second harmonic conversion efficiency in 14 µm-diameter gallium phosphide-on-oxide resonators.

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 ∼ 104, low mode volumes V ∼ 30(λ/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.

Phonon-Polariton Mediated Thermal Radiation and Heat Transfer among Molecules and Macroscopic Bodies: Nonlocal Electromagnetic Response at Mesoscopic Scales.

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 often 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 near macroscopic bodies, conjoining atomistic treatments of electronic and vibrational fluctuations obtained from 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 objects' finite sizes, shapes, and nonlocal or many-body response to electromagnetic fluctuations. We show that, even in small but especially in elongated low-dimensional molecules, 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.

Overcoming limits to near-field radiative heat transfer in uniform planar media through multilayer optimization.

Radiative heat transfer between uniform plates is bounded by the narrow range and limited contribution of surface waves. Using a combination of analytical calculations and numerical gradient-based optimization, we show that such a limitation can be overcome in complicated multilayer geometries, allowing the scattering and coupling rates of slab resonances to be altered over a broad range of evanescent wavevectors. We conclude that while the radiative flux between two inhomogeneous slabs can only be weakly enhanced, the flux between a dipolar particle and an inhomogeneous slab-proportional to the local density of states-can be orders of magnitude larger, albeit at the expense of increased frequency selectivity. A brief discussion of hyperbolic metamaterials shows that they provide far less enhancement than optimized inhomogeneous slabs.

Near-field thermal upconversion and energy transfer through a Kerr medium.

We present an approach for achieving large Kerr χ(3)-mediated thermal energy transfer at the nanoscale that exploits a general coupled-mode description of triply resonant, four-wave mixing processes. We analyze the efficiency of thermal upconversion and energy transfer from mid- to near-infrared wavelengths in planar geometries involving two slabs supporting far-apart surface plasmon polaritons and separated by a nonlinear χ(3) medium that is irradiated by externally incident light. We study multiple geometric and material configurations and different classes of intervening mediums-either bulk or nanostructured lattices of nanoparticles embedded in nonlinear materials-designed to resonantly enhance the interaction of the incident light with thermal slab resonances. We find that even when the entire system is in thermodynamic equilibrium (at room temperature) and under typical drive intensities ~ W/µm2, the resulting upconversion rates can approach and even exceed thermal flux rates achieved in typical symmetric and non-equilibrium configurations of vacuum-separated slabs. The proposed nonlinear scheme could potentially be exploited to achieve thermal cooling and refrigeration at the nanoscale, and to actively control heat transfer between materials with dramatically different resonant responses.

General theory of spontaneous emission near exceptional points.

We present a general theory of spontaneous emission at exceptional points (EPs)-exotic degeneracies in non-Hermitian systems. Our theory extends beyond spontaneous emission to any light-matter interaction described by the local density of states (e.g., absorption, thermal emission, and nonlinear frequency conversion). Whereas traditional spontaneous-emission theories imply infinite enhancement factors at EPs, we derive finite bounds on the enhancement, proving maximum enhancement of 4 in passive systems with second-order EPs and significantly larger enhancements (exceeding 400×) in gain-aided and higher-order EP systems. In contrast to non-degenerate resonances, which are typically associated with Lorentzian emission curves in systems with low losses, EPs are associated with non-Lorentzian lineshapes, leading to enhancements that scale nonlinearly with the resonance quality factor. Our theory can be applied to dispersive media, with proper normalization of the resonant modes.

Topology optimization of multi-track ring resonators and 2D microcavities for nonlinear frequency conversion.

We exploit recently developed topology-optimization techniques to design complex, wavelength-scale resonators for enhancing various nonlinear χ(2) and χ(3) frequency conversion processes. In particular, we demonstrate aperiodic, multi-track ring resonators and two-dimensional slab microcavities exhibiting long lifetimes Q≳104, small modal volumes V≳(λ/2n)3, and among the largest nonlinear overlaps (a generalization of phase matching in large-etalon waveguides) possible, paving the way for efficient, compact, and wide-bandwdith integrated nonlinear devices.

Unifying Microscopic and Continuum Treatments of van der Waals and Casimir Interactions.

We present an approach for computing long-range van der Waals (vdW) interactions between complex molecular systems and arbitrarily shaped macroscopic bodies, melding atomistic treatments of electronic fluctuations based on density functional theory in the former with continuum descriptions of strongly shape-dependent electromagnetic fields in the latter, thus capturing many-body and multiple scattering effects to all orders. Such a theory is especially important when considering vdW interactions at mesoscopic scales, i.e., between molecules and structured surfaces with features on the scale of molecular sizes, in which case the finite sizes, complex shapes, and resulting nonlocal electronic excitations of molecules are strongly influenced by electromagnetic retardation and wave effects that depend crucially on the shapes of surrounding macroscopic bodies. We show that these effects together can modify vdW interaction energies and forces, as well as molecular shapes deformed by vdW interactions, by orders of magnitude compared to previous treatments based on Casimir-Polder, nonretarded, or pairwise approximations, which are valid only at macroscopically large or atomic-scale separations or in dilute insulating media, respectively.

Absolute position total internal reflection microscopy with an optical tweezer.

A noninvasive, in situ calibration method for total internal reflection microscopy (TIRM) based on optical tweezing is presented, which greatly expands the capabilities of this technique. We show that by making only simple modifications to the basic TIRM sensing setup and procedure, a probe particle's absolute position relative to a dielectric interface may be known with better than 10 nm precision out to a distance greater than 1 µm from the surface. This represents an approximate 10× improvement in error and 3× improvement in measurement range over conventional TIRM methods. The technique's advantage is in the direct measurement of the probe particle's scattering intensity vs. height profile in situ, rather than relying on assumptions, inexact system analogs, or detailed knowledge of system parameters for calibration. To demonstrate the improved versatility of the TIRM method in terms of tunability, precision, and range, we show our results for the hindered near-wall diffusion coefficient for a spherical dielectric particle.

Enhanced Spontaneous Emission at Third-Order Dirac Exceptional Points in Inverse-Designed Photonic Crystals.

We formulate and exploit a computational inverse-design method based on topology optimization to demonstrate photonic crystal structures supporting complex spectral degeneracies. In particular, we discover photonic crystals exhibiting third-order Dirac points formed by the accidental degeneracy of monopolar, dipolar, and quadrupolar modes. We show that, under suitable conditions, these modes can coalesce and form a third-order exceptional point, leading to strong modifications in the spontaneous emission (SE) of emitters, related to the local density of states. We find that SE can be enhanced by a factor of 8 in passive structures, with larger enhancements ∼sqrt[n^{3}] possible at exceptional points of higher order n.

Enabling enhanced emission and low-threshold lasing of organic molecules using special Fano resonances of macroscopic photonic crystals.

The nature of light interaction with matter can be dramatically altered in optical cavities, often inducing nonclassical behavior. In solid-state systems, excitons need to be spatially incorporated within nanostructured cavities to achieve such behavior. Although fascinating phenomena have been observed with inorganic nanostructures, the incorporation of organic molecules into the typically inorganic cavity is more challenging. Here, we present a unique optofluidic platform comprising organic molecules in solution suspended on a photonic crystal surface, which supports macroscopic Fano resonances and allows strong and tunable interactions with the molecules anywhere along the surface. We develop a theoretical framework of this system and present a rigorous comparison with experimental measurements, showing dramatic spectral and angular enhancement of emission. We then demonstrate that these enhancement mechanisms enable lasing of only a 100-nm thin layer of diluted solution of organic molecules with substantially reduced threshold intensity, which has important implications for organic light-emitting devices and molecular sensing.

Shape-Independent Limits to Near-Field Radiative Heat Transfer.

We derive shape-independent limits to the spectral radiative heat transfer rate between two closely spaced bodies, generalizing the concept of a blackbody to the case of near-field energy transfer. Through conservation of energy and reciprocity, we show that each body of susceptibility χ can emit and absorb radiation at enhanced rates bounded by |χ|(2)/Im χ, optimally mediated by near-field photon transfer proportional to 1/d(2) across a separation distance d. Dipole-dipole and dipole-plate structures approach restricted versions of the limit, but common large-area structures do not exhibit the material enhancement factor and thus fall short of the general limit. By contrast, we find that particle arrays interacting in an idealized Born approximation (i.e., neglecting multiple scattering) exhibit both enhancement factors, suggesting the possibility of orders-of-magnitude improvement beyond previous designs and the potential for radiative heat transfer to be comparable to conductive heat transfer through air at room temperature, and significantly greater at higher temperatures.

Effectiveness of thin films in lieu of hyperbolic metamaterials in the near field.

We show that the near-field functionality of hyperbolic metamaterials (HMM), typically proposed for increasing the photonic local density of states (LDOS), can be achieved with thin metal films. Although HMMs have an infinite density of internally propagating plane-wave states, the external coupling to nearby emitters is severely restricted. We show analytically that properly designed thin films, of thicknesses comparable to the metal size of a hyperbolic metamaterial, yield an LDOS as high as (if not higher than) that of HMMs. We illustrate these ideas by performing exact numerical computations of the LDOS of multilayer HMMs, along with their application to the problem of maximizing near-field heat transfer, to show that single-layer thin films are suitable replacements in both cases.

Optomechanical and photothermal interactions in suspended photonic crystal membranes.

We present here an optomechanical system fabricated with novel stress management techniques that allow us to suspend an ultrathin defect-free silicon photonic-crystal membrane above a Silicon-on-Insulator (SOI) substrate with a gap that is tunable to below 200 nm. Our devices are able to generate strong attractive and repulsive optical forces over a large surface area with simple in- and out- coupling and feature the strongest repulsive optomechanical coupling in any geometry to date (gOM/2π ≈65 GHz/nm). The interplay between the optomechanical and photo-thermal-mechanical dynamics is explored, and the latter is used to achieve cooling and amplification of the mechanical mode, demonstrating that our platform is well-suited for potential applications in low-power mass, force, and refractive-index sensing as well as optomechanical accelerometry.