Scalable and robust beam shaping using apodized fish-bone grating couplers.

Efficient power coupling between on-chip guided and free-space optical modes requires precision spatial mode matching with apodized grating couplers. Yet, grating apodizations are often limited by the minimum feature size of the fabrication approach. This is especially challenging when small feature sizes are required to fabricate gratings at short wavelengths or to achieve weakly scattered light for large-area gratings. Here, we demonstrate a fish-bone grating coupler for precision beam shaping and the generation of millimeter-scale beams at 461 nm wavelength. Our design decouples the minimum feature size from the minimum achievable optical scattering strength, allowing smooth turn-on and continuous control of the emission. Our approach is compatible with commercial foundry photolithography and has reduced sensitivity to both the resolution and the variability of the fabrication approach compared to subwavelength meta-gratings, which often require electron beam lithography.

Integrating planar photonics for multi-beam generation and atomic clock packaging on chip.

The commercialization of atomic technologies requires replacing laboratory-scale laser setups with compact and manufacturable optical platforms. Complex arrangements of free-space beams can be generated on chip through a combination of integrated photonics and metasurface optics. In this work, we combine these two technologies using flip-chip bonding and demonstrate an integrated optical architecture for realizing a compact strontium atomic clock. Our planar design includes twelve beams in two co-aligned magneto-optical traps. These beams are directed above the chip to intersect at a central location with diameters as large as 1 cm. Our design also includes two co-propagating beams at lattice and clock wavelengths. These beams emit collinearly and vertically to probe the center of the magneto-optical trap, where they will have diameters of ≈100 µm. With these devices we demonstrate that our integrated photonic platform is scalable to an arbitrary number of beams, each with different wavelengths, geometries, and polarizations.

Surface-Normal Free-Space Beam Projection via Slow-Light Standing-Wave Resonance Photonic Gratings.

On-chip grating couplers directly connect photonic circuits to free-space light. The commonly used photonic gratings have been specialized for small areas, specific intensity profiles, and nonvertical beam projection. This falls short of the precise and flexible wavefront control over large beam areas needed to empower emerging integrated miniaturized optical systems that leverage volumetric light-matter interactions, including trapping, cooling, and interrogation of atoms, bio- and chemi- sensing, and complex free-space interconnect. The large coupler size challenges general inverse design techniques, and solutions obtained by them are often difficult to physically understand and generalize. Here, by posing the problem to a carefully constrained computational inverse-design algorithm capable of large area structures, we discover a qualitatively new class of grating couplers. The numerically found solutions can be understood as coupling an incident photonic slab mode to a spatially extended slow-light (near-zero refractive index) region, backed by a reflector. The structure forms a spectrally broad standing wave resonance at the target wavelength, radiating vertically into free space. A reflectionless adiabatic transition critically couples the incident photonic mode to the resonance, and the numerically optimized lower cladding provides 70% overall theoretical conversion efficiency. We have experimentally validated an efficient surface normal collimated emission of ≈90 µm full width at half-maximum Gaussian at the thermally tunable operating wavelength of ≈780 nm. The variable-mesh-deformation inverse design approach scales to extra large photonic devices, while directly implementing the fabrication constraints. The deliberate choice of smooth parametrization resulted in a novel type of solution, which is both efficient and physically comprehensible.

Beating thermal noise in a dynamic signal measurement by a nanofabricated cavity optomechanical sensor.

Thermal fluctuations often impose both fundamental and practical measurement limits on high-performance sensors, motivating the development of techniques that bypass the limitations imposed by thermal noise outside cryogenic environments. Here, we theoretically propose and experimentally demonstrate a measurement method that reduces the effective transducer temperature and improves the measurement precision of a dynamic impulse response signal. Thermal noise-limited, integrated cavity optomechanical atomic force microscopy probes are used in a photothermal-induced resonance measurement to demonstrate an effective temperature reduction by a factor of ≈25, i.e., from room temperature down as low as ≈12 K, without cryogens. The method improves the experimental measurement precision and throughput by >2×, approaching the theoretical limit of ≈3.5× improvement for our experimental conditions. The general applicability of this method to dynamic measurements leveraging thermal noise-limited harmonic transducers will have a broad impact across a variety of measurement platforms and scientific fields.

Highly-twisted states of light from a high quality factor photonic crystal ring.

Twisted light with orbital angular momentum (OAM) has been extensively studied for applications in quantum and classical communications, microscopy, and optical micromanipulation. Ejecting high angular momentum states of a whispering gallery mode (WGM) microresonator through a grating-assisted mechanism provides a scalable, chip-integrated solution for OAM generation. However, demonstrated OAM microresonators have exhibited a much lower quality factor (Q) than conventional WGM resonators (by >100×), and an understanding of the limits on Q has been lacking. This is crucial given the importance of Q in enhancing light-matter interactions. Moreover, though high-OAM states are often desirable, the limits on what is achievable in a microresonator are not well understood. Here, we provide insight on these two questions, through understanding OAM from the perspective of mode coupling in a photonic crystal ring and linking it to coherent backscattering between counter-propagating WGMs. In addition to demonstrating high-Q (105 to 106), a high estimated upper bound on OAM ejection efficiency (up to 90%), and high-OAM number (up to l = 60), our empirical model is supported by experiments and provides a quantitative explanation for the behavior of Q and the upper bound of OAM ejection efficiency with l. The state-of-the-art performance and understanding of microresonator OAM generation opens opportunities for OAM applications using chip-integrated technologies.

Fractional Optical Angular Momentum and Multi-Defect-Mediated Mode Renormalization and Orientation Control in Photonic Crystal Microring Resonators.

Whispering gallery modes (WGMs) in circularly symmetric optical microresonators exhibit integer quantized angular momentum numbers due to the boundary condition imposed by the geometry. Here, we show that incorporating a photonic crystal pattern in an integrated microring can result in WGMs with fractional optical angular momentum. By choosing the photonic crystal periodicity to open a photonic band gap with a band-edge momentum lying between that of two WGMs of the unperturbed ring, we observe hybridized WGMs with half-integer quantized angular momentum numbers (m∈Z+1/2). Moreover, we show that these modes with fractional angular momenta exhibit high optical quality factors with good cavity-waveguide coupling and an order of magnitude reduced group velocity. Additionally, by introducing multiple artificial defects, multiple modes can be localized to small volumes within the ring, while the relative orientation of the delocalized band-edge states can be well controlled. Our Letter unveils the renormalization of WGMs by the photonic crystal, demonstrating novel fractional angular momentum states and nontrivial multimode orientation control arising from continuous rotational symmetry breaking. The findings are expected to be useful for sensing and metrology, nonlinear optics, and cavity quantum electrodynamics.

High Throughput Nanoimaging of Thermal Conductivity and Interfacial Thermal Conductance.

Thermal properties of materials are often determined by measuring thermalization processes; however, such measurements at the nanoscale are challenging because they require high sensitivity concurrently with high temporal and spatial resolutions. Here, we develop an optomechanical cantilever probe and customize an atomic force microscope with low detection noise ≈1 fm/Hz1/2 over a wide (>100 MHz) bandwidth that measures thermalization dynamics with ≈10 ns temporal resolution, ≈35 nm spatial resolution, and high sensitivity. This setup enables fast nanoimaging of thermal conductivity (η) and interfacial thermal conductance (G) with measurement throughputs ≈6000× faster than conventional macroscale-resolution time-domain thermoreflectance acquiring the full sample thermalization. As a proof-of-principle demonstration, 100 × 100 pixel maps of η and G of a polymer particle are obtained in 200 s with a small relative uncertainty (<10%). This work paves the way to study fast thermal dynamics in materials and devices at the nanoscale.

Exceptional points in lossy media lead to deep polynomial wave penetration with spatially uniform power loss.

Waves entering a spatially uniform lossy medium typically undergo exponential intensity decay, arising from either the energy loss of the Beer-Lambert-Bouguer transmission law or the evanescent penetration during reflection. Recently, exceptional point singularities in non-Hermitian systems have been linked to unconventional wave propagation. Here, we theoretically propose and experimentally demonstrate exponential decay free wave propagation in a purely lossy medium. We observe up to 400-wave deep polynomial wave propagation accompanied by a uniformly distributed energy loss across a nanostructured photonic slab waveguide with exceptional points. We use coupled-mode theory and fully vectorial electromagnetic simulations to predict deep wave penetration manifesting spatially constant radiation losses through the entire structured waveguide region regardless of its length. The uncovered exponential decay free wave phenomenon is universal and holds true across all domains supporting physical waves, finding immediate applications for generating large, uniform and surface-normal free-space plane waves directly from dispersion-engineered photonic chip surfaces.

Persistent Nonlinear Phase-Locking and Nonmonotonic Energy Dissipation in Micromechanical Resonators.

Many nonlinear systems are described by eigenmodes with amplitude-dependent frequencies, interacting strongly whenever the frequencies become commensurate at internal resonances. Fast energy exchange via the resonances holds the key to rich dynamical behavior, such as time-varying relaxation rates and signatures of nonergodicity in thermal equilibrium, revealed in the recent experimental and theoretical studies of micro- and nanomechanical resonators. However, a universal yet intuitive physical description for these diverse and sometimes contradictory experimental observations remains elusive. Here we experimentally reveal persistent nonlinear phase-locked states occurring at internal resonances and demonstrate that they are essential for understanding the transient dynamics of nonlinear systems with coupled eigenmodes. The measured dynamics of a fully observable micromechanical resonator system are quantitatively described by the lower-frequency mode entering, maintaining, and exiting a persistent phase-locked period-tripling state generated by the nonlinear driving force exerted by the higher-frequency mode. This model describes the observed phase-locked coherence times, the direction and magnitude of the energy exchange, and the resulting nonmonotonic mode energy evolution. Depending on the initial relative phase, the system selects distinct relaxation pathways, either entering or bypassing the locked state. The described persistent phase locking is not limited to particular frequency fractions or types of nonlinearities and may advance nonlinear resonator systems engineering across physical domains, including photonics as well as nanomechanics.

Overcoming thermo-optical dynamics in broadband nanophotonic sensing.

Advances in integrated photonics open up exciting opportunities for batch-fabricated optical sensors using high-quality-factor nanophotonic cavities to achieve ultrahigh sensitivities and bandwidths. The sensitivity improves with increasing optical power; however, localized absorption and heating within a micrometer-scale mode volume prominently distorts the cavity resonances and strongly couples the sensor response to thermal dynamics, limiting the sensitivity and hindering the measurement of broadband time-dependent signals. Here, we derive a frequency-dependent photonic sensor transfer function that accounts for thermo-optical dynamics and quantitatively describes the measured broadband optomechanical signal from an integrated photonic atomic force microscopy nanomechanical probe. Using this transfer function, the probe can be operated in the high optical power, strongly thermo-optically nonlinear regime, accurately measuring low- and intermediate-frequency components of a dynamic signal while reaching a sensitivity of 0.7 fm/Hz1/2 at high frequencies, an improvement of ≈10× relative to the best performance in the linear regime. Counterintuitively, we discover that a higher transduction gain and sensitivity are achieved with lower quality-factor optical modes for low signal frequencies. Not limited to optomechanical transducers, the derived transfer function is generally valid for describing the small-signal dynamic responses of a broad range of technologically important photonic sensors subject to the thermo-optical effect.

Meta-grating outcouplers for optimized beam shaping in the visible.

Accurate coupling between optical modes at the interface between photonic chips and free space is required for the development of many on-chip devices. This control is critical in quantum technologies where large-diameter beams with designed mode profiles are required. Yet, these designs are often difficult to achieve at shorter wavelengths where fabrication limits the resolution of designed devices. In this work we demonstrate optimized outcoupling of free-space beams at 461 nm using a meta-grating approach that achieves a 16 dB improvement in the apodized outcoupling strength. We design and fabricate devices, demonstrating accurate reproduction of beams with widths greater than 100 µm.

Using thermo-optical nonlinearity to robustly separate absorption and radiation losses in nanophotonic resonators.

Key for optical microresonator engineering, the total intrinsic loss is easily determined by spectroscopy; however, quantitatively separating absorption and radiative losses is challenging, and there is not a general and robust method. Here, we propose and experimentally demonstrate a general all-optical characterization technique for separating the loss mechanisms with high confidence using only linear spectroscopic measurements and an optically measured resonator thermal time constant. We report the absorption, radiation, and coupling losses for ten whispering-gallery modes of three different radial orders on a Si microdisk. Although the total dissipation rates show order-of-magnitude differences, the small absorptive losses are successfully distinguished from the overwhelming radiation losses and show similar values for all the modes as expected for the bulk material absorption.

Kirigami Engineering-Nanoscale Structures Exhibiting a Range of Controllable 3D Configurations.

Kirigami structures provide a promising approach to transform flat films into 3D complex structures that are difficult to achieve by conventional fabrication approaches. By designing the cutting geometry, it is shown that distinct buckling-induced out-of-plane configurations can be obtained, separated by a sharp transition characterized by a critical geometric dimension of the structures. In situ electron microscopy experiments reveal the effect of the ratio between the in-plane cut size and film thickness on out-of-plane configurations. Moreover, geometrically nonlinear finite element analyses (FEA) accurately predict the out-of-plane modes measured experimentally, their transition as a function of cut geometry, and provide the stress-strain response of the kirigami structures. The combined computational-experimental approach and results reported here represent a step forward in the characterization of thin films experiencing buckling-induced out-of-plane shape transformations and provide a path to control 3D configurations of micro- and nanoscale buckling-induced kirigami structures. The out-of-plane configurations promise great utility in the creation of micro- and nanoscale systems that can harness such structural behavior, such as optical scanning micromirrors, novel actuators, and nanorobotics. This work is of particular significance as the kirigami dimensions approach the sub-micrometer scale which is challenging to achieve with conventional micro-electromechanical system technologies.

Fundamental limits and optimal estimation of the resonance frequency of a linear harmonic oscillator.

All physical oscillators are subject to thermodynamic and quantum perturbations, fundamentally limiting measurement of their resonance frequency. Analyses assuming specific ways of estimating frequency can underestimate the available precision and overlook unconventional measurement regimes. Here we derive a general, estimation-method-independent Cramer Rao lower bound for a linear harmonic oscillator resonance frequency measurement uncertainty, seamlessly accounting for the quantum, thermodynamic and instrumental limitations, including Fisher information from quantum backaction- and thermodynamically-driven fluctuations. We provide a universal and practical maximum-likelihood frequency estimator reaching the predicted limits in all regimes, and experimentally validate it on a thermodynamically-limited nanomechanical oscillator. Low relative frequency uncertainty is obtained for both very high bandwidth measurements (≈ 10-5 for τ=30µs) and measurements using thermal fluctuations alone (<10-6). Beyond nanomechanics, these results advance frequency-based metrology across physical domains.

Electron and X-ray Focused Beam-Induced Cross-Linking in Liquids: Toward Rapid Continuous 3D Nanoprinting and Interfacing using Soft Materials.

Multiphoton polymer cross-linking evolves as the core process behind high-resolution additive microfabrication with soft materials for implantable/wearable electronics, tissue engineering, microrobotics, biosensing, drug delivery, etc. Electrons and soft X-rays, in principle, can offer even higher resolution and printing rates. However, these powerful lithographic tools are difficult to apply to vacuum incompatible liquid precursor solutions used in continuous additive fabrication. In this work, using biocompatible hydrogel as a model soft material, we demonstrate high-resolution in-liquid polymer cross-linking using scanning electron and X-ray microscopes. The approach augments the existing solid-state electron/X-ray lithography and beam-induced deposition techniques with a wider class of possible chemical reactions, precursors, and functionalities. We discuss the focused beam cross-linking mechanism, the factors affecting the ultimate feature size, and layer-by-layer printing possibilities. The potential of this technology is demonstrated on a few practically important applications such as in-liquid encapsulation of nanoparticles for plasmonic sensing and interfacing of viable cells with hydrogel electrodes.

Frequency Stabilization of Nanomechanical Resonators Using Thermally Invariant Strain Engineering.

Microfabricated mechanical resonators enable precision measurement techniques from atomic force microscopy to emerging quantum applications. The resonance frequency-based physical sensing combines high precision with long-term stability. However, widely used Si3N4 resonators suffer from frequency sensitivity to temperature due to the differential thermal expansion vs the Si substrates. Here we experimentally demonstrate temperature- and residual stress-insensitive 16.51 MHz tuning fork nanobeam resonators with nonlinear clamps defining the stress and frequency by design, achieving a low fractional frequency sensitivity of (2.5 ± 0.8) × 10-6 K-1, a 72× reduction. On-chip optical readout of resonator thermomechanical fluctuations allows precision frequency measurement without any external excitation at the thermodynamically limited frequency Allan deviation of ≈7 Hz/Hz1/2 and (relative) bias stability of ≈10 Hz (≈ 0.6 × 10-6) above 1 s averaging, remarkably, on par with state-of-the-art driven devices of similar mass. Both the resonator stabilization and the passive frequency readout can benefit a wide variety of micromechanical sensors.

A system for probing Casimir energy corrections to the condensation energy.

In this article, we present a nanoelectromechanical system (NEMS) designed to detect changes in the Casimir energy. The Casimir effect is a result of the appearance of quantum fluctuations in an electromagnetic vacuum. Previous experiments have used nano- or microscale parallel plate capacitors to detect the Casimir force by measuring the small attractive force these fluctuations exert between the two surfaces. In this new set of experiments, we aim to directly detect the shifts in the Casimir energy in a vacuum due to the presence of the metallic parallel plates, one of which is a superconductor. A change in the Casimir energy of this configuration is predicted to shift the superconducting transition temperature (T c) because of the interaction between it and the superconducting condensation energy. In our experiment, we take a superconducting film, carefully measure its transition temperature, bring a conducting plate close to the film, create a Casimir cavity, and then measure the transition temperature again. The expected shifts are smaller than the normal shifts one sees in cycling superconducting films to cryogenic temperatures, so using a NEMS resonator in situ is the only practical way to obtain accurate, reproducible data. Using a thin Pb film and opposing Au surface, we observe no shift in T c >12 µK down to a minimum spacing of ~70 nm at zero applied magnetic field.

Nano-opto-electro-mechanical switches operated at CMOS-level voltages.

Combining reprogrammable optical networks with complementary metal-oxide semiconductor (CMOS) electronics is expected to provide a platform for technological developments in on-chip integrated optoelectronics. We demonstrate how opto-electro-mechanical effects in micrometer-scale hybrid photonic-plasmonic structures enable light switching under CMOS voltages and low optical losses (0.1 decibel). Rapid (for example, tens of nanoseconds) switching is achieved by an electrostatic, nanometer-scale perturbation of a thin, and thus low-mass, gold membrane that forms an air-gap hybrid photonic-plasmonic waveguide. Confinement of the plasmonic portion of the light to the variable-height air gap yields a strong opto-electro-mechanical effect, while photonic confinement of the rest of the light minimizes optical losses. The demonstrated hybrid architecture provides a route to develop applications for CMOS-integrated, reprogrammable optical systems such as optical neural networks for deep learning.

Metasurface-Integrated Photonic Platform for Versatile Free-Space Beam Projection with Polarization Control.

Densely integrated photonic circuits enable scalable, complex processing of optical signals, including modulation, multiplexing, wavelength conversion, and detection. Directly interfacing such integrated circuits to free-space optical modes will enable novel optical functions, such as chip-scale sensing, interchip free-space interconnect and cooling, trapping, and interrogation of atoms. However, doing this within the limits of planar batch fabrication requires new approaches for bridging the large mode scale mismatch. Here, by integrating a dielectric metasurface with an extreme photonic mode converter, we create a versatile nanophotonic platform for efficient coupling to arbitrary-defined free-space radiation of 780 nm wavelength with well-controlled spatially-dependent polarization, phase, and intensity. Without leaving the chip, the high index photonic mode is converted first to a ≈ 200 µm wide, precisely collimated, linearly-polarized Gaussian beam, which is then modified by a planar, integrated, low-loss metasurface. We demonstrate high numerical aperture, diffraction limited focusing to an ≈ 473 nm spot at an ≈ 75 µm working distance, and combine it with simultaneous conversion from linear to elliptical polarization. All device components are lithographically defined and can be batch fabricated, facilitating future chip-scale low-cost hybrid photonic systems for bio-sensing, nonlinear signal processing and atomic quantum sensing, frequency references and memory.

Photonic waveguide to free-space Gaussian beam extreme mode converter.

Integration of photonic chips with millimeter-scale atomic, micromechanical, chemical, and biological systems can advance science and enable new miniaturized hybrid devices and technology. Optical interaction via small evanescent volumes restricts performance in applications such as gas spectroscopy, and a general ability to photonically access optical fields in large free-space volumes is desired. However, conventional inverse tapers and grating couplers do not directly scale to create wide, high-quality collimated beams for low-loss diffraction-free propagation over many millimeters in free space, necessitating additional bulky collimating optics and expensive alignment. Here, we develop an extreme mode converter, which is a compact planar photonic structure that efficiently couples a 300 nm × 250 nm silicon nitride high-index single-mode waveguide to a well-collimated near surface-normal Gaussian beam with an ≈160 µm waist, which corresponds to an increase in the modal area by a factor of >105. The beam quality is thoroughly characterized, and propagation over 4 mm in free space and coupling back into a single-mode photonic waveguide with low loss via a separate identical mode converter is demonstrated. To achieve low phase error over a beam area that is >100× larger than that of a typical grating coupler, our approach separates the two-dimensional mode expansion into two sequential separately optimized stages, which create a fully expanded and well-collimated Gaussian slab mode before out-coupling it into free space. Developed at 780 nm for integration with chip-scale atomic vapor cell cavities, our design can be adapted for visible, telecommunication, or other wavelengths. The technique can be expanded to more arbitrary phase and intensity control of both large-diameter, free-space optical beams and wide photonic slab modes.