Supergrowth and sub-wavelength object imaging.

We further develop the concept of supergrowth [Quantum Stud.: Math. Found.7, 285 (2020)10.1007/s40509-019-00214-5], a phenomenon complementary to superoscillation, defined as the local amplitude growth rate of a function higher than its largest wavenumber. We identify a canonical oscillatory function's superoscillating and supergrowing regions and find the maximum values of local growth rate and wavenumber. Next, we provide a quantitative comparison of lengths and relevant intensities between the superoscillating and the supergrowing regions of a canonical oscillatory function. Our analysis shows that the supergrowing regions contain intensities that are exponentially larger in terms of the highest local wavenumber compared to the superoscillating regions. Finally, we prescribe methods to reconstruct a sub-wavelength object from the imaging data using both superoscillatory and supergrowing point spread functions. Our investigation provides an experimentally preferable alternative to the superoscillation-based superresolution schemes and is relevant to cutting-edge research in far-field sub-wavelength imaging.

Metagrating meets the geometry-based efficiency limit for AR waveguide in-couplers.

Recently, augmented reality (AR) displays have attracted considerable attention due to the highly immersive and realistic viewer experience they can provide. One key challenge of AR displays is the fundamental trade-off between the extent of the field-of-view (FOV) and the size of the eyebox, set by the conservation of etendue sets this trade-off. Exit-pupil expansion (EPE) is one possible solution to this problem. However, it comes at the cost of distributing light over a larger area, decreasing the overall system's brightness. In this work, we show that the geometry of the waveguide and the in-coupler sets a fundamental limit on how efficient the combiner can be for a given FOV. This limit can be used as a tool for waveguide designers to benchmark the in-coupling efficiency of their in-coupler gratings. We design a metasurface-based grating (metagrating) and a commonly used SRG as in-couplers using the derived limit to guide optimization. We then compare the diffractive efficiencies of the two types of in-couplers to the theoretical efficiency limit. For our chosen waveguide geometry, the metagrating's 28% efficiency surpasses the SRG's 20% efficiency and nearly matches the geometry-based limit of 29% due to the superior angular response control of metasurfaces compared to SRGs. This work provides new insight into the efficiency limit of waveguide-based combiners and paves a novel path toward implementing metasurfaces in efficient waveguide AR displays.

Excited-state spin-resonance spectroscopy of V[Formula: see text] defect centers in hexagonal boron nitride.

The recently discovered spin-active boron vacancy (V[Formula: see text]) defect center in hexagonal boron nitride (hBN) has high contrast optically-detected magnetic resonance (ODMR) at room-temperature, with a spin-triplet ground-state that shows promise as a quantum sensor. Here we report temperature-dependent ODMR spectroscopy to probe spin within the orbital excited-state. Our experiments determine the excited-state spin Hamiltonian, including a room-temperature zero-field splitting of 2.1 GHz and a g-factor similar to that of the ground-state. We confirm that the resonance is associated with spin rotation in the excited-state using pulsed ODMR measurements, and we observe Zeeman-mediated level anti-crossings in both the orbital ground- and excited-state. Our observation of a single set of excited-state spin-triplet resonance from 10 to 300 K is suggestive of symmetry-lowering of the defect system from D3h to C2v. Additionally, the excited-state ODMR has strong temperature dependence of both contrast and transverse anisotropy splitting, enabling promising avenues for quantum sensing.

Laser refrigeration of optically levitated sodium yttrium fluoride nanocrystals.

Solid state laser refrigeration can cool optically levitated nanocrystals in an optical dipole trap, allowing for internal temperature control by mitigating photothermal heating. This work demonstrates cooling of ytterbium-doped cubic sodium yttrium fluoride nanocrystals to 252 K on average with the most effective crystal cooling to 241 K. The amount of cooling increases linearly with the intensity of the cooling laser and is dependent on the pressure of the gas surrounding the nanocrystal. Cooling optically levitated nanocrystals allows for crystals prone to heating to be studied at lower pressures than currently achievable and for temperature control and stabilization of trapped nanocrystals.

Experimental demonstration of superresolution of partially coherent light sources using parity sorting.

Analyses based on quantum metrology have shown that the ability to localize the positions of two incoherent point sources can be significantly enhanced over direct imaging through the use of mode sorting. Here we theoretically and experimentally investigate the effect of partial coherence on the sub-diffraction limit localization of two sources based on parity sorting. With the prior information of a negative and real-valued degree of coherence, higher Fisher information is obtained than that for the incoherent case. Our results pave the way to clarifying the role of coherence in quantum-limited metrology.

Metaform optics: Bridging nanophotonics and freeform optics.

The demand for high-resolution optical systems with a compact form factor, such as augmented reality displays, sensors, and mobile cameras, requires creating new optical component architectures. Advances in the design and fabrication of freeform optics and metasurfaces make them potential solutions to address the previous needs. Here, we introduce the concept of a metaform-an optical surface that integrates the combined benefits of a freeform optic and a metasurface into a single optical component. We experimentally realized a miniature imager using a metaform mirror. The mirror is fabricated via an enhanced electron beam lithography process on a freeform substrate. The design degrees of freedom enabled by a metaform will support a new generation of optical systems.

Exciton-Trion Polaritons in Doped Two-Dimensional Semiconductors.

We present a many-body theory of exciton-trion polaritons (ETPs) in doped two-dimensional semiconductor materials. ETPs are robust coherent hybrid excitations involving excitons, trions, and photons. In ETPs, the 2-body exciton states are coupled to the material ground state via exciton-photon interaction, and the 4-body trion states are coupled to the exciton states via Coulomb interaction. The trion states are not directly optically coupled to the material ground state. The energy-momentum dispersion of ETPs exhibit three bands. We calculate the energy band dispersions and the compositions of ETPs at different doping densities using Green's functions. The energy splittings between the polariton bands, as well as the spectral weights of the polariton bands, depend on the strength of the Coulomb coupling between the excitons and the trions, which in turn depends sensitively on the doping density. The doping density dependence of the ETP bands and the charged nature of the trion states could enable novel electrical and optical control of ETPs.

The effects of substitutional Fe-doping on magnetism in MoS2and WS2monolayers.

Doping of two-dimensional (2D) semiconductors has been intensively studied toward modulating their electrical, optical, and magnetic properties. While ferromagnetic 2D semiconductors hold promise for future spintronics and valleytronics, the origin of ferromagnetism in 2D materials remains unclear. Here, we show that substitutional Fe-doping of MoS2and WS2monolayers induce different magnetic properties. The Fe-doped monolayers are directly synthesized via chemical vapor deposition. In both cases, Fe substitutional doping is successfully achieved, as confirmed using scanning transmission electron microscopy. While both Fe:MoS2and Fe:WS2show PL quenching and n-type doping, Fe dopants in WS2monolayers are found to assume deep-level trap states, in contrast to the case of Fe:MoS2, where the states are found to be shallow. Usingµm- and mm-precision local NV-magnetometry and superconducting quantum interference device, we discover that, unlike MoS2monolayers, WS2monolayers do not show a magnetic phase transition to ferromagnetism upon Fe-doping. The absence of ferromagnetism in Fe:WS2is corroborated using density functional theory calculations.

Observation of site-controlled localized charged excitons in CrI3/WSe2 heterostructures.

Isolated spins are the focus of intense scientific exploration due to their potential role as qubits for quantum information science. Optical access to single spins, demonstrated in III-V semiconducting quantum dots, has fueled research aimed at realizing quantum networks. More recently, quantum emitters in atomically thin materials such as tungsten diselenide have been demonstrated to host optically addressable single spins by means of electrostatic doping the localized excitons. Electrostatic doping is not the only route to charging localized quantum emitters and another path forward is through band structure engineering using van der Waals heterojunctions. Critical to this second approach is to interface tungsten diselenide with other van der Waals materials with relative band-alignments conducive to the phenomenon of charge transfer. In this work we show that the Type-II band-alignment between tungsten diselenide and chromium triiodide can be exploited to excite localized charged excitons in tungsten diselenide. Leveraging spin-dependent charge transfer in the device, we demonstrate spin selectivity in the preparation of the spin-valley state of localized single holes. Combined with the use of strain-inducing nanopillars to coordinate the spatial location of tungsten diselenide quantum emitters, we uncover the possibility of realizing large-scale deterministic arrays of optically addressable spin-valley holes in a solid state platform.

Enabling room temperature ferromagnetism in monolayer MoS2 via in situ iron-doping.

Two-dimensional semiconductors, including transition metal dichalcogenides, are of interest in electronics and photonics but remain nonmagnetic in their intrinsic form. Previous efforts to form two-dimensional dilute magnetic semiconductors utilized extrinsic doping techniques or bulk crystal growth, detrimentally affecting uniformity, scalability, or Curie temperature. Here, we demonstrate an in situ substitutional doping of Fe atoms into MoS2 monolayers in the chemical vapor deposition growth. The iron atoms substitute molybdenum sites in MoS2 crystals, as confirmed by transmission electron microscopy and Raman signatures. We uncover an Fe-related spectral transition of Fe:MoS2 monolayers that appears at 2.28 eV above the pristine bandgap and displays pronounced ferromagnetic hysteresis. The microscopic origin is further corroborated by density functional theory calculations of dipole-allowed transitions in Fe:MoS2. Using spatially integrating magnetization measurements and spatially resolving nitrogen-vacancy center magnetometry, we show that Fe:MoS2 monolayers remain magnetized even at ambient conditions, manifesting ferromagnetism at room temperature.

Higher order correlations in a levitated nanoparticle phonon laser.

We present theoretical and experimental investigations of higher order correlations of mechanical motion in the recently demonstrated optical tweezer phonon laser, consisting of a silica nanosphere trapped in vacuum by a tightly focused optical beam [R. M. Pettit et al., Nature Photonics 13, 402 (2019)]. The nanoparticle phonon number probability distribution is modeled with the master equation formalism in order to study its evolution across the lasing threshold. Up to fourth-order equal-time correlation functions are then derived from the probability distribution. Subsequently, the master equation is transformed into a nonlinear quantum Langevin equation for the trapped particle's position. This equation yields the non-equal-time correlations, also up to fourth order. Finally, we present experimental measurements of the phononic correlation functions, which are in good agreement with our theoretical predictions. We also compare the experimental data to existing analytical Ginzburg-Landau theory where we find only a partial match.

Optomechanics with levitated particles.

Optomechanics is concerned with the use of light to control mechanical objects. As a field, it has been hugely successful in the production of precise and novel sensors, the development of low-dissipation nanomechanical devices, and the manipulation of quantum signals. Micro- and nano-particles levitated in optical fields act as nanoscale oscillators, making them excellent low-dissipation optomechanical objects, with minimal thermal contact to the environment when operating in vacuum. Levitated optomechanics is seen as the most promising route for studying high-mass quantum physics, with the promise of creating macroscopically separated superposition states at masses of 106 amu and above. Optical feedback, both using active monitoring or the passive interaction with an optical cavity, can be used to cool the centre-of-mass of levitated nanoparticles well below 1 mK, paving the way to operation in the quantum regime. In addition, trapped mesoscopic particles are the paradigmatic system for studying nanoscale stochastic processes, and have already demonstrated their utility in state-of-the-art force sensing.

Mechanically tunable focusing metamirror in the visible.

A compact, flat lens with dynamically tunable focal length will be an essential component in advanced reconfigurable optical systems. One approach to realize a flat tunable lens is by utilizing metasurfaces, which are two-dimensional nanostructures capable of tailoring the wavefront of incident light. When a metasurface with a hyperboloidal phase profile, i.e., a metalens, is fabricated on a substrate that can be actuated, its focal length can be adjusted dynamically. Here, we design and realize the first reflection type, tunable metalens (i.e., metamirror) operating in the visible regime (670 nm). It is shown that the focal length can be continuously adjusted by up to 45% with a 0% to 20% lateral stretching of the substrate, while maintaining diffraction-limited focusing and high focusing efficiency. Our design as a flat optics element has potential in widespread applications, such as wearable mixed reality systems, biomedical instruments and integrated optics devices.

Polarization-switchable holograms based on efficient, broadband multifunctional metasurfaces in the visible regime.

Gradient metasurfaces provide a novel approach to the phase manipulation of incident electromagnetic waves. Thus, they have the potential to create compact, light-weight optical solutions. An attractive feature of metasurfaces is the ability to integrate multiple optical functionalities into a single surface design. Here we demonstrate a high-efficiency (up to ~60%), reflective meta-hologram for visible light by using an ultra-thin (~λ/4 thick) gap surface plasmon-based metasurface. By precisely sampling the predesigned image phase and amplitude to the unit cells of our device, polarization-controlled dual images are reconstructed with a high polarization extinction ratio and high fidelity. The proposed technique expands the range of possibilities for high-quality hologram generation by using ultra-thin nanophotonic devices and paves the way for variousholography-related applications across the visible band.

Interferometric spatial mode analyzer with a bucket detector.

A spatial mode analyzer based on a Michelson interferometer with a bucket detector is experimentally implemented. The delay line in the interferometer is an optical implementation of the fractional Fourier transform (fFT) which enables the spatial mode analysis of a given input field in the Hermite-Gaussian (HG) mode basis. Modal weights for both 1D and 2D input fields are experimentally measured. Results for input fields comprising of multiple HG modes are also presented.

Phase retrieval in generalized optical interferometry systems.

Modal analysis of an optical field via generalized interferometry (GI) is a novel technique that treats said field as a linear superposition of transverse modes and recovers the amplitudes of modal weighting coefficients. We use phase retrieval by nonlinear optimization to recover the phase of these modal weighting coefficients. Information diversity increases the robustness of the algorithm by better constraining the solution. Additionally, multiple sets of random starting phase values assist the algorithm in overcoming local minima. The algorithm was able to recover nearly all coefficient phases for simulated fields consisting of up to 21 superpositioned Hermite Gaussian modes from simulated data and proved to be resilient to shot noise.

Quantum-Confined Stark Effect of Individual Defects in a van der Waals Heterostructure.

The optical properties of atomically thin semiconductor materials have been widely studied because of the isolation of monolayer transition metal dichalcogenides (TMDCs). They have rich optoelectronic properties owing to their large direct bandgap, the interplay between the spin and the valley degree of freedom of charge carriers, and the recently discovered localized excitonic states giving rise to single photon emission. In this Letter, we study the quantum-confined Stark effect of these localized emitters present near the edges of monolayer tungsten diselenide (WSe2). By carefully designing sequences of metallic (graphene), insulating (hexagonal boron nitride), and semiconducting (WSe2) two-dimensional materials, we fabricate a van der Waals heterostructure field effect device with WSe2 hosting quantum emitters that is responsive to external static electric field applied to the device. A very efficient spectral tunability up to 21 meV is demonstrated. Further, evaluation of the spectral shift in the photoluminescence signal as a function of the applied voltage enables us to extract the polarizability volume (up to 2000 Å3) as well as information on the dipole moment of an individual emitter. The Stark shift can be further modulated on application of an external magnetic field, where we observe a flip in the sign of dipole moment possibly due to rearrangement of the position of electron and hole wave functions within the emitter.

Basis-neutral Hilbert-space analyzers.

Interferometry is one of the central organizing principles of optics. Key to interferometry is the concept of optical delay, which facilitates spectral analysis in terms of time-harmonics. In contrast, when analyzing a beam in a Hilbert space spanned by spatial modes - a critical task for spatial-mode multiplexing and quantum communication - basis-specific principles are invoked that are altogether distinct from that of 'delay'. Here, we extend the traditional concept of temporal delay to the spatial domain, thereby enabling the analysis of a beam in an arbitrary spatial-mode basis - exemplified using Hermite-Gaussian and radial Laguerre-Gaussian modes. Such generalized delays correspond to optical implementations of fractional transforms; for example, the fractional Hankel transform is the generalized delay associated with the space of Laguerre-Gaussian modes, and an interferometer incorporating such a 'delay' obtains modal weights in the associated Hilbert space. By implementing an inherently stable, reconfigurable spatial-light-modulator-based polarization-interferometer, we have constructed a 'Hilbert-space analyzer' capable of projecting optical beams onto any modal basis.

Coherence Constraints and the Last Hidden Optical Coherence.

We have discovered a new domain of optical coherence, and show that it is the third and last member of a previously unreported fundamental triad of coherences. These are unified by our derivation of a parallel triad of coherence constraints that take the form of complementarity relations. We have been able to enter this new coherence domain experimentally and we describe the novel tomographic approach devised for that purpose.

Direct On-Chip Optical Plasmon Detection with an Atomically Thin Semiconductor.

The determination to develop fast, efficient devices has led to vast studies on photonic circuits but it is difficult to shrink these circuits below the diffraction limit of light. However, the coupling between surface plasmon polaritons and nanostructures in the near-field shows promise in developing next-generation integrated circuitry. In this work, we demonstrate the potential for integrating nanoplasmonic-based light guides with atomically thin materials for on-chip near-field plasmon detection. Specifically, we show near-field electrical detection of silver nanowire plasmons with the atomically thin semiconductor molybdenum disulfide. Unlike graphene, atomically thin semiconductors such as molybdenum disulfide exhibit a bandgap that lends itself for the excitation and detection of plasmons. Our fully integrated plasmon detector exhibits plasmon responsivities of ∼255 mA/W that corresponds to highly efficient plasmon detection (∼0.5 electrons per plasmon).