Spectroscopy in Nanoscopic Cavities: Models and Recent Experiments.

The ability of nanophotonic cavities to confine and store light to nanoscale dimensions has important implications for enhancing molecular, excitonic, phononic, and plasmonic optical responses. Spectroscopic signatures of processes that are ordinarily exceedingly weak such as pure absorption and Raman scattering have been brought to the single-particle limit of detection, while new emergent polaritonic states of optical matter have been realized through coupling material and photonic cavity degrees of freedom across a wide range of experimentally accessible interaction strengths. In this review, we discuss both optical and electron beam spectroscopies of cavity-coupled material systems in weak, strong, and ultrastrong coupling regimes, providing a theoretical basis for understanding the physics inherent to each while highlighting recent experimental advances and exciting future directions.

Probing the Polarization of Low-Energy Excitations in 2D Materials from Atomic Crystals to Nanophotonic Arrays Using Momentum-Resolved Electron Energy Loss Spectroscopy.

Spectroscopies utilizing free electron beams as probes offer detailed information on the reciprocal-space excitations of 2D materials such as graphene and transition metal dichalcogenide monolayers. Yet, despite the attention paid to such quantum materials, less consideration has been given to the electron-beam characterization of 2D periodic nanostructures such as photonic crystals, metasurfaces, and plasmon arrays, which can exhibit the same lattice and excitation symmetries as their atomic analogues albeit at drastically different length, momentum, and energy scales. Because of their lack of covalent bonding and influence of retarded electromagnetic interactions, important physical distinctions arise that complicate interpretation of scattering signals. Here we present a fully-retarded theoretical framework for describing the inelastic scattering of wide-field electron beams from 2D materials and apply it to investigate the complementarity in sample excitation information gained in the measurement of a honeycomb plasmon array versus angle-resolved optical spectroscopy in comparison to single monolayer graphene.

Nonlinear effects in single-particle photothermal imaging.

Although photothermal imaging was originally designed to detect individual molecules that do not emit or small nanoparticles that do not scatter, the technique is now being applied to image and spectroscopically characterize larger and more sophisticated nanoparticle structures that scatter light strongly. Extending photothermal measurements into this regime, however, requires revisiting fundamental assumptions made in the interpretation of the signal. Herein, we present a theoretical analysis of the wavelength-resolved photothermal image and its extension to the large particle scattering regime, where we find the photothermal signal to inherit a nonlinear dependence upon pump intensity, together with a contraction of the full-width-at-half-maximum of its point spread function. We further analyze theoretically the extent to which photothermal spectra can be interpreted as an absorption spectrum measure, with deviations between the two becoming more prominent with increasing pump intensities. Companion experiments on individual 10, 20, and 100 nm radius gold nanoparticles evidence the predicted nonlinear pump power dependence and image contraction, verifying the theory and demonstrating new aspects of photothermal imaging relevant to a broader class of targets.

Far-field midinfrared superresolution imaging and spectroscopy of single high aspect ratio gold nanowires.

Limited approaches exist for imaging and recording spectra of individual nanostructures in the midinfrared region. Here we use infrared photothermal heterodyne imaging (IR-PHI) to interrogate single, high aspect ratio Au nanowires (NWs). Spectra recorded between 2,800 and 4,000 cm-1 for 2.5-3.9-µm-long NWs reveal a series of resonances due to the Fabry-Pérot modes of the NWs. Crucially, IR-PHI images show structure that reflects the spatial distribution of the NW absorption, and allow the resonances to be assigned to the m = 3 and m = 4 Fabry-Pérot modes. This far-field optical measurement has been used to image the mode structure of plasmon resonances in metal nanostructures, and is made possible by the superresolution capabilities of IR-PHI. The linewidths in the NW spectra range from 35 to 75 meV and, in several cases, are significantly below the limiting values predicted by the bulk Au Drude damping parameter. These linewidths imply long dephasing times, and are attributed to reduction in both radiation damping and resistive heating effects in the NWs. Compared to previous imaging studies of NW Fabry-Pérot modes using electron microscopy or near-field optical scanning techniques, IR-PHI experiments are performed under ambient conditions, enabling detailed studies of how the environment affects mid-IR plasmons.

Polarization-Resolved Electron Energy Gain Nanospectroscopy With Phase-Structured Electron Beams.

Free-electron-based measurements in scanning transmission electron microscopes (STEMs) reveal valuable information on the broadband spectral responses of nanoscale systems with deeply subdiffraction limited spatial resolution. Leveraging recent advances in manipulating the spatial phase profile of the transverse electron wavefront, we theoretically describe interactions between the electron probe and optically stimulated nanophotonic targets in which the probe gains energy while simultaneously transitioning between transverse states with distinct phase profiles. Exploiting the selection rules governing such transitions, we propose phase-shaped electron energy gain nanospectroscopy for probing the 3D polarization-resolved response field of an optically excited target with nanoscale spatial resolution. Considering ongoing instrumental developments, polarized generalizations of STEM electron energy loss and gain measurements hold the potential to become powerful tools for fundamental studies of quantum materials and their interaction with nearby nanostructures supporting localized surface plasmon or phonon polaritons as well as for noninvasive imaging and nanoscale 3D field tomography.

Nanometer-Scale Spatial and Spectral Mapping of Exciton Polaritons in Structured Plasmonic Cavities.

Exciton polaritons (EPs) are ubiquitous light-matter excitations under intense investigation as test beds of fundamental physics and as components for all-optical computing. Owing to their unique attributes and facile experimental tunability, EPs potentially enable strong nonlinearities, condensation, and superfluidity at room temperature. However, the diffraction limit of light and the momentum content of fast electron probes preclude the characterization of EPs in nanoscale structured cavities exhibiting energy-momentum dispersion. Here we present fully relativistic analytical theory and companion numerical simulations showing that these limitations can be overcome to measure EPs in periodic nanophotonic cavities on their natural energy, momentum, and length scales via lattice electron energy gain spectroscopy. With the combined high momentum resolution of light and nanoscale spatial resolution of focused electron beams, lattice electron energy gain spectroscopy can expose deeply subwavelength EP features using currently available monochromated, aberration-corrected scanning transmission electron microscopes.

Wavelength-Dependent Photothermal Imaging Probes Nanoscale Temperature Differences among Subdiffraction Coupled Plasmonic Nanorods.

Plasmonic structures confine electromagnetic energy at the nanoscale, resulting in local, inhomogeneous, controllable heating, but reading out the temperature using optical techniques poses a difficult challenge. Here, we report on the optical thermometry of individual gold nanorod trimers that exhibit multiple wavelength-dependent plasmon modes resulting in measurably different local temperature distributions. Specifically, we demonstrate how photothermal microscopy encodes different wavelength-dependent temperature profiles in the asymmetry of the photothermal image point spread function. These asymmetries are interpreted through companion numerical simulations to reveal how thermal gradients within the trimer can be controlled by exciting its hybridized plasmon modes. We also find that plasmon modes that are optically dark can be excited by focused laser beam illumination, providing another route to modify thermal profiles beyond wide-field illumination. Taken together these findings demonstrate an all-optical thermometry technique to actively create and measure nanoscale thermal gradients below the diffraction limit.

High spatial and energy resolution electron energy loss spectroscopy of the magnetic and electric excitations in plasmonic nanorod oligomers.

We leverage the high spatial and energy resolution of monochromated aberration-corrected scanning transmission electron microscopy to study the hybridization of cyclic assemblies of plasmonic gold nanorods. Detailed experiments and simulations elucidate the hybridization of the coupled long-axis dipole modes into collective magnetic and electric dipole plasmon resonances. We resolve the magnetic dipole mode in these closed loop oligomers with electron energy loss spectroscopy and confirm the mode assignment with its characteristic spectrum image. The energy splitting of the magnetic mode and antibonding modes increases with the number of polygon edges (n). For the n=3-6 oligomers studied, optical simulations using normal incidence and s-polarized oblique incidence show the respective electric and magnetic modes' extinction efficiencies are maximized in the n=4 arrangement.

Electron Beam Infrared Nano-Ellipsometry of Individual Indium Tin Oxide Nanocrystals.

Leveraging recent advances in electron energy monochromation and aberration correction, we record the spatially resolved infrared plasmon spectrum of individual tin-doped indium oxide nanocrystals using electron energy-loss spectroscopy (EELS). Both surface and bulk plasmon responses are measured as a function of tin doping concentration from 1-10 atomic percent. These results are compared to theoretical models, which elucidate the spectral detuning of the same surface plasmon resonance feature when measured from aloof and penetrating probe geometries. We additionally demonstrate a unique approach to retrieving the fundamental dielectric parameters of individual semiconductor nanocrystals via EELS. This method, devoid from ensemble averaging, illustrates the potential for electron-beam ellipsometry measurements on materials that cannot be prepared in bulk form or as thin films.

Elucidating Energy Pathways through Simultaneous Measurement of Absorption and Transmission in a Coupled Plasmonic-Photonic Cavity.

Control of light-matter interactions is central to numerous advances in quantum communication, information, and sensing. The relative ease with which interactions can be tailored in coupled plasmonic-photonic systems makes them ideal candidates for investigation. To exert control over the interaction between photons and plasmons, it is essential to identify the underlying energy pathways which influence the system's dynamics and determine the critical system parameters, such as the coupling strength and dissipation rates. However, in coupled systems which dissipate energy through multiple competing pathways, simultaneously resolving all parameters from a single experiment is challenging as typical observables such as absorption and scattering each probe only a particular path. In this work, we simultaneously measure both photothermal absorption and two-sided optical transmission in a coupled plasmonic-photonic resonator consisting of plasmonic gold nanorods deposited on a toroidal whispering-gallery-mode optical microresonator. We then present an analytical model which predicts and explains the distinct line shapes observed and quantifies the contribution of each system parameter. By combining this model with experiment, we extract all system parameters with a dynamic range spanning 9 orders of magnitude. Our combined approach provides a full description of plasmonic-photonic energy dynamics in a weakly coupled optical system, a necessary step for future applications that rely on tunability of dissipation and coupling.

Direct Observation of Infrared Plasmonic Fano Antiresonances by a Nanoscale Electron Probe.

In this Letter, we exploit recent breakthroughs in monochromated aberration-corrected scanning transmission electron microscopy (STEM) to resolve infrared plasmonic Fano antiresonances in individual nanofabricated disk-rod dimers. Using a combination of electron energy-loss spectroscopy and theoretical modeling, we investigate and characterize a subspace of the weak coupling regime between quasidiscrete and quasicontinuum localized surface plasmon resonances where infrared plasmonic Fano antiresonances appear. This work illustrates the capability of STEM instrumentation to experimentally observe nanoscale plasmonic responses that were previously the domain only of higher-resolution infrared spectroscopies.

Symmetry-Broken Many-Body Excited States of the Gaseous Atomic Double-Well Bose-Einstein Condensate.

Macroscopic, many-body self-trapped and quantum superposition states of the gaseous double-well Bose-Einstein condensate (BEC) are investigated within the context of a multiconfigurational bosonic self-consistent field theory based upon underlying spatially symmetry-broken one-body wave functions. To aid in the interpretation of our results, an approximate model is constructed in the extreme Fock state limit, in which self-trapped and superposition states emerge in the many-body spectrum, striking a delicate balance between the degree of symmetry breaking, the effects of the condensate's mean field, and that of atomic correlation. It is found, in both the model and full theory, that the superposition state lies energetically below its related self-trapped counterpart even when many configurations are involved. Noticeably different spatial density profiles are associated with each type of excited state, thus providing a rigorous justification for approximate descriptions of high-lying excited states of the BEC.

Sculpting Fano Resonances To Control Photonic-Plasmonic Hybridization.

Hybrid photonic-plasmonic systems have tremendous potential as versatile platforms for the study and control of nanoscale light-matter interactions since their respective components have either high-quality factors or low mode volumes. Individual metallic nanoparticles deposited on optical microresonators provide an excellent example where ultrahigh-quality optical whispering-gallery modes can be combined with nanoscopic plasmonic mode volumes to maximize the system's photonic performance. Such optimization, however, is difficult in practice because of the inability to easily measure and tune critical system parameters. In this Letter, we present a general and practical method to determine the coupling strength and tailor the degree of hybridization in composite optical microresonator-plasmonic nanoparticle systems based on experimentally measured absorption spectra. Specifically, we use thermal annealing to control the detuning between a metal nanoparticle's localized surface plasmon resonance and the whispering-gallery modes of an optical microresonator cavity. We demonstrate the ability to sculpt Fano resonance lineshapes in the absorption spectrum and infer system parameters critical to elucidating the underlying photonic-plasmonic hybridization. We show that including decoherence processes is necessary to capture the evolution of the lineshapes. As a result, thermal annealing allows us to directly tune the degree of hybridization and various hybrid mode quantities such as the quality factor and mode volume and ultimately maximize the Purcell factor to be 104.

Characterizing Localized Surface Plasmons Using Electron Energy-Loss Spectroscopy.

Electron energy-loss spectroscopy (EELS) offers a window to view nanoscale properties and processes. When performed in a scanning transmission electron microscope, EELS can simultaneously render images of nanoscale objects with subnanometer spatial resolution and correlate them with spectroscopic information at a spectral resolution of ∼10-100 meV. Consequently, EELS is a near-perfect tool for understanding the optical and electronic properties of individual plasmonic metal nanoparticles and few-nanoparticle assemblies, which are significant in a wide range of fields. This review presents an overview of basic plasmonics and EELS theory and highlights several recent noteworthy experiments involving the interrogation of plasmonic metal nanoparticle systems using electron beams.

STEM/EELS Imaging of Magnetic Hybridization in Symmetric and Symmetry-Broken Plasmon Oligomer Dimers and All-Magnetic Fano Interference.

Negative-index metamaterials composed of magnetic plasmon oligomers are actively being investigated for their potential role in optical cloaking, superlensing, and nanolithography applications. A significant improvement to their practicality lies in the ability to function at multiple distinct wavelengths in the visible part of spectrum. Here we utilize the nanometer spatial-resolving power of electron energy-loss spectroscopy to conclusively demonstrate hybridization of magnetic plasmons in oligomer dimers that can achieve this goal. We also show that breaking the dimer's symmetry can induce all-magnetic Fano interferences based solely on the interplay of bright and dark magnetic modes, allowing us to further tailor the system's optical responses. These features are engineered through the design of the oligomer's underlying nanoparticle elements as elongated Ag nanodisks with spectrally isolated long-axis plasmon resonances. The resulting magnetic plasmon oligomers and their hybridized assemblies establish a new design paradigm for optical metamaterials with rich functionality.

Spatially Mapping Energy Transfer from Single Plasmonic Particles to Semiconductor Substrates via STEM/EELS.

Energy transfer from plasmonic nanoparticles to semiconductors can expand the available spectrum of solar energy-harvesting devices. Here, we spatially and spectrally resolve the interaction between single Ag nanocubes with insulating and semiconducting substrates using electron energy-loss spectroscopy, electrodynamics simulations, and extended plasmon hybridization theory. Our results illustrate a new way to characterize plasmon-semiconductor energy transfer at the nanoscale and bear impact upon the design of next-generation solar energy-harvesting devices.

Submicrosecond time resolution atomic force microscopy for probing nanoscale dynamics.

We propose, simulate, and experimentally validate a new mechanical detection method to analyze atomic force microscopy (AFM) cantilever motion that enables noncontact discrimination of transient events with ~100 ns temporal resolution without the need for custom AFM probes, specialized instrumentation, or expensive add-on hardware. As an example application, we use the method to screen thermally annealed poly(3-hexylthiophene):phenyl-C(61)-butyric acid methyl ester photovoltaic devices under realistic testing conditions over a technologically relevant performance window. We show that variations in device efficiency and nanoscale transient charging behavior are correlated, thereby linking local dynamics with device behavior. We anticipate that this method will find application in scanning probe experiments of dynamic local mechanical, electronic, magnetic, and biophysical phenomena.