Fractal nanoparticle plasmonics: the Cayley tree

Continuous spectral and coupling-strength encoding with dual-gradient metasurfaces

To control and enhance light-matter interactions at the nanoscale, two parameters are central: the spectral overlap between an optical cavity mode and the material's spectral features (for example, excitonic or molecular absorption lines), and the quality factor of the cavity. Controlling both parameters simultaneously would enable the investigation of systems with complex spectral features, such as multicomponent molecular mixtures or heterogeneous solid-state materials. So far, it has been possible only to sample a limited set of data points within this two-dimensional parameter space. Here we introduce a nanophotonic approach that can simultaneously and continuously encode the spectral and quality-factor parameter space within a compact spatial area. We use a dual-gradient metasurface design composed of a two-dimensional array of smoothly varying subwavelength nanoresonators, each supporting a unique mode based on symmetry-protected bound states in the continuum. This results in 27,500 distinct modes and a mode density approaching the theoretical upper limit for metasurfaces. By applying our platform to surface-enhanced molecular spectroscopy, we find that the optimal quality factor for maximum sensitivity depends on the amount of analyte, enabling effective molecular detection regardless of analyte concentration within a single dual-gradient metasurface. Our design provides a method to analyse the complete spectral and coupling-strength parameter space of complex material systems for applications such as photocatalysis, chemical sensing and entangled photon generation.

Gradient High-Q Dielectric Metasurfaces for Broadband Sensing and Control of Vibrational Light-Matter Coupling

Surface-enhanced infrared absorption spectroscopy (SEIRA) has emerged as a powerful technique for ultrasensitive chemical-specific analysis. SEIRA can be realized by employing metasurfaces that can enhance light-matter interactions in the spectral bands of molecular vibrations. Increasing sample complexity emphasizes the need for metasurfaces that can operate simultaneously at different spectral bands, both accessing rich spectral information over a broad band, and resolving subtle differences in the absorption fingerprints through narrow-band resonances. Here, a novel concept of resonance-gradient metasurfaces is introduced, where the required spectral selectivity is achieved via local high-quality-factor (high-Q) resonances, while the continuous coverage of a broad band is enabled by the gradual adjustment of the unit-cell dimensions along the planar structure. The highly tailorable design of the gradient metasurfaces provides flexibility for shaping the spectral sampling density to match the relevant bands of target analytes while keeping a compact device footprint. The versatility of the gradient metasurfaces is demonstrated through several sensing scenarios, including polymer mixture deconvolution, detecting a multistep bioassay, and identification of the onset of vibrational strong coupling regime. The proposed gradient-resonance platform significantly contributes to the rapidly evolving landscape of nonlocal metasurfaces, enabling applications in molecular detection and analysis of fundamental light-matter interaction phenomena.

Hot-Electron Dynamics Mediated Medical Diagnosis and Therapy

Surface plasmon resonance excitation significantly enhances the absorption of light and increases the generation of "hot" electrons, i.e., conducting electrons that are raised from their steady states to excited states. These excited electrons rapidly decay and equilibrate via radiative and nonradiative damping over several hundred femtoseconds. During the hot-electron dynamics, from their generation to the ultimate nonradiative decay, the electromagnetic field enhancement, hot electron density increase, and local heating effect are sequentially induced. Over the past decade, these physical phenomena have attracted considerable attention in the biomedical field, e.g., the rapid and accurate identification of biomolecules, precise synthesis and release of drugs, and elimination of tumors. This review highlights the recent developments in the application of hot-electron dynamics in medical diagnosis and therapy, particularly fully integrated device techniques with good application prospects. In addition, we discuss the latest experimental and theoretical studies of underlying mechanisms. From a practical standpoint, the pioneering modeling analyses and quantitative measurements in the extreme near field are summarized to illustrate the quantification of hot-electron dynamics. Finally, the prospects and remaining challenges associated with biomedical engineering based on hot-electron dynamics are presented.

Research Progress in Surface-Enhanced Infrared Absorption Spectroscopy: From Performance Optimization, Sensing Applications, to System Integration

Infrared absorption spectroscopy is an effective tool for the detection and identification of molecules. However, its application is limited by the low infrared absorption cross-section of the molecule, resulting in low sensitivity and a poor signal-to-noise ratio. Surface-Enhanced Infrared Absorption (SEIRA) spectroscopy is a breakthrough technique that exploits the field-enhancing properties of periodic nanostructures to amplify the vibrational signals of trace molecules. The fascinating properties of SEIRA technology have aroused great interest, driving diverse sensing applications. In this review, we first discuss three ways for SEIRA performance optimization, including material selection, sensitivity enhancement, and bandwidth improvement. Subsequently, we discuss the potential applications of SEIRA technology in fields such as biomedicine and environmental monitoring. In recent years, we have ushered in a new era characterized by the Internet of Things, sensor networks, and wearable devices. These new demands spurred the pursuit of miniaturized and consolidated infrared spectroscopy systems and chips. In addition, the rise of machine learning has injected new vitality into SEIRA, bringing smart device design and data analysis to the foreground. The final section of this review explores the anticipated trajectory that SEIRA technology might take, highlighting future trends and possibilities.

Metasurface-Enhanced Infrared Spectroscopy: An Abundance of Materials and Functionalities

Infrared spectroscopy provides unique information on the composition and dynamics of biochemical systems by resolving the characteristic absorption fingerprints of their constituent molecules. Based on this inherent chemical specificity and the capability for label-free, noninvasive, and real-time detection, infrared spectroscopy approaches have unlocked a plethora of breakthrough applications for fields ranging from environmental monitoring and defense to chemical analysis and medical diagnostics. Nanophotonics has played a crucial role for pushing the sensitivity limits of traditional far-field spectroscopy by using resonant nanostructures to focus the incident light into nanoscale hot-spots of the electromagnetic field, greatly enhancing light-matter interaction. Metasurfaces composed of regular arrangements of such resonators further increase the design space for tailoring this nanoscale light control both spectrally and spatially, which has established them as an invaluable toolkit for surface-enhanced spectroscopy. Starting from the fundamental concepts of metasurface-enhanced infrared spectroscopy, a broad palette of resonator geometries, materials, and arrangements for realizing highly sensitive metadevices is showcased, with a special focus on emerging systems such as phononic and 2D van der Waals materials, and integration with waveguides for lab-on-a-chip devices. Furthermore, advanced sensor functionalities of metasurface-based infrared spectroscopy, including multiresonance, tunability, dielectrophoresis, live cell sensing, and machine-learning-aided analysis are highlighted.

Dendric nanostructures for SARS-CoV-2 proteins detection based on surface enhanced infrared absorption spectroscopy

Infrared spectroscopy is a non-destructive and rapid characterization tool that can distinguish different viral proteins by spectral details. However, traditional infrared spectroscopy has insufficient absorption signal intensity contrast when measuring low-concentration samples. In this work, surface enhanced infrared absorption (SEIRA) spectroscopy is proposed by deploying a novel nanostructure array as SEIRA substrates. An array of gold dendric nanostructures are designed and fabricated with a precision resonance control to achieve surface enhancement covering a broadband molecular "finger-print" region. The spectral positions of the multiple resonances accurately correspond to the characteristic absorption peaks of the SARS-CoV-2 proteins. An approach for SARS-CoV-2 protein detection based on SEIRA spectroscopy is then proposed. A low concentration detection of 40 μg/ml diluted SARS-CoV-2 nucleocapsid protein is experimentally demonstrated and the enhancement factor (EF) achieved is in good agreement with simulation results. The SEIRA methodology based on broadband resonance nanostructure design provides a systematic approach for sensitive, non-destructive and rapid protein molecular detection, which could be extended to various kind of molecular characterization and biomedical diagnostics.

Towards multi-molecular surface-enhanced infrared absorption using metal plasmonics

Surface-enhanced infrared absorption (SEIRA) leads to a largely improved detection of polar molecules, compared to standard infrared absorption. The enhancement principle is based on localized surface plasmon resonances of the substrate, which match the frequency of molecular vibrations in the analyte of interest. Therefore, in practical terms, the SEIRA sensor needs to be tailored to each specific analyte. We review SEIRA sensors based on metal plasmonics for the detection of biomolecules such as DNA, proteins, and lipids. We further focus this review on chemical SEIRA sensors, with potential applications in quality control, as well as on the improvement in sensor geometry that led to the development of multiresonant SEIRA substrates as sensors for multiple analytes. Finally, we give an introduction into the integration of SEIRA sensors with surface-enhanced Raman scattering (SERS).

Menezes L, Tittl A, Ren H, Maier SA. Optical Metasurfaces for Energy Conversion

Nanostructured surfaces with designed optical functionalities, such as metasurfaces, allow efficient harvesting of light at the nanoscale, enhancing light-matter interactions for a wide variety of material combinations. Exploiting light-driven matter excitations in these artificial materials opens up a new dimension in the conversion and management of energy at the nanoscale. In this review, we outline the impact, opportunities, applications, and challenges of optical metasurfaces in converting the energy of incoming photons into frequency-shifted photons, phonons, and energetic charge carriers. A myriad of opportunities await for the utilization of the converted energy. Here we cover the most pertinent aspects from a fundamental nanoscopic viewpoint all the way to applications.

Controlled assembly of retinal cells on fractal and Euclidean electrodes

Controlled assembly of retinal cells on artificial surfaces is important for fundamental cell research and medical applications. We investigate fractal electrodes with branches of vertically-aligned carbon nanotubes and silicon dioxide gaps between the branches that form repeating patterns spanning from micro- to milli-meters, along with single-scaled Euclidean electrodes. Fluorescence and electron microscopy show neurons adhere in large numbers to branches while glial cells cover the gaps. This ensures neurons will be close to the electrodes’ stimulating electric fields in applications. Furthermore, glia won’t hinder neuron-branch interactions but will be sufficiently close for neurons to benefit from the glia’s life-supporting functions. This cell ‘herding’ is adjusted using the fractal electrode’s dimension and number of repeating levels. We explain how this tuning facilitates substantial glial coverage in the gaps which fuels neural networks with small-world structural characteristics. The large branch-gap interface then allows these networks to connect to the neuron-rich branches.

A microfluidic approach for synthesis and kinetic profiling of branched gold nanostructures

Automatized approaches for nanoparticle synthesis and characterization represent a great asset to their applicability in the biomedical field by improving reproducibility and standardization, which help to meet the selection criteria of regulatory authorities. The scaled-up production of nanoparticles with carefully defined characteristics, including intrinsic morphological features, and minimal intra-batch, batch-to-batch, and operator variability, is an urgent requirement to elevate nanotechnology towards more trustable biological and technological applications. In this work, microfluidic approaches were employed to achieve fast mixing and good reproducibility in synthesizing a variety of gold nanostructures. The microfluidic setup allowed exploiting spatial resolution to investigate the growth evolution of the complex nanoarchitectures. By physically isolating intermediate reaction fractions, we performed an advanced characterization of the shape properties during their growth, not possible with routine characterization methods. Employing an in-house developed method to assign a specific identity to shapes, we followed the particle growth/deformation process and identified key reaction parameters for more precise control of the generated morphologies. Besides, this investigation led to the optimization of a one-pot multi-size and multi-shape synthesis of a variety of gold nanoparticles. In summary, we describe an optimized platform for highly controlled synthesis and a novel approach for the mechanistic study of shape-evolving nanomaterials.

Aluminum Cayley trees as scalable, broadband, multiresonant optical antennas

Optical antennas perform the same functions for light that aerials do for radio waves; they can extract energy from a propagating electromagnetic field, and they can convert localized energy into propagating radiation. Here, we use a fractal-like design, the Cayley tree, to create optical antennas. Implementing this simple iterative design with aluminum as the antenna material, we demonstrate optical antennas with broadband operating range from energies corresponding to thermal radiation up to ultraviolet. The spatial distribution of electromagnetic energy inside the antennas is experimentally imaged using electron energy loss spectroscopy, a technique allowing direct imaging and spectroscopy at the nanoscale. Such antennas are interesting for applications including photodetection, nonlinear frequency conversion, and infrared absorption spectroscopy.

An optical antenna can convert a propagative optical radiation into a localized excitation and the reciprocal. Although optical antennas can be readily created using resonant nanoparticles (metallic or dielectric) as elementary building blocks, the realization of antennas sustaining multiple resonances over a broad range of frequencies remains a challenging task. Here, we use aluminum self-similar, fractal-like structures as broadband optical antennas. Using electron energy loss spectroscopy, we experimentally evidence that a single aluminum Cayley tree, a simple self-similar structure, sustains multiple plasmonic resonances. The spectral position of these resonances is scalable over a broad spectral range spanning two decades, from ultraviolet to midinfrared. Such multiresonant structures are highly desirable for applications ranging from nonlinear optics to light harvesting and photodetection, as well as surface-enhanced infrared absorption spectroscopy.

Multifunctional Chemical Sensing Platform Based on Dual-Resonant Infrared Plasmonic Perfect Absorber for On-Chip Detection of Poly(ethyl cyanoacrylate)

Multifunctional chemical sensing is highly desirable in industry, agriculture, and environmental sciences, but remains challenging due to the diversity of chemical substances and reactions. Surface-enhanced infrared absorption (SEIRA) spectroscopy can potentially address the above problems by ultra-sensitive detection of molecular fingerprint vibrations. Here, a multifunctional chemical sensing platform based on dual-resonant SEIRA device for sensitive and multifunctional on-chip detection of poly(ethyl cyanoacrylate) (PECA) is reported. It is experimentally demonstrated that the SEIRA sensing platform achieves multiple functions required by the PECA glue industry, including vibrational detection, thickness measurement, and in situ observation of polymerization and curing, which are usually realized by separately using a spectrometer, a viscometer, and an ellipsometer in the past. Specifically, the all-in-one sensor offers a dual-band fingerprint vibration identification, sub-nm level detection limit, and ultrahigh sensitivity of 0.76%/nm in thickness measurement, and second-level resolution in real-time observation of polymerization and curing. This work not only provides a valuable toolkit for ultra-sensitive and multifunctional on-chip detection of PECA, but also gives new insights into the SEIRA technology for multi-band, multi-functional, and on-chip chemical sensing.

Constructing Metastructures with Broadband Electromagnetic Functionality

Electromagnetic metastructures stand for the artificial structures with a characteristic size smaller than the wavelength, which may efficiently manipulate the states of light. However, their applications are often restricted by the bandwidth of the electromagnetic response of the metastructures. It is therefore essential to reassert the principles in constructing broadband electromagnetic metastructures. Herein, after summarizing the conventional approaches for achieving broadband electromagnetic functionality, some recent developments in realizing broadband electromagnetic response by dispersion compensation, nonresonant effects, and several trade-off approaches are reviewed, followed by some perspectives for the future development of broadband metamaterials. It is anticipated that broadband metastructures will have even more substantial applications in optoelectronics, energy harvesting, and information technology.

Multi-Frequency Resonance Behaviour of a Si FractalNEMS Resonator

Novel Si-based nanosize mechanical resonator has been top-down fabricated. The shape of the resonating body has been numerically derived and consists of seven star-polygons that form a fractal structure. The actual resonator is defined by focused ion-beam implantation on a SOI wafer where its 18 vertices are clamped to nanopillars. The structure is suspended over a 10 μm trench and has width of 12 μm. Its thickness of 0.040 μm is defined by the fabrication process and prescribes Young’s modulus of 76 GPa which is significantly lower than the value of the bulk material. The resonator is excited by the bottom Si-layer and the interferometric characterisation confirms broadband frequency response with quality factors of over 800 for several peaks between 2 MHz and 16 MHz. COMSOL FEM software has been used to vary material properties and residual stress in order to fit the eigenfrequencies of the model with the resonance peaks detected experimentally. Further use of the model shows how the symmetry of the device affects the frequency spectrum. Also, by using the FEM model, the possibility for an electrical read out of the device was tested. The experimental measurements and simulations proved that the device can resonate at many different excitation frequencies allowing multiple operational bands. The size, and the power needed for actuation are comparable with the ones of single beam resonator while the fractal structure allows much larger area for functionalisation.

Quasi-Periodic Dendritic Metasurface for Integral Operation in Visible Light

A reflective metasurface model composed of silver dendritic units is designed in this study. The integral property of this metasurface, which consists of an upper layer of dendritic structures, a silica spacer, and a bottom silver substrate was demonstrated at visible wavelengths. The simulation results revealed that the metasurface can perform integral operation in the yellow and red bands; this can be easily generalized to the infrared and communication bands by scaling the transverse dimensions of this metasurface. A dendritic metasurface sample responding to red light was prepared via the bottom-up electrochemical deposition method. The integral operation property of the sample was verified experimentally. This dendritic metasurface, which can perform integral operation in visible light, can be used for big data processing technology, real-time signal processing, and beam shaping, and provides a new method for miniaturized and integrated all-optical signal processing systems.

Deep learning: a new tool for photonic nanostructure design

Early results have shown the potential of Deep Learning (DL) to disrupt the fields of optical inverse-design, particularly, the inverse design of nanostructures. In the last three years, the complexity of the optical nanostructure being designed and the sophistication of the employed DL methodology have steadily increased. This topical review comprehensively surveys DL based design examples from the nanophotonics literature. Notwithstanding the early success of this approach, its limitations, range of validity and its place among established design techniques remain to be assessed. The review also provides a perspective on the limitations of this approach and emerging research directions. It is hoped that this topical review may help readers to identify unaddressed problems, to choose an initial setup for a specific problem, and, to identify means to improve the performance of existing DL based workflows.

Miniaturized fractal optical nanoantennas defined by focused helium ion beam milling

It has been shown in the past that fractal geometries are beneficial for radio and communication antenna designs in terms of bandwidth and gain. Recently, this concept was extended to plasmonic nanoantennas. Here, we present a fabrication method based on electron beam lithography and focused helium ion beam milling to further miniaturize dimer nanoantennas of 0th, 1st and 2nd order Sierpiński fractals. With this state-of-the-art approach, it becomes feasible to experimentally move their resonance conditions into the sub-micron wavelength regime, while maintaining excellent pattern definition and achieving sub-10 nm gap sizes for high near-field enhancement. These highly sophisticated nanostructures are numerically simulated and analyzed by dark-field scattering spectroscopy to monitor the effects of the fractal structuring on the scattering spectra and near-field enhancement.

In situ Ga-alloying in germanium nano-twists by the inhibition of fractal growth with fast Li+-mobility

In this study, Ge0.90Ga0.10 nano-twists were prepared by an in situ Ga-alloying method to inhibit the fractal growth of Ge. The mobility of Li+ in the Ge0.90Ga0.10 nano-twists was two orders higher than that in Ge. This advantage promotes fast charging of Li-ion batteries with the rate capability of 819 mA h g-1 at 16 A g-1.

Probing mid-infrared plasmon resonances in extended radial fractal structures

Infrared (IR) antennas made of metallic nanostructures are widely tunable from the near- to the far-IR range. They can be utilized for a variety of applications such as light harvesting and photonic filters, and their structural linear or circular anisotropy can be exploited to further enhance the sensitivity of spectroscopic measurements. Here gold dendritic fractal structures that were optimized to exhibit multiple resonances in the mid-IR range were characterized using a scattering-type scanning near-field optical IR microscope. The spatially resolved IR maps associated with the individual modes serve as a basis to understand the mode evolution between each fractal generation.

Surface-Enhanced Raman Scattering (SERS) Studies of Disc-on-Pillar (DOP) Arrays: Contrasting Enhancement Factor with Analytical Performance

The use of nanomachining methods capable of reproducible construction of nano-arrayed devices have revolutionized the field of plasmonic sensing by the introduction of a diversity of rationally engineered designs. Significant strides have been made to fabricate plasmonic platforms with tailored interparticle gaps to improve their performance for surface-enhanced Raman scattering (SERS) applications. Over time, a dichotomy has emerged in the implementation of SERS for analytical applications, the construction of substrates, optimization of interparticle spacing as a means to optimize electromagnetic field enhancement at the localized surface plasmon level, and the substrate sensitivity over extended areas to achieve quantitative performance. This work assessed the enhancement factor of plasmonic Ag/SiO₂/Si disc-on-pillar (DOP) arrays of variable pitch with its analytical performance for quantitative applications. Experimental data were compared with those from finite-difference time-domain (FDTD) simulations used in the optimization of the array dimensions. A self-assembled monolayer (SAM) of benzenethiol rendered highly reproducible signals (RSD ∼4-10%) and SERS substrate enhancement factor (SSEF) values in the orders of 10⁶-10⁸ for all pitches. Spectra corresponding to rhodamine 6G (R6G) and 4-aminobenzoic acid demonstrated the advantages of using the more densely packed DOP arrays with a 160 nm pitch (gap = 40 nm) for quantitation in spite of the strongest SSEF was attained for a pitch of 520 nm corresponding to a 400 nm gap.

Advancements in fractal plasmonics: structures, optical properties, and applications

Fractal nanostructures exhibit optical properties that span the visible to far-infrared and are emerging as exciting structures for plasmon-mediated applications.

Geometric frustration in a hexagonal lattice of plasmonic nanoelements

We introduce the concept of geometric frustration in plasmonic arrays of nanoelements. In particular, we present the case of a hexagonal lattice of Au nanoasterisks arranged so that the gaps between neighboring elements are small and lead to a strong near-field dipolar coupling. Besides, far-field interactions yield higher-order collective modes around the visible region that follow the translational symmetry of the lattice. However, dipolar excitations of the gaps in the hexagonal array are geometrically frustrated for interactions beyond nearest neighbors, yielding the destabilization of the low energy modes in the near infrared. This in turn results in a slow dynamics of the optical response and a complex interplay between localized and collective modes, a behavior that shares features with geometrically frustrated magnetic systems.

Resolving molecule-specific information in dynamic lipid membrane processes with multi-resonant infrared metasurfaces

A multitude of biological processes are enabled by complex interactions between lipid membranes and proteins. To understand such dynamic processes, it is crucial to differentiate the constituent biomolecular species and track their individual time evolution without invasive labels. Here, we present a label-free mid-infrared biosensor capable of distinguishing multiple analytes in heterogeneous biological samples with high sensitivity. Our technology leverages a multi-resonant metasurface to simultaneously enhance the different vibrational fingerprints of multiple biomolecules. By providing up to 1000-fold near-field intensity enhancement over both amide and methylene bands, our sensor resolves the interactions of lipid membranes with different polypeptides in real time. Significantly, we demonstrate that our label-free chemically specific sensor can analyze peptide-induced neurotransmitter cargo release from synaptic vesicle mimics. Our sensor opens up exciting possibilities for gaining new insights into biological processes such as signaling or transport in basic research as well as provides a valuable toolkit for bioanalytical and pharmaceutical applications.

Modeling the Improved Visual Acuity Using Photodiode Based Retinal Implants Featuring Fractal Electrodes

Electronically restoring vision to patients blinded by severe retinal degenerations is rapidly becoming a realizable feat through retinal implants. Upon receiving an implant, previously blind patients can now detect light, locate objects, and determine object motion direction. However, the restored visual acuity (VA) is still significantly below the legal blindness level (VA < 20/200). The goal of this research is to optimize the inner electrode geometry in photovoltaic subretinal implants in order to restore vision to a VA better than blindness level. We simulated neural stimulation by 20 μm subretinal photovoltaic implants featuring square or fractal inner electrodes by: (1) calculating the voltage generated on the inner electrode based on the amount of light entering the photodiode, (2) mapping how this voltage spreads throughout the extracellular space surrounding retinal bipolar neurons, and (3) determining if these extracellular voltages are sufficient for neural stimulation. By optimizing the fractal inner electrode geometry, we show that all neighboring neurons can be stimulated using an irradiance of 12 mW/mm², while the optimized square only stimulates ~10% of these neurons at an equivalent irradiance. The 20 μm fractal electrode can thus theoretically restore VA up to 20/80, if other limiting factors common to retinal degenerations, such as glia scarring and rewiring of retinal circuits, could be reduced. For the optimized square to stimulate all neighboring neurons, the irradiance has to be increased by almost 300%, which is very near the maximum permissible exposure safety limit. This demonstration that fractal electrodes can stimulate targeted neurons for long periods using safe irradiance levels highlights the possibility for restoring vision to a VA better than the blindness level using photodiode-based retinal implants.

Self-Similarity of Plasmon Edge Modes on Koch Fractal Antennas

We investigate the plasmonic behavior of Koch snowflake fractal geometries and their possible application as broadband optical antennas. Lithographically defined planar silver Koch fractal antennas were fabricated and characterized with high spatial and spectral resolution using electron energy loss spectroscopy. The experimental data are supported by numerical calculations carried out with a surface integral equation method. Multiple surface plasmon edge modes supported by the fractal structures have been imaged and analyzed. Furthermore, by isolating and reproducing self-similar features in long silver strip antennas, the edge modes present in the Koch snowflake fractals are identified. We demonstrate that the fractal response can be obtained by the sum of basic self-similar segments called characteristic edge units. Interestingly, the plasmon edge modes follow a fractal-scaling rule that depends on these self-similar segments formed in the structure after a fractal iteration. As the size of a fractal structure is reduced, coupling of the modes in the characteristic edge units becomes relevant, and the symmetry of the fractal affects the formation of hybrid modes. This analysis can be utilized not only to understand the edge modes in other planar structures but also in the design and fabrication of fractal structures for nanophotonic applications.

Spontaneous Formation of Fractal Aggregates of Au Nanoparticles in Epoxy-Siloxane Films and Their Application as Substrates for NIR Surface Enhanced Raman Spectroscopy

We present a facile, inexpensive route to free-standing, thermo-mechanically robust and flexible epoxy-siloxane substrates embedded with fractal aggregates of Au nanoparticles, and demonstrate their efficiency as substrates for surface enhanced Raman spectroscopy (SERS) at NIR wavelengths. The metallodielectric films are prepared by generating Au nanoparticles through the in-situ reduction of gold (III) chloride trihydrate in epoxypropoxypropyl terminated polydimethyl siloxane (EDMS). The metal nanoparticles spontaneously aggregate into fractal structures in the colloid, which could then be drop-cast onto a substrate. Subsequent UV-initiated cationic polymerization of epoxide moieties in EDMS transforms the fluid colloid into a thin, free-standing film, which contains a dense distribution of fractal aggregates of Au nanoparticles. We used electron and optical microscopy as well as UV⁻Vis⁻NIR spectrometry to monitor the evolution of nanoparticles and to optically and structurally characterize the resulting films. Raman spectroscopy of the chromophore Eosin Y adsorbed onto the metallodielectric films showed that they are excellent SERS substrates at NIR excitation with an enhancement factor of ~9.3 × 10³.

Fractal Electrodes as a Generic Interface for Stimulating Neurons

The prospect of replacing damaged body parts with artificial implants is being transformed from science fiction to science fact through the increasing application of electronics to interface with human neurons in the limbs, the brain, and the retina. We propose bio-inspired electronics which adopt the fractal geometry of the neurons they interface with. Our focus is on retinal implants, although performance improvements will be generic to many neuronal types. The key component is a multifunctional electrode; light passes through this electrode into a photodiode which charges the electrode. Its electric field then stimulates the neurons. A fractal electrode might increase both light transmission and neuron proximity compared to conventional Euclidean electrodes. These advantages are negated if the fractal’s field is less effective at stimulating neurons. We present simulations demonstrating how an interplay of fractal properties generates enhanced stimulation; the electrode voltage necessary to stimulate all neighboring neurons is over 50% less for fractal than Euclidean electrodes. This smaller voltage can be achieved by a single diode compared to three diodes required for the Euclidean electrode’s higher voltage. This will allow patients, for the first time, to see with the visual acuity necessary for navigating rooms and streets.

Dendritic optical antennas: scattering properties and fluorescence enhancement

With the development of nanotechnologies, researchers have brought the concept of antenna to the optical regime for manipulation of nano-scaled light matter interactions. Most optical nanoantennas optimize optical function, but are not electrically connected. In order to realize functions that require electrical addressing, optical nanoantennas that are electrically continuous are desirable. In this article, we study the optical response of a type of electrically connected nanoantennas, which we propose to call “dendritic” antennas. While they are connected, they follow similar antenna hybridization trends to unconnected plasmon phased array antennas. The optical resonances supported by this type of nanoantennas are mapped both experimentally and theoretically to unravel their optical response. Photoluminescence measurements indicate a potential Purcell enhancement of more than a factor of 58.

Dynamics of a Polymer Network Based on Dual Sierpinski Gasket and Dendrimer: A Theoretical Approach

In this paper we focus on the relaxation dynamics of a multihierarchical polymer network built through the replication of the dual Sierpinski gasket in the form of a regular dendrimer. The relaxation dynamics of this multihierarchical structure is investigated in the framework of the generalized Gaussian structure model using both Rouse and Zimm approaches. In the Rouse-type approach, we show a method whereby the whole eigenvalue spectrum of the connectivity matrix of the multihierarchical structure can be determined iteratively, thereby rendering possible the analysis of the Rouse-dynamics at very large generations. Remarkably, the general picture that emerges from both approaches, even though we have a mixed growth algorithm and the monomers interactions are taken into account specifically to the adopted approach, is that the multihierarchical structure preserves the individual relaxation behaviors of its constituent components. The theoretical findings with respect to the splitting of the intermediate domain of the relaxation quantities are well supported by experimental results.

Synergistic Effects of Plasmonics and Electron Trapping in Graphene Short-Wave Infrared Photodetectors with Ultrahigh Responsivity

Graphene's unique electronic and optical properties have made it an attractive material for developing ultrafast short-wave infrared (SWIR) photodetectors. However, the performance of graphene SWIR photodetectors has been limited by the low optical absorption of graphene as well as the ultrashort lifetime of photoinduced carriers. Here, we present two mechanisms to overcome these two shortages and demonstrate a graphene-based SWIR photodetector with high responsivity and fast photoresponse. In particular, a vertical built-in field is employed in the graphene channel for trapping the photoinduced electrons and leaving holes in graphene, which results in prolonged photoinduced carrier lifetime. On the other hand, plasmonic effects were employed to realize photon trapping and enhance the light absorption of graphene. Thanks to the above two mechanisms, the responsivity of this proposed SWIR photodetector is up to a record of 83 A/W at a wavelength of 1.55 μm with a fast rising time of less than 600 ns. This device design concept addresses key challenges for high-performance graphene SWIR photodetectors and is promising for the development of mid/far-infrared optoelectronic applications.

Enhanced Graphene Photodetector with Fractal Metasurface

Graphene has been demonstrated to be a promising photodetection material because of its ultrabroadband optical absorption, compatibility with CMOS technology, and dynamic tunability in optical and electrical properties. However, being a single atomic layer thick, graphene has intrinsically small optical absorption, which hinders its incorporation with modern photodetecting systems. In this work, we propose a gold snowflake-like fractal metasurface design to realize broadband and polarization-insensitive plasmonic enhancement in graphene photodetector. We experimentally obtain an enhanced photovoltage from the fractal metasurface that is an order of magnitude greater than that generated at a plain gold-graphene edge and such an enhancement in the photovoltage sustains over the entire visible spectrum. We also observed a relatively constant photoresponse with respect to polarization angles of incident light, as a result of the combination of two orthogonally oriented concentric hexagonal fractal geometries in one metasurface.

Relaxation dynamics of Sierpinski hexagon fractal polymer: Exact analytical results in the Rouse-type approach and numerical results in the Zimm-type approach

In this paper, we focus on the relaxation dynamics of Sierpinski hexagon fractal polymer. The relaxation dynamics of this fractal polymer is investigated in the framework of the generalized Gaussian structure model using both Rouse and Zimm approaches. In the Rouse-type approach, by performing real-space renormalization transformations, we determine analytically the complete eigenvalue spectrum of the connectivity matrix. Based on the eigenvalues obtained through iterative algebraic relations we calculate the averaged monomer displacement and the mechanical relaxation moduli (storage modulus and loss modulus). The evaluation of the dynamical properties in the Rouse-type approach reveals that they obey scaling in the intermediate time/frequency domain. In the Zimm-type approach, which includes the hydrodynamic interactions, the relaxation quantities do not show scaling. The theoretical findings with respect to scaling in the intermediate domain of the relaxation quantities are well supported by experimental results.

Realization of Fractal-Inspired Thermoresponsive Quasi-3D Plasmonic Metasurfaces with EOT-Like Transmission for Volumetric and Multispectral Detection in the Mid-IR Region

We use a paradigmatic mathematic model known as Sierpiński fractal to reverse-engineer artificial nanostructures that can potentially serve as plasmonic metasurfaces as well as nanogap electrodes. Herein, we particularly demonstrate the possibility of obtaining multispectral extraordinary optical transmission-like transmission peaks from fractal-inspired geometries, which can preserve distinct spatial characteristics. To achieve enhanced volumetric interaction and thermal responsiveness within the framework, we consider a bilayer, quasi-three-dimensional (3D) configuration that relies on the unique approach of combining complementary and noncomplementary surfaces, while avoiding the need for multilayer alignment on the nanoscale. We implement an improved version of the model to (1) increase the volume of quasi-3D nanochannels and enhance the lightening-rod effect of the metasurfaces, (2) harness cross-coupling as a mechanism for achieving better sensitivity, and (3) exploit optical magnetism for pushing the resonances to longer wavelengths on a miniaturized platform. We further demonstrate vertical coupling as an effective route for ultimate miniaturization of such quasi-3D nanostructures. We report a wavelength shift up to 1666 nm/refractive index unit and 2.5 nm/°C, implying the usefulness of the proposed devices for applications such as dielectrophoretic sensing and nanothermodynamic study of molecular reactions in the chemically active mid-IR spectrum.

Plasmonic Circuit Theory for Multiresonant Light Funneling to a Single Spatial Hot Spot

We present a theoretical framework, based on plasmonic circuit models, for generating a multiresonant field intensity enhancement spectrum at a single "hot spot" in a plasmonic device. We introduce a circuit model, consisting of an array of coupled LC resonators, that directs current asymmetrically in the array, and we show that this circuit can funnel energy efficiently from each resonance to a single element. We implement the circuit model in a plasmonic nanostructure consisting of a series of metal bars of differing length, with nearest neighbor metal bars strongly coupled electromagnetically through air gaps. The resulting nanostructure resonantly traps different wavelengths of incident light in separate gap regions, yet it funnels the energy of different resonances to a common location, which is consistent with our circuit model. Our work is important for a number of applications of plasmonic nanoantennas in spectroscopy, such as in single-molecule fluorescence spectroscopy or Raman spectroscopy.

Midrefractive Dielectric Modulator for Broadband Unidirectional Scattering and Effective Radiative Tailoring in the Visible Region

Nanoantennas have found many applications in ultrasmall sensors, single-molecule detection, and all-optical communication. Conventional nanoantennas are based on noble-metal plasmonic structures, but suffer from large ohmic loss and only possess dipolar plasmon modes. This has driven an intense search for all-dielectric materials beyond noble metals. Here, we propose midrefractive nanospheres as a novel all-dielectric material to realize broadband unidirectional radiation and effective radiative tailoring in the visible region. Midrefractive all-dielectric materials such as boron nanospheres possess broad and overlapping electric and magnetic dipole modes. The internal interaction between these two modes can route the radiation almost on the one side covering the whole visible range. Unlike the elaborate design in plasmonic nanostructures to obtain strong coupled broad and narrow modes, the bright mode in boron nanospheres is intrinsic, independent, and easily coupled with adjacent narrow modes. So the strong interaction in boron-based heterodimer is able to realize an independent and precise tailoring of the radiant and subradiant states by simply changing the particle sizes, respectively. Our findings imply midrefractivity materials like boron are excellent building blocks to support electromagnetic coupling operation in nanoscale devices, which will lead to a variety of emerging applications such as nanoantennas with directing exciton emission, ultrasensitive nanosensors, or even potential new construction of photonic metamaterials.

Impact of local-field effects on the plasmonic enhancement of vibrational signals by infrared nanoantennas

We have developed an analytical model that provides a mechanistic description of the plasmonic enhancement of vibrational signals by infrared nanoantennas. Our treatment is based on a coupled-point-dipole model which considers the interaction between a point-like nanoantenna and a single vibrational dipole moment. This idealized model is refined in two consecutive steps. The first step generalizes the model to make the treatment of non-point-like nanoantennas possible. The second step deals with local-field effects originating from the mutual interaction of the molecular vibrations. We have compared the results of our model with finite-difference time-domain simulations, and we find that our model predicts both the lineshapes and the amplitudes of the vibrational signals in a quantitative manner. Our analysis shows that the local-field effects play a surprisingly dominant role in the plasmonic enhancement, and we discuss possibilities of engineering this local field in order to further boost the plasmonic amplification.

Biotags Based on Surface-Enhanced Raman Can Be as Bright as Fluorescence Tags

Surface enhanced Raman spectroscopy (SERS) is a powerful analytical technique that has been proposed as a substitute for fluorescence for biological imaging and detection but is not yet commercially utilized. The reason lies primarily in the lower intensity and poor reproducibility of most metal nanoparticle-based tags as compared to their fluorescence-based counterparts. Here, using a technique that scrupulously preserves the same number of dye molecules in both the SERS and fluorescence measurements, we show that SERS-based biotags (SBTs) with highly reproducible optical properties can be nanoengineered such that their brightness is at least equal to that of fluorescence-based tags.

A mechanically driven form of Kirigami as a route to 3D mesostructures in micro/nanomembranes

Assembly of 3D micro/nanostructures in advanced functional materials has important implications across broad areas of technology. Existing approaches are compatible, however, only with narrow classes of materials and/or 3D geometries. This paper introduces ideas for a form of Kirigami that allows precise, mechanically driven assembly of 3D mesostructures of diverse materials from 2D micro/nanomembranes with strategically designed geometries and patterns of cuts. Theoretical and experimental studies demonstrate applicability of the methods across length scales from macro to nano, in materials ranging from monocrystalline silicon to plastic, with levels of topographical complexity that significantly exceed those that can be achieved using other approaches. A broad set of examples includes 3D silicon mesostructures and hybrid nanomembrane-nanoribbon systems, including heterogeneous combinations with polymers and metals, with critical dimensions that range from 100 nm to 30 mm. A 3D mechanically tunable optical transmission window provides an application example of this Kirigami process, enabled by theoretically guided design.