Subwavelength Cross Section Research Articles

Bottom-up Filling of Nanosized Trenches with Silver to Fabricate Transparent Conducting Electrodes

Transparent conducting electrodes (TCEs) are essential in many optoelectronic devices including solar cells, sensors, displays, and LEDs. The use of transparent metal oxide layers, in particular Indium tin oxide (ITO), is the most common used approach. However, ITO comes with numerous drawbacks such as the relatively rarity of indium and hence high cost, fragility, strong UV absorption and relative high sheet resistance. An exciting alternative TCE is the use of interconnected metallic nanowires, where their sub-wavelength cross-sections makes them transparent to visible light, where especially silver nanowires are a good candidate because of their high conductivity.Here we show a promising cost-effective method called selective-area electrochemical deposition (SAEC) for the fabrication of these metal nanostructures. SAEC is based on a through-the-mask electrochemical deposition method, where the mask is made using substrate conformal imprint lithography. Next to the inherent low fabrication cost of the electrochemical deposition, it has numerous advantages such as bottom-up growth, scalability, operate at ambient conditions, control over nucleation, and yields high purity deposits. While submicron sized features have been already demonstrated by SAEC, obtaining homogeneous void free filling of features below 100 nm using direct plating is a major challenge because of the terminal effect and the poor control of nucleation of the seed layer.In this work, we have explored the SAEC fabrication of large area silver nanowire grids on ITO substrates and on TOPCon solar cells. We show that the nucleation density of the silver nanoparticles is the key parameter for the successful homogenous void-free filling of the trenches. The nucleation density namely determines the coalescence thickness, which sets a minimum thickness for the silver nanowires in order to be connected. We control the nucleation density of the silver nanoparticles by making use of the double pulse method, where a high overpotential nucleation pulse is applied for controlling the nucleation density. After nucleation, we merge the silver nuclei by applying a low overpotential growth pulse.After the successful filling of the trenches, we have compared the optical and electrical performance of the SAEC fabricated silver nanowire grids to those using conventional thermal or e-beam evaporation followed by lift-off. The SAEC-fabricated TCEs show high transmission (>96%) and extreme low resistance (as low as 3 Ω/sq), resulting into a superior figure of merit (FoM). Due to the bottom-up nature of this technique, arbitrary high aspect ratio nanowires can be achieved and therefore the relationship of decreasing transmission with decreasing sheet resistance is broken.Furthermore, we have also incorporated the silver NW grids in TOPCon cells and compared the performance to similar cells based on ITO. This work represents a low-cost and scalable strategy to fabricate sub 100 nm predefined metal structures, enabling the commercial viable fabrication of nanostructure based transparent conductive electrodes for optoelectronic devices.

Photoemission Electron Microscopy of Blue and UV Surface Plasmons on Nanostructured Aluminum Films

We image surface plasmons on aluminum surfaces in the ultraviolet and blue spectral range with photoemission electron microscopy (PEEM). Plasmon excitation is mediated by light incident on straight aluminum ridges with subwavelength cross section on flat aluminum films. We observe interference patterns due to light/plasmon interaction, with distinct periodicity and orientation depending on the light in-plane incidence angle with respect to the ridge orientation. From the interference patterns, we deduce the surface plasmon propagation directions and decay lengths. The latter are remarkably high with 2.8 μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu$$\\end{document}m and 8.4 μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu$$\\end{document}m for excitation wavelengths of 273 nm and 410 nm, respectively. Our results extend PEEM imaging of surface plasmons into the ultraviolet region.

Elastic Gallium Phosphide Nanowire Optical Waveguides-Versatile Subwavelength Platform for Integrated Photonics.

Emerging technologies for integrated optical circuits demand novel approaches and materials. This includes a search for nanoscale waveguides that should satisfy criteria of high optical density, small cross-section, technological feasibility and structural perfection. All these criteria are met with self-assembled gallium phosphide (GaP) epitaxial nanowires. In this work, the effects of the nanowire geometry on their waveguiding properties are studied both experimentally and numerically. Cut-off wavelength dependence on the nanowire diameter is analyzed to demonstrate the pathways for fabrication of low-loss and subwavelength cross-section waveguides for visible and near-infrared (IR) ranges. Probing the waveguides with a supercontinuum laser unveils the filtering properties of the nanowires due to their resonant action. The nanowires exhibit perfect elasticity allowing fabrication of curved waveguides. It is demonstrated that for the nanowire diameters exceeding the cut-off value, the bending does not sufficiently reduce the field confinement promoting applicability of the approach for the development of nanoscale waveguides with a preassigned geometry. Optical X-coupler made of two GaP nanowires allowing for spectral separation of the signal is fabricated. The results of this work open new ways for the utilization of GaP nanowires as elements of advanced photonic logic circuits and nanoscale interferometers.

Retrieving the subwavelength cross-section of dielectric nanowires with asymmetric excitation of Bloch surface waves.

Optical microscopy with a diffraction limit cannot distinguish nanowires with sectional dimensions close to or smaller than the optical resolution. Here, we propose a scheme to retrieve the subwavelength cross-section of nanowires based on the asymmetric excitation of Bloch surface waves (BSWs). Leakage radiation microscopy is used to observe the propagation of BSWs at the surface and to collect far-field scattering patterns in the substrate. A model of linear dipoles induced by tilted incident light is built to explain the directional imbalance of BSWs. It shows the potential capability in precisely resolving the subwavelength cross-section of nanowires from far-field scattering without the need for complex algorithms. Through comparing the nanowire widths measured by this method and those measured by scanning electron microscopy (SEM), the transverse resolutions of the widths of two series of nanowires with heights 55 nm and 80 nm are about 4.38 nm and 6.83 nm. All results in this work demonstrate that the new non-resonant far-field optical technology has potential application in metrology measurements with high precision by taking care of the inverse process of light-matter interaction.

High-acoustic-index-contrast phononic circuits: Numerical modeling

We numerically model key building blocks of a phononic integrated circuit that enable phonon routing in high-acoustic-index waveguides. Our particular focus is on the gallium nitride-on-sapphire phononic platform which has recently demonstrated high acoustic confinement in its top layer without the use of suspended structures. We start with the systematic simulation of various transverse phonon modes supported in strip waveguides and ring resonators with sub-wavelength cross section. Mode confinement and quality factors of phonon modes are numerically investigated with respect to geometric parameters. A quality factor of up to 108 is predicted in optimized ring resonators. Next, we study the design of the phononic directional couplers and present key design parameters for achieving strong evanescent couplings between modes propagating in parallel waveguides. Last, interdigitated transducer electrodes are included in the simulation for direct excitation of a ring resonator and critical coupling between microwave input and phononic dissipation. Our work provides a comprehensive numerical characterization of phonon modes and functional phononic components in high-acoustic-index phononic circuits, which supplements previous theories and contributes to the emerging field of phononic integrated circuits.

Polarization mode hybridization and conversion in phononic wire waveguides

Phononic wire waveguides of subwavelength cross sections support two orthogonal polarization modes: the out-of-plane motion dominated Rayleigh-like and the in-plane motion dominated Love-like modes, analogous to transverse-electric and transverse-magnetic modes in photonic waveguides. Due to the anisotropic elasticity of the substrate material, the polarization states of phonons propagating along certain crystallographic orientations can strongly hybridize. Here, we experimentally investigate the orientation-dependent mode hybridization in phononic wire waveguides patterned from GaN-on-sapphire thin films. Such mode hybridization allows efficient actuation of piezoelectrically inactive Love-like modes using common interdigital electrodes designed for Rayleigh-like modes and further enables on-chip polarization conversion between guided transverse modes. Both are important for on-chip implementation of complex phononic circuits.

Optical trapping of sub-wavelength objects with point-like slot waveguides

An optical tweezer capable of picking up dielectric as well as metallic objects of sizes much smaller than the light wavelength is proposed based on point-like two-dimensionally slotted waveguides. Slot waveguides transport light based on evanescent modes, therefore, with sub-wavelength resolution. A point-like slot waveguide confines light within a sub-wavelength cross-section, and a strong gradient electric field is formed. A radiation force is induced by the strong gradient field, and the force is strong enough for optically trapping and manipulating small objects of different sizes and refractive indice with sub-wavelength resolution. As an example, the proposed device is numerically simulated with a rectangular slot waveguide so as to confirm its feasibility. Since the assumed device profile and materials are common for chip formation, the proposed device has the potential to become a lab-on-a-chip opto-electric tool for biologic analysis.

Microstructures for lowering the quarter wavelength resonance frequency of a hard-backed rigid-porous layer

The frequency of the quarter wavelength resonance in the sound absorption spectra due to a thin hard-backed rigid-porous layer can be influenced by the design of its microstructure as well as its thickness. Microstructures considered include parallel arrays of identical cylindrical, slit-like or rectangular pores with deep sub-wavelength cross sections inclined to the surface normal, cylindrical annular pores, slits with log-normal width distributions, slits with cross sections that vary in a sinusoidal manner and slits with two distinct widths (dual porosity). Formulae that predict the bulk acoustical properties due to these microstructures are presented and used to explore the extent to which specific microstructures could be used separately or in combination to improve low-frequency absorption. Predicted normal incidence absorption coefficient spectra are compared using microstructural dimensions that would be feasible for 3D printing. The most effective microstructures are predicted to be slits with sinusoidally-varying widths, or with two distinct widths, inclined to the surface normal at 70°. The quarter wavelength layer resonances predicted in absorption coefficient spectra using these microstructures are comparable with those predicted for layers of the same thickness and bulk porosity having cylindrical pores with dead-end branches.

3-D near-field imaging of guided modes in nanophotonic waveguides

Abstract Highly evanescent waveguides with a subwavelength core thickness present a promising lab-on-chip solution for generating nanovolume trapping sites using overlapping evanescent fields. In this work, we experimentally studied Si3N4 waveguides whose sub-wavelength cross-sections and high aspect ratios support fundamental and higher order modes at a single excitation wavelength. Due to differing modal effective indices, these co-propagating modes interfere and generate beating patterns with significant evanescent field intensity. Using near-field scanning optical microscopy (NSOM), we map the structure of these beating modes in three dimensions. Our results demonstrate the potential of NSOM to optimize waveguide design for complex field trapping devices. By reducing the in-plane width, the population of competing modes decreases, resulting in a simplified spectrum of beating modes, such that waveguides with a width of 650 nm support three modes with two observed beats. Our results demonstrate the potential of NSOM to optimize waveguide design for complex field trapping devices.

Shaping a Subwavelength Needle with Ultra-long Focal Length by Focusing Azimuthally Polarized Light.

Flat optics, which could planarize and miniaturize the traditional optical elements, possesses the features of extremely low profile and high integration for advanced manipulation of light. Here we proposed and experimentally demonstrated a planar metalens to realize an ultra-long focal length of ~240λ with a large depth of focus (DOF) of ~12λ, under the illumination of azimuthally polarized beam with vortical phase at 633 nm. Equally important is that such a flat lens could stably keep a lateral subwavelength width of 0.42λ to 0.49λ along the needle-like focal region. It exhibits one-order improvement in the focal length compared to the traditional focal lengths of 20~30λ of flat lens, under the criterion of having subwavelength focusing spot. The ultra-long focal length ensures sufficient space for subsequent characterization behind the lens in practical industry setups, while subwavelength cross section and large DOF enable high resolution in transverse imaging and nanolithography and high tolerance in axial positioning in the meantime. Such planar metalens with those simultaneous advantages is prepared by laser pattern generator rather than focused ion beam, which makes the mass production possible.

Subwavelength light confinement and propagation: A numerical study of a two-layer silver film with perforated holes

Confinement and propagation of light under the diffraction limit is a substantial challenge for the development of waveguides as components in subwavelength optical devices. Light confinement and propagation at optical frequencies in a two-layer silver film with a periodic array of holes is investigated in a numerical study using the discrete dipole approximation method. Extraordinary subwavelength confinement and propagation of light can be obtained along an extremely subwavelength cross section of a region as small as 10 × 20 nm2 at a distance of over 10 μm. This study provides rational design of waveguides under subwavelength dimensions.

Experimental realization of optical lumped nanocircuits at infrared wavelengths

The integration of radiofrequency electronic methodologies on micro- as well as nanoscale platforms is crucial for information processing and data-storage technologies. In electronics, radiofrequency signals are controlled and manipulated by 'lumped' circuit elements, such as resistors, inductors and capacitors. In earlier work, we theoretically proposed that optical nanostructures, when properly designed and judiciously arranged, could behave as nanoscale lumped circuit elements--but at optical frequencies. Here, for the first time we experimentally demonstrate a two-dimensional optical nanocircuit at mid-infrared wavelengths. With the guidance of circuit theory, we design and fabricate arrays of Si3N4 nanorods with specific deep subwavelength cross-sections, quantitatively evaluate their equivalent impedance as lumped circuit elements in the mid-infrared regime, and by Fourier transform infrared spectroscopy show that these nanostructures can indeed function as two-dimensional optical lumped circuit elements. We further show that the connections among nanocircuit elements, in particular whether they are in series or in parallel combination, can be controlled by the polarization of impinging optical signals, realizing the notion of 'stereo-circuitry' in metatronics-metamaterials-inspired optical circuitry.

Guiding light at the nanoscale: numerical optimization of ultrasubwavelength metallic wire plasmonic waveguides

We present a comprehensive numerical analysis of the guiding of a photonic signal in the form of a strongly confined asymmetric surface plasmon polariton (SPP) mode along metallic nanowire waveguides. The proposed approach provides extremely high localization of the SPP mode, nanoscale integration density, and a feasible technological platform. The waveguide performance was studied over a broad range of subwavelength cross sections at a telecommunication wavelength. It was optimized using a conventional figure of merit for data transfer along a straight waveguide and an all-inclusive figure of merit has been introduced.

Transmission of electromagnetic waves through sub-wavelength channels

We propose a method of tunneling electromagnetic (EM) waves through a channel with sub-wavelength cross section. By filling the channel with high-epsilon isotropic material and implementing two matching layers with uniaxial metamterial substrates, the guided waves can go through the narrow channel without being cut off, as if it has just passed through the original empty waveguide. Both the magnitude and phase information of the EM fields can be effectively restored after passing this channel, regardless of the polarization of the incoming wave. The performance of this sub-wavelength channel, which is designed with coordinate transformation methodology, is studied theoretically and numerically.

A light touch on nanotubes: femtonewton force sensing and nanometric spatial resolution

Light can exert a mechanical action onmatter. Although this simple concept has been known for centuries (Kepler’s explanation of comet tails is based on it), the advent of the laser age has led to tremendous experimental advances and understanding of this phenomenon. Optical tweezers, instruments based on a tightly focused laser beam, have been used to trap, manipulate, control, and assemble dielectric particles, single atoms, cells, metal, and semiconducting nanostructures, leading to a real optical revolution in physics, biology, and nanotechnology. When used as force transducer, optical tweezers can measure forces in the piconewton range. In this context, the concept of photonic force microscopy (PFM) has been developed by scanning a dielectric sphere over surfaces in a liquid environment and sensing the force interaction. While the lateral resolution in PFM applications is related to particle size, the extension of conventional optical trapping to nanoparticles is a difficult task, since the radiation force scales with the volume of the trapped particle. Recently, optical trapping of carbon nanotube bundles was realized in aqueous environments. The almost linear geometry of these nanostructures, which have a subwavelength cross section and very high aspect ratio, is of crucial importance for bridging the gap between the micro and nano-world. In our work we demonstrated that the nanotubes’ small transverse size is key to achieving nanometric resolution for PFM applications, while an axial dimension in the micron range ensures stable trapping and allows force sensing in the femtonewton regime. A critical element in force sensing with optical tweezers is Brownian motion—random fluctuations of particles in a fluid. Performing statistical analysis of an optically trapped particle’s fluctuations about equilibrium enables force measurements. The Figure 1. (a) Optical trapping geometry. A laser beam is expanded to over-fill the back aperture of a high numerical microscope objective. The laser light propagates along the z axis (oriented as k wavevector) while x is the polarization axis (oriented as E=electric field). The light is focused in a chamber containing the nanotube solution; here the cylinder represents a randomly oriented nanotube. (b) A laser trapped bundle oriented by radiation torque along the optical axis. (c) The same bundle un-trapped (laser is off) and randomly oriented by Brownian motion.

Three-dimensional numerical modeling of photonic integration with dielectric-loaded SPP waveguides

Using full three-dimensional numerical modeling, we demonstrate highly efficient passive and active photonic circuit elements based on dielectric-loaded surface plasmon polariton waveguides (DLSPPWs). Highly confined surface plasmon polariton (SPP) mode having subwavelength cross section allows high level of integration of DLSPPW circuitry. We demonstrate very efficient guiding and routing of SPP signals with the passive waveguide elements such as bends, splitters, and Bragg reflectors, having a functional size of just a few microns at telecommunication wavelengths. Introducing a gain in the dielectric, we have found the requirement for lossless waveguiding and estimated the performance of DLSPPW lossless and active elements. DLSPPW based components have prospective implementation in photonic integrated chips, hybrid optical-electronic circuits, and lab-on-a-chip applications.

Theory of supercoupling, squeezing wave energy, and field confinement in narrow channels and tight bends usingεnear-zero metamaterials

In this work, we investigate the detailed theory of the supercoupling, anomalous tunneling effect, and field confinement originally identified by Silveirinha and Engheta [Phys. Rev. Lett. 97, 157403 (2006)], where we demonstrated the possibility of using materials with permittivity $\ensuremath{\epsilon}$ near zero to drastically improve the transmission of electromagnetic energy through a narrow irregular channel with very subwavelength transverse cross section. Here, we present additional physical insights, describe applications of the tunneling effect in relevant waveguide scenarios (e.g., the ``perfect'' or ``super'' waveguide coupling), and study the effect of metal losses in the metallic walls and the possibility of using near-zero $\ensuremath{\epsilon}$ materials to confine energy in a subwavelength cavity with gigantic field enhancement. In addition, we systematically study the propagation of electromagnetic waves through narrow channels filled with anisotropic near-zero $\ensuremath{\epsilon}$ materials. It is demonstrated that these materials may have interesting potentials, and that for some particular geometries, the reflectivity of the channel is independent of the specific dimensions or parameters of near-zero $\ensuremath{\epsilon}$ transition. We also describe several realistic metamaterial implementations of the studied problems, based on standard metallic waveguides, microstrip line configurations, and wire media.

Crystalline structure’s influence on the near-field optical properties of single plasmonic nanowires

The finite difference time domain method is employed to study the crystalline structure’s influence on the propagation of a local excitation along metallic nanowires of subwavelength cross section. The metallic nanowires are elongated cylinders deposited on a transparent substrate. A tightly focused gaussian beam illuminates one end of the nanowires. According to recent experimental studies, the authors show that the propagation length of the localized surface plasmon excitations depends on the crystalline structure of the nanowire. Thus, they are able to determine the effective permittivity of metals in such a nanostructure versus its crystalline properties. The authors also demonstrate that the field of optical information transport could greatly benefit from the care of the subwavelength optical waveguide’s crystallinity.

Passive photonic elements based on dielectric-loaded surface plasmon polariton waveguides

The authors present full three-dimensional numerical modeling of passive photonic elements based on dielectric-loaded surface plasmon polariton waveguides (DLSPPWs). They demonstrate that at telecom wavelengths a highly confined SPP mode can be guided in a single mode DLSPPW of subwavelength cross section and estimate the achievable density of photonic integration. The size of bending and splitting photonic elements based on DLSPPW can be as small as a few micrometers with pure bend loss less than 10% (0.4dB) and the transmission efficiency exceeding 70% (total loss of about 1.3dB). Such DLSPPW elements are important for implementation of photonic integrated circuits, guiding optical and electric signals in the same circuitry, and lab-on-a-chip applications.

Near-field optical properties of single plasmonic nanowires

The authors apply the finite difference time domain method to study the propagation of a local excitation along metallic nanowires of subwavelength cross section. The metallic nanowires are elongated cylinders deposited on a transparent substrate. A tightly focused Gaussian beam illuminates one end of the nanowires. The localized surface plasmon excitations propagate along the nanowire over distances much larger than the incident wavelength. According to recent experimental studies, they show that such nanostructures behave like a Fabry-Pérot cavity with large value of surface plasmon propagation length.