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Quantum states of cylindrical surface charge density for modeling plasmonic circuit elements: Nanowires, nanorods, cavities, and waveguides
Abstract
Nanostructures in the form of ellipsoids, prolate spheroids, rings, and cylinders are known to exhibit resonant surface and cavity modes with applications in nanophotonics and plasmonics and, more recently, in novel quantum experiments, in which control of plasmons and their interactions with plasmons, photons, phonons, excitons, and quantum emitters are desired. Nanorods and nanowires are examples of plasmonic structures with spectral properties of potential use as interconnects and circuit components. Estimates of the surface properties of these components are needed in circuit design and integrated systems. Here, we present a quantum Hamiltonian for the cylindrical surface charge density. We then study the photon excitation of plasmons on the cylindrical surface and calculate their scattering and radiative decay rate. Nonradiative decay of plasmons induces an efficient heating of the nanoparticle and can photoacoustically excite mechanical oscillations. Computational calculations are also presented for the plasmonic modes and the ensuing excitations of nanomechanical eigenmodes of nanoparticles with near-cylindrical symmetries.
... To construct effective nano photonic devices [1] with ultra-fast operational speed and the capability to concentrate the electromagnetic field into a region which is significantly narrower than the operating wavelength [2], using SPPs ensures that the objectives of the nanophotonic branch [3] are addressed. SPPs have been used extensively in several technologies, including waveguides [4], modulators [5], nano-lasers [6], nano rings [7], nano wires [8] and nano-antennas [9]. These can be advantageous because of their rapid transient response, compactness, and adjustability in efficiency parameters. ...
Photonic researchers are increasingly exploiting nanotechnology due to the development of numerous prevalent nanosized manufacturing technologies, which has enabled novel shape-optimized nanostructures to be manufactured and investigated. Hybrid nanostructures that integrate dielectric resonators with plasmonic nanostructures are also offering new opportunities. In this work, we have explored a hybrid coupled nano-structured antenna with stacked multilayer lithium tantalate (LiTaO3) and Aluminum oxide (Al2O3), operating at wavelength ranging from 400 nm to 2000 nm. Here, the sensitivity response has been explored of these nano-structured hybrid arrays. It shows a strong electromagnetic confinement in the separation gap (g) of the dimers due to strong surface plasmon resonance (SPR). The influences of the structural dimensions have been investigated to optimize the sensitivity. The designed hybrid coupled nanostructure with the combination of 10 layers of gold (Au) and Lithium tantalate (LiTaO3) or Aluminum oxide (Al2O3) (five layers each) having height, h1 = h2 = 10 nm exhibits 730 and 660 nm/RIU sensitivity, respectively. The sensitivity of the proposed hybrid nanostructure has been compared with a single metallic (only gold) elliptical paired nanostructure. Depending on these findings, we demonstrated that a roughly two-fold increase in the sensitivity (S) can be obtained by utilizing a hybrid coupled nanostructure compared to an identical nanostructure, which competes with traditional sensors of the same height, (h). Our innovative novel plasmonic hybrid nanostructures provide a framework for developing plasmonic nanostructures for use in various sensing applications.
Previously, rotons were observed in correlated quantum systems at low temperatures, including superfluid helium and Bose-Einstein condensates. Here, following a recent theoretical proposal, we report the direct experimental observation of roton-like dispersion relations in two different three-dimensional metamaterials under ambient conditions. One experiment uses transverse elastic waves in microscale metamaterials at ultrasound frequencies. The other experiment uses longitudinal air-pressure waves in macroscopic channel–based metamaterials at audible frequencies. In both experiments, we identify the roton-like minimum in the dispersion relation that is associated to a triplet of waves at a given frequency. Our work shows that designed interactions in metamaterials beyond the nearest neighbors open unprecedented experimental opportunities to tailor the lowest dispersion branch—while most previous metamaterial studies have concentrated on shaping higher dispersion branches.
We have theoretically studied the designable quantum beamsplitter of single photons interacting with the two-level quantum dot placed in the node of a Y-type waveguide on the basis of the real-space approach. We showed that splitting of incoming single photons from one quantum channel to the others could be achieved by controlling the coupling strength of two-level quantum dot with waveguide, detuning between the quantum dot and the incoming single photon, and so on. Such quantum devices based on the controllable single photon transport behave as quantum beamsplitter at the single photon level, which provides us rich ways of configuration of important elements for the practical realization of the quantum information network.
Physical mechanisms of electron emission from fibre optic nanotips, namely, tunnelling, multi-photon, and thermionic emission, either prevent fast switching or require intense laser fields. Time-resolved electron emission from nano-sized sources finds applications ranging from material characterisation to fundamental studies of quantum coherence. We present a nano-sized electron source capable of fast-switching (⩽1 ns) that can be driven with low-power femtosecond lasers. The physical mechanism that can explain emission at low laser power is surface plasmon enhanced above-threshold photoemission. An electron emission peak is observed and provides support for resonant plasmonic excitation. The electron source is a metal-coated optical fibre tapered into a nano-sized tip. The fibre is flexible and back illuminated facilitating ease of positioning. The source operates with a few nJ per laser pulse, making this a versatile emitter that enables nanometrology, multisource electron-lithography and scanning probe microscopy.
It is widely recognized that nanoscience and nanotechnology and their subfields, such as nanophotonics, nanoelectronics, and nanomechanics, have had a tremendous impact on recent advances in sensing, imaging, and communication, with notable developments, including novel transistors and processor architectures. For example, in addition to being supremely fast, optical and photonic components and devices are capable of operating across multiple orders of magnitude length, power, and spectral scales, encompassing the range from macroscopic device sizes and kW energies to atomic domains and single-photon energies. The extreme versatility of the associated electromagnetic phenomena and applications, both classical and quantum, are therefore highly appealing to the rapidly evolving computing and communication realms, where innovations in both hardware and software are necessary to meet the growing speed and memory requirements. Development of all-optical components, photonic chips, interconnects, and processors will bring the speed of light, photon coherence properties, field confinement and enhancement, information-carrying capacity, and the broad spectrum of light into the high-performance computing, the internet of things, and industries related to cloud, fog, and recently edge computing. Conversely, owing to their extraordinary properties, 0D, 1D, and 2D materials are being explored as a physical basis for the next generation of logic components and processors. Carbon nanotubes, for example, have been recently used to create a new processor beyond proof of principle. These developments, in conjunction with neuromorphic and quantum computing, are envisioned to maintain the growth of computing power beyond the projected plateau for silicon technology. We survey the qualitative figures of merit of technologies of current interest for the next generation computing with an emphasis on edge computing.
We present the results of a theoretic study of the electromagnetic field imbalance in surface plasmon polaritons (SPPs), which reveal that the magnetic field components induced by the electric fields normal and parallel to a metal surface cancel each other in SPPs, resulting in an imbalance. A group velocity analysis shows that this imbalance contributes significantly to the slow propagation of SPPs. We also analyze the enhanced spontaneous emission and nonlinearity in plasmonic cavities, and the results indicate that the electromagnetic field imbalance must be considered to correctly estimate the interaction strength.
Surface plasmons are coherent and collective electron oscillations confined at the dielectric–metal interface. Benefitting from the inherent subwavelength nature of spatial profile, surface plasmons can greatly accumulate the optical field and energy on the nanoscale and dramatically enhance various light–matter interactions. The properties of surface plasmons are strongly related to materials and structures, so that metals, semiconductors and two-dimensional materials with various morphologies and structures can have alternating plasmonic wavelengths ranging from ultraviolet, visible, near infrared to far infrared. Because the electric field can be enhanced by orders of magnitude within plasmonic structures, various light–matter interaction processes including fluorescence, Raman scattering, heat generation, photoacoustic effects, photocatalysis, nonlinear optical conversion, and solar energy conversion, can be significantly enhanced and these have been confirmed by both theoretical, computational and experimental studies. In this review, we present a concise introduction and discussion of various plasmon-enhanced light–matter interaction processes. We discuss the physical and chemical principles, influencing factors, computational and theoretical methods, and practical applications of these plasmon-enhanced processes and phenomena, with a hope to deliver guidelines for constructing future high-performance plasmonic devices and technologies.
The discrete quantum nature of plasmons may be exploited to make efficient single-photon sources. Despite the losses associated with metallic resonators, advantages over dielectric counterparts exist when it comes to producing efficient quantum emitters.
Significance
Antennas, from radiofrequencies to optics, are forced to transmit and receive with the same efficiency to/from the same direction. The same constraint applies to thermophotovoltaic systems, which are forced to emit as well as they can absorb, limiting their efficiency. In this paper, we show that it is possible to efficiently overcome these bounds using temporally modulated traveling-wave circuits. Beyond the basic physics interest of our theoretical and experimental findings, we also prove that the proposed temporally modulated antenna can be efficiently used to transmit without being forced to listen to echoes and reflections, with important implications for radio-wave communications. Similar concepts may be extended to infrared frequencies, with relevant implications for energy harvesting.
Electronic excitations in metallic nanoparticles in the optical regime that
have been of great importance in surface enhanced spectroscopy and emerging
applications of molecular plasmonics, due to control and confinement of
electromagnetic energy, may also be of potential to control the motion of
nanoparticles and molecules. Here, we propose a concept for trapping
polarizable particles and molecules using toroidal metallic nanoparticles.
Specifically, gold nanorings are investigated for their scattering properties
and field distribution to computationally show that the response of these
optically resonant particles to incident photons permit the formation of a
nanoscale trap when proper aspect ratio, photon wavelength and polarization are
considered. However, interestingly the resonant plasmonic response of the
nanoring is shown to be detrimental to the trap formation. The results are in
good agreement with analytic calculations in the quasi-static limit within the
first-order perturbation of the scalar electric potential. The possibility of
extending the single nanoring trapping properties to two-dimensional arrays of
nanorings is suggested by obtaining the field distribution of nanoring dimers
and trimers.
We study the surface plasmon modes in a silver double-nanowire system by employing the eigenmode analysis approach based on the finite element method. Calculated dispersion relations, surface charge distributions, field patterns and propagation lengths of ten lowest energy plasmon modes in the system are presented. These ten modes are categorized into three groups because they are found to originate from the monopole-monopole, dipole-dipole and quadrupole-quadrupole hybridizations between the two wires, respectively. Interestingly, in addition to the well studied gap mode (mode 1), the other mode from group 1 which is a symmetrically coupled charge mode (mode 2) is found to have a larger group velocity and a longer propagation length than mode 1, suggesting mode 2 to be another potential signal transporter for plasmonic circuits. Scenarios to efficiently excite (inject) group 1 modes in the two-wire system and also to convert mode 2 (mode 1) to mode 1 (mode 2) are demonstrated by numerical simulations.
In 2004, the authors reported two coupling schemes based on the thermo-optic properties of thin metallic films and their associated sub-and superstrates, by utilizing surface plasmons. These studies showed a potential for all-optical modulation at low rates that may be used for sensing purposes. In this article, they continue by investigating thermal processes involved in thin metallic films with different approaches. They first experimentally imaged the shift of the surface plasmon dispersion relation in the visible spectrum, as the thin film temperature is externally varied. They then reinforce the previous observations by collecting the absorption curves at selected visible photon energies of excitation, as the film temperature in the excitation region increases. Utilizing the absorption measurements, they briefly address how one may obtain the real and imaginary parts of the index of refraction of the thin film as a function of temperature for each involved wavelength. Finally, they investigate the local physical state of the film by optically profiling the surface plasmon excitation region. © 2008 American Vacuum Society.
We study the nonlocal response of a confined electron gas within the
hydrodynamical Drude model. We address the question whether plasmonic
nanostructures exhibit nonlocal resonances that have no counterpart in the
local-response Drude model. Avoiding the usual quasi-static approximation, we
find that such resonances do indeed occur, but only above the plasma frequency.
Thus the recently found nonlocal resonances at optical frequencies for very
small structures, obtained within quasi-static approximation, are unphysical.
As a specific example we consider nanosized metallic cylinders, for which
extinction cross sections and field distributions can be calculated
analytically.
A form of optical modulation at low pulse rates is reported in the case of surface plasmons excited by 1.55 ‐ µ m photons in a thin gold foil. Several visible-photon energies are shown to be pulsed by the action of the infrared pulses, the effect being maximized when each visible beam also excites surface plasmons. The infrared surface plasmons are implicated as the primary cause of thermally induced changes in the foil. The thermal effects dissipate in sufficiently small times so that operation up to the kilohertz range in pulse repetition frequency is obtained. Unlike direct photothermal phenomena, no phase change is necessary for the effect to be observed.
Collective electronic excitations at metal surfaces are well known to play a key role in a wide spectrum of science, ranging from physics and materials science to biology. Here we focus on a theoretical description of the many-body dynamical electronic response of solids, which underlines the existence of various collective electronic excitations at metal surfaces, such as the conventional surface plasmon, multipole plasmons, and the recently predicted acoustic surface plasmon. We also review existing calculations, experimental measurements, and applications. Comment: 54 pages, 33 figures, to appear in Rep. Prog. Phys
Plasmonic sensors based on metallic nanorings benefit from resonances covering a wide spectral range and homogeneous cavity fields. Here, we explore the potential for nanorings in active plasmonics by examining the tunability of plasmon resonances due to external magnetic fields. Within the electrostatic approximation, we compute plasmon resonances and their shifts in magnetic fields for both solid and planar nanorings. In particular, solid nanorings of circular, elliptical, and disk-shaped cross sections are critically examined and compared to planar rings. Overall, we find that magnetoplasmon shifts in nanorings are greatly reduced compared to standard nanoparticles. However, flat geometries are found to be preferable and allow for relatively large shifts.
Twisted nanoribbons from two-dimensional materials possess many unusual properties tunable by changing the twist angle, for example, electro- and thermal conductivity, chemical properties, and stability against buckling. New interesting phenomena can be observed when a twisted nanoribbon interacts with a substrate. Here we report the results of a classical molecular dynamics study of a graphene nanoribbon twisted about its long axis and interacting with a graphite substrate. Van der Waals interactions with the substrate lead to localization of twisting and the formation of topological solitons called twistons. The topological charge of a twiston obtained with the twist angle β multiple of π can be defined as q=β/π; it can be positive or negative. Twistons can move along the nanoribbon with very little radiation in the form of small-amplitude phonons. Scenarios of twiston collisions are described depending on their topological charge and on the nanoribbon width. In narrow nanoribbons twistons collide practically elastically, preserving their profiles and speeds after the collision, and inelasticity of collisions increases with increasing nanoribbon width. Our results contribute to an understanding of the behavior of two-dimensional material nanoribbons on a substrate.
Photon scattering and the ensuing excitation of surface plasmons in single rings, single composite rings, and many-ring systems was recently shown to provide dispersion and field distributions [K. V. Garapati et al., J. Phys. Commun. 2, 015031 (2018)] of potential for specific applications in particle and molecular trapping [R. Alaee et al., Appl. Phys. Lett. 109, 141102 (2016); M. Salhi et al., Phys. Rev. A 92, 033416 (2015)], in addition to metamaterials and sensing. Following photon or electron interactions with metallic nanorings, both radiative and nonradiative decay channels are important in the consideration of the nanoparticle as a photon or phonon source, and in related applications. Here, we quantize the electronic normal modes of the ring torus and obtain the radiative decay of plasmons. Due to a geometry-related complexity, we employ a perturbation approach to obtain analytical expressions for the radiative decay channel for a vacuum bounded single solid nanoring. In quantizing the fields, the frequency spectrum of the charge density normal modes of the nanoring is obtained and shown to agree with the exact quasistatic plasmon dispersion relations. Higher-order corrections beyond the presented zero- and first-order calculations may be obtained following the presented results. The results are of potential interest in quantum sensing such as entangling photons and plasmons, or plasmons and trapped molecules.
The growing need for classical as well as quantum optical sensing places increasingly stringent requirements upon the desired characteristics of the engendered fields. Specifically, achieving superior field enhancement plays a critical role in applications ranging from chem-bio sensing, Raman and infrared spectroscopies to ion trapping and qubit control in emerging quantum-information science. Due to their low optical losses and ability to exhibit resonant field enhancements, all dielectric multilayers are emerging as an optical material system not only useful to classical photonics and sensing but also of potential to be integrated with quantum materials and quantum sensing. The recently introduced concept of zero-admittance layers [1] within dielectric multilayer materials, enables the creation and control of resonant fields orders of magnitude larger than the exciting field. Here, invoking the zero-admittance concept, we design, fabricate, and characterize an all-dielectric nonabsorbing stack and demonstrate the engendered huge field enhancement. Describing the fields in terms of Bloch surface waves, we connect the surface field to the semiperiodicity in the dielectric domains of the stack. As a specific application of the resonant field, we propose and demonstrate refractive-index sensing for the detection of trace amounts of an analyte. The results include a quantification of the sensitivity of the device with respect to the profile of the exciting field. The experimental results are shown to be in good agreement with theoretical calculations.
The curvature in coiled single walled carbon nanotubes (SWCNTs) rings impacts on their properties rela-tive to straight CNTs, but the availability of such rings is limited. This has been addressed in developing a continuous flow method for fabricating coiled SWCNTs rings in high yield (80%) using a vortex fluid-ic device (VFD), in the absence of any toxic chemicals and surfactants. The VFD thin film microfluidic platform has a rapidly rotating angled glass tube with the processed liquid driven up and out of the tube. Magnetic force microscopy (MFM) established that the magnetic interaction of the resulting rings is strongly dependent on the thickness of the coiled SWCNT rings.
It is shown that focusing circularly polarized 800 nm light pulses of duration 100 fs on the tips of p-GaAs crystalline shards having no negative electron affinity (NEA) activation results in electron emission that is both fast and spin-polarized. The 400 fs duration of the emission process was determined by pump/probe measurements. The three samples we investigated produced electron polarizations of 13.1(0.9)%, 13.3(0.7)%, and 10.4(0.2)%. Emission currents ranged between 50 pA and 3 nA with a sample bias of-100 V and an average laser power of 100 mW. The electron emission exhibited linear dichroism and was obtained under moderate vacuum conditions, similar to that of metallic tips. This source of spin-polarized electron pulses is "fast" in the sense that the electron emission process is of comparable duration to the laser pulses that initiate it.
Here, we present an optical fiber-based electron gun designed for the ultrafast streaking of low-energy electron bunches. The temporal profile of the few tens of the picosecond long electron bunch composed of 200 electrons is well characterized using a customized streak camera. Detailed analysis reveals that the stretched optical trigger pulse owing to the dispersion effects inside the waveguide dominantly determines the temporal length of the low density electron bunch. This result illustrates the capability to control the observable time-window in the streak diffraction experiment by tailoring geometrical parameters of the fiber source and its coupling condition. With the electrostatic Einzel lens system integrated on the fiber-based cathode, we also demonstrate spatial focusing of the electron beam with the RMS spot size of 98 μm and imaging of the static low-energy electron diffraction pattern of monolayer graphene in the electron kinetic energy range of 1.0–2.0 keV.
Field quantization in high curvature geometries help understanding the elastic and inelastic scattering of photons and electrons in nanostructures and probelike metallic domains. The results find important applications in high-resolution photonic and electronic modalities of scanning probe microscopy, nano-optics, plasmonics, and quantum sensing. We present a calculation of relevant photon interactions in both hyperboloidal and paraboloidal material domains. The two morphologies are compared for their plasmon dispersion properties, field distributions, and radiative decay rates, which are shown to be consistent with the corresponding quantities for the finite prolate spheroidal domains. The results are relevant to other material domains that model a nanostructure such as a probe tip, quantum dot, or nanoantenna.
It is shown that the mixed quantum/classical theory (MQCT) for the description of molecular scattering is considerably improved by using integer values of orbital angular momentum l, just like in quantum theory, instead of treating it as a continuous classical variable related to the impact parameter. This conclusion is justified by the excellent accuracy of the modified theory for prediction of the differential cross sections, at various values of collision energy and in both forward and backward scattering regimes. This approach requires fewer trajectories, compared to the random Monte-Carlo sampling, and the only convergence parameter is lmax (maximum orbital angular momentum) similar to Jmax in the full quantum theory (maximum total angular momentum). Calculations of differential and integral cross sections for elastic and inelastic channels are presented, and the role of the scattering phase is discussed. The low energy range is analyzed in detail to obtain insight into how the mixed quantum/classical treatment works in the scattering regime dominated by resonances. The differential cross section for rotationally inelastic scattering, computed by MQCT approach, is presented for the first time.
Magnetism in carbon nanostructures is a rapidly expanding field of current materials science. Its progress is driven by the wide range of applications for magnetic carbon nanosystems, including transmission elements in spintronics, building blocks of cutting-edge nanobiotechnology, and qubits in quantum computing. These systems also provide novel paradigms for basic phenomena of quantum physics, and are thus of great interest for fundamental research. This comprehensive survey emphasizes both the fundamental nature of the field, and its groundbreaking nanotechnological applications, providing a one-stop reference for both the principles and the practice of this emerging area. With equal relevance to physics, chemistry, engineering and materials science, senior undergraduate and graduate students in any of these subjects, as well as all those interested in novel nanomaterials, will gain an in-depth understanding of the field from this concise and self-contained volume.
Dissipative entanglement-generation protocols embrace environmental interactions to generate long-lived entangled states. In this paper, we report on the antibunching dynamics for a pair of actively driven quantum emitters coupled to a shared dissipative plasmonic reservoir. We find that antibunching is a universal signature for entangled states generated by dissipative means and examine its use as an entanglement diagnostic. We discuss the experimental validation of plasmonically mediated entanglement generation by Hanbury Brown-Twiss interferometry with picosecond timing resolution determined by an effective two-qubit Rabi frequency, and we analyze the robustness of entanglement generation with respect to perturbations in local detunings, couplings, and driving fields.
The optical constants n and k were obtained for the noble metals (copper, silver, and gold) from reflection and transmission measurements on vacuum-evaporated thin films at room temperature, in the spectral range 0.5-6.5 eV. The film-thickness range was 185-500 Å. Three optical measurements were inverted to obtain the film thickness d as well as n and k. The estimated error in d was ± 2 Å, and that in n, k was less than 0.02 over most of the spectral range. The results in the film-thickness range 250-500 Å were independent of thickness, and were unchanged after vacuum annealing or aging in air. The free-electron optical effective masses and relaxation times derived from the results in the near infrared agree satisfactorily with previous values. The interband contribution to the imaginary part of the dielectric constant was obtained by subtracting the free-electron contribution. Some recent theoretical calculations are compared with the results for copper and gold. In addition, some other recent experiments are critically compared with our results.
The classical and quantum physics seem to divide nature into two domains macroscopic and microscopic. It is also certain that they accurately predict experimental results in their respective regions. However, the reduction theory, namely, the general derivation of classical results from the quantum mechanics is still a far cry. The outcome of some recent investigations suggests that there possibly does not exist any universal method for obtaining classical results from quantum mechanics. In the present work we intend to investigate the problem phenomenonwise and address specifically the phenomenon of scattering. We suggest a general approach to obtain the classical limit formula from the phase shiftδ
l, in the limiting value of a suitable parameter on whichδ
l depends. The classical result has been derived for three different potential fields in which the phase shifts are exactly known. Unlike the current wisdom that the classical limit can be reached only in the high energy regime it is found that the classical limit parameter in addition to other factors depends on the details of the potential fields. In the last section we have discussed the implications of the results obtained.
The angle-energy distribution of a fast electron losing energy to the conduction electrons in a thick metallic foil has been derived assuming that the conduction electrons constitute a Fermi-Dirac gas and that the fast electron undergoes only small fractional energy and momentum changes. This distribution exhibits both collective interaction characteristics and individual interaction characteristics, and is more general than the result obtained by other workers. Describing the conduction electrons by the hydro-dynamical equations of Bloch, it has been shown that for very thin idealized foils energy loss may occur at a value which is less than the plasma energy, while as the foil thickness decreases below ~vomegap the loss at the plasma energy becomes less than that predicted by more conventional theories. The net result is an increase in the energy loss per unit thickness as the foil thickness is decreased. It is suggested that the predicted loss at subplasma energies may correspond to some of the low-lying energy losses which have been observed by experimenters using thin foils.
A critical anlysis of the difference between the classical and
quantum mechanical definitions of scattering cross sections
for particles is presented. This leads to a clarification of
the classical limit problem and suggests precise criteria for
its validity. In particular these criteria are derived for
both finite and infinite range potentials.
The normal modes of oscillation of a cold dielectric plasma ring are analysed in the quasi-electrostatic approximation. An exact dispersion relation is derived, valid for all aspect ratios. Its solutions are shown to be extremely close to those of an infinite cylindrical plasma with cross-section equal to the minor cross-section of the ring, when the cylinder is considered as a wavelength-preserving limit of the toroidal geometry.
Theoretical studies of surface plasmon polaritons in cylindrical structures consistent of concentric layers are presented. The complete set of Maxwell's equations with appropriate boundary conditions are solved and expressed in a matrix form for a system with a finite number of shells imbedded in an environment. Numerical evaluations of the transcendental equation for the dispersion relation are given to analyze the role of factors such as number of shells, dielectric properties of the materials and the environment, curvature and size of the system.
The paper is an attempt to present, in the simplest possible terms, a unified picture of the theory of various forms of surface wave and a clear physical interpretation of their behaviour. The Zenneck wave, the radial cylindrical surface wave and the Sommerfeld-Goubau or axial cylindrical surface wave are each discussed and shown to represent basically one and the same phenomenon. The link with the Brewster angle, for which a wave incident on a surface suffers no reflection, is clearly established. The transition from a TEM wave supported by a parallel-strip transmission line, with metal plates close together, to two Zenneck waves independently supported by the plates, when these are separated by a very large distance, is demonstrated. The effect of bends in the supporting surface is considered, and methods of reducing radiation are explained. Finally the principles governing the launching of surface waves are surveyed with particular reference to the Brewster-angle approach.
Raman spectroscopy and confocal Raman imaging with 514 nm excitation was performed on recently developed ultralong carbon nanotubes grown by the "fast-heating" chemical vapor deposition (CVD) method. The ultralong nanotubes are found to consist of both semiconducting and metallic types, with spectra that are consistent with the nanotubes being single walled. Characterization of nanotube diameters shows that short nanotubes appearing near the sample catalyst region have a broader distribution than is observed for the ultralong nanotubes. The narrow diameter distribution is determined by uniformity of catalyst particle size and gives additional evidence for the proposed "kite" mechanism for long nanotube growth. Raman imaging was performed over large length scales (up to 140 microm). Imaging reveals the ultralong nanotubes to be of high quality, with a very low defect density. Variations in G-band frequencies and intensity demonstrate the occurrence of minor structural changes and variations in nanotube-substrate interaction along the length of the nanotubes. Evidence also demonstrates that larger structural changes resulting in a full chirality change can occur in these nanotube types to produce a metal-to-semiconductor intramolecular junction.
Nanocrystalline nanowires (NCNW) are fragments of bulk crystals that are infinite in only one direction. A construction is given for calculating eigenstates belonging to the symmetry labels (k,m) (wavevector and rotational quantum number). Vibrational harmonic eigenstates are worked out explicitly for a simple model, illustrating the general results: the LA mode has m=0, while with sufficient rotational symmetry, the TA branch is doubly degenerate, has m=+/-1, and has quadratic dispersion with k for k less than the reciprocal diameter of the NCNW. The twiston branch (a fourth Goldstone boson) is an acoustic m=0 branch, additional to the LA and two TA branches.
In approaching a discussion of this matter, it is most important to ensure general agreement about the particular features that characterize the so-called surface wave. An attempt has been made to formulate in simple and unambiguous terms a definition of this form of wave, distinguishing it from the various other waves known to be associated with an interface between two different media. It is maintained that there are really two closely allied aspects of the problem of surface wave propagation, one of which is more particularly concerned with launching the wave from a given aerial over the surface and the other with the capabilities of that surface in supporting such a wave. The present paper deals with the latter consideration in relation to surfaces slightly curved in the direction of the propagation of the wave. Recognizing the evanescent character of the surface wave field distribution over the equiphase surfaces and the important part played by the inclination of these surfaces with the normal to the interface when power is transferred across it, a method is discussed of calculating the radiation which arises when a wave of this kind circulates around a highly reactive supporting surface of cylindrical form. It is concluded that when the surface has a finite loss there will be a particular radius of curvature for which no power is transferred across the interface.
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