Transverse and longitudinal components of the propagating and evanescent waves associated to radially-polarized nonparaxial fields

A comparison is established between the contributions of transverse and longitudinal components of both the propagating and the evanescent waves associated to freely propagating radially polarized nonparaxial beams. Attention is focused on those fields that remain radially polarized upon propagation. In terms of the plane-wave angular spectrum of these fields, analytical expressions are given for determining both the spatial shape of the above components and their relative weight integrated over the whole transverse plane. The results are applied to two kinds of doughnut-like beams with radial polarization, and we compare the behavior of such fields at two transverse planes.

A linear model for the structure of turbulence beneath surface water waves

The structure of turbulence in the ocean surface layer is investigated using a simplified semi-analytical model based on rapid-distortion theory. In this model, which is linear with respect to the turbulence, the flow comprises a mean Eulerian shear current, the Stokes drift of an irrotational surface wave, which accounts for the irreversible effect of the waves on the turbulence, and the turbulence itself, whose time evolution is calculated. By analysing the equations of motion used in the model, which are linearised versions of the Craik–Leibovich equations containing a ‘vortex force’, it is found that a flow including mean shear and a Stokes drift is formally equivalent to a flow including mean shear and rotation. In particular, Craik and Leibovich’s condition for the linear instability of the first kind of flow is equivalent to Bradshaw’s condition for the linear instability of the second. However, the present study goes beyond linear stability analyses by considering flow disturbances of finite amplitude, which allows calculating turbulence statistics and addressing cases where the linear stability is neutral. Results from the model show that the turbulence displays a structure with a continuous variation of the anisotropy and elongation, ranging from streaky structures, for distortion by shear only, to streamwise vortices resembling Langmuir circulations, for distortion by Stokes drift only. The TKE grows faster for distortion by a shear and a Stokes drift gradient with the same sign (a situation relevant to wind waves), but the turbulence is more isotropic in that case (which is linearly unstable to Langmuir circulations).

SURFACE SOLITARY WAVES IN A DOUBLE DIFFUSIVE SYSTEM

We show that a surface solitary wave governed by the Korteweg-de Vries equation can develop in a fluid acted upon by fluxes of heat and of a second diffusive element. This solitary wave appears as a manifestation of a hydrodynamical instability which sets in only when a certain relation involving the parameters of the system is satisfied.

Effects of a temperature dependent viscosity in surface nonlinear waves propagating in a shallow fluid heated from below

The effects of a temperature dependent viscosity in surface nonlinear waves propagating in a shallow fluid heated from below are investigated. It is shown that the (2+1)-dimensional Burgers equation may appear as the equation governing the upper free surface perturbations of a Bénard system, even when the viscosity is assumed to depend on temperature. The critical Rayleigh number for the appearance of waves governed by the Kadomtsev-Petviashvili equation, however, will be smaller than R=30, which is the critical number obtained for a constant viscosity. © 1992.

Coupling light into graphene plasmons with the help of surface acoustic waves

We propose a scheme for coupling laser light into graphene plasmons with the help of electrically generated surface acoustic waves. The surface acoustic wave forms a diffraction grating which allows us to excite the long lived phononlike branch of the hybridized graphene plasmon-phonon dispersion with infrared laser light. Our approach avoids patterning the graphene sheet, does not rely on complicated optical near-field techniques, and allows us to electrically switch the coupling between far-field radiation and propagating graphene plasmons.

Effects of a steady nonuniform current on the characteristics of surface gravity waves /

"December 1974."

The optical response of nanostructured surfaces and the composite diffracted evanescent wave model

Investigations of the optical response of subwavelength-structure arrays milled into thin metal films have revealed surprising phenomena, including reports of unexpectedly high transmission of light. Many studies have interpreted the optical coupling to the surface in terms of the resonant excitation of surface plasmon polaritons (SPPs), but other approaches involving composite diffraction of surface evanescent waves (CDEW) have also been proposed. Here we present a series of measurements on very simple one-dimensional subwavelength structures to test the key properties of the surface waves, and compare them to the CDEW and SPP models. We find that the optical response of the silver metal surface proceeds in two steps: a diffractive perturbation in the immediate vicinity (2–3 mu m) of the structure, followed by excitation of a persistent surface wave that propagates over tens of micrometres. The measured wavelength and phase of this persistent wave are significantly shifted from those expected for resonance excitation of a conventional SPP on a pure silver surface.

Ocean bottom pressure records from the Cascadia array and short surface gravity waves

The ocean bottom pressure records from eight stations of the Cascadia array are used to investigate the properties of short surface gravity waves with frequencies ranging from 0.2 to 5 Hz. It is found that the pressure spectrum at all sites is a well-defined function of the wind speed U10 and frequency f, with only a minor shift of a few dB from one site to another that can be attributed to variations in bottom properties. This observation can be combined with the theoretical prediction that the ocean bottom pressure spectrum is proportional to the surface gravity wave spectrum E(f) squared, times the overlap integral I(f) which is given by the directional wave spectrum at each frequency. This combination, using E(f) estimated from modeled spectra or parametric spectra, yields an overlap integral I(f) that is a function of the local wave age inline image. This function is maximum for f∕fPM = 8 and decreases by 10 dB for f∕fPM = 2 and f∕fPM = 30. This shape of I(f) can be interpreted as a maximum width of the directional wave spectrum at f∕fPM = 8, possibly equivalent to an isotropic directional spectrum, and a narrower directional distribution toward both the dominant low frequencies and the higher capillary-gravity wave frequencies.

Shaping surface acoustic waves for cardiac tissue engineering

The heart is a non-regenerating organ that gradually suffers a loss of cardiac cells and functionality. Given the scarcity of organ donors and complications in existing medical implantation solutions, it is desired to engineer a three-dimensional architecture to successfully control the cardiac cells in vitro and yield true myocardial structures similar to native heart. This thesis investigates the synthesis of a biocompatible gelatin methacrylate hydrogel to promote growth of cardiac cells using biotechnology methodology: surface acoustic waves, to create cell sheets. Firstly, the synthesis of a photo-crosslinkable gelatin methacrylate (GelMA) hydrogel was investigated with different degree of methacrylation concentration. The porous matrix of the hydrogel should be biocompatible, allow cell-cell interaction and promote cell adhesion for growth through the porous network of matrix. The rheological properties, such as polymer concentration, ultraviolet exposure time, viscosity, elasticity and swelling characteristics of the hydrogel were investigated. In tissue engineering hydrogels have been used for embedding cells to mimic native microenvironments while controlling the mechanical properties. Gelatin methacrylate hydrogels have the advantage of allowing such control of mechanical properties in addition to easy compatibility with Lab-on-a-chip methodologies. Secondly in this thesis, standing surface acoustic waves were used to control the degree of movement of cells in the hydrogel and produce three-dimensional engineered scaffolds to investigate in-vitro studies of cardiac muscle electrophysiology and cardiac tissue engineering therapies for myocardial infarction. The acoustic waves were characterized on a piezoelectric substrate, lithium niobate that was micro-fabricated with slanted-finger interdigitated transducers for to generate waves at multiple wavelengths. This characterization successfully created three-dimensional micro-patterning of cells in the constructs through means of one- and two-dimensional non-invasive forces. The micro-patterning was controlled by tuning different input frequencies that allowed manipulation of the cells spatially without any pre- treatment of cells, hydrogel or substrate. This resulted in a synchronous heartbeat being produced in the hydrogel construct. To complement these mechanical forces, work in dielectrophoresis was conducted centred on a method to pattern micro-particles. Although manipulation of particles were shown, difficulties were encountered concerning the close proximity of particles and hydrogel to the microfabricated electrode arrays, dependence on conductivity of hydrogel and difficult manoeuvrability of scaffold from the surface of electrodes precluded measurements on cardiac cells. In addition, COMSOL Multiphysics software was used to investigate the mechanical and electrical forces theoretically acting on the cells. Thirdly, in this thesis the cardiac electrophysiology was investigated using immunostaining techniques to visualize the growth of sarcomeres and gap junctions that promote cell-cell interaction and excitation-contraction of heart muscles. The physiological response of beating of co-cultured cardiomyocytes and cardiac fibroblasts was observed in a synchronous and simultaneous manner closely mimicking the native cardiac impulses. Further investigations were carried out by mechanically stimulating the cells in the three-dimensional hydrogel using standing surface acoustic waves and comparing with traditional two-dimensional flat surface coated with fibronectin. The electrophysiological responses of the cells under the effect of the mechanical stimulations yielded a higher magnitude of contractility, action potential and calcium transient.

Gravimetric and density profiling using the combination of surface acoustic waves and neutron reflectivity

A new approach is described herein, where neutron reflectivity measurements that probe changes in the density profile of thin films as they absorb material from the gas phase have been combined with a Love wave based gravimetric assay that measures the mass of absorbed material. This combination of techniques not only determines the spatial distribution of absorbed molecules, but also reveals the amount of void space within the thin film (a quantity that can be difficult to assess using neutron reflectivity measurements alone). The uptake of organic solvent vapours into spun cast films of polystyrene has been used as a model system with a view to this method having the potential for extension to the study of other systems. These could include, for example, humidity sensors, hydrogel swelling, biomolecule adsorption or transformations of electroactive and chemically reactive thin films. This is the first ever demonstration of combined neutron reflectivity and Love wave-based gravimetry and the experimental caveats, limitations and scope of the method are explored and discussed in detail.

Solitary waves on a free surface of a heated Maxwell fluid

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

New biosensor applications of surface plasmon and hydrogel optical waveguide spectroscopy

Rapid and sensitive detection of chemical and biological analytes becomes increasingly important in areas such as medical diagnostics, food control and environmental monitoring. Optical biosensors based on surface plasmon resonance (SPR) and optical waveguide spectroscopy have been extensively pushed forward in these fields. In this study, we combine SPR, surface plasmon-enhanced fluorescence spectroscopy (SPFS) and optical waveguide spectroscopy with hydrogel thin film for highly sensitive detection of molecular analytes.rnrnA novel biosensor based on SPFS which was advanced through the excitation of long range surface plasmons (LRSPs) is reported in this study. LRSPs are special surface plasmon waves propagating along thin metal films with orders of magnitude higher electromagnetic field intensity and lower damping than conventional SPs. Therefore, their excitation on the sensor surface provides further increased fluorescence signal. An inhibition immunoassay based on LRSP-enhanced fluorescence spectroscopy (LRSP-FS) was developed for the detection of aflatoxin M1 (AFM1) in milk. The biosensor allowed for the detection of AFM1 in milk at concentrations as low as 0.6 pg mL-1, which is about two orders of magnitude lower than the maximum AFM1 residue level in milk stipulated by the European Commission legislation.rnrnIn addition, LRSPs probe the medium adjacent to the metallic surface with more extended evanescent field than regular SPs. Therefore, three-dimensional binding matrices with up to micrometer thickness have been proposed for the immobilization of biomolecular recognition elements with large surface density that allows to exploit the whole evanescent field of LRSP. A photocrosslinkable carboxymethyl dextran (PCDM) hydrogel thin film is used as a binding matrix, and it is applied for the detection of free prostate specific antigen (f-PSA) based on the LRSP-FS and sandwich immunoassay. We show that this approach allows for the detection of f-PSA at low femto-molar range, which is approximately four orders of magnitude lower than that for direct detection of f-PSA based on the monitoring of binding-induced refractive index changes.rnrnHowever, a three dimensional hydrogel binding matrix with micrometer thickness can also serve as an optical waveguide. Based on the measurement of binding-induced refractive index changes, a hydrogel optical waveguide spectroscopy (HOWS) is reported for a label-free biosensor. This biosensor is implemented by using a SPR optical setup in which a carboxylated poly(N-isoproprylacrylamide) (PNIPAAm) hydrogel film is attached on a metallic surface and modified by protein catcher molecules. Compared to regular SPR biosensor with thiol self-assembled monolayer (SAM), HOWS provides an order of magnitude improved resolution in the refractive index measurements and enlarged binding capacity owing to its low damping and large swelling ratio, respectively. A model immunoassay experiment revealed that HOWS allowed detection of IgG molecules with a 10 pM limit of detection (LOD) that was five-fold lower than that achieved for SPR with thiol SAM. For the high capacity hydrogel matrix, the affinity binding was mass transport limited.rnrnThe mass transport of target molecules to the sensor surface can play as critical a role as the chemical reaction itself. In order to overcome the diffusion-limited mass transfer, magnetic iron oxide nanoparticles were employed. The magnetic nanoparticles (MNPs) can serve both as labels providing enhancement of the refractive index changes, and “vehicles” for rapidly delivering the analytes from sample solution to an SPR sensor surface with a gradient magnetic field. A model sandwich assay for the detection of β human chorionic gonadotropin (βhCG) has been utilized on a gold sensor surface with metallic diffraction grating structure supporting the excitation of SPs. Various detection formats including a) direct detection, b) sandwich assay, c) MNPs immunoassay without and d) with applied magnetic field were compared. The results show that the highly-sensitive MNPs immunoassay improves the LOD on the detection of βhCG by a factor of 5 orders of magnitude with respect to the direct detection.rn

Behavior of propagating and evanescent components in azimuthally polarized non-paraxial fields

The contribution of the propagating and the evanescent waves associated with freely propagating non-paraxial light fields whose transverse component is azimuthally polarized at some plane is investigated. Analytic expressions are derived for describing both the spatial shape and the relative weight of the propagating and the evanescent components integrated over the transverse plane. The analysis is carried out within the framework of the plane-wave angular spectrum approach. These results are used to illustrate the behavior of a kind of donut-like beams with transverse azimuthal polarization at some plane.

Approximations to the scattering of water waves by steep topography

A new method is developed for approximating the scattering of linear surface gravity waves on water of varying quiescent depth in two dimensions. A conformal mapping of the fluid domain onto a uniform rectangular strip transforms steep and discontinuous bed profiles into relatively slowly varying, smooth functions in the transformed free-surface condition. By analogy with the mild-slope approach used extensively in unmapped domains, an approximate solution of the transformed problem is sought in the form of a modulated propagating wave which is determined by solving a second-order ordinary differential equation. This can be achieved numerically, but an analytic solution in the form of a rapidly convergent infinite series is also derived and provides simple explicit formulae for the scattered wave amplitudes. Small-amplitude and slow variations in the bedform that are excluded from the mapping procedure are incorporated in the approximation by a straightforward extension of the theory. The error incurred in using the method is established by means of a rigorous numerical investigation and it is found that remarkably accurate estimates of the scattered wave amplitudes are given for a wide range of bedforms and frequencies.

The Stokes conjecture for waves with vorticity

We study stagnation points of two-dimensional steady gravity free-surface water waves with vorticity. We obtain for example that, in the case where the free surface is an injective curve, the asymptotics at any stagnation point is given either by the “Stokes corner flow” where the free surface has a corner of 120°, or the free surface ends in a horizontal cusp, or the free surface is horizontally flat at the stagnation point. The cusp case is a new feature in the case with vorticity, and it is not possible in the absence of vorticity. In a second main result we exclude horizontally flat singularities in the case that the vorticity is 0 on the free surface. Here the vorticity may have infinitely many sign changes accumulating at the free surface, which makes this case particularly difficult and explains why it has been almost untouched by research so far. Our results are based on calculations in the original variables and do not rely on structural assumptions needed in previous results such as isolated singularities, symmetry and monotonicity.