Scattering Of Evanescent Waves Research Articles

Scattering of evanescent wave generated by total reflection

An exact semi-analytical solution to a scattering problem of evanescent wave incident on a particle is obtained. The evanescent wave is generated by total reflection as an electromagnetic plane wave propagates from an optically denser medium to an optically thinner one. The scattered fields by and internal fields within the particle are expanded in terms of spherical vector wave functions, and an integral representation of spherical vector wave functions over cylindrical ones is used to compute the reflection of the scattered fields on the interface between the optically denser and thinner media. By applying the boundary conditions and projection technique, the unknown expansion coefficients of the scattered fields are determined. The scattering cross sections are evaluated, and the scattering characteristics are analyzed briefly.

Scattering of evanescent wave by multiple parallel infinite cylinders near a surface

This paper presents an exact analytical solution for the scattering of evanescent wave by an arbitrary collection of parallel infinite cylinders located near the surface of an optically denser substrate. The evanescent wave is generated by total internal reflection of the source wave propagating within the substrate at greater than the critical angle. The source wave is arbitrarily polarized and propagates in the plane perpendicular to the axes of the cylinders. The theoretical formulation utilizes Hertz potentials, which accounts for the near-field scattering between the cylinders and Fresnel reflection of angular distribution of scattered waves from the surface. Analytical formulas are derived for the electric and magnetic fields and Poynting vector of the scattered radiation in the near field, as well as their asymptotic forms in the far-field. Numerical results are presented to illustrate the scattering of evanescent wave by several configurations of cylinders located near the surface.

Near-field optical transducer for nanomechanical resonators

We show that a single-mode tapered-fiber waveguide can be used as a sensitive transducer to couple to the motion of a nanomechanical resonator. When the waveguide and the resonator are sufficiently close to each other, small mechanical oscillations of the resonator can be actuated efficiently by the optical dipole force. Scattering of evanescent waves confined around the waveguide and the ensuing modulation in the optical transmission through the waveguide allow for sensitive detection of the resonator oscillations. Using this technique, we have measured high-frequency nanomechanical resonances with a ∼150 fm Hz−1/2 noise floor at a detection power of ∼100 μW. The tapered-fiber waveguide provides a single seamless transduction interface between the device chip and the measurement equipment, thus offering potential for use outside of the research laboratory.

Scattering of P-polarized evanescent waves by a spherical dielectric particle

The scattering of plane waves by dielectric particles is an age-old problem for which a complete solution was given by Gustav Mie (1908). Mie's solution to the plane-wave case was later extended to the evanescent case in order to achieve resolutions beyond the Rayleigh limit. Solutions exist based on the multipole expansion method and group-theory method. Present work suggests an alternative solution to the scattering of evanescent waves by a spherical dielectric particle, by obtaining the scattering coefficients from Debye's potentials as solved by Born and Wolf in the plane-wave case.

Resonant Effects in Evanescent Wave Scattering of Polydisperse Colloids

Measurements and predictions are reported to understand large variations in evanescent wave (EW) scattering intensities between different particles from the same batch of single mode, polydisperse colloids. Measured EW scattering intensity distributions are obtained for three different micrometer sized latex particles irreversibly deposited onto glass surfaces. Predicted EW scattering intensity distributions are obtained using measured particle size distributions as input in a Mie theory for the three-dimensional scattering of a sphere under EW illumination. Good agreement is observed between measured and predicted EW scattering intensity distributions using no adjustable parameters. Our results indicate how finite polydispersity together with resonant effects produce large, nonlinear intensity variations between particles that appear to be physically and chemically uniform. Our findings allow such resonant effects to be understood and exploited in EW based particle-surface characterization techniques (e.g., using total internal reflections, surface plasmons) and chemical and biomolecular sensing applications (e.g., using whispering gallery modes).

Scattering of evanescent waves incident on targets in a simulated sediment

When a sound beam in water is incident on a sediment at a sufficiently small grazing angle, the resulting wave field in the sediment is complicated, even for the case of flat, fluidlike sediments. The wave field in the sediment for a sound beam from a simple transducer has an evanescent component and diffractive components. This situation has been experimentally simulated by using a combination of previously described immiscible liquids [Osterhoudt et al., J. Acoust. Soc. Am. 117, 2483 (2005)]. Measured wave-field features are similar to those seen in a wave-number-integration-based synthesis (using OASES) for a related problem. Targets are placed in the evanescent wave field to simulate scattering by targets buried in marine sediments. Features of the observed backscattering are relevant to detecting and clarifying objects in sediments. Measurements include the resonant excitation of the organ-pipe mode of open water-filled cylinders previously studied with free-field illumination [Osterhoudt and Marston, J. Acoust. Soc. Am. 113, 2334 (2003)]. The degradation of the backscattering with increasing target depth and with target tilt were measured and modeled. Simple approximate models of these properties are facilitated by the localized coupling processes for the excitation of (and radiation by) organ-pipe modes. [Work supported by ONR.]

Analysis of Evanescent Waves Scattering by a Single Particle in Total Internal Reflection Microscopy

Since its invention in the mid of eighties (1) Total Internal Reflection Microscopy (TIRM) has proven to be an effective technique to measure weak interactions between spherical colloidal particles and surfaces with a resolution of a few femtonewton. It is a single particle evanescent light scattering technique. In an experimental setup a laser beam is coupled into a prism and hits the glass-water interface with an angle slightly above the critical angle of total internal reflection. This generates an evanescent field near the interface that decays in the lower refractive index medium (water) with a characteristic penetration depth which depends on the angle of incidence. A colloidal particle that is dispersed in the medium will scatter light from the evanescent wave if it is in the vicinity of the surface. By registering a scattered intensity it is possible to deduce the particle- substrate distance. Compared to other methods for measure particle wall interactions like the surface force apparatus or the atomic force microscopy where a colloidal particle is attached to the tip, TIRM is the most sensitive technique because thermal fluctuations where limit the other methods in their resolution are exploited to determine the interaction potential. In this way forces in the order of a few femtonewton can be detected. TIRM has proven to be a valuable tool for the precise measurement of weak colloidal interactions as double layer forces, van der Waals forces, magnetic interactions and depletion forces. Review on TIRM can be found for example in (2,3). To compare experimental results with results of mathematical modeling an effective light scattering method is needed. For this purpose the Discrete Sources Method (DSM) has been chosen. The DSM is a well-known method for light scattering analysis, which has recently been applied for evanescent wave scattering (4). 1. Discrete Sources Method For the theoretical modeling the Discrete Sources Method (DSM) has been chosen. The DSM is a well-known method for the analysis of light scattering. It has recently been applied to the evanescent wave scattering (4). In frame of the DSM the mathematical statement can be presented as follows:

Analysis of Spectral Characteristics of Scattering of Evanescent Waves

The spectral scattering characteristics of nanoscale particles exhibited in the field of evanescent waves are analyzed using the method of discrete sources. The effect of various parameters on the behavior of the scattering characteristics is studied. The material of the particles is shown to have the most substantial effect on the scattering cross section. © 2005 Pleiades Publishing, Inc.

Optical fiber humidity sensor based on evanescent-wave scattering.

The phenomenon of evanescent-wave scattering (EWS) is used to design an optical-fiber humidity sensor. Porous solgel silica (PSGS) coated on the surface of a silica optical-fiber core scatters evanescent waves that penetrate the coating layer. Water molecules in the gas phase surrounding the optical fiber can be absorbed into the inner surface of the pores of the porous silica. The absorbed water molecules form a thin layer of liquid water on the inner surface of the porous silica and enhance the EWS. The amount of water absorbed into the PSGS coating is in dynamic equilibrium with the water-vapor pressure in the gas phase. Therefore the humidity in the air can be quantitatively determined with fiber-optic EWS caused by the PSGS coating. The humidity sensor reported here is fast in response, reversible, and has a wide dynamic range. The possible interference caused by EWS to an optical-fiber gas sensor with a reagent-doped PSGS coating as a transducer is also discussed.

Scattering of evanescent waves by a sensor tip near a plane surface

The paper is devoted to the application of a rigorous approach for analyzing the evanescent wave scattering by sensor tip near a plane surface. On the basis of the discrete sources method a numerical schemes was developed and implemented in computer program. Numerical results related to the influence of the position of the sensor tip on the scattering characteristics are discussed.

Scattering of evanescent waves by a particle on or near a plane surface

The paper is devoted to semi-analytical approaches for analyzing the evanescent wave scattering by penetrable scatterers on a plane surface. On the basis of the discrete sources method and the T-matrix method numerical schemes were developed and implemented in computer programs. Numerical results related to the influence of the plane surface on the scattering characteristics are discussed.

Scattering and extinction of evanescent waves by small particles

Expressions have been obtained for the total cross sections for extinction and scattering of evanescent waves by small spherical particles. Due to the different structure of p- and s-polarized waves, cross sections for both extinc- tion and scattering of p-polarised evanescent waves exceed those for s-polarised waves, as long as the Mie coefficients for magnetic multipoles are smaller than those for electric mul- tipoles for each multipolar order, i.e. for sufficiently small particles. The difference increases with the angle of incidence of the totally reflected wave. The definition of cross sections for evanescent-wave excitation with variable intensity over the cross-sectional area of the particle allows quantitative comparison with the case of plane-wave excitation. For ex- ample, within the dipole approximation the cross sections for plane-wave excitation lie between those for p- and s-polarised evanescent-wave excitation, respectively. Due to the inhomo- geneity of the evanescent field higher multipole contributions are strongly enhanced as compared to plane-wave excitation and increase further with the angle of incidence, resulting in corresponding changes in the scattering and extinction spec- tra. These effects are demonstrated in the specific case of scattering of evanescent waves by small silver particles.

Application of Evanescent Wave Scattering to the Study of the Motion of Liposomes near a Solid Surface

This report presents measurements and calculations of dynamic light scattering of evanescent waves from negatively and positively charged liposomes diffusing near a glass-solution interface. Scattering from the glass interface provides the reference beam for heterodyne detection. The measured short time decay of the autocorrelation functions for negatively charged liposomes is consistent with the response calculated using a model with unrestricted diffusion in half space with reflecting boundary conditions at the glass interface. In contrast, positively charged liposomes show significant deviations from the model predictions. In both cases, the short time response is significantly slower than the bulk value. The diffusion coefficient of negatively charged liposomes is nearly independent of the scattering angle. The technique gives information on the effects of "association" with the interface on the diffusive motion near an interface.

Application of Mie Scattering of Evanescent Waves to Scanning Tunnelling Optical Microscopy Theory

Abstract In this paper we present a macroscopic theory for scanning tunnelling optical microscopy where the sample is a grating and the tip is modelled by a dielectric sphere. The sphere is immersed in the near-field above the grating and is excited by the diffracted orders which can be evanescent. The detected signal is supposed to be the diffracted intensity by the sphere which is calculated by using Mie theory. When studying Mie scattering of one evanescent wave we show that the multipolar series is perturbed compared to scattering of a homogeneous wave. Even for a small sphere multipolar terms have to be taken into account. We have then proposed a formula for the intensity leading to calculations of intensity profile and surfaces and to discuss the influence of tip radius on resolution of the images.

Choked jet edge tones, continued again: Scattering of evanescent waves as the sound source

The early suggestion of monopole sources due to the high-impedance supersonic jet switching above and below the edge resulted in excessive acoustic radiation estimates. It is now proposed that the sound is better attributable to the growing then decaying ‘‘evanescent wave’’ of the sinuous jet instability, estimated by Rayleigh’s formula applied to a plane just outside the jet flow. The wave amplitude, growth and decay rates (both taken as a cosine form), wavelength, and convection speed (Mach number=0.6 for pressure ratio 3.07) are all estimated from schlieren and shadowgraph photographs. For the nozzle aspect ratio of 4.8, the two limiting cases calculated are (i) two-dimensional and (ii) acoustically equivalent line source. The preferred downstream radiation calculated in both cases is consistent with experiment, while the amplitudes calculated appear somewhat high, (ii) being within difficult measurement error (3–4 dB). [Work supported by Texas Advanced Research Program.]

Scattering of evanescent waves with application to atom-surface interactions.

This paper first develops the general S-matrix theory for evanescent (negative-energy) waves ``incident'' on a localized scattering center. Next, an exact expression is derived for the interaction energy of an evanescent wave with a short-range scattering center in terms of elements of the scattering matrix. Finally, these results are applied to the calculation of the repulsive interaction between a He atoms and a metal surface. A difficulty, in principle caused by the ${r}^{\mathrm{\ensuremath{-}}4}$ polarization potential between an electron and a He atom, is discussed.

Scattering of Evanescent Waves by Cylindrical Structures

Abstract : Research is presented on the diffraction of an electromagnetic evanescent wave by an infinitely conducting half plane and by an infinitely conducting cylinder of circular cross section. General formulas are given for the near and far fields. Scattering patterns are shown in several particular cases. This study is intended as a first step toward finding the best grating structure which makes it possible to abstract the greatest amount of energy, at a prescribed frequency, from a beam of charged particles in uniform straight motion. (Author)