A multiple scattering problem

The present work deals with the problem of the interaction of the electromagnetic radiation with a statistical distribution of nonmagnetic dielectric particles immersed in an infinite homogeneous isotropic, non-magnetic medium. The wavelength of the incident radiation can be less, equal or greater than the linear dimension of a particle. The distance between any two particles is several wavelengths. A single particle in the absence of the others is assumed to scatter like a Rayleigh-Gans particle, i.e. interaction between the volume elements (self-interaction) is neglected. The interaction of the particles is taken into account (multiple scattering) and conditions are set up for the case of a lossless medium which guarantee that the multiple scattering contribution is more important than the self-interaction one. These conditions relate the wavelength λ and the linear dimensions of a particle a and of the region occupied by the particles D. It is found that for constant λ/a, D is proportional to λ and that |Δχ|, where Δχ is the difference in the dielectric susceptibilities between particle and medium, has to lie within a certain range.

The total scattering field is obtained as a series the several terms of which represent the corresponding multiple scattering orders. The first term is a single scattering term. The ensemble average of the total scattering intensity is then obtained as a series which does not involve terms due to products between terms of different orders. Thus the waves corresponding to different orders are independent and their Stokes parameters add.

The second and third order intensity terms are explicitly computed. The method used suggests a general approach for computing any order. It is found that in general the first order scattering intensity pattern (or phase function) peaks in the forward direction Θ = 0. The second order tends to smooth out the pattern giving a maximum in the Θ = π/2 direction and minima in the Θ = 0 , Θ = π directions. This ceases to be true if ka (where k = 2π/λ) becomes large (> 20). For large ka the forward direction is further enhanced. Similar features are expected from the higher orders even though the critical value of ka may increase with the order.

The first order polarization of the scattered wave is determined. The ensemble average of the Stokes parameters of the scattered wave is explicitly computed for the second order. A similar method can be applied for any order. It is found that the polarization of the scattered wave depends on the polarization of the incident wave. If the latter is elliptically polarized then the first order scattered wave is elliptically polarized, but in the Θ = π/2 direction is linearly polarized. If the incident wave is circularly polarized the first order scattered wave is elliptically polarized except for the directions Θ = π/2 (linearly polarized) and Θ = 0, π (circularly polarized). The handedness of the Θ = 0 wave is the same as that of the incident whereas the handedness of the Θ = π wave is opposite. If the incident wave is linearly polarized the first order scattered wave is also linearly polarized. The second order makes the total scattered wave to be elliptically polarized for any Θ no matter what the incident wave is. However, the handedness of the total scattered wave is not altered by the second order. Higher orders have similar effects as the second order.

If the medium is lossy the general approach employed for the lossless case is still valid. Only the algebra increases in complexity. It is found that the results of the lossless case are insensitive in the first order of k_imD where k_im = imaginary part of the wave vector k and D a linear characteristic dimension of the region occupied by the particles. Thus moderately extended regions and small losses make (k_imD)² ≪ 1 and the lossy character of the medium does not alter the results of the lossless case. In general the presence of the losses tends to reduce the forward scattering.

High-density holographic recording parameters under different wavelength of a two dyes-sensitized photopolymer

The high-density holographic recording parameters of a novel two dyes-sensitized photopolymer under different exposure wavelengths are studied. The results show that the maximum diffraction efficiency, exposure sensitivity, maximum refraction index modulation, dynamic range, and the exposure time constant increases with the increase of the exposure wavelength. The analysis indicates that the scattering has an important role in the forming of the holographic grating. (c) 2005 Elsevier GmbH. All rights reserved.

Effect of processing parameters on the optical properties of TiO2/ormosil planar waveguide

Hybrid TiO2/ormosil waveguiding films have been prepared by the sol-gel method at low thermal treatment temperature of 150° C. The influence of processing parameters including the molar ratios of titanium butoxide (Ti(OBu)(4))/3-glycidoxypropyltrimethoxysilane (GLYMO) and H2O/Ti(OBu)(4) (expressed as R), especially aging of sot on the optical properties was investigated. The optical properties of films were measured with scanning electron microscope (SEM), UV/VIS/NIR spectrophotometer (UV-Vis), m-line and the scattering-detection method. The results indicate that the film thickness increases with the increase of sol aging time, but the variation of refractive index as a function of sot aging time depends on the relative ratios of GLYMO to Ti(OBu)(4). Higher transmittance and lower attenuation of the planar waveguide can be obtained in the sol with lower Ti(OBu)(4) contents and shorter aging time.

Energy scattering in weakly non-linear systems.

The Chinese Tam-Tam exhibits non-linear behavior in its vibro-acoustic response. The frequency content of the response during free, unforced vibration smoothly changes, with energy being progressively smeared out over a greater bandwidth with time. This is used as a motivating case for the general study of the phenomenon of energy cascading through weak nonlinearity. Numerical models based upon the Fermi-Pasta-Ulam system of non-linearly coupled oscillators, modified with the addition of damping, have been developed. These were used to study the response of ensembles of systems with randomized natural frequencies. Results from simulations will be presented here. For un-damped systems, individual ensemble members exhibit cyclical energy exchange between linear modes, but the ensemble average displays a steady state. For the ensemble response of damped systems, lightly damped modes can exhibit an effective damping which is higher than predicated by linear theory. The presence of a non-linearity provides a path for energy flow to other modes, increasing the apparent damping spectrum at some frequencies and reducing it at others. The target of this work is a model revealing the governing parameters of a generic system of this type and leading to predictions of the ensemble response.

Optimized vertical carbon nanotube forests for multiplex surface-enhanced raman scattering detection

The highly sensitive and molecule-specific technique of surface-enhanced Raman spectroscopy (SERS) generates high signal enhancements via localized optical fields on nanoscale metallic materials, which can be tuned by manipulation of the surface roughness and architecture on the submicrometer level. We investigate gold-functionalized vertically aligned carbon nanotube forests (VACNTs) as low-cost straightforward SERS nanoplatforms. We find that their SERS enhancements depend on their diameter and density, which are systematically optimized for their performance. Modeling of the VACNT-based SERS substrates confirms consistent dependence on structural parameters as observed experimentally. The created nanostructures span over large substrate areas, are readily configurable, and yield uniform and reproducible SERS enhancement factors. Further fabricated micropatterned VACNTs platforms are shown to deliver multiplexed SERS detection. The unique properties of CNTs, which can be synergistically utilized in VACNT-based substrates and patterned arrays, can thus provide new generation platforms for SERS detection. © 2012 American Chemical Society.

The microstructure of hydrogenated microcrystalline silicon thin films studied by small-angle x-ray scattering

The microstructures of hydrogenated microcrystalline silicon (tic-Si: H) thin films, prepared by plasma-enhanced chemical vapor deposition (PECVD), hot wire CVD(HWCVD) and plasma assisted HWCVD (PE-HWCVD), have been analyzed by the small angle x-ray scattering(SAXS) measurement. The SAXS data show that the microstructures of the μ c-Si: H films display different characteristics for different deposition techniques. For films deposited by PECVD, the volume fraction of micro-voids and mean size are smaller than those in HWCVD sample. Aided by suitable ion-bombardment, PE-HWCVD samples show a more compact structure than the HWCVD sample. The microstructure parameters of the μ c-Si: H thin films deposited by two-steps HWCVD and PE-HWCVD with Ar ions are evidently improved. The result of 45° tilting SAXS measurement indicates that the distribution of micro-voids in the film is anisotropic. The Fouriertransform infrared spectra confirm the SAXS data.

Scattering-parameter measurements of laser diodes

An accurate and simple technique for measuring the input reflection coefficient and the frequency response of semiconductor laser diode chips is proposed and demonstrated. All the packaging parasitics could be obtained accurately using a calibrated probe, and the impedance of the intrinsic diode chip is deduced from the directly measured reflection coefficient. The directly measured impedance of a laser diode is affected strongly by the short bond wire. In the frequency response (S(2)1) measurements of semiconductor laser diode chips, the test fixture consists of a microwave probe, a submount, and a bond wire. The S-parameters of the probe could be determined using the short-open-match (SOM) method. Both the attenuation and the reflection of the test fixture have a strong influence on the directly measured frequency response, and in our proposed technique, the effect of test fixture is completely removed.

Investigation of excited states in 22Mg via resonant elastic scattering of 21Na+p and its astrophysical implications

The excited states in 22Mg have been investigated by the resonant elastic scattering of 21Na + p.A 4.0 MeV/nucleon 21Na beam was separated by the Center for Nuclear Study (CNS) radioactive ion beam separator (CRIB) and then used to bombard a thick (CH2)n target. The energy spectra of recoiled protons were measured at scattering angles of θc.m. ≈ 172◦, 146◦, and 134◦, respectively. A wide energy-range of excitation function in 22Mg (up to Ex ∼ 8.9 MeV) was obtained simultaneously with a thick-target method, and a state at 7.06 MeV was newly observed. The resonant parameters were deduced from an R-matrix analysis of the center-of-mass (c.m.) differential cross-section data with a SAMMY-M6-BETA code. The astrophysical resonant reaction rate for the 18Ne(α,p)21Na reactionwas recalculated based on the present parameters.Generally speaking,the present rates are much smaller than the previous ones.

Quasi-Elastic Scattering of C-16 from C-12 at 47.5 MeV/Nucleon

Differential cross sections for the quasi-elastic scattering of C-16 at 47.5 MeV/nucleon from C-12 target are measured. Coupled-channels calculations are carried out and the optical potential parameters are obtained by fitting the experimental angular distribution.

Investigation of excited states in Mg-22 via resonant elastic scattering of Na-21+p and its astrophysical implications

The excited states in 22Mg have been investigated by the resonant elastic scattering of 21Na + p. A 4.0 MeV/nucleon 21Na beam was separated by the Center for Nuclear Study (CNS) radioactive ion beam separator (CRIB) and then used to bombard a thick (CH2)n target. The energy spectra of recoiled protons were measured at scattering angles of θc.m. ≈ 172◦ , 146◦, and 134◦, respectively. A wide energy-range of excitation function in 22Mg (up to Ex ∼ 8.9 MeV) was obtained simultaneously with a thick-target method, and a state at 7.06 MeV was newly observed. The resonant parameters were deduced from an R-matrix analysis of the center-of-mass (c.m.) differential cross-section data with a SAMMY-M6-BETA code. The astrophysical resonant reaction rate for the 18Ne(α,p)21Na reactionwas recalculated based on the present parameters. Generally speaking, the present rates are much smaller than the previous ones.

Rectangular Silver Nanorods: Controlled Preparation, Liquid-Liquid Interface Assembly, and Application in Surface-Enhanced Raman Scattering

In this paper, we for the first time report a polyol method for large-scale synthesis of rectangular silver nanorods in the presence of directing agent and seeds. This method has some clear advantages including simplicity, high quality, and ease of scaleup. Silver nanowires or silver nanorods with a submicrometer diameter could also be facilely prepared when the reaction parameters are slightly changed. Furthermore, a liquid-liquid assembly strategy has been employed to construct uniform rectangular silver nanorod arrays on a solid substrate which could be used as surface-enhanced Raman scattering (SERS) substrates with high SERS activity, stability, and reproducibility. It is found that the SERS spectra obtained from the probe molecules with the different concentrations show different SERS intensifies. As the concentration of 4-aminothiophenol (4-ATP) or rhodamine 6G (R6G) increases, the SERS intensities progressively increase. The enhancement factor for 4-ATP and R6G should be as large as 5.06 x 10(4) or much larger than the value of 5.06 x 10(8), respectively.

Variation of crystallographic parameters in PEEKK with heat treatment temperature

Using the wide-angle X-ray diffraction method, the variation of crystallographic parameters of poly(aryl ether ether ketone ketone) (PEEKK) has been studied in different heat treatment temperatures. All the reflections and their intensities as well as their Miller indices are presented in detail according to an orthorhombic system. The investigation indicates that the unit cell parameters a, b, c and the unit cell volume V systematically decrease with increasing heat treatment temperature. This variation is interpreted by the change of conformation of polymer molecular chains during thermal treatment. The results calculated from the formula of degree of crystallinity (W-c,W-x) for PEEKK, which was derived based on X-ray scattering intensity theory and the graphic multipeak resolution method, are compatible with the density measurement (W-c,W-d) and calorimetry (W-c,W-h) values. (C) 1997 Elesevier Science Ltd.

Effect of heat treatment on the parameters of crystal structure and degree of crystallinity of poly(aryl-ether-ether-ketone)

The variations of unit cell parameters and crystallite size of nine PEEK samples treated at various temperatures have been studied by using Wide-Angle X-ray Diffraction (WAXD), The results indicate a decrease in unit cell parameter a,b and c but an increase in crystallite size L(hkl) With the increase beat treatment temperature. Based on X-ray scattering intensity theory and using the graphic multipeak resolution method, the formula of degree of crystallinity (W-c,W-X) for PEEK is derived. The results calculated are compatible with the density measurement and calorimetry.

THE CHAIN STRUCTURE AND LIGHT-SCATTERING-STUDIES FOR ACRYLAMIDE-SODIUM ACRYLIC-ACID (AM-AA) COPOLYMERS

A set of AM-AA copolymer samples with the same comonomer content and different average molecular weight have been characterized by C-13 NMB and light scattering methods in this paper. The chemical composition (comonomer AA, mole content 16.9 +/- 1.1%) of these samples is uniform. the sequence of AA in the macromolecular chain is of alone and random distribution and the light scattering theory from polyelectrolyte in added-salt solutions is suitable for the AM-AA copolymers-0.12 mol/L NaCl water systems. The actual values of M(w), the second Virial coefficient A(2) and the mean square radius of gyration (R(2)), for the studied samples have been obtained. The relationships between the molecular parameters are as follows: A(2)=0.0619 ($) over bar M(w)(-0.24), < R(2) >(1/2)(t)= 0.0210 ($) over bar M(w)(0.54).

Aqueous solutions of HEC and hmHEC: effects of molecular mass versus hydrophobic associations on hydrodynamic and thermodynamic parameters.

Aqueous solutions of amphiphilic polymers usually comprise of inter- and intramolecular associations of hydrophobic groups often leading to a formation of a rheologically significant reversible network at low concentrations that can be identified using techniques such as static light scattering and rheometry. However, in most studies published till date comparing water soluble polymers with their respective amphiphilic derivatives, it has been very difficult to distinguish between the effects of molecular mass versus hydrophobic associations on hydrodynamic (intrinsic viscosity [g]) and thermodynamic parameters (second virial coefficient A2), owing to the differences between their degrees of polymerization. This study focuses on the dilute and semi-dilute solutions of hydroxyethyl cellulose (HEC) and its amphiphilic derivatives (hmHEC) of the same molecular mass, along with other samples having a different molecular mass using capillary viscometry, rheometry and static light scattering. The weight average molecular masses (MW) and their distributions for the nonassociative HEC were determined using size exclusion chromatography. Various empirical approaches developed by past authors to determine [g] from dilute solution viscometry data have been discussed. hmHEC with a sufficiently high degree of hydrophobic modification was found to be forming a rheologically significant network in dilute solutions at very low concentrations as opposed to the hmHEC with a much lower degree of hydrophobic modification which also enveloped the hydrophobic groups inside the supramolecular cluster as shown by their [g] and A2. The ratio A2MW/[g], which takes into account hydrodynamic as well as thermodynamic parameters, was observed to be less for associative polymers compared to that of the non-associative polymers.