A Second-Order Method for the Electromagnetic Scattering from a Large Cavity

In this paper,we study the electromagnetic scattering from a two dimen- sional large rectangular open cavity embedded in an infinite ground plane,which is modelled by Helmholtz equations.By introducing nonlocal transparent boundary con- ditions,the problem in the open cavity is reduced to a bounded domain problem.A hypersingular integral operator and a weakly singular integral operator are involved in the TM and TE cases,respectively.A new second-order Toeplitz type approximation and a second-order finite difference scheme are proposed for approximating the hyper- singular integral operator on the aperture and the Helmholtz in the cavity,respectively. The existence and uniqueness of the numerical solution in the TE case are established for arbitrary wavenumbers.A fast algorithm for the second-order approximation is pro- posed for solving the cavity model with layered media.Numerical results show the second-order accuracy and efficiency of the fast algorithm.More important is that the algorithm is easy to implement as a preconditioner for cavity models with more general media.

Study of scattering from time-varying Gerstners sea surface using second-order small slope approximation

Backscattered fields from one-dimensional time-varying Gerstners sea surface are calculated utilising the secondorder small slope approximation. It is well known that spectral properties of the backscattered echoes relate to the velocity of the small elementary scatterers on sea surface profiles. Therefore, modeling Doppler spectra from the ocean requires an accurate description of the sea surface motion. The profile of nonlinear Gerstners sea surface shows verticalskewness of sea waves, it is sharper at the crest and flatter at the trough than linear waves, and its maximum slope position is closer to the crest than to the trough. Furthermore, the horizontal component of the small elementary scatterers orbit velocity on the sea surface, which yields noticeable influence on Doppler spectra, can be obtained conveniently by Gerstners sea surface model. In this study the characteristics of Doppler spectra of backscattered fields from time-varying Gerstners sea surface are investigated and the dependences of the Doppler frequency and the Doppler bandwidth on the parameters, such as the wind speed, the radar frequency, the incident angle, etc. are discussed. It is shown that the Doppler bandwidth of microwave scattered fields from Gerstners sea surface is considerably broadened. For the case of high frequency backscattered fields, the values of the higher-order spectrum peaks are larger than those obtained by linear sea surface.

Determination of Matrine and Oxymatrine in Radix Sophorae Flavescentis by Resonance Rayleigh Scattering, Second-order Scattering and Frequency Doubling Scattering Technique

In 0.1 mol/L HCl medium, 12-tungstophosphoric（TP） acid reacted with matrine（Mat） and oxymatrine（Oxy） to form an ion-association complex. As a result, the new spectra of resonance Rayleigh scattering（RRS）, second-order scattering（SOS） and frequency doubling scattering（FDS） appeared and their intensities were enhanced greatly. The maximum scattering wavelengths of RRS, SOS and FDS were located at 370, 670 and 390 nm, respectively. The in-crements of scattering intensity were directly proportional to the concentration of Mat and Oxy in a certain range. Based on this, the method for the determination of matrine and oxymatrine has been established. It has been applied to the determination of matrine and oxymatrine in samples of Radix sophorae flavescentis with satisfactory result. The reaction mechanism and reasons of RRS enhancement were discussed.

Second-order Nonlinearities of CdS Nanoparticles Studied by Hyper-Rayleigh Scattering Technique

A series of CdS nanoparticles with different surfaces were prepared by colloidal chemical method and reverse micelle method. Their second-order nonlinear optical (NLO) properties were experimentally studied in solution by newly developed hyper-Rayleigh scattering (HRS) technique. The results show that 'per particle' first-order hyperpolarizability beta values are sensitive To the synthetic method and the surface chemical modification.

EFFECT OF SOLVENT ON SURFACE ENHANCED RAMAN SCATTERING SPECTRA OF COLLOIDAL SILVER

The effect of solvent on surface enhanced Raman scattering [SERS) of colloidal silver has been studied. Experiments show that the intensity of SERS is related to the polarity and molecular constitution of the solvent. The influence of solvent is due to the change of the adsorption quantity and adsorption intensity.

Influence of the Pseudogap on the Inelastic Neutron Scattering Spectra of the Underdoped Lanthanum Cuprate

The influence of pseudogap on the inelastic neutron scattering spectra of the underdoped lanthanum cuprate is studied on the basis of the model which incorporates both the superconducting state and pseudogap state. It is found that the striking effects of the influence of the pseudogap on the incommensurability of the spin excitation spectrum are that in the superconducting state the pseudogap makes the intensity of the incommensurate peak increase, in the normal state the pseudogap not only makes the intensity of the incommensurate peak increase, but also sharpens the incommensurate peak and increases incommensurability.

Doppler spectral analysis for time-evolving sea surfaces using second-order small slope approximation

The second-order small slope approximation （SSA2） method is introduced to study the Doppler characteristics from time-evolving sea surfaces. Simulation results show better agreement between the SSA2 model and the numerical method for both vertical and horizontal polarizations, meaning that SSA2 gives a satisfactory prediction of the spectral difference between two po- larizations; while such discrepancy cannot be captured using the lowest-order SSA （SSA1） model. In particular, the Doppler shifts and spectral widths for different incident angles, wind directions and polarizations are analyzed, demonstrating correct variations with respect to such parameters. Those observations prove that the SSA2 provides an efficient and relatively fast tool for sea surface Doppler spectral analysis.

Studies on convergence and scaling law of Thomson backscattering spectra in strong fields

With the saddle point analysis method for the Bessel function structure and property, the convergence problem and the scaling laws of Thomson backscattering spectra are solved and studied in both cases that are for the plane wave laser field without and with applied external constant magnetic field. Some unclear points appeared in previous work are clarified. The extension of the method to a general situation for the laser field with an arbitrary polarization is discussed. We also make a simple analysis and discussion about the optimal spectra dependence of field parameters and its implication to practical applications.

Seismic inversion with generalized Radon transform based on local second-order approximation of scattered field in acoustic media

Sound velocity inversion problem based on scattering theory is formulated in terms of a nonlinear integral equation associated with scattered field. Because of its nonlinearity, in practice, linearization algorisms （Born/ single scattering approximation） are widely used to obtain an approximate inversion solution. However, the linearized strategy is not congruent with seismic wave propagation mechanics in strong perturbation （heterogeneous） medium. In order to partially dispense with the weak perturbation assumption of the Born approximation, we present a new approach from the following two steps： firstly, to handle the forward scattering by taking into account the second- order Born approximation, which is related to generalized Radon transform （GRT） about quadratic scattering poten- tial; then to derive a nonlinear quadratic inversion formula by resorting to inverse GRT. In our formulation, there is a significant quadratic term regarding scattering potential, and it can provide an amplitude correction for inversion results beyond standard linear inversion. The numerical experiments demonstrate that the linear single scattering inversion is only good in amplitude for relative velocity perturbation （3c/c0） of background media up to 10 %, andits inversion errors are unacceptable for the perturbation beyond 10 %. In contrast, the quadratic inversion can give more accurate amplitude-preserved recovery for the per- turbation up to 40 %. Our inversion scheme is able to manage double scattering effects by estimating a trans- mission factor from an integral over a small area, and therefore, only a small portion of computational time is added to the original linear migration/inversion process.

A study on resonance Rayleigh scattering spectra of Humic Acid (HA)

This paper deals with the influences of pH, acidity and ionic intensity of the solutions on the resonance Rayleigh scattering spectra and fluorescence spectra of humic acid. When the pH value is low and the acidity and ionic intensity are high, the resonance Rayleigh spectra and fluorescence spectra both show a tendency of increasing, though the former's intensity is much higher. In combination with the transmission electron microscope data, the factors leading to the occurrence and enhancement of the resonance Rayleigh scattering spectra of humic acid were explored. It is considered that particle enlargement caused by aggregation, the increase of heterogeneity, the increase of hydrophobility, the formation of interface, etc., are the factors leading to the occurrence and enhancement of the resonance Rayleigh scattering spectra of humic acid. As the intensity of the resonance Rayleigh scattering spectra of humic acid is much higher, resonance Rayleigh scattering spectroscopy can be used as a newly developed spectrum technology, which is more sensitive and simpler, to study humic acid and its complicated behaviors.

Surface-enhanced Raman Scattering of Aflatoxin B1 on Silver by DFT Method

The structure, electrostatic properties, and Raman spectra of aflatoxin B1 （AFB1） and AFB1-Ag complex are studied by density functional theory with B3LYP/6- 311G（d,p）/Lan12dz basis set. The results show that the surface-enhanced Raman scattering （SERS） and pre-resonance Raman spectra of AFB1-Ag complex strongly depend on the adsorption site and the excitation wavelength found to enhance 102-103 order compared to of the incident light. The SERS factors are normal Raman spectrum of AFB1 molecule due to the larger static polarizabilities of the AFB1-Ag complex, which directly results in the stronger chemical enhancement in SERS spectra. The pre-resonance Raman spectra of AFB1-Ag complex are explored at 266, 482, 785, and 1064 nm incident light wavelength, in which the enhancement factors are about 10^2-10^4, mainly caused by the charge-transfer excitation resonance. The vibrational modes are analyzed to explain the relationship between the vibrational direction and the enhanced Raman intensities.

Lensless ghost imaging through the strongly scattering medium

Lensless ghost imaging has attracted much interest in recent years due to its profound physics and potential applications. In this paper we report studies of the robust properties of the lensless ghost imaging system with a pseudo-thermal light source in a strongly scattering medium. The effects of the positions of the strong medium on the ghost imaging are investigated. In the lensless ghost imaging system, a pseudo-thermal light is split into two correlated beams by a beam splitter. One beam goes to a charge-coupled detector camera, labeled as CCD2. The other beam goes to an object and then is collected in another charge-coupled detector camera, labeled as CCD1, which serves as a bucket detector. When the strong medium, a pane of ground glass disk, is placed between the object and CCD1, the bucket detector, the quality of ghost imaging is barely affected and a good image could still be obtained. The quality of the ghost imaging can also be maintained, even when the ground glass is rotating, which is the strongest scattering medium so far. However, when the strongly scattering medium is present in the optical path from the light source to CCD2 or the object, the lensless ghost imaging system hardly retrieves the image of the object. A theoretical analysis in terms of the second-order correlation function is also provided.

Dynamic behaviors of water contained in calcium-silicate-hydrate gel at different temperatures studied by quasi-elastic neutron scattering spectroscopy

The dynamic behaviors of water contained in calcium-silicate-hydrate（C-S-H） gel with different water content values from 10%to 30%（by weight）,are studied by using an empirical diffusion model（EDM） to analyze the experimental data of quasi-elastic neutron scattering（QENS） spectra at measured temperatures ranging from 230 K to 280 K.In the study,the experimental QENS spectra with the whole Q-range are considered.Several important parameters including the bound/immobile water elastic coefficient A,the bound water index BWI,the Lorentzian with a half-width at half-maximum（HWHM） Γ;（Q） and Γ;（Q）,the self-diffusion coefficients D;and D;of water molecules,the average residence times τ;and τ;,and the proton mean squared displacement（MSD）(u;) are obtained.The results show that the QENS spectra can be fitted very well not only for small Q（≤1 A;） but also for large Q.The bound/immobile water fraction in a C-S-H gel sample can be shown by the fitted BWI.The distinction between bound/immobile and mobile water,which includes confined water and ultra-confined water,can be seen by the fitted MSD.All the MSD tend to be the smallest value below 0.25 A;（the MSD of bound/immobile water） as the Q increases to 1.9 A;no matter what the temperature and water content are.Furthermore,by the abrupt changes of the fitted values of D;,τ;,and Γ;（Q）,a crossover temperature at 250 K,namely the liquid-to-crystal-like transition temperature,can be identified for confined water in large gel pores（LGPs） and/or small gel pores（SGPs） contained in the C-S-H gel sample with 30% water content.

16-Moment Approximation for Ion Velocity Distribution and its Application in Calculations of Incoherent Scatter Spectra

A sixteen moment approximation based on a bi-Maxwellian that contains the stress tensor and the heat flow vector is applied to describe the ion velocity distribution which influences the incoherent scatter spectra. A discussion is made about the effects on the incoherent scatter spectra caused by different values of the normalized perpendicular drift velocity D, aspect angle Φ between the magnetic field and the line-of-sight direction, and the ratio α of the ion-neutral collision to ion cyclotron frequency. Numerical results show that the shifting and asymmetry of incoherent scatter spectra appear parallel to E × B and E as the normalized perpendicular drift velocity D increases due to the ion drift velocity, the stress tensor and the heat flow vector respectively. However, the spectrum is always typically double-humped Maxwellian parallel to B. The ion velocity distribution is more distorted from the Maxwellian as the aspect angle Φ increases from 0° to 90°, and consequently the incoherent scatter spectra is no longer typically double-humped Maxwellian. Asαincreases, the ion velocity distribution becomes Maxwellian and the incoherent scatter spectra become typically double-humped Maxwellian even with a large value of the normalized perpendicular drift velocity D. It is reasonable to use the sixteen-moment approximation to describe the non-Maxwellian plasma characterized by the large temperature anisotropy.

Scattering of elastic wave by a cylindrical shell deeply embeded in saturated soils

The compression of soil grain and pore fluid as well as viscid coupling of pore fluid and soil skeleton is considered, the scattering problem of incident plane P1 wave （fast compressional wave） by an infinite cylindrical shell deeply embedded in isotropic saturated soils is studied by adopting the amended Biot model, amplitude equations about potential functions of scattering and refracting fields are obtained, and the effect of dimensionless frequencies and shell thickness on the back-scattering spectra and dynamic stress concentration factors of two types of cylindrical shells with high and low rigidity are numerically computed and analyzed.

Reversible Aggregation Kinetics of Poly(N-isopropylacrylamide-co-N-vinylpyrrolidone) in Aqueous Solutions Revealed by Elastic Light Scattering Spectroscopy

Poly（N-isopropylacrylamide-co-N-vinylpyrrolidone） [P（NIPAM-co-NVP）] copolymers with different content of N-vinylpyrrolidone （NVP） were synthesized, and reversible aggregation kinetics of the copolymers in aqueous solutions was investigated with elastic light scattering （ELS） spectra. The results indicated that the apparent activation energy of aggregation process during heating and dissociation process during cooling increased with the NVP content increasing. The phase transition temperature also increased as the content of NVP increased, suggesting that the hydrophilic nature of NVP strongly affected the phase behavior of the copolymer solutions. The higher the content of NVP, the higher the temperature required to break the balance between the hydrophilic and hydrophobie interaction. Besides, during heating and cooling process, the phase transition hysteresis of P（NIPAM-co-NVP） chains decreased when the hydrophilic comonomer increased.

Generalized 3D Scattering Channel Model with MIMO Antenna Systems

In this paper, a generalized three-dimensional(3D) scattering channel model for macrocellular land mobile environments is considered. This model simultaneously describes angular arrival of multi-path signals in the azimuth and elevation planes in an environment where uniformly distributed scatterers are assumed to be present in hemispheroids around the base station(BS) and mobile station(MS). Using this channel model, we first derive the closed-form expression for the joint and marginal probability density functions of the angle-of-arrival and time-of-arrival measured at the BS and the MS corresponding to the azimuth and elevation angles. Next, we derive an expression for the Doppler spectral distribution caused by motion of the MSs. Furthermore, we analyze the performance of multiple-input multiple-output antenna systems numerically. The results show that the proposed 3D scattering channel model performs better than previously proposed two-dimensional(2D) models for indoor and outdoor environments. We compare the results with previous scattering channel models and measurement results to validate the generalizability of our model.

Resonance Rayleigh Scattering and Resonance Nonlinear Scattering Methods for Determination of Methylene Blue with 12-Tungstophosphoric Acid

In a pH=0.65―1.5 NaAc-HCl medium, methylene blue（MB） reacts with 12-tungstophosphoric acid （TPA） by virtue of electrostatic attraction and hydrophobic force to form a 3：2 ion-association complex. As a result, the intensities of resonance Rayleigh scattering（RRS）, second-order scattering（SOS） and frequency doubling scatte- ring（FDS） are enhanced greatly. The maximum scattering wavelengths of RRS, SOS and FDS are located at 316, 647 and 311 nm. The increments of scattering intensity（△I） are directly proportional to the concentration of MB in a certain range. The methods exhibited high sensitivity, and the detection limits（3s） for MB are 2.3 ng/mL（RRS method）, 5.6 ng/mL（SOS method） and 6.4 ng/mL（FDS method）, respectively. The effects of coexisting substances have been examined, and the results indicate that the methods have good selectivity. Based on the above researches, a new spectral method for the determination of trace amounts of MB has been developed. It can be applied to the determination of MB in human serum, and the recoveries are 97.5%―105.0%. The results are in good agreement with those obtained by the pharmacopoeia method. In this work, the optimum conditions of the reaction and the influencing factors were investigated. In addition, the reaction mechanism and the reasons of the enhancement of resonance light scattering were discussed.

Size Dependence of First-order Hyperpolarizability of CdS Nanoparticles Studied by Hyper-Rayleigh Scattering

The second-order optical nonlinearity of CdS nanoparticles with different diameters of 28.0, 30.0, 31.5, 50.0, and 91.0 A was studied by hyper-Rayleigh scattering technique. Results show that the first-order hyperpolarizability P value per CdS partiele decreases as size is reduced to diameter of 31.5 A; however, as CdS size further decreases, this trend is reversed and (J value increases. Substantially, the normalized P value per CdS formula unit, β0, exhibits systematic enhancement with decreasing size. This phenomenon is interpreted in terms of a so-called surfaee contribution mechanism.

Study of second-order nonlinear hyperpolarisability of all-trans-β-carotene in solutions by linear spectroscopic technique

This paper demonstrates the second-order nonlinear hyperpolarisability γ of all-trans-β-carotene in different solvents by linear spectroscopic technique that is based on resonance Raman scattering and UV-VIS （Ultraviolet-visible） absorption spectroscopy. Owing to the two-level model well describing the link that exists between the resonance Raman scattering and stimulated Raman scattering, the stimulated Raman polarisability αR can be calculated through the two-photon resonance system. The value of γ of all-trans-β-carotene in carbon bisulfide solution is 6.435×10^-33 esu （1 esu of resistance = 8.98755×10^11Ω） that is close to the true value, because the solution of all-trans-β-carotene in carbon bisulfide satisfies the rigid resonance Raman scattering condition. This method is expected to be worthy of applications to measure the second-order nonlinear hyperpolaxisability of a conjugate organic molecule.