Verification of Physical Optics Approximation by the Discrete Dipole Method in Calculations of Light Backscattering

Using the discrete dipole method, exact and approximate analytical solutions for orientation-averaged cross sections for extinction, absorption, and scattering of light are obtained. The analytical solutions can be applied to the calculation of integrated cross sections of fractal clusters formed by primary particles with different optical properties (soot in air and aqueous suspensions of aggregates of polystyrene, gold, and silver nanoparticles). It is shown that two models of aggregates that differ only in trajectories (ballistic or Brownian) of primary particles and intermediate clusters and in average fractal dimensions give close values of averaged extinction cross sections.

The formulas for light scattering amplitude and phase function [or element of scattering matrixf11] of hexagonal column with concave ends in the Rayleigh-Gans-Debye (RGD) approximation are derived. Numerical results for the phase function of light scattering of hexagonal column with pyramidal hollow ends in the RGD approximation and in the method of Purcell-Pennypacker (or discrete dipole method, or coupled dipole method) are compared. The good agreement for hexagonal columns having small phase shifts has been found.

Nanoparticles optimal shape designing in the cylindrical coordinate to use for optical devices

The interaction between metal particles was calculated based on the discrete dipole method. The calculated results revealed that the multiple interactions in a collection of metal particles are dominated by the interaction between the neighboring particles. Thus, a two-particle approximation was deduced and applied to estimate the optical absorption and near-field enhancement property of Ag-Si3N4 composite films. The calculated results indicated that the interaction between Ag particles will induce extra absorption near the surface plasmon resonance peak and improve the near-field enhancement property of composite films. Calculated results were consistent with the experimental results.

The main results of studying the synthesis, growth mechanisms, and optical properties of gold nanorods published in the last 5–8 years are briefly reviewed. Hydrosols of gold nanorods with variable axial ratios are synthesized in the micellar solution of ionic surfactants by sead-mediated growth procedure using the stage of particle separation in the glycerol concentration gradient. Results of synthesis in systems containing one surfactant, albeit with different Ag/Au molar ratios and different amounts of gold seeding particles, agree with the published data. It is shown that, in the case of the mixture of two surfactants, the Ag/Au ratio is an efficient controlling parameter of the synthesis of nanorods with large axial ratios. The extinction and differential light scattering, spectra dynamic light scattering, and the depolarization of laser light scattering at 90° are used for the optical control of synthesis. Three fractions are observed in separated samples. One of these fractions is characterized by the only short wavelength plasmon resonance at 570 nm corresponding, in agreement with the published data, to cubic particles. Measurements of the extinction spectra of nanorods in water-glycerol mixtures reveal higher sensitivity of the longitudinal plasmon resonance to the dielectric environment relative to the transverse resonance. It is shown theoretically and experimentally that the relative shift of plasmon resonance is proportional to the relative increment of refractive index of the surrounding medium. To calculate optical properties of nanorods, we employed a model of cylinders with semispherical ends (s-cylinders) corresponding to the shape of real particles and admitting the exact solution by the T-matrix method with a computational burden that is an order of magnitude lower than that used in the discrete dipole method. The set of dependences of the longitudinal resonance wavelength on the axial ratio of different-thickness particles complies with our data and published measurements. Theoretical and experimental values of depolarization ratio I VH/I VV for nanorods and nanospheres with different sizes prepared with both citrate (15–46 nm) and original thiocyanate (90 nm) reduction of HAuCl4 are compared. It is shown that the depolarization parameter of light scattered by a nanorod suspension can exceed the theoretical limit (1/3) for common dielectric particles. The measured 10%-depolarization ratio for 90-nm spheres was far beyond the set of “size-depolarization” measurements for 15–46-nm-dia particles prepared by the citrate method and is indicative of the improved spherical morphology of 90-nm particles. This assumption was confirmed by TEM data, which also revealed both the presence of a noticeable amount of nanorods with a large axial ratio and “nanowires” of about the same thickness. A new analytic calibration for determining the diameter of spherical particles (5–100 nm) by the spectral position of the sol extinction maximum is proposed.

Reflectance anisotropies of silicon surfaces: analysis of spectra in terms of surface excess susceptibilities

The angular spectrum method (ASM) is commonly used for reconstructing images in digital holography for applications such as lens-free holography and metasurface design. The lack of Fraunhofer or Fresnel approximations and computational speed due to the fast Fourier transform makes ASM a competitive field propagation method. Using a thin-object approximation, ASM can also efficiently compute fields over large areas, enabling faster calculations than those using other methods such as finite difference time domain or Mie theory. However, thin-object approximations are not accurate for nanoscale objects and so ASM is currently unable to accurately recover nanoscale object information. Here we test three ASM transmission models that use a scalar description to model the interaction of a plane wave with a plane of randomly assembled nanoparticles and evaluate the accuracy of each against the discrete dipole method (DDA). Random distributions of nanoparticles are often used in super-resolution, sub-diffraction limit, or specialized sensing applications as they are easy to place. We study the performance of the three transmission models for gold and polystyrene nanospheres of 30 nm, 60 nm, and 100 nm in diameter for different particle densities. The performance of the models is evaluated against simulations using DDA, which is validated against Mie theory calculations, for the same configurations. We show transmission models in ASM that perform within 20% accuracy of the fields calculated using DDA.

In this paper we analyze optical properties and plasmonic field enhancements in large aperiodic nanostructures. We introduce extension of Generalized Ohm's Law approach to estimate electromagnetic properties of Fibonacci, Rudin-Shapiro, cluster-cluster aggregate and random deterministic clusters. Our results suggest that deterministic aperiodic structures produce field enhancements comparable to random morphologies while offering better understanding of field localizations and improved substrate design controllability. Generalized Ohm's law results for deterministic aperiodic structures are in good agreement with simulations obtained using discrete dipole method.

Fast shadowing test algorithm based on target division by cubes

In this study, fast calculations for the electromagnetic (EM) scattering of complex targets coated by radar absorbing materials have been reported. The Geometric Optics and Physical Optics (GO/PO) methods are combined with the modified surface reflection coefficient method, to solve the problem of EM scattering. Moreover, two acceleration techniques have been employed to improve the efficiency of computations. Firstly, the neighbor search technique is adopted to accelerate the ray tracing process in GO/PO. In this technique, an Octree structure is applied to divide the space into multiple subspaces, namely sub-nodes, where the efficiency of ray tracing can be improved through Morton code transform. In order to further reduce the computational time, parallel acceleration technique, based on GPU platform within the Compute Unified Device Architecture (CUDA) framework is introduced. Our proposed method has been verified from the nice correlation of simulated and multilevel fast multipole method (MLFMM) and CPU-based GO/PO methods. The runtime is compared with that of GO/PO method in serial model, responsible for a good speedup ratio. Finally, the influence of coating thicknesses and types of material on the EM scattering characteristics of the coated targets are also analyzed.

In most of the electromagnetic problems, the number of unknowns to evaluate the scattered fields grows whenever the size of the antenna, device or scenario increases or the working frequency becomes higher. In this context, the rigorous full-wave methods –e.g. Method of Moments (MoM), Fast Multipole Method (FMM) (Engheta et al., 1992), Finite-Difference Time-Domain (FDTD) (Taflove & Umashankar, 1987) or Finite-Difference FrequencyDomain (FDFD) (Rappaport & McCartin, 1991), Finite Element Method (FEM) (Kempel et al., 1998) – can not tackle the analysis of such problems beyond an upper limit determined by the computational requirements in terms of time and memory. High frequency techniques consist in the asymptotic evaluation of the Maxwell’s equations. As a consequence, they provide good accuracy when dealing with electrically large geometries meanwhile the computational needs diminish with respect to the aforementioned methods. Within the high frequency techniques, the Geometrical Optics (GO) and the Physical Optics (PO) approximation are the most extended methods due to the successful results obtained in various fields such as Radar Cross Section (RCS), design of reflector antennas or radioelectric coverage calculation. Since the Physical Optics approximation is detailed in the following section, the Geometrical Optics is briefly summarised. The main interest in the GO lies in the fact that incident, reflected and transmitted electromagnetic waves are studied based on the conservation of the energy flux along a ray tube between a source and an observation point. Therefore, the Geometrical Optics is usually referred to as Ray Optics. The GO comprises two different methodologies (Rossi & Gabillet, 2002): Ray Tracing (Glassner, 1989) – the starting point is the receiver or observation point and a path to the source is sought analysing the reflections on walls, buildings, mountains – and Ray Launching – multiple rays are launched from the source, so they are independently followed until an observation point or the receiver is reached. One of the common applications of the GO is the evaluation of radio electric coverage or the channel characterization in urban scenarios. Both the GO and the PO techniques require of an additional method to compute the contribution due to the diffraction phenomenon. The GO can be complemented by means of the Geometrical Theory of Diffraction (GTD) (Keller, 1962) or the Uniform Theory of

The aim of this paper is to explore a high-precision, a wide range of a frequency discrimination technique, and to study the application of this technique in the optical air data system (MOADS). To overcome the traditional equipment's shortcomings of short velocity detecting range such as pilot static tubes and wind wane, this technique can provide precision aviation data for various aerocrafts , without influencing pneumatic shape and performance of aerocraft. A tunable dual channel Fabry-Perot interferometer is used as a frequency discriminator in an airborne wind lidar system. This new frequency discriminator has been proposed to overcome the exiting frequency discriminator shortcoming. By adjusting the cavity length of interferometer, the speed of aerocraft can be detected and cut into several dynamic range. By this way, the Doppler wind lidar system can detect atmospheric parameters at the meantime, such as speed of aerocraft and temperature of atmosphere around the aerocraft, by analyzing the information of Rayleigh backscattering light. There are three main contribution in this paper: the first is discussing the basic theory of MOADS, calculational method and mathematic model of relative wind velocity between aircraft and wind are put forward.; the second is the parameter optimization of the dual-channel Fabry-Perot interferometer and the structure design of the interferometer; the third is the simulation of the performance and the accuracy of this system. Theory analysis and simulation results show this method is reasonable and practical.

This paper describes the contributions of tip scattering, first-order rim diffraction and tip-rim interaction to the high-frequency scattering from a finite perfectly conducting right-circular cone. Empirical correction factors are introduced to the classical physical optics (PO) approximation. It is shown that the contribution due to tip scattering as obtained from physical optics approximation, with a correction factor included, closely matches with Felsen's result for small angle cones and for a wide range of aspect angle. It is also shown for axial incidence that the firstorder diffraction from the rim is expressible in terms of the PO integral after incorporating a correction factor. Axial radar cross section measurement results on narrow and large angle cones are presented and compared with the results of the modified PO result thus obtained in this paper and geometrical theory of diffraction (GTD). The contribution of the proposed tip-rim interaction is subsequently discussed and it is shown that this interaction is significant only for narrow angle cones. Backscattering measurement results on two cones over a wide range of aspect angle are also compared with the classical results of PO and GTD. From this comparison, it is inferred that for large angle cones, second order diffraction mechanisms contribute insignificantly when the incident wave is vertically polarized. This shows that PO can be a reasonably accurate analytical tool for large angle cones and for vertical polarization, except at axial incidence. At axial incidence, the correction factor introduced in this paper has to be used in the PO solution to make it match with experiment.

This paper describes how to synthesize a tapered resistive grid that produces a desired backscattering pattern. The grid consists of equally spaced, equal width strips. Each strip has a resistivity that is found by using a genetic algorithm. Physical optics is used to calculate the backscattering. The results are compared with the method of moments calculations.

The calculation of Radar Cross Section (RCS) of arbitrarily large perfectly conducting body is presented. The body is modelled as triangular meshes of any size by the help of graphical tools. For the calculation of scattered field, Physical Optics(P0) surface integral is analytically evaluated over each of the triangular meshes. Due to the analytical integration, there is no limitation on the size of the triangles.