Scattering center models of backscattering waves by dielectric spheroid objects.

Scattering center models provide a simple and effective way of describing the complex electromagnetic scattering phenomena of targets and have been successfully applied in radar applications. However, the existing models are limited to conducting objects. Numerical results show that scattering centers of dielectric objects are far more complex than conducting objects and most of them are distributed beyond the object. For the lossless and low-loss media, the major scattering contributions to total fields are surface waves and multiple internal reflections rather than the direct reflection. Concise scattering center models for backscattering from dielectric spheroid objects are proposed in this work, which can characterize the backscattered waves by scattering centers with sparse and physical parameters. Good agreement has been demonstrated between the high resolution range profiles simulated by this model with those obtained by Mie series and the full wave numerical method.

Computation of radiation pressure force exerted on arbitrary shaped homogeneous particles by high-order Bessel vortex beams using MLFMA.

Due to special characteristics of nondiffraction and self reconstruction, the Bessel beams have attracted wide attention in optical trapping and appear to be a dramatic alternative to Gaussian beams. We present in this paper an efficient approach based on the surface integral equations (SIE) to compute the radiation pressure force (RPF) exerted on arbitrary shaped homogeneous particles by high-order Bessel vortex beam (HOBVB). The incident beam is described by vector expressions perfectly satisfy Maxwell's equations. The problem is formulated with the combined tangential formulation (CTF) and solved iteratively with the aid of the multilevel fast multipole algorithm (MLFMA). Then RPF is computed by vector flux of the Maxwell's stress tensor over a spherical surface tightly enclosing the particle and analytical expression for electromagnetic fields of incident beam in near region are used. The numerical predictions are compared with the results of the rigorous method for spherical particle to validate the accuracy of the approach. Some numerical results on relative large particles of complex shape, such as biconcave cell-like particles with different geometry parameters are given, showing powerful capability of our approach. These results are expected to provide useful insights into the RPF exerted on complex shaped particles by HOBVB.

Prediction of metallic nano-optical trapping forces by finite element-boundary integral method.

The hybrid of finite element and boundary integral (FE-BI) method is employed to predict nano-optical trapping forces of arbitrarily shaped metallic nanostructures. A preconditioning strategy is proposed to improve the convergence of the iterative solution. Skeletonization is employed to speed up the design and optimization where iteration has to be repeated for each beam configuration. The radiation pressure force (RPF) is computed by vector flux of the Maxwell's stress tensor. Numerical simulations are performed to validate the developed method in analyzing the plasmonic effects as well as the optical trapping forces. It is shown that the proposed method is capable of predicting the trapping forces of complex metallic nanostructures accurately and efficiently.

Computational study of radiation torque on arbitrary shaped particles with MLFMA.

The surface integral equation (SIE) method is used for the computational study of radiation torque on arbitrarily shaped homogeneous particles. The Multilevel Fast Multipole Algorithm (MLFMA) is employed to reduce memory requirements and improve the capability of SIE. The resultant matrix equations are solved iteratively to obtain equivalent electric and magnetic currents. Then, radiation torque is computed using the vector flux of the pseudotensor over a spherical surface tightly enclosing the particle. We use, therefore, the analytical electromagnetic field expression for incident waves in the near region, instead of the far-field approximation. This avoids the error which may be caused when describing the incident beam. The numerical results of three kinds of non-spherical particles are presented to illustrate the validity and capability of the developed method. It is shown that our method can be applied to predict, in the rigorous sense, the torque from a beam of any shape on a particle of complex configuration with a size parameter as large as 650. The radiation torques on large ellipsoids are exemplified to show the performance of the method and to study the influence that different aspect ratios have on the results. Then, the code is used for the calculation of radiation torque on objects of complex shape including a biconcave cell-like particle and a motor with a non-smooth surface.

Prediction of radiation pressure force exerted on moving particles by the two-level skeletonization.

A fast full-wave method for computing radiation pressure force (RPF) exerted by shaped light beams on moving particles is presented. The problem of evaluating RPF exerted on a moving particle by a single excitation beam is converted into that of computing RPF's exerted on a static particle by multiple beams. The discretization of different beams leads to distinct right hand sides (RHS's) for the matrix system. To avoid solving each RHS by the brute-force manner, the algorithm conducts low-rank decomposition on the excitation matrix consisting of all RHS's to figure out the so-called skeleton light beams by interpolative decomposition (ID). The peak memory requirement of the skeletonization is a bottle-neck if the particle is large. A two-level skeletonization scheme is proposed to solve this problem. Some numerical experiments on arbitrarily shaped homogeneous particles are performed to illustrate the performance and capability of the developed method.

Accurate modeling of high order spatial dispersion of wire medium.

The wire medium consisting of an array of parallel thin metallic wires was previously studied by using an effective medium with spatial dispersion. In this paper, the validity of conventional effective model was examined analytically and numerically by studying a canonical structure of the wire medium. It is noted that the conventional model fails for high transversal spatial harmonics, which consequently results in discrepancy in the scattering between the effective model and the physical structure. In this study, we propose a new effective model to include higher order spatial dispersions: instead of the second-order expansion, the proposed dispersion equation is based on the fourth-order expansion of the dispersion equation of the photonic states. Compared with the 3D full-wave simulation results of the wire medium, the proposed model has demonstrated significant improvement in numerical accuracy in characterizing the EM behavior in this type of metamaterials.

Computation of radiation pressure force on arbitrary shaped homogenous particles by multilevel fast multipole algorithm.

A full-wave numerical method based on the surface integral equation for computing radiation pressure force (RPF) exerted by a shaped light beam on arbitrary shaped homogenous particles is presented. The multilevel fast multipole algorithm is employed to reduce memory requirement and to improve its capability. The resultant matrix equation is solved by using an iterative solver to obtain equivalent electric and magnetic currents. Then RPF is computed by vector flux of the Maxwell's stress tensor over a spherical surface tightly enclosing the particle. So the analytical expressions for electromagnetic fields of incident beam in near region are used. Some numerical results are performed to illustrate the validity and capability of the developed method. Good agreements between our method and the Lorenz-Mie theory for spherical and small spheroidal particle are found while our method has powerful capability for computing RPF of any shaped beam on a relatively large particle of complex shape. Tests for ellipsoidal and red blood cell-like particles illuminated by Gaussian beam have shown that the size of the particle can be as large as 50-100 wavelengths, respectively, for the relative refractive of 1.33 and 1.1.

Effective media properties of hyperuniform disordered composite materials.

The design challenge of new functional composite materials consisting of multiphase materials has attracted an increasing interest in recent years. In particular, understanding the role of distributions of ordered and disordered particles in a host media is scientifically and technologically important for designing novel materials and devices with superior spectral and angular properties. In this work, the effective medium property of disordered composite materials consisting of hyperuniformly distributed hard particles at different filling fractions is investigated. To accurately extract effective permittivity of a disordered composite material, a full-wave finite element method and the transmission line theory are used. Numerical results show that the theory of hyperuniformity can be conveniently used to design disordered composite materials with good accuracy compared with those materials with randomly dispersed particles. Furthermore, we demonstrate that a Luneburg lens based on the proposed hyperuniform media has superior radiation properties in comparison with previously reported metamaterial designs and it may open up a new avenue in electromagnetic materials-by-design.

Full-wave modeling of broadband near field scanning microwave microscopy.

A three-dimensional finite element numerical modeling for the scanning microwave microscopy (SMM) setup is applied to study the full-wave quantification of the local material properties of samples. The modeling takes into account the radiation and scattering losses of the nano-sized probe neglected in previous models based on low-frequency assumptions. The scanning techniques of approach curves and constant height are implemented. In addition, we conclude that the SMM has the potential for use as a broadband dielectric spectroscopy operating at higher frequencies up to THz. The results demonstrate the accuracy of previous models. We draw conclusions in light of the experimental results.

Computation of stress on the surface of a soft homogeneous arbitrarily shaped particle.

Prediction of the stress on the surface of an arbitrarily shaped particle of soft material is essential in the study of elastic properties of the particles with optical force. It is also necessary in the manipulation and sorting of small particles with optical tweezers, since a regular-shaped particle, such as a sphere, may be deformed under the nonuniform optical stress on its surface. The stress profile on a spherical or small spheroidal soft particle trapped by shaped beams has been studied, however little work on computing the surface stress of an irregular-shaped particle has been reported. We apply in this paper the surface integral equation with multilevel fast multipole algorithm to compute the surface stress on soft homogeneous arbitrarily shaped particles. The comparison of the computed stress profile with that predicted by the generalized Lorenz-Mie theory for a water droplet of diameter equal to 51 wavelengths in a focused Gaussian beam show that the precision of our method is very good. Then stress profiles on spheroids with different aspect ratios are computed. The particles are illuminated by a Gaussian beam of different waist radius at different incidences. Physical analysis on the mechanism of optical stress is given with help of our recently developed vectorial complex ray model. It is found that the maximum of the stress profile on the surface of prolate spheroids is not only determined by the reflected and refracted rays (orders p=0,1) but also the rays undergoing one or two internal reflections where they focus. Computational study of stress on surface of a biconcave cell-like particle, which is a typical application in life science, is also undertaken.