Analysis of scattering from complex dielectric objects using the generalized method of moments.

Integral equation-based analysis of scattering from dielectric objects has been a topic of research for many decades. Different integral equation formulations, discretization methods, and comparative data of their relative advantages have been well studied. Traditional discretization methods typically rely on a tight coupling between the underlying geometry discretization and the approximation function space that is defined on this discretization. As a result, it is difficult to stitch together different approximation spaces or nonconformal domains or match basis sets to local physics. Furthermore, the basis sets most commonly used in discretizing dielectric boundary integral operators impose limits on the variety of integral equation formulations that can be employed. We recently published a methodology [J. Opt. Soc. Am. A28, 328 (2011)10.1364/JOSAA.28.000328JOAOD61084-7529] that overcomes several of these bottlenecks. In the present paper, we introduce several extensions to these concepts for dielectric scattering problems. Specifically, we present a method that (i) uses mixed higher order local geometric descriptions and (ii) mixes multiple basis sets defined on this geometry, including higher order polynomials and classical Rao-Wilton-Glisson functions. Furthermore, we provide a unified description of different integral equation formulations that can be used for the analysis of scattering from dielectric objects, and show that the present approach admits a larger range of formulations than existing methods. A number of results demonstrating the efficiency of the method (in terms of accuracy and capability) together with applicability to different formulations are presented.

A quasianalytical time domain solution for scattering from a homogeneous sphere.

A transient spherical multipole expansion-like solution for acoustic scattering from a spherical object is derived within a mesh-free and singularity-free time domain integral equation (TDIE) framework for the sound-soft, sound-rigid and penetrable cases. The method is based on an expansion of the time domain Green's function that allows independent evaluation of spatial and temporal convolutions. The TDIE system is solved by descretizing the integral equations in space and time, forming a matrix system via the method of moments, and solving the system with the marching on in time algorithm. Spatial discretization using tesseral harmonics leads to closed form expressions for spatial integrals, and use of a strictly band limited temporal interpolant permits efficient, accurate computation of temporal convolutions via numerical quadrature. The accuracy of these integrations ensures late time stability and accuracy of the deconvolution data. Results presented demonstrate the accuracy and convergence of the approach for broadband simulations compared with Fourier transformed analytical data.

Rapid analysis of scattering from periodic dielectric structures using accelerated Cartesian expansions.

The analysis of fields in periodic dielectric structures arise in numerous applications of recent interest, ranging from photonic bandgap structures and plasmonically active nanostructures to metamaterials. To achieve an accurate representation of the fields in these structures using numerical methods, dense spatial discretization is required. This, in turn, affects the cost of analysis, particularly for integral-equation-based methods, for which traditional iterative methods require O(N2) operations, N being the number of spatial degrees of freedom. In this paper, we introduce a method for the rapid solution of volumetric electric field integral equations used in the analysis of doubly periodic dielectric structures. The crux of our method is the accelerated Cartesian expansion algorithm, which is used to evaluate the requisite potentials in O(N) cost. Results are provided that corroborate our claims of acceleration without compromising accuracy, as well as the application of our method to a number of compelling photonics applications.

Generalized method of moments: a framework for analyzing scattering from homogeneous dielectric bodies.

In this paper, we present a novel framework for discretizing integral equations--specifically, those used for analyzing scattering from dielectric bodies. The candidate integral equations chosen for the analysis are the well-known Poggio-Miller-Chang-Harrington-Wu-Tsai (PMCHWT) and the Müller equations. Discrete solutions to these equations are typically obtained by representing the spatial variation of the currents using the Rao-Wilton-Glisson (RWG) basis functions or their higher order equivalents. In this paper, we propose a framework for defining basis functions that departs significantly from those of RWG functions in that approximation functions can be chosen independent of continuity constraints. We will show that using this framework together with a quasi-Helmholtz type representation has a number of benefits. Namely, (i) it shows excellent convergence, (ii) it permits inclusion of different orders of polynomials or different functions as basis functions without imposition of additional constraints, (iii) the method can easily handle nonconformal meshes, and (iv) the method is well conditioned at all frequencies. These features will be demonstrated via a number of numerical experiments.

Nanoresonant signal boosters for carbon nanotube based infrared detectors.

We report the development of a sensitive carbon nanotube (CNT) infrared detector whose signals are boosted by nanoantenna-like features. This assembly is fabricated using nanoassembly of CNTs and a standard photolithographic process, together with nanoantenna-like features that are designed to create a resonance structure necessary to boost the electric field intensity at the CNT sensor. A novel approach is employed to find the near-field effect of the antenna. As a result, these effects are verified and demonstrated experimentally in this paper. The first experimental demonstration of a practical infrared device with nanoantenna-like structures is reported; it shows that the photocurrent is increased by an order of magnitude. The proposed fabrication and design process enables a ready integration of resonance structures into the manufacture of infrared devices, and opens the possibility of developing high fidelity infrared sensors with wide sensing range.

Plane-wave-time-domain-enhanced marching-on-in-time scheme for analyzing scattering from homogeneous dielectric structures.

A novel and fast integral-equation-based scheme is presented for analyzing transient electromagnetic scattering from homogeneous, isotropic, and nondispersive bodies. The computational complexity of classical marching-on-in-time (MOT) methods for solving time-domain integral equations governing electromagnetic scattering phenomena involving homogeneous penetrable bodies scales as O(NtNs2). Here, Nt represents the number of time steps in the analysis, and Ns denotes the number of spatial degrees of freedom of the discretized electric and magnetic currents on the body's surface. In contrast, the computational complexity of the proposed plane-wave-time-domain-enhanced MOT solver scales as O(NtNs log2Ns). Numerical results that demonstrate the accuracy and the efficacy of the scheme are presented.