Denis Tihon

Characterization of power absorption response of periodic three-dimensional structures to partially coherent fields

In many applications of absorbing structures it is important to understand their spatial response to incident fields, for example in thermal solar panels, bolometric imaging, and controlling radiative heat transfer. In practice, the illuminating field often originates from thermal sources and is only partially spatially coherent when it reaches the absorbing device. In this paper, we present a method to fully characterize the way a structure can absorb such partially coherent fields. The method is presented for any three-dimensional material and accounts for the partial coherence and partial polarization of the incident light. This characterization can be achieved numerically using simulation results or experimentally using the energy absorption interferometry that has been described previously in the literature. The absorbing structure is characterized through a set of absorbing functions onto which any partially coherent field can be projected. This set is compact for any structure of finite extent, and the absorbing function is discrete for periodic structures.

Fast FMIR-MoM implementation using analytical singularity evaluation

Frequency-domain Method of Moments (MoM) is a mature numerical technique that is formulated in the frequency domain, as opposed to time-domain methods. For that reason, computation time can increase rapidly when results are required over a large number of frequencies. This is also true when material properties are varied. In this paper, we show that rapid computation of the impedance matrix for various wave-vectors can be obtained combining the Frequency and Material Independent Reaction MoM (FMIR-MoM) with the analytical evaluation of the MoM integrals. The resulting formulation works well in the near-field, and is competitive with classical techniques, even for the computation of the impedance matrix at a single frequency.

Computation of the absorption of partially coherent fields using traditional coherent solvers

We present an exact formulation for the computation of the power absorbed by lossy structures that can deal with partially spatially coherent fields. The absorbing structure is characterized through a discrete number of natural absorption modes, leading to a compact representation of the absorption capabilities of the structure when subjected to any kind of incident fields. The method can be easily combined with any kind of commercial software since only the response of the structure to fully coherent fields is required.

Numerically Stable Eigenmode Extraction in 3-D Periodic Metamaterials

A numerical method is presented to compute the eigenmodes supported by 3-D metamaterials using the method of moments. The method relies on interstitial equivalent currents between layers. First, a parabolic formulation is presented. Then, we present an iterative technique that can be used to linearize the problem. In this way, all the eigenmodes characterized by their transmission coefficients and equivalent interstitial currents can be found using a simple eigenvalue decomposition of a matrix. The accuracy that can be achieved is limited only by the quality of simulation, and we demonstrate that the error introduced when linearizing the problem decreases doubly exponentially with respect to the time devoted to the iterative process. We also draw a mathematical link and distinguish the proposed method from other transfer-matrix-based methods available in the literature.

SVD post-compression combined with shielded-block preconditioner

We present a post-compression method based on the Singular Value Decomposition that can be used to retrieve the low-rank representation of the Method of Moments interaction matrix after using the shielded-block preconditioner. A compression ratio of more than 17 has be achieved without significant loss of accuracy. The time needed to compress the preconditioned matrix is negligible with respect to the preconditioning time. We also show that the compression can decrease the solution complexity using iterative solvers or multiple-scattering MBFs, thereby significantly decreasing the total computation time.

Krylov subspace-based and MBF-based analysis of large finite arrays of silver nanorods in the presence of a scatterer

Metamaterials receive increasing attention at optical frequencies due to their potential for subwavelength imaging. Among the possible structures are dense, doubly periodic arrays of silver nanorods where image transmission is achieved via surface plasmon polaritons. However, the numerical simulation of such dense structures may require excessive computational resources without employing an efficient numerical approach. In this paper, the multiple-scattering based Macro Basis Function (MBF) method is applied to the shielded-block preconditioned matrix, which represents interactions between different elements of the array (subdomains). The “rule of thumb” that relates the number of MBFs generated on a subdomain to the number of iterations required by the Full Orthogonalization Method (FOM) for the same error level is investigated. For high levels of error, the number of MBFs are observed to be smaller than the number of iterations required. Conversely, for low levels of error, the FOM converges faster.