Computing the T-matrix of a scattering object with multiple plane wave illuminations

Abstract

Given an arbitrarily complicated object, it is often difficult to say immediately how it interacts with a specific illumination. Optically small objects, e.g., spheres, can often be modeled as electric dipoles, but which multipole moments are excited for larger particles possessing a much more complicated shape? The T-matrix answers this question, as it contains the entire information about how an object interacts with any electromagnetic illumination. Moreover, a multitude of interesting properties can be derived from the T-matrix such as the scattering cross section for a specific illumination and information about symmetries of the object. Here, we present a method to calculate the T-matrix of an arbitrary object numerically, solely by illuminating it with multiple plane waves and analyzing the scattered fields. Calculating these fields is readily done by widely available tools. The finite element method is particularly advantageous, because it is fast and efficient. We demonstrate the T-matrix calculation at four examples of relevant optical nanostructures currently at the focus of research interest. We show the advantages of the method to obtain useful information, which is hard to access when relying solely on full wave solvers.

Describing Meta-Atoms Using the Exact Higher-Order Polarizability Tensors

“…However, recently emerged high-refractive-index particles [5,8,27,28,49] and coupled plasmonic systems [17,43] often involve higher-order multipole transitions. It should be noted that T-matrix of meta-atoms can be systematically retrieved for arbitrary multipole order [17], but detailed analysis on their properties from their T-matrix is difficult due to the spherical basis, while retrieval of higherorder α-tensor can be cumbersome [43]. In this section, we analyze several meta-atoms from their α-tensors, which are transformed from T-matrix using Eqn.…”

“…Hybridized plasmonic structures can exhibit higherorder multipole modes even with subwavelength feature sizes [17,43]. Among them, plasmonic double bars (PDB) has exhibited strong MD mode even at the visible regime [50].…”

“…They also proposed that two oppositely dual particles are completely uncoupled to each other, and a media consisting of dual particles with a single handedness will be completely transparent to one helicity and opaque to the other helicity [68]. Demonstration of this concept is difficult, because purely dual particles have not been discovered, although approximately dual particles have been studied [17,68]. Still, we can theoretically investigate the concepts above using α-tensors and MST, because arbitrary α-tensors without physical parameters can be devised, which cannot be done using the traditional numerical methods.…”

“…Formulation of multipole radiation is a textbook problem [15], but given the importance of the multipole approach, expressions for multipoles are still under research [2,16,17] with possibility on toroidal multipoles as an extra multipole family [6,18]. In general, the multipoles under discussion are excited at a specific illumination, but they do not provide complete information of highly anisotropic meta-atoms.…”

“…In nanophotonics, analysis of meta-atoms based on their T-matrix started to become remarked rather recently [17,21]. It has been pointed out that complicated coupled configurations involving multiple meta-atoms can be efficiently studied by describing the meta-atoms in terms of α-tensor (or T-matrix) and using the multiple-scattering theory (MST) [17]. Electromagnetically coupled discrete scattering objects can be self-consistently treated to describe for collective responses of multiple particles [22][23][24] and periodic particle arrays [25][26][27][28][29][30][31], and this approach significantly reduces the calculation loads for complicated, random [32,33], or multi-scale systems [34][35][36].…”